Chapter 9 Data Handling (Additional Questions)

The correct option is (B).

The question asks for the term that describes a collection of raw facts, which can include numbers, words, measurements, observations, or descriptions.

Let's examine the options:

(A) Information: Information is data that has been processed, organized, or structured in a way that makes it meaningful and useful. It is derived from data, but is not the raw collection itself.

(B) Data: Data is the term used for raw facts and figures collected for study or analysis. It is the foundational material from which information is derived.

(C) Survey: A survey is a method or technique used to collect data from a sample of individuals or groups. It is a process of data collection, not the collection of facts itself.

(D) Analysis: Analysis is the process of inspecting, cleansing, transforming, and modeling data with the goal of discovering useful information, informing conclusions, and supporting decision-making. It is what you do *with* data, not the data itself.

Based on the definitions, the term that best describes a collection of raw facts such as numbers, words, measurements, observations, or descriptions is Data.

The correct option is (B).

When information is initially collected from a source, it is in its original, unprocessed form. This is known as Raw data.

Let's look at the other options:

(A) Primary data: Primary data is data collected directly by the researcher or investigator for their specific purpose. While often collected as raw data, 'primary data' refers to the source, not necessarily the state (raw or processed).

(C) Organized data: Organized data is raw data that has been structured, classified, or arranged in a specific manner to make it easier to analyze or understand. The collected information is raw *before* it is organized.

(D) Secondary data: Secondary data is data that has been collected by someone else and is available from other sources (like reports, databases, etc.). The collected information in the context of initial gathering is not secondary.

Therefore, the information collected, in its initial state, is called Raw data.

The correct option is (B).

The process of taking raw data and arranging it in a structured format, such as grouping it or putting it into tables, is known as the Organization of data.

Let's distinguish this from the other options:

(A) Collection of data: This is the initial step where data is gathered from its source.

(C) Interpretation of data: This step involves analyzing the organized data to draw conclusions or infer meaning.

(D) Presentation of data: This is the stage where the organized and analyzed data is displayed in a clear and easily understandable format, often using charts, graphs, or well-structured tables, for others to view and understand.

Arranging the collected data into a systematic form like a table is specifically the act of organizing it before it is interpreted or presented.

The correct option is (B).

In the tally mark system, vertical strokes are used to represent counts. For convenience and ease of counting, every fifth stroke is drawn diagonally across the previous four strokes.

The symbol $||||$ represents a count of 4.

When the fifth item is counted, a diagonal line is drawn across these four strokes:

$\bcancel{||||}$

This group represents a count of 5.

Therefore, the symbol $\bcancel{||||}$ represents 5.

The correct option is (C).

The question asks for the term that defines how often a specific value or category appears within a dataset. This is the definition of frequency.

Let's consider the options:

(A) Range: The range of a dataset is the difference between the highest and lowest values.

(B) Mean: The mean (or average) is calculated by summing all the values in a dataset and dividing by the number of values.

(C) Frequency: Frequency is defined as the number of times a particular observation, value, or category appears in a dataset.

(D) Mode: The mode is the value that appears most frequently in a dataset. While related to frequency, the mode is the value itself, not the count of its occurrences.

Based on these definitions, the number of times a particular observation occurs in a data set is its Frequency.

The correct option is (B).

A pictograph, also known as a pictogram or picture graph, is a statistical graph in which the data is represented by pictures or symbols.

Let's look at the other options:

(A) Bars: Data represented using bars is typically found in a bar graph.

(C) Numbers: Numbers are the actual data values themselves, not the visual representation method used in a pictograph.

(D) Lines: Data represented using lines connecting points is typical of a line graph.

Therefore, a pictograph represents data using Pictures or symbols, where each picture or symbol represents a specific quantity.

The correct option is (C).

The pictograph uses a symbol of a car ($\textsf{🚗}$) to represent a certain number of cars sold. The key provided tells us that each $\textsf{🚗}$ symbol represents 10 cars.

To find the number of cars sold in March, we need to count the number of car symbols shown for March in the pictograph.

According to the description in the image alt text, the number of car symbols shown for March is 5.

Since each symbol represents 10 cars, the total number of cars sold in March is the number of symbols multiplied by the value of each symbol:

Number of cars sold in March = (Number of symbols for March) $\times$ (Value of each symbol)

Number of cars sold in March = $5 \times 10$

$5 \times 10 = 50$

Therefore, 50 cars were sold in March.

The correct option is (B).

To find the month with the least number of cars sold, we need to calculate the total number of cars sold in each month based on the pictograph and its key.

The key is: $\textsf{🚗}$ = 10 cars.

Let's find the number of cars sold in each month:

January: There are 4 car symbols. Number of cars = $4 \times 10 = 40$.

February: There are 3 car symbols. Number of cars = $3 \times 10 = 30$.

March: There are 5 car symbols. Number of cars = $5 \times 10 = 50$.

April: There are 3.5 car symbols (implied by a half car symbol). Number of cars = $3.5 \times 10 = 35$.

Now, let's compare the number of cars sold in each month:

January: 40 cars

February: 30 cars

March: 50 cars

April: 35 cars

The least number of cars sold is 30, which occurred in February.

The correct option is (A).

From the pictograph and the key ($\textsf{🚗}$ = 10 cars), we find the number of cars sold in January and February.

Number of cars sold in January = 4 symbols $\times$ 10 cars/symbol = $4 \times 10 = 40$ cars.

Number of cars sold in February = 3 symbols $\times$ 10 cars/symbol = $3 \times 10 = 30$ cars.

To find how many more cars were sold in January than in February, we subtract the number of cars sold in February from the number of cars sold in January:

Difference = (Cars sold in January) - (Cars sold in February)

Difference = $40 - 30$

$40 - 30 = 10$

So, 10 more cars were sold in January than in February.

The correct option is (C).

A bar graph is a visual display of data using bars of different heights or lengths. A fundamental characteristic of a standard bar graph is that the bars are of uniform width and are drawn with equal spacing between them.

Let's look at the other options:

(A) Lines: Lines are used to connect data points, typically seen in a line graph, not a bar graph.

(B) Circles: Circles or sectors of a circle are used in a pie chart to represent parts of a whole.

(D) Points: Points are individual markers used to represent data values, often connected by lines in a line graph or scattered in a scatter plot.

The defining visual elements of a bar graph are Bars or rectangles of uniform width.

The correct option is (B).

In a bar graph, data is represented by rectangular bars. These bars can be vertical or horizontal. The key feature is that the length or height of each bar corresponds to the quantity, value, or count it represents.

Specifically, the height of a bar in a bar graph is proportional to the frequency of the data category or observation it represents. A longer or taller bar indicates a higher frequency, while a shorter bar indicates a lower frequency.

