NCERT Solutions for Class 6 Maths Chapter 04 Data Handling and Presentation

 

Page 75

Question. Naresh and Navya decided to go to each student in the class and ask what their favourite game is. Then they prepared a list. Navya is showing the list:
Answer: The table displays the game preferences that students favor. Looking at the data, we can work out which game is liked the most by counting how many times each game appears in the list.

Exam Tip: When given raw data, always organize it by counting the frequency of each item to find patterns and identify the most common choice.

 

Question. Figure it Out

1. What would you do to find the most popular game among Naresh's and Navya's classmates?
Answer: To find the most popular game, I would count how many times each game appears in the list. The game that is mentioned the most times is the one that the majority of students prefer.

Exam Tip: Always organize unstructured data through tallying or counting frequencies before drawing any conclusions.

 

2. What is the most popular game in their class?
Answer: Hockey is the most popular game, with 7 students choosing it.

Exam Tip: Provide the exact count when stating the most frequent item to show you have analyzed the data thoroughly.

 

3. Try to find out the most popular game among your classmates.
Answer: To find the most popular game in my class, I would follow a similar process. I would ask each classmate their favorite game, write down their responses, and then tally the results to see which game appears most frequently in our list.

Exam Tip: Always record data systematically and ensure each person is counted exactly once to avoid errors in your final count.

 

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Question 4. Pari wants to respond to the questions given below. Put a tick (✓) for the questions where she needs to carry out data collection and put a cross (✗) for the questions where she doesn't need to collect data. Discuss your answers in the classroom.
(a) What is the most popular TV show among her classmates?
(b) When did India get independence?
(c) How much water is getting wasted in her locality?
(d) What is the capital of India?
Answer:
(a) What is the most popular TV show among her classmates? (✓) Tick - Data collection is needed since she must ask her classmates about their viewing habits.
(b) When did India get independence? (✗) Cross - No data collection is needed; this is a historical fact that is already known.
(c) How much water is getting wasted in her locality? (✓) Tick - Data collection is needed to measure or observe the water usage in her locality.
(d) What is the capital of India? (✗) Cross - No data collection is needed; this is a known fact.
In simple words: Questions about something that already has a known answer don't need data collection. Questions about something new we need to find out about our own group or area do need us to gather information.

Exam Tip: The key difference is whether the information is already known and fixed (no data collection needed) or whether it depends on gathering new information from a specific group or location (data collection is needed).

 

Page 76

Question. Figure it Out - Complete the table to help Shri Nilesh to purchase the correct numbers of sweets:
Answer: Based on the tally marks shown, the table should be completed as follows:

In simple words: Count the tally marks in each row - every group of 5 lines crossed equals 5, and any leftover lines equal 1 each. Add them together to get the total number for that sweet.

Exam Tip: Always remember that a group of 5 tally marks (four vertical lines with one diagonal line through them) represents 5 items, not 4.

 

Question. How many students chose jalebi?
Answer: 6 students chose jalebi.

Exam Tip: Read the number directly from the completed column of the table.

 

Question. Barfi was chosen by _______ students?
Answer: Barfi was chosen by 3 students.

Exam Tip: Match the sweet name to its corresponding row and read the number value.

 

Question. How many students chose gujiya?
Answer: 13 students chose gujiya.

Exam Tip: When reading from a tally table, count each complete group of 5 and add any remaining marks.

 

Question. Rasgulla was chosen by _______ students?
Answer: Rasgulla was chosen by 7 students.

Exam Tip: Double-check your tally counting by adding up the total of all sweets to verify it matches the total number of students surveyed.

 

Question. How many students chose gulab jamun?
Answer: 9 students chose gulab jamun.

Exam Tip: Adding all the numbers (6 + 9 + 13 + 3 + 7) should give you the total number of students surveyed - this is a good check on your work.

 

Question. Is the above table sufficient to distribute each type of sweet to the correct student? Explain. If it is not sufficient, what is the alternative?
Answer: No, the table is not sufficient to distribute each sweet correctly to individual students. The table only shows the total count of how many students prefer each sweet type, but it does not show which specific student likes which sweet. To properly distribute the sweets to individual students, we would need a separate list that links each student's name to their sweet preference. This could be done by adding another column showing the names of students next to their chosen sweet in the table. This way, Shri Nilesh would know exactly which student gets which sweet.

Exam Tip: Understand the difference between grouped summary data (which shows totals) and individual-level data (which shows specific details about each person). Summary tables are useful for finding patterns but not for individual assignments or distributions.

 

Page 77

Question. Figure it Out - Sushri Sandhya asked her students about the sizes of the shoes they wear. She noted the data on the board: 4 5 3 4 3 4 5 5 4 / 5 5 4 5 6 4 3 5 6 / 4 6 4 5 7 5 6 4 5. She then arranged the shoe sizes of the students in ascending order: 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 7
Answer:
(1.) Help her to figure out the following:
- The largest shoe size in the class is 7.
- The smallest shoe size in the class is 3.
- There are 10 students who wear shoe size 5.
- There are 15 students who wear shoe sizes larger than 4.

(2.) How did arranging the data in ascending order help to answer these questions?
Arranging data in ascending order makes it quick to spot the smallest and largest values, making it easier to compare and analyze the dataset. It helps you count frequencies more easily and identify patterns, like how many students fall into specific categories, simplifying the process of answering data-based questions.

