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Class 6 Ganita Prakash · Chapter 4
Data Handling and Presentation

Page-wise textbook solutions (pages 74–105) · Every step · Figures · Common mistakes · Tips

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🗝️ Key ideas of this chapter

Data: facts, numbers, measures or observations that give information. Collect → organise → present → interpret.
Tally marks: | for each item; the 5th mark crosses the four (||||/). The count is the frequency.
Pictograph: pictures show data; always give the key (☺ = 5 students). Choose a key that divides the numbers.
Bar graph: bars of equal width and equal gaps; length/height = frequency; the scale starts at 0.
Heights → vertical bars (columns); lengths/distances → horizontal bars.
Fancy pictures (infographics) can mislead — compare only the heights/lengths.

📖 Textbook Page 74

📖 Page 74Think · What is data?

Which of these is data: a list of your classmates’ favourite colours, the weights of all students, the name of our country’s capital?

1Data is a collection of facts, numbers, measures or observations that give information about things.

2Favourite colours of classmates → a collection of observations → data.

3Weights of all students → a collection of measures → data.

4The capital of India is a single known fact; we do not need to collect it.

✅ Answer: The list of favourite colours and the list of weights are data.

📖 Textbook Page 75

📖 Page 75Figure it Out · Q1

What would you do to find the most popular game among Naresh’s and Navya’s classmates?

1List every game named.

2Go through the names one by one and put a tally mark against the game each child chose.

3Count the tally marks for each game.

4The game with the most marks is the most popular.

✅ Answer: Organise the list in a table with tally marks, count each game and compare the counts.

📖 Page 75Figure it Out · Q2

What is the most popular game in their class?

1Count each game from the list of 31 children:

2Hockey 8, Kabaddi 6, Cricket 6, Satoliya 5, Football 4, Badminton 2.

3Check: 8 + 6 + 6 + 5 + 4 + 2 = 31 ✔

4Hockey has the largest count.

✅ Answer: Hockey (8 children). Cricket is NOT the most popular — Navya’s guess was wrong.

📖 Page 75Figure it Out · Q3

Try to find out the most popular game among your classmates.

1Ask every classmate their favourite game and write the answers.

2Make a table with tally marks for each game.

3Count the marks; the game with the highest frequency is the most popular.

✅ Answer: Answers depend on your class — follow the steps (collect → tally → count → compare).

📖 Page 75Figure it Out · Q4

Tick (✓) the questions where Pari must collect data and cross (✗) where she need not: (a) most popular TV show among classmates (b) when India got independence (c) water wasted in her locality (d) capital of India.

1(a) Different classmates like different shows → she must ask them → ✓.

2(b) A known fact (1947) → ✗.

3(c) She must measure/observe in her locality → ✓.

4(d) A known fact (New Delhi) → ✗.

✅ Answer: (a) ✓ (b) ✗ (c) ✓ (d) ✗

📖 Textbook Page 76

📖 Page 76Figure it Out · Q1 (Sweets)

Complete Shri Nilesh’s tally table. How many students chose (a) jalebi (b) barfi (c) gujiya (d) rasgulla (e) gulab jamun?

1Each ‘||||/’ (four lines with a line across) means 5.

2Gujiya: ||||/ ||||/ ||| = 5 + 5 + 3 = 13.

3Barfi: ||| = 3. Rasgulla: ||||/ || = 7.

4Jalebi: ||||/ | = 6. Gulab jamun: ||||/ |||| = 9.

✅ Answer: (a) 6 (b) 3 (c) 13 (d) 7 (e) 9 — total 38 sweets.

📖 Textbook Page 77

📖 Page 77Figure it Out · Q2 (Sweets)

Is the table enough to give each type of sweet to the correct student? If not, what is the alternative?

1The table tells only HOW MANY students chose each sweet.

2It does not tell WHICH student chose which sweet.

3Alternative: write each student’s name next to the sweet they chose (a list of name – sweet), or let students pick their sweet from the box.

✅ Answer: No. It gives counts, not names. Keep a list of each student’s name with their choice.

📖 Page 77Figure it Out · Q1 (Shoe sizes)

From 3, 3, 3, 4, 4, …, 6, 7 find (a) the largest size (b) the smallest size (c) students who wear size 5 (d) students who wear sizes larger than 4.

1(a) The last number in ascending order is 7.

2(b) The first number is 3.

3(c) Count the 5s: 10.

4(d) Sizes 5, 6, 7: 10 + 4 + 1 = 15.

✅ Answer: (a) 7 (b) 3 (c) 10 (d) 15

📖 Page 77Figure it Out · Q2 (Math Talk)

How did arranging the data in ascending order help to answer these questions?

