Data Handling and Presentation — Class 6 Mathematics
Ganita Prakash · Chapter 4
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- Space weighted by chapter size
- Charts from the book's own data
- Traps corrected
- Space weighted by chapter size
- Charts from the book's own data
- Traps corrected
- Space weighted by chapter size
- Charts from the book's own data
- Traps corrected
- Space weighted by chapter size
- Charts from the book's own data
- Traps corrected
- Space weighted by chapter size
- Charts from the book's own data
- Traps corrected
Chapter summary
Key ideas & terms
- 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.
Extra questions & answers
What is data?
Data is any collection of facts, numbers, measures, observations or descriptions that conveys information about things.
Why do we organise raw data?
Because an unorganised list is hard to interpret; organising it (for example into a frequency table) lets us read information easily.
What are tally marks used for?
Tally marks are used to count how many times each value occurs, usually grouped in fives.
What does frequency mean?
Frequency is the number of times a particular observation or category appears in the data.
What is a pictograph?
A pictograph represents data using a picture or symbol, where one symbol stands for a fixed number of items as given by the key.
Why is a key important in a pictograph?
The key tells how many items each symbol represents, so the picture can be read correctly.
What is a bar graph?
A bar graph shows data using bars of equal width whose lengths or heights are proportional to the values.
Why must bars in a bar graph have equal width?
So that only the length represents the value, making fair and easy comparison between categories.
What is the purpose of a scale in a bar graph?
The scale fixes how much each unit of length on the axis stands for, allowing large values to be drawn neatly.
How can a bar graph help in decision making?
By showing at a glance which category is largest or smallest, it helps us draw inferences and make correct decisions.
Figure it Out
1. What would you do to find the most popular game among Naresh’s and Navya’s classmates?
To find the most popular game, collect each student's favourite game, then organise the list by counting how many times each game appears. The game with the highest frequency is the most popular. This can be done with tally marks or a frequency table.
2. What is the most popular game in their class?
Count the names for each game. Hockey appears the most (8 times), so it is the most popular game. The next most popular are Kabaddi and Cricket, which tie at 6 each.
3. Try to find out the most popular game among your classmates.
Ask every classmate for their one favourite game, record the answers, make a tally table counting each game, and see which game has the largest count. The result will depend on your own class data.
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?
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?
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?
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?
Figure it Out
1. Complete the table to help Shri Nilesh to purchase the correct numbers of sweets: a. How many students chose jalebi?
From the tally marks
1. Complete the table to help Shri Nilesh to purchase the correct numbers of sweets: b. Barfi was chosen by students?
The tally for Barfi is
1. Complete the table to help Shri Nilesh to purchase the correct numbers of sweets: c. How many students chose gujiya?
The tally for Gujiya is
1. Complete the table to help Shri Nilesh to purchase the correct numbers of sweets: d. Rasgulla was chosen by students?
The tally for Rasgulla is
1. Complete the table to help Shri Nilesh to purchase the correct numbers of sweets: e. How many students chose gulab jamun?
The tally for Gulab jamun is
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?
No, the frequency table is not sufficient for distribution. It tells only how many students like each sweet, not which student likes which sweet. To distribute correctly, Shri Nilesh needs a list that links each student's name to their chosen sweet, or to group students by their choice and then distribute.
Figure it Out
1. Help her to figure out the following: a. The largest shoe size in the class is _________.
The largest shoe size is
1. Help her to figure out the following: b. The smallest shoe size in the class is _________.
The smallest shoe size is
1. Help her to figure out the following: c. There are _________ students who wear shoe size 5.
There are
1. Help her to figure out the following: d. There are _________ students who wear shoe sizes larger than 4.
There are
2. How did arranging the data in ascending order help to answer these questions?
Arranging in ascending order brings the smallest value to the start and the largest to the end, and groups equal values together. This makes counting frequencies and identifying minimum and maximum much quicker and avoids missing values.
3. Are there other ways to arrange the data?
Yes. Data can be arranged in descending order, or organised into a frequency table with tally marks showing how many students wear each size, such as size
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?