(3.) Are there other ways to arrange the data?
Yes, data can be arranged in descending order to find the largest values first, or grouped by frequency to quickly see the most common entries. Another method is grouping data into ranges, helping identify patterns or distributions across broader categories, making analysis more manageable and clear.

(4.) Write the names of a few trees you see around you. When you observe a tree on the way from your home to school (or while walking from one place to another place), record the data and fill in the following table:
In simple words: Putting numbers in order from smallest to biggest helps you quickly find the smallest and biggest values. It also makes it easier to count how many of each number you have and spot patterns in the data.

Exam Tip: When faced with messy raw data, always organize it first - whether in ascending or descending order, or by counting frequencies - before trying to answer questions about it. This step is essential for accurate analysis.

 

Question. (5.) Take a blank piece of paper and paste any small news item from a newspaper. Each student may use a different article. Now, prepare a table on the piece of paper as given below. Count the number of each of the letters 'c', 'e', 'i', 'r', 'x' and 'x' in the words of the news article, and fill in the table.
Answer:
(a) The letter found the most number of times is: e
(b) The letter found the least number of times is: x

Exam Tip: When counting letter frequencies in a text, use tally marks to track as you go through the article systematically to avoid missing any letters or double-counting.

 

Page 77 (continued)

Question. (c) List the five letters 'c', 'e', 'i', 'r', 'x' in ascending order of frequency. Now, compare the order of your list with that of your classmates. Is your order the same or nearly the same as theirs? (Almost everyone is likely to get the order 'x, c, r, i, e'.) Why do you think this is the case?
Answer: When we list these letters in ascending order by how often they appear, most people get approximately the same order: x, c, r, i, e. This happens because the English language follows predictable patterns in which letters appear most and least frequently. The letter 'e' is one of the most common letters in English text, while 'x' is uncommon. This pattern is consistent across different texts and writers, which is why most people find similar results.

Exam Tip: Recognize that language and nature have underlying patterns - the frequency of letters in English text is not random but follows consistent rules, which is why different people analyzing different texts still get similar frequency distributions.

 

Question. (d) Write the process you followed to complete this task.
Answer: I selected a small news article and pasted it on paper. Then, I counted how many times each letter (c, e, i, r, and x) appeared in the article by going through it word by word. I recorded the frequencies in a table. After completing this, I listed the letters in ascending order based on their frequency counts.

Exam Tip: When describing your process, explain each step clearly and in order so that someone else could follow the same steps and achieve the same result.

 

Question. (e) Discuss with your friends the processes they followed.
Answer: When I discussed with my friends, I found that some classmates had counted manually by scanning the article, while others used a more systematic approach like highlighting or underlining the target letters. Some had used tally marks, which helped them keep track more accurately. Although our processes varied, our final frequency counts were quite similar because we were all analyzing the same or similar news articles.

Exam Tip: Different methods can lead to the same correct answer - the key is using a systematic, careful approach to avoid errors rather than relying on memory or quick guesses.

 

Question. (f) If you do this task with another news item, what process would you follow?
Answer: For another news item, I would first highlight each target letter as I find it to ensure I don't miss any or count them twice. Then, I would tally the count for each letter in a separate column. Finally, I would create the frequency table and arrange the letters in ascending order of their frequencies.

Exam Tip: Having a refined process based on what you learned from the first task makes the second task faster and more accurate.

 

Page 82

Question. If they want to show their data through a pictograph, where they also use one symbol for each student, as Lakhanpal did, what are the challenges they might face?
Answer: If Jarina and Sangita want to show their data through a pictograph using one symbol for each student, like Lakhanpal did, the challenges they face include:

• Space and Clarity: Since there are a large number of students, using one symbol for each student would require a lot of space, making the pictograph crowded and difficult to interpret.
• Time Consumption: Drawing individual symbols for every student would be very time-consuming, especially when the number of students is high.
• Handling Non-Exact Numbers: If the number of students isn't a simple multiple of the symbols used (for example, 33 or 27), it would be challenging to represent these values accurately without adjusting the scale (for example, 1 symbol representing 5 or 10 students).

In simple words: When you have many students, drawing one symbol for each person makes the picture too full and takes too much time. Also, if the number doesn't divide evenly, you can't show it clearly.

Exam Tip: Understand that pictographs are best used when data values are small or can be represented with a reasonable scale - when numbers are large, a different representation method is more practical.

 

Page 83

Question. What could be the problems faced in preparing such a pictograph, if the total number of students present in a class is 33 or 27?
Answer: If the total number of students in a class is 33 or 27, the problems faced in preparing a pictograph are:

• Difficulty in Representation: Since 33 and 27 are not exact multiples of 5 or 10, using one symbol to represent 5 or 10 students would create fractions or incomplete symbols, which can be challenging to represent accurately in a simple pictograph.
• Inconsistent Scaling: If we choose a scale where 1 symbol represents 5 or 10 students, it becomes difficult to visually represent numbers like 33 or 27 without breaking a symbol into parts, leading to a lack of clarity in the pictograph.
• Visual Confusion: Using fractional symbols can make the pictograph harder to interpret, especially for those unfamiliar with the concept of proportional representation.

In simple words: When the total is 33 or 27, and you try to use symbols representing 5 or 10 students each, you end up with fractions of symbols. This makes the pictograph confusing and hard to read.

Exam Tip: When choosing a scale for a pictograph, always pick a value that divides evenly into your total or most of your data values to avoid messy fractional symbols.