1The smallest value is at the start and the largest at the end — no searching.

2Equal values come together, so they are easy to count.

3Values larger than 4 are all together at the end.

✅ Answer: Ordering puts equal values together and the smallest/largest at the ends, so counting and comparing becomes easy.

📖 Page 77Figure it Out · Q3

Are there other ways to arrange the data?

1Descending order (largest to smallest).

2A frequency table with tally marks (size → number of students).

3A pictograph or a bar graph.

✅ Answer: Yes — descending order, a tally/frequency table, a pictograph or a bar graph.

📖 Textbook Page 78

📖 Page 78Figure it Out · Q4 (Trees)

Record the trees you see on your way to school in a table. Which tree was found most, least, and were any two found equally?

1Make a table: Tree | Tally | Number.

2Each time you see a tree, put a tally mark against its name.

3Count and compare the numbers.

4Example: Neem 9, Peepal 4, Mango 6, Banyan 1, Coconut 6 → most: Neem; least: Banyan; Mango and Coconut are equal.

✅ Answer: Answers depend on your route — see the example.

📖 Page 78Figure it Out · Q5 (Letters)

Count the letters c, e, i, r, x in a news item. Which letter is found most and least? Why do almost all get the order x, c, r, i, e?

1Go through the article word by word and put a tally for each c, e, i, r, x.

2Usually: e is the most common, x is the rarest.

3Order from least to most is nearly always x, c, r, i, e.

4This is because ‘e’ is the most used letter in English words, and ‘x’ is used in very few words — the pattern holds for any long English text.

✅ Answer: Most: e; least: x. The order x, c, r, i, e repeats because English uses these letters with nearly fixed frequencies.

💡 Tip: (d)–(f): explain your steps — read slowly, tally, recount to check. With a new article, follow the same steps.

📖 Textbook Page 79

📖 Page 79Pictograph · Modes of travel

Which mode of travel is used by the most students? Which by the least?

1Each ☺ = 1 student.

2Private car 4, public bus 5, school bus 11, cycle 3, walking 7.

3Longest row: school bus. Shortest row: cycle.

✅ Answer: Most: school bus (11). Least: cycle (3).

📖 Textbook Page 80

📖 Page 80Example · Sleep pictograph

Using the pictograph (▲ = 10 children): how many children (1) always (2) sometimes slept at least 9 hours? (3) always slept less than 9 hours?

1(1) Always: 5 symbols → 5 × 10 = 50.

2(2) Sometimes: 2 full + 1 half → 20 + 5 = 25.

3(3) ‘Never’ slept 9 hours = always slept less: 4 × 10 = 40.

✅ Answer: (1) 50 (2) 25 (3) 40

📖 Textbook Page 81

📖 Page 81Drawing a pictograph

Lakhanpal drew a pictograph of students absent (☺ = 1 student). Draw it.

1One symbol for each absent student.

2Class I: 3, II: 5, III: 4, IV: 2, V: 0 (empty row), VI: 1, VII: 5, VIII: 7.

✅ Answer: See the pictograph.

📖 Textbook Page 82

📖 Page 82Think · Large numbers

Jarina and Sangita want to show students PRESENT (20 to 35 per class). What problems come if ☺ = 1 student? How did they solve it?

1With ☺ = 1 student, Class II needs 35 symbols — it takes a lot of time and space.

2Jarina used ☺ = 5 students: 30 → 6 symbols, 35 → 7, 25 → 5.

3Sangita used ☺ = 10 students and a half symbol for 5: 25 → 2½, 35 → 3½.

✅ Answer: Use a bigger scale (key). Both pictographs are shown.

📖 Textbook Page 83

📖 Page 83Math Talk

What problems come in drawing such a pictograph if the number present is 33 or 27?

1With ☺ = 5 students: 33 = 6 symbols + 3 students, and 3 is 3/5 of a symbol — hard to draw exactly.

2With ☺ = 10: 27 = 2 symbols + 7/10 of a symbol.

3So we have to draw parts of symbols that are hard to read, or round off (33 ≈ 35, 27 ≈ 25).

✅ Answer: The numbers are not multiples of the key, so we must draw awkward parts of a symbol (or round the numbers).

📖 Page 83Figure it Out · Q1

The pictograph shows books borrowed in a week (one book symbol = 1 book). (a) Minimum on which day? (b) Total in the week? (c) Maximum on which day? A possible reason?

1Read the rows: Mon 5, Tue 4, Wed 2, Thu 0, Fri 5, Sat 8.

2(a) Thursday — no books (0).

3(b) 5 + 4 + 2 + 0 + 5 + 8 = 24.

