Class 6 › Mathematics › Ganita Prakash Data Handling and Presentation Class 6 Mathematics · Ganita Prakash · Chapter 4
Practice all → Summary Questions & answers Practise this chapter → This chapter explains how to collect, organise and present data. Any collection of facts, numbers, measures or observations that conveys information is called data. Raw data, such as a list of classmates\u2019 favourite games, is hard to interpret, so it is first organised using tally marks into a frequency table, where the frequency is how many times each value occurs. The chapter then presents two main visual displays. A pictograph (or pictogram) uses a picture or symbol to stand for a chosen number of items, with a key telling how much one symbol represents; part-symbols show smaller counts. A bar graph uses bars of equal width whose lengths or heights are proportional to the values, drawn on a scale, making comparisons easy at a glance. Students learn to read information from pictographs and bar graphs, to choose a sensible scale, and to draw their own displays from a frequency table. The chapter stresses interpreting and drawing inferences from data \u2014 finding the most and least popular categories \u2014 so that data can be used to make decisions correctly.
Data
Any collection of facts, numbers, measures or observations that conveys information about things.
Tally marks
Strokes used to count occurrences while organising data, grouped in fives for easy counting.
Frequency
The number of times a particular value or category occurs in the data.
Frequency table
A table that lists each category alongside its frequency.
Pictograph
A display that uses a picture or symbol to represent a fixed number of items, with a key.
Bar graph
A display using bars of equal width whose lengths are proportional to the values they represent.
Q2 Why do we organise raw data? Answer Q3 What are tally marks used for? Answer Q4 What does frequency mean? Answer Q5 What is a pictograph? Answer Q6 Why is a key important in a pictograph? Answer Q7 What is a bar graph? Answer Q8 Why must bars in a bar graph have equal width? Answer Q9 What is the purpose of a scale in a bar graph? Answer Q10 How can a bar graph help in decision making? Answer Q1 1. What would you do to find the most popular game among Naresh’s and Navya’s classmates? Answer Q2 2. What is the most popular game in their class? Answer Q3 3. Try to find out the most popular game among your classmates. Answer Q4 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? Answer Q5 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. b. When did India get independence? Answer Q6 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. c. How much water is getting wasted in her locality? Answer Q7 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. d. What is the capital of India? Answer Q1 1. Complete the table to help Shri Nilesh to purchase the correct numbers of sweets: a. How many students chose jalebi? Answer Q2 1. Complete the table to help Shri Nilesh to purchase the correct numbers of sweets: b. Barfi was chosen by students? Answer Q3 1. Complete the table to help Shri Nilesh to purchase the correct numbers of sweets: c. How many students chose gujiya? Answer Q4 1. Complete the table to help Shri Nilesh to purchase the correct numbers of sweets: d. Rasgulla was chosen by students? Answer Q5 1. Complete the table to help Shri Nilesh to purchase the correct numbers of sweets: e. How many students chose gulab jamun? Answer Q6 2. 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 Q1 1. Help her to figure out the following: a. The largest shoe size in the class is _________. Answer Q2 1. Help her to figure out the following: b. The smallest shoe size in the class is _________. Answer Q3 1. Help her to figure out the following: c. There are _________ students who wear shoe size 5. Answer Q4 1. Help her to figure out the following: d. There are _________ students who wear shoe sizes larger than 4. Answer Q5 2. How did arranging the data in ascending order help to answer these questions? Answer Q6 3. Are there other ways to arrange the data? Answer Q7 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: a. Which tree was found in the greatest number? Answer Q8 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: b. Which tree was found in the smallest number? Answer Q9 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: c. Were there any two trees found in the same numbers? Answer Q10 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’, and ‘x’ in the words of the news article, and fill in the table. a. The letter found the most number of times is ________. Answer Q11 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’, and ‘x’ in the words of the news article, and fill in the table. b. The letter found the least number of times is ________. Answer Q12 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’, and ‘x’ in the words of the news article, and fill in the table. 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 Q13 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’, and ‘x’ in the words of the news article, and fill in the table. d. Write the process you followed to complete this task. Answer Q14 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’, and ‘x’ in the words of the news article, and fill in the table. e. Discuss with your friends the processes they followed. Answer Q15 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’, and ‘x’ in the words of the news article, and fill in the table. f. If you do this task with another news item, what process would you follow? Answer Q1 1. The following pictograph shows the number of books borrowed by students, in a week, from the library of Middle School, Ginnori: a. On which day were the minimum number of books borrowed? Answer Q2 1. The following pictograph shows the number of books borrowed by students, in a week, from the library of Middle School, Ginnori: b. What was the total number of books borrowed during the week? Answer Q3 1. The following pictograph shows the number of books borrowed by students, in a week, from the library of Middle School, Ginnori: c. On which day were the maximum number of books borrowed? What may be the possible reason? Answer Q4 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 — Prepare a pictograph using the symbol to represent 100 kites. Answer Q5 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 — a. How many symbols represent the kites that Rani purchased? Answer Q6 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 — b. Who purchased the maximum number of kites? Answer Q7 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 — c. Who purchased more kites, Jasmeet or Chaman? Answer Q8 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 — d. Rukhsana says Poonam Ben purchased more than double the number of kites that Rani purchased. Is she correct? Why? Answer Q1 1. How many total cars passed through the crossing between 6 a.m. and noon? Answer Q2 2. Why do you think so little traffic occurred during the hour of 6–7 a.m., as compared to the other hours from 7 a.m.