 

Page 83

Question. Figure it Out - (1.) The following pictograph shows the number of books borrowed by students, in a week, from the library of Middle School, Ginnori:
Answer:
(a) The day with the minimum number of books borrowed was Thursday, when 0 books were borrowed.

Exam Tip: Always scan all days or categories shown in a pictograph to identify which has the fewest symbols.

 

Question. (1.) (b) What was the total number of books borrowed during the week?
Answer: Total number of books borrowed during the week is 24.

Exam Tip: Add up the number of books for each day to get the weekly total.

 

Question. (1.) (c) On which day were the maximum number of books borrowed? What may be the possible reason?
Answer: The maximum number of books (8 books) were borrowed on Saturday. A possible reason for this is that more students might visit the library on weekends or near the end of the week, possibly because they have more free time to read or borrow books for the upcoming week.

Exam Tip: When explaining patterns in data, think about real-world factors like weekends, holidays, or people's daily routines that might cause variations in borrowing or usage patterns.

 

Question. (2.) Magan Bhai sells kites at Jamnagar. Six shopkeepers from nearby villages come to purchase kites from him. The number of kites he sold to these six shopkeepers are given below:
Answer:

Prepare a pictograph using the symbol to represent 100 kites. Answer the following questions:

(a) Rani purchased 300 kites, therefore there are 3 symbols representing Rani's kites.

(b) Poonam Ben purchased the maximum number of kites, with a total of 700 kites.

(c) Jasmeet purchased 450 kites, which is more than the 250 kites purchased by Chaman.

(d) Rukhsana says Poonam Ben purchased more than double the number of kites that Rani purchased. Is she correct? Why?
Yes, Rukhsana is correct. Poonam Ben purchased 700 kites, which is more than double Rani's 300 kites. Double of 300 is 600, and 700 exceeds this amount.
In simple words: When you use symbols to stand for a number, count the symbols for each shopkeeper and multiply by what each symbol represents to find the total.

Exam Tip: Always verify numerical comparisons by doing the actual calculation - double-checking prevents errors when interpreting pictograph data.

 

Page 86

Question. Answer the following questions using the bar graph: (1.) In Class 2, _______ students were absent that day.
Answer: In Class 2, 5 students were absent that day.

Exam Tip: Read bar graph values carefully by checking where the top of each bar aligns with the vertical axis scale.

 

Question. (2.) In which class were the maximum number of students absent?
Answer: In class 8, the maximum number of students (7) were absent.

Exam Tip: To find the maximum or minimum value in a bar graph, compare the heights of all bars and identify the tallest or shortest one.

 

Question. (3.) Which class had full attendance that day?
Answer: Class 5 had full attendance that day (0 students absent).

Exam Tip: A bar showing zero height or a bar at the bottom of the graph indicates no absence, meaning full attendance for that class.

 

Page 88

Question. Figure it Out - (1.) How many total cars passed through the crossing between 6 am and noon?
Answer: The total number of cars passed during each hour:
6-7 am : 150 cars
7-8 am : 1200 cars
8-9 am : 1000 cars
9-10 am : 800 cars
10-11 am : 600 cars
11-12 pm : 600 cars

Total = 150 + 1200 + 1000 + 800 + 600 + 600 = 4350 cars

Exam Tip: When reading horizontal bar graphs, carefully match each bar to its label on the vertical axis and read the value from the horizontal axis.

 

Question. (2.) Why do you think so little traffic occurred during the hour of 6-7 am, as compared to the other hours from 7 am-noon?
Answer: Traffic is typically low between 6-7 am because it is early in the morning and fewer people are on the roads at that time. Most people might not have started their daily activities or commutes yet, so there are fewer vehicles traveling.

Exam Tip: When analyzing traffic patterns, consider people's daily routines - early morning hours generally have less activity than typical working hours.

 

Question. (3.) Why do you think the traffic was the heaviest between 7 am and 8 am?
Answer: Traffic is usually heaviest between 7 am and 8 am because this is a common time for people to commute to work, school, or other activities. This period marks the start of the morning rush hour.

Exam Tip: The peak traffic hours correspond to when most people are starting their daily commutes - typically morning rush hour (7-9 am) and evening rush hour (4-6 pm).

 

Question. (4.) Why do you think the traffic was lesser and lesser each hour after 8am all the way until noon?
Answer: After 8 am, the morning rush hour gradually decreases as most people have already reached their destinations. As the day progresses, traffic naturally reduces because fewer people are on the road during mid-morning, until lunchtime or afternoon activities begin.

Exam Tip: Understand that traffic patterns follow people's daily schedules - once the initial rush passes, traffic naturally decreases until the next peak period begins.

 

Page 93

Question. Use the bar graph to answer the following questions: (1.) On which item does Imran's family spend the most and the second most?
Answer: Imran's family spends the most on food. The second most is spent on house rent.

Exam Tip: When comparing items on a bar graph, identify the tallest bar and the second tallest bar to find the top two spending categories.

 

Question. (2.) Is the cost of electricity about one-half the cost of education?
Answer: Yes, the cost of electricity (Rs. 400) is about half the cost of education (Rs. 800), as Rs. 400 is exactly 50% of Rs. 800.

Exam Tip: When comparing values, use proportional reasoning - check if one value is roughly half, double, or equal to another value from the graph.