Let's consider the other options:

(A) Mean: The mean is a single average value calculated from the entire dataset or a subset, not represented by the height of individual bars for different categories.

(C) Width: The width of the bars is typically kept uniform across all categories in a bar graph.

(D) Scale: The scale is marked on the axis (usually the vertical axis for vertical bars) and indicates the units of measurement for the frequency or value being represented by the height of the bars.

Therefore, the height of each bar in a bar graph represents the Frequency of the corresponding observation.

The correct option is (C).

The bar graph represents the number of students in different classes using the height of the bars.

We need to look at the bar corresponding to Class 7 and read the value on the vertical axis that aligns with the top of this bar.

According to the description of the bar graph provided (in the alt text), the number of students for each class is given as:

• Class 6: 40 students
• Class 7: 50 students
• Class 8: 45 students

Therefore, the number of students in Class 7 is 50.

The correct option is (B).

To find the class with the maximum number of students, we need to compare the number of students in each class as shown by the heights of the bars in the bar graph from Question 12.

Based on the bar graph, the number of students in each class is:

Number of students in Class 6 = 40

Number of students in Class 7 = 50

Number of students in Class 8 = 45

Comparing these numbers, we see that 50 is the largest number:

40 (Class 6) < 50 (Class 7)

45 (Class 8) < 50 (Class 7)

The class with the maximum number of students is Class 7, with 50 students.

The correct option is (B).

From the bar graph in Question 12, we have the number of students in each class:

Number of students in Class 6 = 40

Number of students in Class 8 = 45

To find the total number of students in Class 6 and Class 8 combined, we add the number of students in these two classes:

Total students = (Students in Class 6) + (Students in Class 8)

Total students = $40 + 45$

We can perform the addition:

$\begin{array}{cc} & 4 & 0 \\ + & 4 & 5 \\ \hline & 8 & 5 \\ \hline \end{array}$

Total students = 85

Therefore, the total number of students in Class 6 and Class 8 combined is 85.

The correct option is (C).

Tally marks are a way to keep track of counts when collecting or organizing data. Each tally mark represents one occurrence of an observation. Groups of five are typically marked as $\bcancel{||||}$.

The purpose of using tally marks for different observations is to count how many times each distinct observation appears in the raw data. The number of times an observation occurs is called its frequency.

Let's consider why the other options are not the primary purpose of tally marks:

(A) Total sum: Tally marks count occurrences, which can be used to find the total number of observations, but not directly the sum of the values themselves unless each tally mark represents a specific value (which is typically 1).

(B) Average: The average (mean) requires summing the values and dividing by the total number of observations. Tally marks help find the number of observations but don't directly provide the sum of values unless used in conjunction with the value of each category.

(D) Range: The range requires finding the highest and lowest values in the dataset, which is not directly determined by tallying frequencies.

Therefore, the primary use of tally marks when organizing raw data is to find the Frequency of each observation.

All the given options are methods of representing data.

Let's explain why each option is a method of representing data:

(A) Raw data table: A raw data table is the simplest form of representing data where the collected facts are listed as they are obtained, usually in a table format. This is the initial representation of the data before any organization or processing.

(B) Tally marks: Tally marks are used to organize raw data by counting the frequency of each observation. While they are a counting tool, they are used within a frequency distribution table, which is a common way to represent organized data, showing how many times each value or category appears. Thus, they are integral to a tabular representation of frequency.

(C) Pictograph: A pictograph is a graphical representation of data where pictures or symbols are used to represent quantities. This provides a visual way to compare data across different categories.

(D) Bar graph: A bar graph is another graphical representation that uses bars (rectangles) of uniform width, with heights proportional to the values or frequencies they represent. This is a common and effective method for comparing discrete categories.

Each of these methods serves to display or show data in a structured or visual format, making them methods of data representation.

The correct option is (A).

Let's evaluate the Assertion (A) and the Reason (R).

Assertion (A): A bar graph is a visual representation of data.

A bar graph uses bars to display data, allowing for easy comparison of quantities. This is indeed a visual method for presenting data. Thus, Assertion (A) is True.

Reason (R): The bars in a bar graph show the frequency of different categories.

In a typical bar graph, the height (or length) of each bar is proportional to the frequency or value of the category it represents. This is how bar graphs convey information about the data distribution across categories. Thus, Reason (R) is True.

Now, let's consider if Reason (R) is the correct explanation for Assertion (A).

Assertion (A) states that a bar graph is a visual representation. Reason (R) explains *how* it visually represents data – by using bars whose lengths correspond to frequencies. The fact that bar heights represent frequencies is the fundamental principle by which a bar graph visually organizes and displays data for comparison. Therefore, Reason (R) correctly explains *why* a bar graph serves as a visual representation of data.

Since both the Assertion and the Reason are true, and the Reason provides a valid explanation for the Assertion, option (A) is the correct answer.

The correct option is (A).

We are given a list of favourite fruits and need to find the frequency of each fruit using tally marks.

Let's count the occurrences of each fruit in the given list:

• Apple: Appears 5 times.
• Mango: Appears 5 times.
• Banana: Appears 3 times.
• Orange: Appears 2 times.

Now, we convert these frequencies into tally marks according to the standard system where $\bcancel{||||}$ represents 5:

• Apple (Frequency 5): $\bcancel{||||}$
• Mango (Frequency 5): $\bcancel{||||}$
• Banana (Frequency 3): $|||$
• Orange (Frequency 2): $||$

Comparing these tally marks with the given options, we find that option (A) matches our results.

Based on the data provided in the Case Study of Question 18, the frequency of each fruit is determined by counting how many times it appears in the list:

The list of favourite fruits is:
Apple, Mango, Banana, Apple, Mango, Apple, Banana, Orange, Mango, Apple, Banana, Mango, Orange, Apple, Mango

Let's count the frequency of each fruit:

• Apple: Appears 5 times.
• Mango: Appears 5 times.
• Banana: Appears 3 times.
• Orange: Appears 2 times.

The frequency of each fruit is:

Apple: 5

Mango: 5

Banana: 3

Orange: 2

The "most popular" fruit is the one with the highest frequency. Comparing the frequencies (5, 5, 3, 2), the highest frequency is 5.

Both Apple and Mango have a frequency of 5, which is the highest frequency in this data set. This means that both Apple and Mango are equally popular and are the modes of the dataset.

Given the options (A) Apple, (B) Mango, (C) Banana, (D) Orange, and acknowledging that both Apple and Mango are tied for the highest popularity, both options (A) and (B) represent a fruit that is most popular.

