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Solutions

Overview

Step-by-step NCERT solutions for Data Handling and Presentation (Chapter 4, NCERT Class 6 Mathematics) — every question and answer worked out in full, not just the final result. You can also read the Data Handling and Presentation textbook chapter.

Solved

What these solutions cover

All 25 questions in Data Handling and Presentation are solved in the PDF. Here's what's inside, exercise by exercise:

Collecting and Organising Data

  1. What would you do to find the most popular game among Naresh's and Navya's classmates?
  2. What is the most popular game in their class?
  3. 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. 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?

Collecting and Organising Data — Tally Table

  1. Complete the table to help Shri Nilesh to purchase the correct numbers of sweets: a. How many students chose jalebi? b. Barfi was chosen by _____ students? c. How many students chose gujiya? d. Rasgulla was chosen by _____ students? e. How many students chose gulab jamun?
  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?

Collecting and Organising Data — Shoe Sizes

  1. Help her to figure out the following: a. The largest shoe size in the class is _________. b. The smallest shoe size in the class is _________. c. There are _________ students who wear shoe size 5. d. There are _________ students who wear shoe sizes larger than 4.

Pictographs — Books Borrowed

  1. The following pictograph shows the number of books borrowed by students in a week from the library of Middle School, Ginnori (each symbol = 1 book): Monday: 5 books, Tuesday: 4 books, Wednesday: 2 books, Thursday: 0 books, Friday: 5 books, Saturday: 8 books. a. On which day were the minimum number of books borrowed? b. What was the total number of books borrowed during the week? c. On which day…
  2. Magan Bhai sells kites at Jamnagar. Six shopkeepers from nearby villages come to purchase kites from him. The number of kites sold: Chaman – 250, Rani – 300, Rukhsana – 100, Jasmeet – 450, Jetha Lal – 250, Poonam Ben – 700. Prepare a pictograph using the symbol to represent 100 kites. Answer the following: a. How many symbols represent the kites that Rani purchased? b. Who purchased the maximum…

Bar Graphs — Vehicular Traffic

  1. Use the bar graph of the number of students absent in each class (1 unit length = 1 student; Class I – 3, II – 5, III – 4, IV – 2, V – 0, VI – 1, VII – 5, VIII – 7) to answer: a. In Class 2, ___________ students were absent that day. b. In which class were the maximum number of students absent? c. Which class had full attendance that day?
  2. How many total vehicles passed through the crossing between 6 a.m. and noon? (The bar graph shows: 6–7 a.m. ≈ 150, 7–8 a.m. = 1200, 8–9 a.m. = 1000, 9–10 a.m. = 800, 10–11 a.m. = 700, 11 a.m.–noon ≈ 600 vehicles.)