 

Question. (3.) Is the cost of education less than one-fourth the cost of food?
Answer: No, the cost of education (Rs. 800) is not less than one-fourth the cost of food (Rs. 3400). One-fourth of Rs. 3400 is Rs. 850 and the cost of education is only slightly less than this, but not noticeably less than one-fourth.

Exam Tip: To check if a value is less than a fraction of another value, calculate that fraction first, then compare - this ensures accuracy in your answer.

 

Question. Figure it Out - (1.) Samantha visited a tea garden and collected data of the insects and critters she saw there. Here is the data she collected:
Answer: Help her prepare a bar graph representing this data. The bar graph should show each type of insect on the horizontal axis and the number of each insect on the vertical axis. Mites (6), Caterpillars (10), Beetles (5), Butterflies (3), and Grasshoppers (2) should each have a bar corresponding to their count.

Exam Tip: When preparing a bar graph from a data table, ensure each category gets its own bar with a height proportional to its value, and clearly label both axes.

 

Question. (2.) Pooja collected data on the number of tickets sold at the Bhopal railway station for a few different cities of Madhya Pradesh over a 2-hour period.
Answer: She used this data and prepared a bar graph on the board to discuss the data with her students, but someone erased a portion of the graph. The erased portion can be reconstructed by using the data table provided. The missing bar for Sagar should be drawn at a height of 16 units to match the data table. The bar for Seoni also appears to need adjustment if it was erased.

Exam Tip: When a graph is incomplete or partially erased, always refer back to the original data table to reconstruct the missing parts accurately.

 

Question. (a) Write the number of tickets sold for Vidisha above the bar.
Answer: The number of tickets sold for Vidisha is 24.

Exam Tip: Always verify graph readings against the data table provided with the graph.

 

Question. (b) Write the number of tickets sold for Jabalpur above the bar.
Answer: The number of tickets sold for Jabalpur is 20.

Exam Tip: Match each bar in the graph to its corresponding data value in the table.

 

Question. (c) The bar for Vidisha is 6 unit lengths and the bar for Jabalpur is 5 unit lengths. What is the scale for this graph?
Answer: The scale for this graph is 1 unit length = 4 tickets. This is because Vidisha has 24 tickets and 6 unit lengths (24 ÷ 6 = 4), and Jabalpur has 20 tickets and 5 unit lengths (20 ÷ 5 = 4).

Exam Tip: To find the scale of a bar graph, divide the actual value by the bar length to find what each unit represents.

 

Question. (d) Draw the correct bar for Sagar.
Answer: For Sagar, we have 16 tickets sold. Using the scale of 1 unit length = 4 tickets, we need to draw a bar of length 4 units (16 ÷ 4 = 4). This bar should be placed above the "Sagar" label on the horizontal axis.

Exam Tip: When drawing a bar on a graph with a known scale, divide the data value by the scale to find the correct bar length.

 

Question. (e) Add the scale of the bar graph placing the correct numbers on the vertical axis.
Answer: The vertical axis should be labeled with the scale: 0, 4, 8, 12, 16, 20, 24, 28, etc., increasing by 4 each time to match the scale of 1 unit = 4 tickets.

Exam Tip: When labeling the vertical axis of a bar graph, use consistent intervals that match your chosen scale to make the graph easy to read.

 

Question. (f) Are the bars for Seoni and Indore correct in this graph? If not, draw the correct bar(s).
Answer: Seoni has 16 tickets, which should be represented by a bar of 4 unit lengths. Indore has 28 tickets, which should be represented by a bar of 7 unit lengths. Check the graph to see if these bars match the correct lengths. If they don't, redraw them to the correct proportions using the scale of 1 unit = 4 tickets.

Exam Tip: Always double-check that all bars in a graph are correctly drawn to scale by verifying each value against the data table.

 

Question. (3.) Chinu listed the various means of transport that passed across the road in front of his house from 9 AM to 10 AM:
Answer:
(a) Prepare a frequency distribution table for the data.
Looking at the transport data, we can organize it as follows:

(b) Which means of transport was used the most?
Bike was the most frequently used means of transport with 12 occurrences.

(c) If you were there to collect this data, how could you do it? Write the steps or process.
To collect this data, I would stand at the location and observe all vehicles passing by. I would use tally marks to record each vehicle type I see. I would organize the tally marks in a table with columns for each transport type. After the observation period, I would count the tally marks for each type to get the total frequency.
In simple words: Stand in one spot and watch the road. Every time you see a vehicle, make a mark next to its type. Count all the marks at the end.

Exam Tip: The most systematic way to collect raw data like this is to use tally marks in real time, as it prevents counting errors and is faster than trying to count from memory later.

 

Question. (4.) Roll a die 30 times and record the number you obtain each time. Prepare a frequency distribution table using tally marks. Find the number that appeared:
Answer:

(a) The minimum number of times:
Each number appears 5 times (assuming a fair die and random rolls).

(b) The maximum number of times:
Each number appears 5 times (assuming a fair die and random rolls).

(c) Find numbers that appeared an equal number of times:
All numbers (1, 2, 3, 4, 5, 6) appeared an equal number of times - 5 times each.
In simple words: When you roll a fair die many times, each number should show up about the same number of times. This is called probability.

Exam Tip: With a fair die, over many rolls, each face should appear roughly equally often. Significant deviations might suggest the die is biased.

 

Question. (5.) Faiz prepared a frequency distribution table of data on the number of wickets taken by Jaspreet Bumrah in his last 30 matches:
Answer:

(a) What information is this table giving?
This table shows how many matches Jaspreet Bumrah took 0, 1, 2, 3, 4, 5, 6, or 7 wickets in over his last 30 matches. For example, he took 0 wickets in 2 matches, 1 wicket in 4 matches, and so on.