Assuming the question expects a single answer from the options, and both Apple and Mango are equally most popular, we select one of the options that represents a most popular fruit. Option (A) is Apple, which has the highest frequency (tied with Mango).

The correct option is (A).

The correct option is (A).

Let's match each term with its correct description:

(i) Raw Data: This refers to data collected in its original, unprocessed form. The corresponding description is (b) Data in its original form.

So, (i) matches with (b).

(ii) Frequency: This is the number of times a particular observation occurs in a data set. The corresponding description is (a) How many times an observation occurs.

So, (ii) matches with (a).

(iii) Pictograph: This is a method of representing data using pictures or symbols, where each symbol represents a specific quantity. The corresponding description is (d) Data shown using symbols.

So, (iii) matches with (d).

(iv) Scale (Bar Graph): In a bar graph, the scale on the axis represents the unit length chosen to represent a certain number of actual units of the data (e.g., 1 cm representing 10 students). The corresponding description is (c) A chosen unit length representing a certain number of units.

So, (iv) matches with (c).

Putting the matches together, we get: (i)-(b), (ii)-(a), (iii)-(d), (iv)-(c).

This sequence matches option (A).

The correct option is (A).

Let's analyze each statement regarding a standard bar graph:

(A) The width of the bars can be different. In a standard bar graph, the bars should have a uniform width. Having different widths for bars representing different categories can be misleading as it might visually suggest a different proportion or significance than intended by the height alone. Therefore, this statement is NOT correct.

(B) The bars can be drawn vertically or horizontally. Bar graphs can be oriented either way; the bars can extend upwards from a horizontal axis (vertical bars) or extend sideways from a vertical axis (horizontal bars). This statement is correct.

(C) There should be equal spacing between the bars. Equal spacing between bars is a standard convention to clearly distinguish between categories and prevent the graph from looking like a histogram (which represents continuous data and has no space between bars). This statement is correct.

(D) The height of a bar represents the frequency. The length or height of a bar in a bar graph is directly proportional to the value or frequency of the category it represents. This is the primary way a bar graph displays quantitative data. This statement is correct.

Based on the analysis, the statement that is NOT correct about a bar graph is that the width of the bars can be different.

The correct option is (C).

We are given that one symbol in the pictograph represents 5 students.

The total number of students we need to represent is 25.

To find the number of symbols needed, we divide the total number of students by the number of students each symbol represents:

Number of symbols = $\frac{\text{Total number of students}}{\text{Number of students per symbol}}$

Number of symbols = $\frac{25}{5}$

Calculating the division:

$\frac{25}{5} = 5$

So, 5 symbols are needed to represent 25 students.

Let's check the options:

(A) 3

(B) 4

(C) 5

(D) $\bcancel{||||}$ (This represents 5 in tally marks, which corresponds to option C)

The number of symbols needed is 5, which corresponds to option (C).

The correct option is (C).

Data can be classified based on how it is collected. When data is collected directly from the source by the investigator or researcher for their specific study or purpose, it is called Primary data.

Let's consider the other options:

(A) Secondary data: This refers to data that has already been collected by someone else and is available from existing sources, such as publications, databases, or previous research.

(B) Organized data: This describes data that has been arranged or structured in a systematic way (e.g., in tables), usually after it has been collected (either as raw primary or secondary data).

(D) Published data: This is data that is available in published form (books, journals, websites, etc.). Published data is generally considered a type of secondary data because it was collected and processed by someone else.

Therefore, data collected directly from the source is called Primary data.

The correct option is (A).

We are given the total number of students surveyed and the number of students who like cricket and football.

Total number of students = 30

Number of students who like cricket = 12

Number of students who like football = 8

The number of students who like hockey is the remaining number of students after accounting for those who like cricket and football.

First, find the total number of students who like either cricket or football:

Students (Cricket or Football) = Students (Cricket) + Students (Football)

Students (Cricket or Football) = $12 + 8$

$12 + 8 = 20$

Now, subtract this number from the total number of students to find the number of students who like hockey:

Students (Hockey) = Total students - Students (Cricket or Football)

Students (Hockey) = $30 - 20$

$30 - 20 = 10$

Therefore, 10 students like hockey.

The correct option is (C).

We need to choose the most suitable method to visually represent the population of different states in India. Population figures are typically large numbers.

Let's evaluate the suitability of each option:

(A) Tally marks: Tally marks are used for counting frequencies, usually for small counts of distinct items. Representing millions or tens of millions of people using tally marks would be highly impractical and unintelligible.

(B) Pictograph (if scale is manageable): A pictograph uses symbols. While a large scale could be used (e.g., one symbol represents 1 million people), representing exact populations that are not perfect multiples of the scale can be difficult, requiring fractions of symbols which can be imprecise and hard to interpret quickly for comparison across many states.

(C) Bar graph: A bar graph uses bars whose heights (or lengths) are proportional to the quantities they represent. With a suitably chosen scale on the axis (e.g., in millions or ten millions), a bar graph can effectively display and compare the populations of multiple states visually. The relative heights of the bars immediately show which states have larger or smaller populations.

(D) Raw data table: A raw data table lists the names of the states and their population numbers. While it provides the exact data, it is a numerical representation rather than a visual representation that allows for quick comparison of magnitudes at a glance.

Considering the need for a visual representation to compare large numerical data (populations) across multiple categories (states), the Bar graph is the most suitable method among the given options.

The correct option is (B).

We are given that the number of bicycles produced in April is 750.

The pictograph uses a key where one symbol represents 100 bicycles.

To find the number of symbols needed to represent 750 bicycles, we divide the total number of bicycles by the value each symbol represents:

Number of symbols = $\frac{\text{Total bicycles}}{\text{Bicycles per symbol}}$

Calculating the value from equation (i):

So, you would need 7.5 symbols to represent 750 bicycles.

This means 7 full symbols and one half symbol.

Looking at the options, option (B) is the numerical value 7.5, which is the correct number of symbols required.

Option (D) is a description "7 and a half symbol", which is equivalent to 7.5 symbols.

In this case, both options (B) and (D) convey the same correct quantity. However, option (B) provides the direct numerical result of the calculation.

The correct option is (B).

The number of bicycles produced each month are: January: 400, February: 600, March: 500, April: 750.

The vertical axis of a bar graph represents the quantity being measured, which in this case is the number of bicycles produced. We need to choose a scale such that these values can be clearly represented by the height of the bars, and the graph is easy to read and interpret.

Let's evaluate the given options for the scale (where 1 unit on the axis corresponds to the given number of bicycles):

(A) 1 unit = 1 bicycle: The maximum value is 750. Using this scale would require the vertical axis to extend up to at least 750 units. This would result in a very tall graph, which is usually not practical or easy to plot and read.