Drawing a Bar Graph

  1. Use the bar graph of Imran's family monthly expenditure (House rent: ₹3000, Food: ₹3400, Education: ₹800, Electricity: ₹400, Transport: ₹600, Miscellaneous: ₹1200) to answer: On which item does Imran's family spend the most and the second most?
  2. Is the cost of electricity about one-half the cost of education?
  3. Is the cost of education less than one-fourth the cost of food?
  4. Samantha visited a tea garden and collected data of the insects and critters she saw there: Mites – 6, Caterpillars – 10, Beetles – 5, Butterflies – 3, Grasshoppers – 2. Help her prepare a bar graph representing this data.
  5. Pooja collected data on tickets sold at Bhopal railway station: Vidisha – 24, Jabalpur – 20, Seoni – 16, Indore – 28, Sagar – 16. The bar graph has a portion erased. a. Write the number of tickets sold for Vidisha above the bar. b. Write the number of tickets sold for Jabalpur above the bar. c. The bar for Vidisha is 6 unit lengths and the bar for Jabalpur is 5 unit lengths. What is the scale…
  6. 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. (50 vehicles listed). a. Prepare a frequency distribution table for the data. b. Which means of transport was used the most? c. If you were there to collect this data, how could you do it? Write the steps or process.
  7. Faiz prepared a frequency distribution table of data on the number of wickets taken by Jaspreet Bumrah in his last 30 matches: Wickets: 0–2, 1–4, 2–6, 3–8, 4–3, 5–5, 6–1, 7–1 matches. a. What information is this table giving? b. What may be the title of this table? c. What caught your attention in this table? d. In how many matches has Bumrah taken 4 wickets? e. Mayank says, 'If we want to know…
  8. The following pictograph shows the number of tractors in five different villages (1 symbol = 1 tractor): Village A – 6, Village B – 5, Village C – 8, Village D – 3, Village E – 6. a. Which village has the smallest number of tractors? b. Which village has the most tractors? c. How many more tractors does Village C have than Village B? d. Komal says, 'Village D has half the number of tractors as…
  9. The number of girl students in each class is depicted by a pictograph (1 symbol = 4 girls): Class 1 – 6 symbols, Class 2 – 4½ symbols, Class 3 – 5 symbols, Class 4 – 3½ symbols, Class 5 – 2½ symbols, Class 6 – 4 symbols, Class 7 – 3 symbols, Class 8 – 1½ symbols. a. Which class has the least number of girl students? b. What is the difference between the number of girls in Classes 5 and 6? c. If…
  10. Mudhol Hounds in six villages: Village A – 18, Village B – 36, Village C – 12, Village D – 48, Village E – 18, Village F – 24. Prepare a pictograph and answer: a. What will be a useful scale or key to draw this pictograph? b. How many symbols will you use to represent the dogs in Village B? c. Kamini said that the number of these dogs in Village B and Village D together will be more than the…
  11. A survey of 120 school students: Playing – 45, Reading story books – 30, Watching TV – 20, Listening to music – 10, Painting – 15. Draw a bar graph using scale 1 unit length = 5 students. Which activity is preferred by most students other than playing?
  12. Students and teachers planted saplings during the first week of July. The bar graph shows: Monday – 50, Tuesday – 40, Wednesday – 30, Thursday – 40, Friday – 50, Saturday – 60, Sunday – 40 saplings. 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…
  13. Shagufta and Divya prepared a bar graph for the number of tigers in India (2006: 1400, 2010: 1700, 2014: 2200, 2018: 3000, 2022: 3700), but there are a few mistakes in the graph. Can you find those mistakes and fix them?

Artistic and Aesthetic Considerations

  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?
  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?
Sample

Worked examples

3 questions from Data Handling and Presentation, solved step by step.

Collecting and Organising Data

What is the most popular game in their class?

Counting each game from the list:

Kabaddi: Mehnoor, Anaya, Simran, Ankita, Arsh, Sarah = 6

Satoliya (Pittu): Pushkal, Jivisha, Jivika, Nand, Hemal = 5

Badminton: Densy, Aarna = 2

Hockey: Jubimon, Leela, Afshan, Imon, Navjot, Gurpreet, Rehana, Ananya = 8

Football: Rajesh, Thara, Debabrata, Kompal = 4

Cricket: Soumya, Keerat, Yuvraj, Bhavya, Hardik, Tahira = 6

Hockey has the highest frequency of 8.

Answer: Hockey (8 students) is the most popular game.

Drawing a Bar Graph

Is the cost of electricity about one-half the cost of education?

Electricity = ₹400

Education = ₹800

Half of education = ₹800 ÷ 2 = ₹400

₹400 = ₹400, so electricity is exactly half the cost of education.

Answer: Yes; electricity (₹400) = education (₹800) ÷ 2, so it is exactly half.

Drawing a Bar Graph

Is the cost of education less than one-fourth the cost of food?

Food = ₹3400

One-fourth of food = ₹3400 ÷ 4 = ₹850

Education = ₹800

₹800 < ₹850, so education is less than one-fourth the cost of food.

Answer: Yes; one-fourth of food = ₹850, and education = ₹800 < ₹850.

All 25 questions in Data Handling and Presentation are solved step by step in the Solutions PDF above.

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More solutions in Ganita Prakash

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More NCERT Solutions for Class 6

Read the Data Handling and Presentation textbook chapter / PDF, or browse all NCERT Class 6 Mathematics solutions.

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