(b) What may be the title of this table?
A suitable title could be: "Frequency Distribution of Wickets Taken by Jaspreet Bumrah in His Last 30 Matches" or simply "Bumrah's Wicket Distribution".

(c) What caught your attention in this table?
The most striking feature is that Bumrah took 3 wickets in the most matches (8 matches), showing that taking 3 wickets in a match is his most common performance level.

(d) In how many matches has Bumrah taken 4 wickets?
Bumrah has taken 4 wickets in 3 matches.

(e) Mayank says "If we want to know the total number of wickets taken in this way, we have to add the numbers 0, 1, 2, 3 ..., up to 7." Can Mayank get the total number of wickets taken in this way? Why?
No, Mayank cannot get the total number of wickets taken by simply adding 0 + 1 + 2 + 3 + 4 + 5 + 6 + 7. Instead, he must multiply each wicket count by how many matches he took that many wickets, then add all those products together. For example: (0 x 2) + (1 x 4) + (2 x 6) + (3 x 8) + (4 x 3) + (5 x 5) + (6 x 1) + (7 x 1).

(f) How would you correctly figure out the total number of wickets taken by Bumrah in his last 30 matches, using this table?
To find the total wickets, multiply each wicket value by its frequency (number of matches) and then add all products: (0 x 2) + (1 x 4) + (2 x 6) + (3 x 8) + (4 x 3) + (5 x 5) + (6 x 1) + (7 x 1) = 0 + 4 + 12 + 24 + 12 + 25 + 6 + 7 = 90 total wickets in 30 matches.
In simple words: To get a total from a frequency table, you must multiply each value by how many times it happened, not just add the numbers together.

Exam Tip: When working with frequency tables, remember that the total is found by: (each value × its frequency), then summing all these products - never just add the values or frequencies alone.

 

Question. (6.) The following pictograph shows the number of tractors in five different villages.
Answer:
Observe the pictograph and answer the following questions:

(a) Which village has the smallest number of tractors?
Village D has the smallest number of tractors with 3 tractors.

(b) Which village has the most tractors?
Village C has the most tractors with 8 tractors.

(c) How many more tractors does Village C have than Village B?
Village C has 8 tractors and Village B has 5 tractors. The difference is 8 - 5 = 3 more tractors in Village C.

(d) Komal says, "Village D has half the number of tractors as Village E." Is she right?
Village D has 3 tractors and Village E has 6 tractors. Half of 6 is 3, so yes, Komal is correct.
In simple words: Count the tractor symbols for each village and compare them. If one village has half as many symbols as another, then one has half the tractors.

Exam Tip: When comparing values in a pictograph, count symbols carefully and verify numerical relationships like double, half, or equal before making statements.

 

Question. (7.) The number of girl students in each class of a school is depicted by a pictograph:
Answer:
Observe this pictograph and answer the following questions:

(a) Which class has the least number of girl students?
Class 8 has the least number of girl students with 2 girls.

(b) What is the difference between the number of girls in Class 5 and 6?
Class 5 has 2 girls and Class 6 has 4 girls. The difference is 4 - 2 = 2 girls.

(c) If 2 more girls were admitted in Class 2, how would the graph change?
If 2 more girls were admitted in Class 2, the current count of 4 girls would increase to 6 girls. On the pictograph, one more symbol (representing 4 girls) would need to be added to the Class 2 row, along with a half symbol for the remaining 2 girls.

(d) How many girls are there in Class 7?
Class 7 has 3 girls.

(e) Mudhol Hounds (a type of breed of Indian dogs) are largely found in North Karnataka's Bagalkote and Vijaypura districts. The government took an initiative to protect this breed by providing support to those who adopted these dogs. Due to this initiative, the number of these dogs increased. The number of Mudhol dogs in six villages of Karnataka are as follows -
Village A: 18, Village B: 36, Village C: 12, Village D: 48, Village E: 18, Village F: 24
Prepare a pictograph and answer the following questions:

(a) What will be a useful scale or key to draw this pictograph?
A useful scale would be: 1 symbol = 6 dogs. This allows all numbers to divide evenly and keeps the pictograph manageable in size.

(b) How many symbols will you use to represent the dogs in Village B?
Village B has 36 dogs. Using a scale of 1 symbol = 6 dogs, we need 36 ÷ 6 = 6 symbols for Village B.

(c) Kamini said that the number of dogs in Village B and Village D together will be more than the number of dogs in the other 4 villages. Is she right? Give reasons for your response.
Village B has 36 dogs and Village D has 48 dogs, totaling 36 + 48 = 84 dogs. The other 4 villages (A, C, E, F) have: 18 + 12 + 18 + 24 = 72 dogs. Since 84 > 72, yes, Kamini is correct. The dogs in Villages B and D together are more than in the other four villages combined.

Exam Tip: When making comparative statements about data, always calculate the exact values and compare them to verify the claim is true.

 

Question 9. A survey of 120 school students was conducted to find out which activity they preferred to do in their free time.

Draw a bar graph to illustrate the above data taking the scale of 1 unit length = 5 students. Which activity is preferred by most students other than playing?
Answer: A bar graph with the given scale would show Playing with 9 units, Reading story books with 6 units, Watching TV with 4 units, Listening to music with 2 units, and Painting with 3 units on the vertical axis. Reading story books is the activity preferred by most students after playing, as 30 students chose this option.
In simple words: Reading story books is liked by the second-most number of students (30 out of 120).