(B) 1 unit = 10 bicycles: The maximum value is 750. The height of the bar for April would be $750/10 = 75$ units. The heights for the other months would be $400/10 = 40$, $600/10 = 60$, and $500/10 = 50$ units. An axis extending up to 75 or 80 units is quite manageable, and this scale allows for clear representation of the values, including the 750 value which results in a height ending in .5 if the scale were, say, 20. With a scale of 10, all values are multiples of 10 or 50, making them easy to represent precisely.

(C) 1 unit = 50 bicycles: The maximum value is 750. The height of the bar for April would be $750/50 = 15$ units. The heights for the other months would be $400/50 = 8$, $600/50 = 12$, and $500/50 = 10$ units. An axis extending up to 15 or 20 units is very compact. While possible, it makes the differences between the values less visually prominent compared to a scale of 10.

(D) 1 unit = 1000 bicycles: The maximum value is 750. Using this scale, even the largest value (750) would result in a bar height of $750/1000 = 0.75$ units. All bars would be less than 1 unit high, making the graph very short and the differences between months extremely difficult to discern.

Comparing the options, a scale of 1 unit = 10 bicycles provides a good balance between graph size and the ability to clearly represent and compare the data values which are in the hundreds. It is a commonly used scale for data in this range.

The correct option is (C).

Raw data, as collected, is often unorganized and may consist of a large number of individual facts or observations. In this form, it can be difficult to see patterns, trends, or summarize the information effectively.

To make raw data easily understandable, it needs to go through processing steps:

• Organization: This involves sorting, grouping, and classifying the data, often into frequency tables. This structure helps in summarizing the data.
• Presentation: Once organized, the data can be presented visually using charts and graphs such as bar graphs, pictographs, etc. Visual presentation allows for quick comparison and identification of key features of the data.

Let's look at the other options:

(A) Ignored: Ignoring data means not using it, which certainly doesn't lead to understanding it.

(B) Collected: Collection is the first step, but collected data in its raw form is precisely what is *not* easily understandable without further processing.

(D) Destroyed: Destroying data makes it impossible to work with or understand.

Therefore, raw data needs to be Organized and presented to make it easily understandable.

The correct option is (C).

We are looking for a method of data representation that facilitates a quick visual comparison of quantities (like frequencies or values) across different categories.

Let's consider how each method represents data and its effectiveness for visual comparison:

(A) Tally marks: Tally marks are primarily used for counting frequencies. While they give a count, comparing counts across many categories by just looking at tally marks is not a quick visual process.

(B) Simple frequency table: A frequency table lists categories and their corresponding numerical frequencies. Comparing numbers in a table requires reading and numerical comparison, which is not as quick or intuitive as visual comparison.

(C) Bar graph: A bar graph uses bars of varying heights (or lengths) for different categories, where the height of each bar is proportional to the quantity it represents. The relative heights of the bars immediately provide a visual comparison of the magnitudes across categories, making it easy to see which category is largest, smallest, or how categories compare to each other.

(D) Listing raw data: This is the original list of data points. It is unstructured and does not provide any visual summary or easy way to compare quantities across categories.

The method best suited for quick visual comparison of quantities across different categories is the Bar graph.

The correct option is (B).

We are given that one symbol in the pictograph represents 20 people.

The total number of people we need to represent is 70.

To find the number of symbols needed, we divide the total number of people by the number of people each symbol represents:

Number of symbols = $\frac{\text{Total number of people}}{\text{Number of people per symbol}}$

Calculating the value from equation (i):

So, 3.5 symbols are needed to represent 70 people. This means we need 3 full symbols and 0.5 (or half) of a symbol.

Looking at the options, option (B) states "3 and a half", which accurately describes the requirement of 3.5 symbols.

The correct option is (C).

A frequency distribution table lists each distinct observation or category present in the data and shows how many times each observation appears. The number of times an observation occurs is called its frequency.

When you sum up the frequencies for all the different observations or categories in the table, you are essentially counting the total number of individual data points that were recorded in the original dataset.

Therefore, the sum of all frequencies must equal the total number of observations that were collected initially.

Let's look at why the other options are incorrect:

(A) The number of categories is the count of unique values or groups, not the total count of all data points.

(B) The highest frequency is just the count of the most frequent observation.

(D) The lowest frequency is the count of the least frequent observation.

Thus, the total of the frequencies in a frequency distribution table is equal to the Total number of observations.

The correct option is (B).

In a bar graph, the height of each bar is directly proportional to the quantity it represents, which is typically the frequency of the corresponding category.

Let $H_{\text{Red}}$ be the height of the bar for 'Red', and $H_{\text{Blue}}$ be the height of the bar for 'Blue'.

We are given that the bar for 'Red' is twice the height of the bar for 'Blue'.

The height of a bar represents the frequency. Let $F_{\text{Red}}$ be the frequency of 'Red' and $F_{\text{Blue}}$ be the frequency of 'Blue'. Assuming a constant scale $k$ (where $H = k \times F$), we have:

Substitute equations (ii) and (iii) into equation (i):

Assuming the scale $k$ is not zero, we can cancel $k$ from both sides:

This shows that the frequency of Red is twice the frequency of Blue.

Let's check the options:

(A) The frequency of Red is half the frequency of Blue. This is incorrect.

(B) The frequency of Red is twice the frequency of Blue. This is correct.

(C) There are more categories than colors. This statement is not directly related to the relative heights of the bars for 'Red' and 'Blue'.

(D) The scale is incorrect. The heights being proportional to frequencies is how the scale works. Different heights simply reflect different frequencies according to the scale.

Therefore, if the bar for 'Red' is twice the height of the bar for 'Blue', it means the frequency of Red is twice the frequency of Blue.

The correct option is (B).

Let's analyze the characteristics of a pictograph in relation to the given options:

(A) It is very accurate even for large data sets. Pictographs can struggle with accuracy for large datasets, especially when values are not exact multiples of the symbol's value. Representing fractions of symbols can be imprecise or difficult to interpret precisely.

(B) It is easy to read and understand for beginners. Pictographs use pictures, which makes them visually intuitive and engaging, especially for those who are new to data representation, like young students. They provide a simple way to compare quantities visually. This is a significant advantage.

(C) It is always quick to draw. While simple pictographs might be quick, drawing or finding appropriate symbols, especially for large datasets or when needing to represent fractions of symbols, can be time-consuming. Other methods like bar graphs might be quicker to draw for many datasets.

(D) It can represent any type of data easily. Pictographs are best suited for discrete data where symbols can represent whole units. They are less suitable for continuous data or data where the values vary greatly in magnitude or are complex.

Considering these points, the main advantage of a pictograph among the given options is that it is easy to read and understand, particularly for beginners or a general audience.