–noon? Answer Q3 3. Why do you think the traffic was the heaviest between 7–8 a.m.? Answer Q4 4. Why do you think the traffic was lesser and lesser each hour after 8 a.m. all the way until noon? Answer Q1 1. Samantha visited a tea garden, and collected data of the insects and critters she saw there. Here is the data she collected: Help her prepare a bar graph representing this data. Answer Q2 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 two-hour period. 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. a. Write the number of tickets sold for Vidisha above the bar. Answer Q3 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 two-hour period. 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. b. Write the number of tickets sold for Jabalpur above the bar. Answer Q4 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 two-hour period. 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. 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 Q5 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 two-hour period. 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. d. Draw the correct bar for Sagar. Answer Q6 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 two-hour period. 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. e. Add the scale of the bar graph by placing the correct numbers on the vertical axis. Answer Q7 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 two-hour period. 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. f. Are the bars for Seoni and Indore correct in this graph? If not, draw the correct bar(s). Answer Q8 3. Chinu listed the various means of transport that passed across the road in front of his house from 9 a.m. to 10 a.m.: a. Prepare a frequency distribution table for the data. Answer Q9 3. Chinu listed the various means of transport that passed across the road in front of his house from 9 a.m. to 10 a.m.: b. Which means of transport was used the most? Answer Q10 3. Chinu listed the various means of transport that passed across the road in front of his house from 9 a.m. to 10 a.m.: c. If you were there to collect this data, how could you do it? Write the steps or process. Answer Q11 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: a. The minimum number of times. Answer Q12 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: b. The maximum number of times. Answer Q13 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: c. Find numbers that appeared an equal number of times. Answer Q14 5. Faiz prepared a frequency distribution table of data on the number of wickets taken by Jaspreet Bumrah in his last 30 matches: a. What information is this table giving? Answer Q15 5. Faiz prepared a frequency distribution table of data on the number of wickets taken by Jaspreet Bumrah in his last 30 matches: b. What may be the title of this table? Answer Q16 5. Faiz prepared a frequency distribution table of data on the number of wickets taken by Jaspreet Bumrah in his last 30 matches: c. What caught your attention in this table? Answer Q17 5. Faiz prepared a frequency distribution table of data on the number of wickets taken by Jaspreet Bumrah in his last 30 matches: d. In how many matches has Bumrah taken 4 wickets? Answer Q18 5. Faiz prepared a frequency distribution table of data on the number of wickets taken by Jaspreet Bumrah in his last 30 matches: e. Mayank says, “If we want to know the total number of wickets he has taken in his last 30 matches, 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? Answer Q19 5. Faiz prepared a frequency distribution table of data on the number of wickets taken by Jaspreet Bumrah in his last 30 matches: f. How would you correctly figure out the total number of wickets taken by Bumrah in his last 30 matches, using this table? Answer Q20 6. The following pictograph shows the number of tractors in five different villages. Observe the pictograph and answer the following questions— a. Which village has the smallest number of tractors? Answer Q21 6. The following pictograph shows the number of tractors in five different villages. Observe the pictograph and answer the following questions— b. Which village has the most tractors? Answer Q22 6. The following pictograph shows the number of tractors in five different villages. Observe the pictograph and answer the following questions— c. How many more tractors does Village C have than Village B? Answer Q23 6. The following pictograph shows the number of tractors in five different villages. Observe the pictograph and answer the following questions— d. Komal says, “Village D has half the number of tractors as Village E.” Is she right? Answer Q24 7. The number of girl students in each class of a school is depicted by the pictograph: Observe this pictograph and answer the following questions: a. Which class has the least number of girl students? Answer Q25 7. The number of girl students in each class of a school is depicted by the pictograph: Observe this pictograph and answer the following questions: b. What is the difference between the number of girls in Classes 5 and 6? Answer Q26 7. The number of girl students in each class of a school is depicted by the pictograph: Observe this pictograph and answer the following questions: c. If two more girls were admitted in Class 2, how would the graph change? Answer Q27 7. The number of girl students in each class of a school is depicted by the pictograph: Observe this pictograph and answer the following questions: d. How many girls are there in Class 7? Answer Q28 8. 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? Answer Q29 8. 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: b. How many symbols will you use to represent the dogs in Village B? Answer Q30 8. 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: c. Kamini said that the number of these dogs in Village B and Village D together will be more than the number of these dogs in the other 4 villages. Is she right? Give reasons for your response. Answer Q31 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 Q32 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 ___________. Answer Q33 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— b. The total number of saplings planted during the whole week is ___________. Answer Q34 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— 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 Q35 11. The number of tigers in India went down drastically between 1900 and 1970. Project Tiger was launched in 1973 to track and protect the 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 four-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 Q1 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 Q2 2. If you were making a table of the longest rivers on each continent and their lengths, would you prefer to use a bar 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
Any collection of facts, numbers, measures or observations is called
A a frequency B a graph C data D a tally
Flashcards & interactive practice 
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