Exam Tip: Always check the scale carefully and ensure each bar's height matches the frequency divided by the scale factor - this prevents drawing errors.

 

Question 10. Students and teachers of a primary school decided to plant tree saplings in the school campus and in the surrounding village during the first week of July. Details of the saplings they planted are as follows -
(a) The total number of saplings planted on Wednesday and Thursday is _______.
(b) The total number of saplings planted during the whole week is _______.
(c) The greatest number of saplings were planted on _______, and the least number of saplings were planted on _______.
Why do you think that is the case? Why were more saplings planted on certain days of the week and less on others? Can you think of possible explanations or reasons? How could you try and figure out whether your explanations are correct?
Answer:
(a) The total number of saplings planted on Wednesday and Thursday is 30 + 40 = 70.
(b) The total number of saplings planted during the whole week is 52 + 40 + 30 + 40 + 50 + 60 + 40 = 312.
(c) The greatest number of saplings were planted on Saturday and the least number of saplings were planted on Wednesday.
The most saplings were planted on Saturday likely due to greater volunteer availability on weekends, when students feel free from homework and school work. In contrast, fewer saplings were planted on Wednesday because of midweek commitments. To confirm this, check volunteer participation data, event schedules and weather conditions to understand why certain days saw more or less activity.
In simple words: Saturday had the most planting because more helpers were free on weekends. Wednesday had the least because people were busy in the middle of the week.

Exam Tip: When reading bar graphs, read values directly from the bar height against the y-axis scale - double-check your scale interpretation before calculating totals.

 

Question 11. The number of tigers in India went down drastically between 1900 and 1970. Project Tiger was launched in 1973 to track and protect tigers in India. Starting in 2006, the exact number of tigers in India was tracked. Shagufta and Divya looked up information about the number of tigers in India between 2006 and 2022 in 4-year intervals. They prepared a frequency table for this data and a bar graph to present this data, but there are a few mistakes in the graph. Can you find those mistakes and fix them?

Answer: The mistakes in the original graph are: (1) The horizontal bar graph shows 2022 at the top and 2006 at the bottom, but the bars do not accurately represent the values from the table. The bar for 2022 should be the longest (3700 tigers), but it appears shorter than expected. (2) The scale on the x-axis and the bar lengths do not match the actual data values. (3) Some bars are not proportional to the numbers they represent. The corrected bar graph should show 2006 with a bar extending to 1400, 2010 to 1700, 2014 to 2200, 2018 to 3000, and 2022 to 3700, with each bar's length accurately reflecting its value according to a consistent scale (e.g., 1 unit = 500 tigers).
In simple words: The bars in the original graph do not match the numbers in the table. Each bar should be drawn to show the exact number of tigers for that year, with longer bars for bigger numbers.

Exam Tip: When correcting graphs, always verify that the bar length is proportional to the data value and that the scale is applied consistently across all bars.

 

Question 1. The bar graph representing the insects and critters in a tea garden:
Answer: The bar graph shows the frequency of different insects and critters found in a tea garden. Mites appear 6 times, Caterpillars appear 10 times, Beetles appear 5 times, Butterflies appear 3 times, and Grasshoppers appear 2 times. Caterpillars are the most common insect in this tea garden, appearing nearly twice as often as Mites. The scale uses 1 unit to represent 1 insect or critter, making it easy to read exact counts from the bar heights.
In simple words: The graph shows how many of each type of bug was found. Caterpillars are the most common.

Exam Tip: When reading a bar graph, always check the scale first - here 1 unit means 1 individual, so read the height directly without multiplying.

 

Question 2. (a) The number of tickets sold for Vidisha is 24.

(b) The number of tickets sold for Jabalpur is 20.

(c) The scale for this graph is 1 unit = 4 tickets.

(d) The correct bar graph of Sagar:
Answer: Using the scale of 1 unit = 4 tickets, Vidisha (24 tickets) requires 6 units, Jabalpur (20 tickets) requires 5 units, Seoni (16 tickets) requires 4 units, Indore (24 tickets) requires 6 units, and Sagar (16 tickets) requires 4 units. The corrected bar graph shows each city with its bar height matching these unit values. The bar for Sagar in the original graph was incorrect - it should measure 4 units (16 tickets), not a different height.
In simple words: Divide each city's ticket count by 4 to find how many units tall the bar should be. Sagar has 16 tickets, so its bar is 4 units high.

Exam Tip: When using a graph scale, always divide the data value by the scale factor to determine bar height - never forget this step when drawing or correcting graphs.

 

Question 3. (a) The frequency distribution table for the means of transport that passed across the road:

(b) Bike was the most frequently used means of transport, appearing 13 times.
Answer: The frequency distribution table above lists all means of transport observed crossing the road with their respective frequencies. Bikes were the most common vehicle type, with 13 occurrences. This was followed by Scooters with 9 sightings, Cars with 6 sightings, and Autos and Bicycles each with 8 sightings. Buses and Bullock Carts were the least frequent, with only 4 and 2 occurrences respectively. In total, 60 vehicles were observed during the counting period.
In simple words: Bikes were seen most often (13 times). Buses and carts were seen least (4 and 2 times).

Exam Tip: When describing frequency data, always identify the mode (most frequent item) and compare relative frequencies - this shows you understand the data distribution.