The correct option is (A).

Let's analyze each method in the context of representing continuous data.

Continuous data is data that can take any value within a given range (e.g., height, weight, temperature). To represent continuous data, it is typically grouped into class intervals.

(A) Bar graph: Bar graphs are primarily used to represent and compare discrete categories. The bars in a standard bar graph are separated by gaps, which visually implies distinct, separate categories. While you can create a bar graph showing the frequencies of continuous data grouped into intervals, the gaps between the bars are misleading because the data is continuous across the intervals. A bar graph is therefore generally NOT suitable for correctly representing the distribution of continuous data in the way a histogram does.

(B) Pictograph: Pictographs use symbols to represent quantities. Like bar graphs, they are best suited for discrete data where symbols can represent whole units of a category. Representing continuous data, especially when grouped into intervals that might result in fractional symbol counts, can be difficult and often lacks the precision and visual representation of continuity needed for this type of data.

(C) Frequency table: A frequency table can be used to organize both discrete and continuous data. For continuous data, it lists the class intervals and the frequency (number of observations) falling into each interval. This is a suitable method for summarizing continuous data.

(D) Histogram: A histogram is a specific type of bar graph designed for continuous data. It uses bars of equal width representing class intervals, and the height of each bar represents the frequency of observations in that interval. The bars in a histogram are drawn adjacent to each other (without gaps) to visually emphasize the continuous nature of the data. A histogram is the standard graphical representation for the distribution of continuous data.

Comparing the options, a standard Bar graph, with its separated bars, is considered the least suitable method for representing the distribution of continuous data compared to a frequency table (for organization) or a histogram (for graphical representation). While a pictograph is also not ideal, the distinction between bar graphs (discrete) and histograms (continuous) is a fundamental concept in data representation.

The correct option is (B).

Tally marks are used for counting items. The standard method is to draw a vertical stroke for each item up to four. For the fifth item, a diagonal stroke is drawn across the previous four vertical strokes, forming a group of five.

To represent 5 students, we count:

• 1st student: $|$
• 2nd student: $||$
• 3rd student: $|||$
• 4th student: $||||$
• 5th student: $\bcancel{||||}$ (crossing the first four)

So, the tally mark representation for 5 is $\bcancel{||||}$.

Let's look at the options:

(A) $||||$ represents 4.

(B) $\bcancel{||||}$ represents 5 (the standard way). This is correct.

(C) $|||||$ represents 5, but this is not the standard grouping method which uses a diagonal stroke for the fifth mark.

(D) $\bcancel{||||} |$ represents a group of 5 plus one more, so it represents $5+1 = 6$.

Therefore, the correct representation for 5 using standard tally marks is $\bcancel{||||}$.

In the context of statistics, data refers to raw facts, figures, observations, or measurements collected for analysis or study. It can be in the form of numbers, words, measurements, observations, or descriptions.

These collected facts are typically unorganized and need to be processed, organized, and analyzed to derive meaningful information, patterns, or conclusions.

Raw data refers to data collected in its original form, before any statistical techniques are applied to organize, process, or analyze it.

These are the unprocessed and unclassified facts or figures obtained from observations, surveys, experiments, or other sources. For example, a list of heights of students in a class as they were measured, without arranging them in any order, is raw data.

The frequency of an observation in a data set is defined as the number of times that specific observation or value appears in the data set.

It indicates how often a particular item or value occurs within the collection of data.

The purpose of using tally marks is to easily and systematically count the frequency of observations or items in a data set as they occur.

They help in organizing raw data by providing a quick way to keep a running count, especially when dealing with a large number of observations. Each tally mark represents one occurrence, and groups of five ($\bcancel{||||}$) are used for easier counting.

The tally marks for the number $9$ are shown by first making a group of five, represented by a diagonal line crossing four vertical lines, and then adding four more vertical lines.

The tally marks for $9$ are: $\bcancel{||||}\ ||||$

The tally marks for the number $5$ are represented by a group of five, which consists of four vertical lines crossed by a diagonal line.

The tally marks for $5$ are: $\bcancel{||||}$

A pictograph (or pictogram) is a way of representing data using pictures or symbols.

Each picture or symbol represents a certain quantity or frequency. Pictographs are often used to make data easier to understand and more visually appealing, especially for presenting simple comparisons.

The 'key' (also known as a legend) in a pictograph indicates the quantity or numerical value that each single picture or symbol represents.

It is crucial for interpreting the pictograph correctly, as it tells the reader how to convert the count of symbols into the actual frequency or number being represented.

Given that one symbol 🚗 represents $5$ cars.

To find out how many symbols are needed to represent $20$ cars, we need to divide the total number of cars by the value each symbol represents.

Number of symbols = $\frac{\text{Total number of cars}}{\text{Value represented by one symbol}}$

Number of symbols = $\frac{20}{5}$

Number of symbols = $4$

Therefore, $4$ symbols would represent $20$ cars.

This can be shown as: 🚗 🚗 🚗 🚗

A bar graph (or bar chart) is a visual representation of data using rectangular bars.

The bars are drawn either horizontally or vertically, with lengths proportional to the values or frequencies they represent. Bar graphs are used to compare data among different categories.

The two axes in a bar graph are usually called the horizontal axis and the vertical axis.

Conventionally, in many bar graphs, the horizontal axis represents the categories being compared, and the vertical axis represents the frequency or value associated with each category. However, the axes can be switched.

In a bar graph where the bars are drawn vertically, the height of each bar represents the frequency or the numerical value of the category it corresponds to.

If the bars are drawn horizontally, then the length of the bar represents the frequency or value.

Yes, the bars in a bar graph should always have uniform width.

This is important because the visual comparison between the categories is based on the height (or length) of the bars, which represents the frequency or value. If the bars had different widths, the area of the bars would become inconsistent with the values they represent, potentially misleading the viewer and making accurate comparisons difficult. Maintaining uniform width ensures that the height alone correctly reflects the magnitude of the data for each category.

Yes, the gaps between the bars in a bar graph should be uniform.

Maintaining uniform gaps is important for several reasons:

It ensures that the visual representation is clear and unambiguous, making it easy for the viewer to understand that each bar represents a distinct, separate category.

Uniform spacing prevents the visual distortion of the graph that could occur with unequal gaps, which might otherwise suggest false relationships or differences between categories.

Along with uniform bar width, uniform gaps contribute to the overall consistency and readability of the bar graph, ensuring that the focus remains on comparing the heights (or lengths) of the bars, which represent the data values.

A frequency distribution table is a tabular summary of data that shows the frequency (or count) of each distinct value or category within a dataset.

It systematically organizes raw data into classes or categories and lists the number of times each class or value occurs. This makes it easier to analyze and understand the distribution of the data.