The answer depends on your local survey. After filling the table, look for the tree with the highest frequency. For example, if you counted
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?
This is the tree with the lowest count in your table. It will be the one you saw the fewest times on your route.
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?
Compare the frequencies in your table. If two trees have the same count, record them as equal. For example, Peepal and Neem both
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 ________.
After counting, the letter with the highest frequency is usually
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 ________.
Typically
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?
Ascending order is most likely
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.
I pasted the news item, created the table, read the text letter by letter ignoring case, made a tally mark for each occurrence of
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.
Friends followed similar steps but some counted by underlining letters with different colours or by scanning word by word. Comparing methods shows all need systematic tallying to avoid missing or double-counting letters.
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?
I would repeat the same systematic process: paste new item, make the same table, go through the text sequentially, tally each target letter, and then total the tallies. The process stays the same for any text.
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: a. On which day were the minimum number of books borrowed?
Thursday had the minimum — its row is empty, i.e. 0 books were borrowed on Thursday.
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?
Counting the symbols (each symbol = 1 book): Monday 5, Tuesday 4, Wednesday 2, Thursday 0, Friday 5, Saturday 8. Total for the week = 5+4+2+0+5+8 = 24 books.
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?
Saturday had the maximum, with 8 books. A possible reason is that students borrow more books before the weekend/holiday.
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.
Using
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?
Rani purchased
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?
Poonam Ben purchased the maximum,
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?
Jasmeet purchased
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?
Yes, she is correct. Double of Rani's
Figure it Out
1. How many total cars passed through the crossing between 6 a.m. and noon?
Add the approximate heights:
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?
At
3. Why do you think the traffic was the heaviest between 7–8 a.m.?
4. Why do you think the traffic was lesser and lesser each hour after 8 a.m. all the way until noon?
After the morning rush, people have reached their destinations. As the morning progresses, fewer commuters are traveling, so traffic gradually decreases toward midday.
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: Help her prepare a bar graph representing this data.
Draw two perpendicular axes, mark insects Mites, Caterpillars, Beetles, Butterflies, Grasshoppers on the horizontal axis and number of insects
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.
Vidisha sold
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.
Jabalpur sold
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?
Since
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.
Sagar sold
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.
Mark the vertical axis starting at
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).
Seoni sold
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.
Counting with tally: Bike
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?
Bike was the most frequent with
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.
Prepare a table with categories for each vehicle type, stand at the road from
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.
After rolling
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.
The face with the largest tally is the maximum. For example, face
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.
Look for two or more faces with the same frequency, for example faces
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?
The table shows how many matches in which Bumrah took a particular number of wickets. For example, in
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?
A suitable title is
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?
It is striking that he took
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?
In
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?
No. Adding
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?
Multiply wickets by number of matches and add:
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?
Village D has the smallest number of tractors, with 3.
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?
Village C has the most tractors, with 8.
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?
Village C has 8 tractors and Village B has 5, so Village C has
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?
Yes. Village D has 3 tractors and Village E has 6, and
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?
With
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?
With the key of 4 girls per symbol: Class 5 shows
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?
Each symbol is
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?
Class
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?
All numbers are multiples of
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?
Village B has
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.
Yes.
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?
Draw vertical bars with heights: Playing
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 ___________.
Reading the bar heights, Wednesday about
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 ___________.
Add all days: Monday
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?
Greatest on Saturday, least on Wednesday. Possible reasons: Saturday may have had more volunteers or a special planting drive, while Wednesday may have been a regular school day with fewer participants or rain. To verify, you could check attendance records, weather data, or ask teachers why the schedule varied.
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?
Mistakes: bars do not start at
Figure it Out
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?
Use vertical bars or column graph. Heights are naturally vertical from the ground, so vertical bars intuitively look like people standing and make comparison of heights easy at a glance.
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?
Use horizontal bars. River lengths extend horizontally along the ground, so horizontal bars suggest distance naturally. Example table: Nile in Africa ≈