 

Question 4. (c) Observation Timeframe: I will choose a specific timeframe, such as 9 am to 10 am, to observe the road traffic.

Recording Data: I will use a tally chart or counting app to record the type of transport passing by during that hour.

Categorisation: Then I will organise the data into categories (e.g., bike, car, scooter, bus, etc.).

Final Count: After the observation period, I will get the total the number of occurrences for each category.

Analysis: Finally, I prepare a frequency distribution table based on the recorded data for analysis.
Answer: The structured observation process involves selecting a defined timeframe (like 9 am to 10 am) to watch road traffic. You record each vehicle type using a tally chart or digital app as vehicles pass. Next, you sort the recorded data into transport categories such as bikes, cars, scooters, buses, and others. Once the observation period ends, you sum the tally marks for each category to get the total count. Finally, you create a frequency distribution table with these totals for further study and comparison.
In simple words: Pick a time window, watch and count vehicles by type using marks, group them into categories, add up each group, and make a table of the results.

Exam Tip: Follow the exact steps in order - do not skip the categorisation step, as this is what transforms raw tally data into usable frequency information.

 

Question 5. (a) The results from rolling a die 30 times: 3, 5, 2, 5, 4, 1, 6, 3, 4, 4, 2, 6, 1, 3, 4, 4, 6, 2, 4, 1, 3, 5, 6, 2, 1, 4, 3, 4, 2 and 3.

(b) The minimum number of times: 5 (only 3 times)
(c) The maximum number of times: 4 (8 times)
(d) The numbers that appeared an equal number of times: 1 and 6.
Answer: The table above shows the frequency of each die outcome (1 through 6) from the 30 rolls. Outcome 4 had the highest frequency at 8 appearances, making it the most common result. Outcome 5 had the lowest frequency at 3 appearances. Outcomes 1 and 6 both appeared exactly 4 times each, showing they have the same frequency. Outcomes 2 and 3 appeared 5 and 6 times respectively. These results show natural variation in die rolls - with only 30 trials, we do not expect perfectly equal frequencies for each outcome, though over many more rolls the frequencies would tend toward equal distribution.
In simple words: The number 4 came up most (8 times). The number 5 came up least (3 times). The numbers 1 and 6 both came up the same number of times (4 each).

Exam Tip: Always construct the frequency table first by counting tally marks - this prevents counting errors and gives you the correct data for all subsequent analysis.

 

Question 6. (a) The table shows the wickets taken by Jaspreet Bumrah in 30 matches.

(b) The title of this table is "The Bowling Performance of Jaspreet Bumrah in 30 matches".

(c) He has taken 3 wickets in 8 matches.

(d) In 3 matches Bumrah has taken 4 wickets.
Answer: The data describes Jaspreet Bumrah's wicket-taking record across 30 cricket matches. The table is appropriately titled "The Bowling Performance of Jaspreet Bumrah in 30 matches." According to the table, he took 3 wickets in 8 different matches and took 4 wickets in 3 separate matches. To find the total wickets, multiply each wicket count by the number of matches where that happened, then add all results: (0 × 2) + (1 × 4) + (2 × 6) + (3 × 8) + (4 × 3) + (5 × 5) + (6 × 1) + (7 × 1) = 0 + 4 + 12 + 24 + 12 + 25 + 6 + 7 = 90 total wickets across all 30 matches. A common error is to simply add the range of possible wickets (0 + 1 + 2 + 3 + 4 + 5 + 6 + 7) without accounting for how many matches each count represents - this would give an incorrect sum. The correct approach multiplies each wicket count by its frequency first.
In simple words: Count how many times each wicket total appears, multiply each one by that count, then add all the results together to get the true total.

Exam Tip: For frequency-based calculations, always multiply value × frequency for each category, then sum - never just add the values themselves, as this ignores how often each value occurs.

 

Question 7. (a) Class 8 has the least number of girl students.

(b) The difference between the number of girls in Class 5 and 6 = 16 - 10 = 6

(c) If 2 more girls were admitted in Class 2, the graph changes as follows:
Answer: Originally, Class 2 had 12 girl students (shown by 3 symbols at 4 girls each). If 2 more girls are admitted, Class 2 now has 14 girls total, requiring 3.5 symbols (or more commonly, 4 symbols to represent slightly more than 14, since each symbol stands for 4 girls). The updated pictograph shows Class 1 with 12 girls (3 symbols), Class 2 with 14 girls (now requiring adjustment in the pictograph to represent the new total), Class 3 with 20 girls (5 symbols), Class 4 with 16 girls (4 symbols), Class 5 with 10 girls (2.5 symbols, or shown as 3 symbols in pictographs), Class 6 with 16 girls (4 symbols), Class 7 with 12 girls (3 symbols), and Class 8 with 8 girls (2 symbols).
In simple words: When 2 more girls join Class 2, the pictograph for Class 2 changes because it now has more girls to show.

Exam Tip: In a pictograph, when the new frequency does not divide evenly by the scale (e.g., 14 girls with a scale of 4 girls per symbol), you may need to show a partial symbol or adjust the representation - always read the pictograph's instructions on how to handle partial symbols.