The tally mark $\bcancel{||||}$ represents a count of $5$.

The additional tally marks $||$ represent a count of $2$.

To find the total frequency, we add the counts represented by the tally marks.

Frequency = Count of $\bcancel{||||}$ + Count of $||$

Frequency = $5 + 2$

Frequency = $7$

Therefore, if the tally mark is $\bcancel{||||}\text{ }||$, the frequency is $7$.

The main advantage of representing data using pictographs or bar graphs is that they make the data visually understandable and easy to interpret and compare.

Instead of looking at raw numbers in a table, a visual representation allows people to quickly grasp patterns, trends, and differences between categories. This makes complex data more accessible and easier to communicate.

Given that one symbol 🧍 represents $4$ students.

To represent $10$ students, we need to find out how many symbols are required.

Number of symbols = $\frac{\text{Total number of students}}{\text{Value represented by one symbol}}$

Number of symbols = $\frac{10}{4} = 2.5$

This means we need $2$ full symbols and $0.5$ (half) of a symbol.

A full symbol 🧍 represents $4$ students.

Half of a symbol represents half the value of a full symbol, which is $\frac{4}{2} = 2$ students.

So, to represent $10$ students, we would use:

$2$ full symbols 🧍 (representing $2 \times 4 = 8$ students)

$1$ half symbol (representing $2$ students)

The representation for $10$ students would be two full symbols and one half symbol:

🧍 🧍 (and a visual representation of half of the symbol 🧍)

If a bar in a bar graph showing monthly expenses represents 'groceries' and its height reaches up to the level marked $\textsf{₹}5000$ on the value axis (usually the vertical axis), it means that the monthly expense incurred on groceries was $\textsf{₹}5000$.

The height of the bar directly corresponds to the magnitude of the data it represents, according to the scale shown on the axis.

One example of data that could be collected in a classroom and represented using a pictograph is the number of students who prefer different types of fruits.

For example, you could ask students to name their favourite fruit from a list (like Apple, Banana, Orange, Grapes) and count how many students choose each fruit.

This data can then be represented using a pictograph where a symbol, like a drawing of a fruit or a smiling face, represents a certain number of students (e.g., one symbol = $2$ students). The number of symbols shown next to each fruit name would indicate the number of students who prefer that fruit.

One example of data that could be collected in a school and represented using a bar graph is the number of students enrolled in different classes or grades.

For instance, you could collect data on how many students are in Class 6, Class 7, Class 8, Class 9, and Class 10. This would give you different categories (the classes) and the frequency (the number of students) for each category.

A bar graph could then be drawn with the names of the classes on one axis and the number of students on the other axis. Each class would have a bar whose height corresponds to the number of students in that class, allowing for a clear comparison of the student strength across different grades.

It is important to give a title to a pictograph or a bar graph because the title tells the viewer what the graph is about.

The title provides the context for the data being displayed. Without a title, the audience would not know what the pictures, symbols, or bars represent, making it impossible to understand the information or draw meaningful conclusions from the graph.

In a standard pictograph, it is not typical to use entirely different symbols for different categories.

The standard practice is to use a single, uniform symbol throughout the pictograph. The symbol itself represents a unit of the data being measured (as defined by the key), and the frequency of each category is shown by the number of times that same symbol is repeated for that category.

Using different symbols for different categories would generally defeat the purpose of using a single symbol to represent a unit of frequency and could make the pictograph difficult to read and interpret.

No, it is not necessary for the horizontal axis to always represent categories and the vertical axis to represent values in a bar graph.

The axes can be swapped. When the categories are on the horizontal axis and the values (frequencies) are on the vertical axis, it is called a vertical bar graph (or column graph), and the height of the bars represents the values.

When the categories are on the vertical axis and the values are on the horizontal axis, it is called a horizontal bar graph, and the length of the bars represents the values. Both orientations are valid ways to represent data using a bar graph.

Organizing data refers to the process of arranging and presenting raw, unclassified data in a systematic and orderly manner.

The main purpose of organizing data is to make it meaningful, understandable, and easy to analyze.

This can involve grouping data, creating frequency tables, arranging data in ascending or descending order, or representing it visually using graphs or charts. Organized data simplifies interpretation and facilitates the extraction of insights and conclusions.

To answer this question, we first need to collect the data on the favourite subject of $25$ students. Since we cannot actually collect data from a specific class, let's create a sample dataset of $25$ favourite subjects.

Sample Data (Favourite Subjects of $25$ Students):

Maths, Science, English, Maths, Social Studies, Science, English, Maths, Art, Science, Maths, English, Social Studies, Maths, Science, English, Maths, Social Studies, Science, Maths, Art, English, Maths, Science, Social Studies

Now, we will organize this data into a frequency distribution table using tally marks. We list the unique subjects and count how many times each subject appears in the list.

Frequency Distribution Table of Favourite Subjects:

In this table:

The first column lists the different categories of favourite subjects.

The second column shows the tally marks, where each mark represents one student's preference for that subject. Groups of five are indicated by $\bcancel{||||}$.

The third column shows the frequency, which is the total count of students for each subject obtained from the tally marks.

Steps to follow to draw a pictograph:

Step 1: Collect the Data

Gather the raw data that needs to be represented visually.

Step 2: Choose a Suitable Symbol

Select a relevant picture or symbol that can represent the item or unit being counted in the data. The symbol should be simple and easy to understand.

Step 3: Define the Key (or Legend)

Determine the quantity that each single symbol will represent. This is the key. Choosing an appropriate value for the key depends on the range of the data; a larger value per symbol can make the pictograph less crowded for large numbers, while a smaller value allows for more precision. If necessary, decide how to represent fractions of the key value.

Step 4: Draw the Pictograph

For each category or item in the data, draw the corresponding number of symbols based on the frequency and the key. Arrange the symbols neatly, often in rows or columns, next to the category labels.

Step 5: Add a Title and Labels

Provide a clear title for the pictograph that describes what the data is about. Label the categories clearly so the viewer knows what each row or column of symbols represents.

Step 6: Include the Key

Clearly state the key used, explaining what each symbol represents in terms of quantity.

Drawing a pictograph for the given data on absent students:

Given Data:

Monday: 5 absent students

Tuesday: 3 absent students

Wednesday: 0 absent students

Thursday: 7 absent students

Friday: 4 absent students

Chosen Symbol and Key:

Let 🧍 represent 1 absent student.

Pictograph showing the number of absent students during a week:

Key: 🧍 = 1 student

Steps to follow to draw a bar graph:

Step 1: Collect and Organize the Data

Gather the data that needs to be represented. Ensure the data is categorized and the values for each category are clear.

Step 2: Draw the Axes

Draw two perpendicular lines, one horizontal (x-axis) and one vertical (y-axis). These are the axes of the bar graph.

Step 3: Label the Axes

Decide which axis will represent the categories (e.g., subjects, days of the week) and which axis will represent the values or frequencies (e.g., marks, number of students). Label each axis clearly with what it represents.

Step 4: Choose and Mark the Scale on the Value Axis

Select an appropriate scale for the axis that represents the values. The scale should start from zero and cover the entire range of the data values. Mark equal divisions on this axis according to the chosen scale. The choice of scale affects how the bar graph looks; a smaller interval makes the differences between bars more pronounced.

Step 5: Draw the Bars

For each category, draw a rectangular bar. The bars should be of uniform width. The height (if vertical bars) or length (if horizontal bars) of each bar should correspond to the value of that category on the scale of the value axis. Ensure there are equal gaps between the bars.

Step 6: Label the Categories

Write the name of each category clearly below or beside its corresponding bar.

Step 7: Add a Title

Give the bar graph a clear and descriptive title that summarizes the information presented.

Drawing a bar graph for the given data on marks obtained:

Given Data:

To draw the bar graph:

We will draw two axes. The horizontal axis will represent the subjects, and the vertical axis will represent the marks obtained.

We need to choose a scale for the vertical axis. The marks range from 60 to 90. A suitable scale could be divisions of 10 marks, going from 0 to 100.

We draw bars of uniform width for each subject with equal gaps. The height of the bar for Hindi will reach up to 75 on the vertical scale, English up to 60, Maths up to 90, Science up to 85, and Social Studies up to 70.

Labels will be added to the horizontal axis for each subject (Hindi, English, Maths, Science, Social Studies) and the vertical axis will be labeled 'Marks Obtained' with scale markings (0, 10, 20, ..., 100).

A title such as 'Marks Obtained by a Student in Five Subjects' will be added.

Since drawing a graphical bar graph directly in this text format is not possible, the above describes how it would be constructed based on the given data and the steps explained.

Since the pictograph image is not available, we will assume the number of symbols for each colony to answer the questions based on a typical representation.

Let's assume the pictograph shows the following number of symbols:

Colony A: 🌳 🌳 🌳 🌳 🌳 (5 symbols)

Colony B: 🌳 🌳 🌳 (3 symbols)

Colony C: 🌳 🌳 🌳 🌳 🌳 🌳 (6 symbols)

Colony D: 🌳 🌳 🌳 🌳 (4 symbols)

Key: $\text{🌳} = 10$ trees

(a) How many trees were planted in Colony C?

Colony C has 6 symbols. Each symbol represents 10 trees.

Number of trees in Colony C = Number of symbols $\times$ Value per symbol

Number of trees in Colony C = $6 \times 10 = 60$ trees.

(b) In which colony was the maximum number of trees planted?

Calculate the total trees for each colony:

Colony A: $5 \times 10 = 50$ trees

Colony B: $3 \times 10 = 30$ trees

Colony C: $6 \times 10 = 60$ trees

Colony D: $4 \times 10 = 40$ trees

Comparing the number of trees (50, 30, 60, 40), the maximum number of trees planted is 60.

This occurred in Colony C.

(c) How many more trees were planted in Colony A than in Colony D?

Number of trees in Colony A = 50 trees

Number of trees in Colony D = 40 trees

Difference = Number of trees in Colony A $-$ Number of trees in Colony D

Difference = $50 - 40 = 10$ trees.

10 more trees were planted in Colony A than in Colony D.

(d) What was the total number of trees planted in all four colonies?

Total trees = Trees in Colony A + Trees in Colony B + Trees in Colony C + Trees in Colony D

Total trees = $50 + 30 + 60 + 40$

Total trees = $180$ trees.

The total number of trees planted in all four colonies was 180.

Since the image of the bar graph is not available, we will answer the questions based on assumed typical values for the number of students in each class, which would be read from the heights of the bars.

Let's assume the bar graph shows the following number of students:

Class 6: 120 students

Class 7: 100 students

Class 8: 150 students

(a) What is the number of students in Class 7?

Based on our assumption, the bar for Class 7 reaches the level indicating 100 students on the vertical axis.

The number of students in Class 7 is 100.

(b) Which class has the maximum number of students?

Comparing the number of students in each class (120, 100, 150), the maximum number is 150.

This corresponds to Class 8.

(c) What is the difference between the number of students in Class 8 and Class 6?

Number of students in Class 8 = 150

Number of students in Class 6 = 120

Difference = Number of students in Class 8 $-$ Number of students in Class 6

Difference = $150 - 120 = 30$

The difference is 30 students.

(d) What is the total number of students in Class 6, 7, and 8?

Total students = Students in Class 6 + Students in Class 7 + Students in Class 8

Total students = $120 + 100 + 150$

Total students = $370$

The total number of students in Class 6, 7, and 8 is 370.

Given data:

Steps to construct the bar graph:

1. Draw two perpendicular axes, the horizontal axis (x-axis) and the vertical axis (y-axis).

2. Label the horizontal axis as 'Day of the Week' and the vertical axis as 'Number of Visitors'.

3. Choose an appropriate scale for the vertical axis. The number of visitors ranges from 80 to 200. A scale of 1 unit representing 20 visitors ($1 \text{ unit} = 20 \text{ visitors}$) would be suitable, marking points at 0, 20, 40, 60, ..., 200.

4. Mark equal divisions on the horizontal axis for each day of the week (Monday, Tuesday, Wednesday, Thursday, Friday), leaving equal gaps between them.

5. Draw rectangular bars of uniform width for each day. The height of each bar should correspond to the number of visitors on that day according to the chosen scale on the vertical axis.

- Monday: Bar height up to 120.

- Tuesday: Bar height up to 100.

- Wednesday: Bar height up to 80.

- Thursday: Bar height up to 150.

- Friday: Bar height up to 200.

6. Label the title of the bar graph as 'Number of Museum Visitors During a Week'.

Since drawing the bar graph here is not possible, the above description details how it would be constructed.

First, we organize the given data into a frequency distribution table using tally marks.

Given data: Red, Blue, Green, Yellow, Red, Blue, Red, Green, Yellow, Blue, Red, Green, Blue, Blue, Red, Green, Yellow, Red, Blue, Green

Frequency Distribution Table of Favourite Colours:

Now, we draw a pictograph to represent this data. We are asked to choose a key where one symbol represents 2 children.

Let us use the symbol 🧑 to represent 2 children.