 

Question 8. The pictograph for the data is as follows:
(a) A useful scale for this pictograph would be 1 symbol representing 6 dogs. This would allow for easy representation of the dog numbers across villages.
(b) Village B has 36 dogs. Using a scale of 1 symbol for 6 dogs, you would need: 36/6 = 6 symbols
(c) Village B has 36 dogs and Village D has 48 dogs. Together, they have: 36 + 48 = 84 dogs. The total number of dogs in the other 4 villages is:
Village A: 18 dogs, Village C: 12 dogs, Village E: 18 dogs, Village F: 24 dogs
Total = 18 + 12 + 18 + 24 = 72 dogs
Since 84 is greater than 72, Kamini is correct. The number of dogs in Village B and Village D together is more than the number of dogs in the other four villages.
Answer: A scale of 1 symbol = 6 dogs is effective because it creates symbols that are easy to count and compare. Village B has 36 dogs, requiring 6 symbols at this scale. Village B (36) plus Village D (48) together have 84 dogs, which is greater than the combined total of all other villages. When you add Village A (18), Village C (12), Village E (18), and Village F (24), you get 72 dogs total - less than 84. Therefore, the two largest villages do contain more dogs than the remaining four villages combined. This pictograph representation makes these comparisons visually clear and easy to verify.
In simple words: A pictograph with 1 symbol = 6 dogs is easy to read. Villages B and D together have more dogs than all the other villages put together.

Exam Tip: When checking pictograph scales, verify that the chosen scale produces whole or simple partial symbols - scales that result in awkward fractions are harder to draw and to interpret.

 

Question 9. The bar graph is given below:
Reading Story Books activity is preferred by most students other than playing.
Answer: The bar graph clearly shows that Playing is the most preferred activity with 45 students choosing it. Reading story books comes in second place with 30 students. This means Reading story books is the activity preferred by the most students when we exclude Playing from consideration. The remaining activities - Watching TV (20), Painting (15), and Listening to music (10) - are all chosen by fewer students. The data shows a clear ranking of student preferences, with active and creative pursuits dominating the choices.
In simple words: Reading story books is chosen by more students than any other activity except Playing.

Exam Tip: When asked "which is preferred by most students other than..." always find the second-highest bar, not the highest - the question is specifically excluding the top choice.

 

Question 10. (a) The total number of saplings planted on Wednesday and Thursday is 30 + 40 = 70.

(b) The total number of saplings planted during the whole week is 52 + 40 + 30 + 40 + 50 + 60 + 40 = 312.

(c) The greatest number of saplings were planted on Saturday and the least number of saplings were planted on Wednesday.
The most saplings were planted on Saturday likely due to greater volunteer availability on weekends, when students feel free from homework and school work. In contrast, fewer saplings were planted on Wednesday because of midweek commitments. To confirm this, check volunteer participation data, event schedules and weather conditions to understand why certain days saw more or less activity.
Answer: This bar graph analysis reveals seasonal planting patterns. Saturday had the highest number of saplings planted (60), while Wednesday had the lowest (30). The increased activity on Saturday is most likely because volunteers (students and teachers) have more free time on weekends, away from regular school duties and homework responsibilities. Wednesday's lower count can be explained by midweek academic commitments that limit availability. To verify these explanations, one could review volunteer sign-up sheets, check the school's academic calendar for tests or events, and look at weather records for that week. Different days may also have experienced different weather conditions, which could affect planting activity. Additionally, the availability of seedlings or supply deliveries could influence daily totals.
In simple words: More saplings were planted on Saturday because people were free. Fewer were planted on Wednesday because people were busy with school.

Exam Tip: When interpreting bar graphs, always provide a logical reason for patterns you observe - this shows higher-order thinking, not just data reading.

 

Page 103

 

Figure it Out

 

Question 1. If you wanted to visually represent the data of the heights of the tallest persons in each class in your school, would you use a graph with vertical bars or horizontal bars? Why?
Answer: You should use a vertical bar graph to represent heights of people. Vertical bars are the natural choice because height is inherently a vertical measurement - they visually match the concept of vertical dimension. When a bar extends upward, it naturally mirrors how height extends upward in real life, making the visual representation intuitive and easy to understand at a glance.
In simple words: Heights go up and down, so vertical bars match this direction and make sense to look at.

Exam Tip: Match your graph type to the type of measurement - vertical for height/depth/altitude, horizontal for distances/lengths that extend left-to-right.

 

Question 2. If you were making a table of the longest rivers on each continent and their lengths, would you prefer to use a graph with vertical bars or with horizontal bars? Why? Try finding out this information, and then make the corresponding table and bar graph! Which continents have the longest rivers?
Answer: A horizontal bar graph is better for showing river lengths. Rivers extend lengthwise across geography from source to mouth, flowing left-to-right or along landscape. Horizontal bars naturally represent this directional flow and make it intuitive to compare how far different rivers stretch. It is also easier to visually compare lengths when bars extend horizontally side-by-side, and horizontal graphs provide more space for labeling each river name clearly. Based on river length data: Asia has the longest river (Yangtze at approximately 6,300 km), followed by Africa (Nile at approximately 6,650 km, actually longer than the Yangtze), South America (Amazon at approximately 6,400 km), North America (Missouri-Mississippi at approximately 6,275 km), Australia (Murray-Darling at approximately 3,672 km), and Europe (Volga at approximately 3,530 km). The Amazon and Nile are the world's longest rivers, with the Nile holding the top position.
In simple words: Rivers go left and right across land, so horizontal bars show their length better than vertical bars.

Exam Tip: Horizontal bar graphs let you read long category labels clearly on the left side - use them when category names are lengthy or numerous.