Key: 🧑 = 2 children

To represent the frequencies using this key, we divide the frequency by the value of the key (2):

Red: $6 \div 2 = 3$ symbols

Blue: $6 \div 2 = 3$ symbols

Green: $5 \div 2 = 2.5$ symbols (2 full symbols and 1 half symbol)

Yellow: $3 \div 2 = 1.5$ symbols (1 full symbol and 1 half symbol)

Pictograph of Favourite Colours of Children:

Key: 🧑 = 2 children

(Note: A visual representation of half a symbol 🧑 would typically be half of the drawing of the symbol itself.)

Given data:

Steps to construct the bar graph:

1. Draw two perpendicular axes, the horizontal axis (x-axis) and the vertical axis (y-axis).

2. Label the horizontal axis as 'Day' and the vertical axis as 'Sale (in $\textsf{₹}$)'.

3. Choose an appropriate scale for the vertical axis (Sale). The sales values range from 200 to 550. A suitable scale could be 1 unit representing $\textsf{₹}50$ or $\textsf{₹}100$. Let's use a scale of 1 unit representing $\textsf{₹}50$ ($1 \text{ unit} = \textsf{₹}50$) to show clearer differences. Mark points at 0, 50, 100, 150, ..., 600 on the vertical axis.

4. Mark equal divisions on the horizontal axis for each day (Day 1, Day 2, Day 3, Day 4, Day 5), leaving equal gaps between them.

5. Draw rectangular bars of uniform width for each day. The height of each bar should correspond to the sale value on that day according to the chosen scale on the vertical axis:

- Day 1: Bar height up to 300.

- Day 2: Bar height up to 450.

- Day 3: Bar height up to 200.

- Day 4: Bar height up to 550.

- Day 5: Bar height up to 400.

6. Label the title of the bar graph as 'Daily Sales of Stationery Items'.

Since drawing the bar graph directly in this text format is not possible, the above description details how it would be constructed based on the given data and the steps explained.

Comparing Pictographs and Bar Graphs:

Advantages of using a Pictograph:

1. Visually Appealing and Engaging: Pictographs use pictures or symbols related to the data, which makes them more interesting and easier to understand, especially for children or a general audience.

2. Simple Representation: They offer a straightforward visual count of items, making it easy to quickly grasp the magnitude of data for each category, particularly when frequencies are small or can be easily divided by the key value.

Disadvantages of using a Pictograph:

1. Difficulty Representing Large Numbers: If the frequencies are very large, a pictograph can become cluttered and difficult to read unless the key represents a very large value per symbol, which might reduce precision.

2. Difficulty Representing Fractional Values: Representing fractions or parts of a symbol (e.g., half a tree, a quarter of a person) can be awkward or ambiguous and requires creating modified symbols, which is not always straightforward.

3. Requires Careful Design: Choosing an appropriate symbol and key is crucial. A poorly chosen symbol or key can make the pictograph misleading or confusing.

Advantages of using a Bar Graph (compared to Pictographs):

1. Easier to Represent Large Numbers and Precise Values: Bar graphs use a numerical scale, which allows for the representation of a wide range of values accurately, including large numbers and precise measurements, simply by adjusting the scale.

2. Simple Comparison of Magnitudes: The heights (or lengths) of the bars directly represent the values, making it very easy to compare the magnitudes across different categories visually.

3. Handles Fractional/Decimal Values Easily: The scale on a bar graph can easily accommodate fractional or decimal values accurately.

Disadvantages of using a Bar Graph (compared to Pictographs):

1. Less Engaging Visually: While clear, bar graphs are generally less visually stimulating or engaging than pictographs, especially for young audiences.

2. Requires Understanding of Scales: Interpreting a bar graph accurately requires understanding the numerical scale on the value axis.

Example where a Bar Graph might be Preferred over a Pictograph:

A bar graph would be preferred over a pictograph when representing the monthly rainfall in different cities, where the values might be large numbers or include decimal points (e.g., City A: 125.5 mm, City B: 98 mm, City C: 210.75 mm).

It would be difficult and inaccurate to represent precise decimal values like 125.5 or 210.75 using discrete symbols in a pictograph, even with fractional symbols. A bar graph with a continuous numerical scale allows for the precise height of the bar to represent these exact values, making the comparison and interpretation of rainfall amounts accurate and clear.

Given data on the number of different types of pets owned by students:

To represent this data using a pictograph, we need to choose a suitable symbol and a key.

Let us choose the symbol 🐾 (paw print) or 🐕 (dog) or 🐈 (cat) etc. Let's use a generic animal symbol 🐾.

The numbers are 8, 6, 4, and 2. All are even numbers. An appropriate key would be one symbol representing 2 students.

Key: 🐾 = 2 students

Now, we calculate the number of symbols needed for each type of pet:

Dog: $8 \div 2 = 4$ symbols

Cat: $6 \div 2 = 3$ symbols

Fish: $4 \div 2 = 2$ symbols

Bird: $2 \div 2 = 1$ symbol

Pictograph showing the number of different types of pets owned by students:

Key: 🐾 = 2 students

Given data on the population of a town over five consecutive years:

Steps to construct the bar graph:

1. Draw two perpendicular axes, the horizontal axis (x-axis) and the vertical axis (y-axis).

2. Label the horizontal axis as 'Year' and the vertical axis as 'Population'.

3. Choose an appropriate scale for the vertical axis (Population). The population values range from 15000 to 21000. It's best to start the scale at 0. A suitable scale could be 1 unit representing 1000 or 2000 people. Let's use a scale of 1 unit representing 1000 people ($1 \text{ unit} = 1000 \text{ people}$). Mark points at 0, 1000, 2000, and so on, up to at least 21000 (e.g., up to 22000 or 25000) on the vertical axis.

4. Mark equal divisions on the horizontal axis for each year (2016, 2017, 2018, 2019, 2020), leaving equal gaps between them.

5. Draw rectangular bars of uniform width for each year. The height of each bar should correspond to the population value for that year according to the chosen scale on the vertical axis:

- Year 2016: Bar height up to 15000.

- Year 2017: Bar height up to 16500.

- Year 2018: Bar height up to 18000.

- Year 2019: Bar height up to 19500.

- Year 2020: Bar height up to 21000.

6. Label the title of the bar graph as 'Population of a Town Over Five Years'.

Since drawing the bar graph directly in this text format is not possible, the above description details how it would be constructed based on the given data and the steps explained.

To organize the given data into a frequency distribution table, we list the distinct values for the number of hours spent reading and then use tally marks to count how many students read for each number of hours.

Given data for 15 students (in hours):

1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 5

Frequency Distribution Table of Reading Hours:

In this table, the 'Reading Hours' column lists the number of hours students read. The 'Tally Marks' column shows the count for each hour using tally marks. The 'Frequency' column gives the total count derived from the tally marks.