4(c) Saturday (8). Reason: a holiday (Sunday) comes next, so students borrow books to read at home; Thursday the library may have been closed.

✅ Answer: (a) Thursday (b) 24 books (c) Saturday — students borrow books for the weekend.

📖 Textbook Page 84

📖 Page 84Figure it Out · Q2

Make a pictograph of kites sold (one kite symbol = 100 kites). (a) Symbols for Rani? (b) Who bought most? (c) Jasmeet or Chaman — who bought more? (d) Rukhsana says Poonam Ben bought more than double Rani’s kites. Is she right?

1Symbols = kites ÷ 100: Chaman 2½, Rani 3, Rukhsana 1, Jasmeet 4½, Jetha Lal 2½, Poonam Ben 7.

2(a) Rani: 3 symbols.

3(b) Poonam Ben (700).

4(c) Jasmeet (450) bought more than Chaman (250).

5(d) Double of Rani = 2 × 300 = 600; 700 > 600 → Yes, she is right.

✅ Answer: (a) 3 (b) Poonam Ben (c) Jasmeet (d) Yes — 700 is more than 600.

📖 Textbook Page 86

📖 Page 86Bar graph · Absent students

From the bar graph of absent students: (1) how many were absent in Class 2? (2) Which class had the most absent? (3) Which class had full attendance?

1Read the height of each bar (1 unit = 1 student).

2Class 2 bar reaches 5.

3Tallest bar: Class 8 (7).

4Class 5 has no bar (0 absent).

✅ Answer: (1) 5 (2) Class 8 (3) Class 5

📖 Textbook Page 88

📖 Page 88Figure it Out · Q1

How many vehicles passed through the crossing between 6 a.m. and noon?

1Read each bar: 150, 1200, 1000, 800, 700, 600.

2Total = 150 + 1200 + 1000 + 800 + 700 + 600 = 4450.

✅ Answer: About 4,450 vehicles.

📖 Page 88Figure it Out · Q2–Q4

Why was traffic (2) so little between 6–7 a.m. (3) heaviest between 7–8 a.m. (4) less and less each hour after 8 a.m.?

1(2) Early morning — most people have not yet started for work or school; shops and offices are closed.

2(3) 7–8 a.m. is the rush hour: school buses, office-goers and workers all travel at the same time.

3(4) After 8–9 a.m. most people have reached school or office, so fewer vehicles are on the road until lunchtime.

✅ Answer: Early morning is quiet; 7–8 a.m. is the school-and-office rush; later most people have already reached.

📖 Page 88Example · Population of India

How much did India’s population increase in 50 years (1951–2001)? How much in each decade?

11951: 36 crore; 2001: 102 crore → increase 102 − 36 = 66 crore.

2Each decade: 44 − 36 = 8, 54 − 44 = 10, 68 − 54 = 14, 84 − 68 = 16, 102 − 84 = 18 (crore).

3The increase gets bigger every decade.

✅ Answer: 66 crore in 50 years; decade increases 8, 10, 14, 16, 18 crore.

📖 Textbook Page 89

📖 Page 89Drawing a bar graph · Sweets

Draw a bar graph of the sweet choices (jalebi 6, gulab jamun 9, gujiya 13, barfi 3, rasgulla 7) with 1 unit = 1 student.

1Draw a horizontal line (sweets) and a vertical line (number of students).

2Mark 0, 1, 2, …, 14 on the vertical line with equal gaps.

3Draw bars of equal width and equal gaps; heights 6, 9, 13, 3, 7.

✅ Answer: See the bar graph.

📖 Textbook Page 90

📖 Page 90Example · Smriti’s runs

Draw a bar graph of Smriti’s runs 80, 50, 10, 100, 90, 0, 90, 50 using 1 unit = 10 runs. In which match did she score the most? How many runs in all?

1Scale: 1 unit = 10 runs, so the axis goes 0, 10, 20, …, 100.

2Bar heights: 8, 5, 1, 10, 9, 0, 9, 5 units.

3Most: Match 4 (100).

4Total = 80 + 50 + 10 + 100 + 90 + 0 + 90 + 50 = 470.

✅ Answer: Most in Match 4 (100 runs); total 470 runs.

📖 Textbook Page 93

📖 Page 93Imran’s family · Questions

Using the bar graph of Imran’s family expenses: (1) on which item do they spend the most and second most? (2) Is electricity about half of education? (3) Is education less than one-fourth of food?

1Scale: 1 unit = ₹200.

2(1) Food ₹3400 (most), house rent ₹3000 (second).

3(2) Half of 800 = 400 = electricity → Yes.

4(3) One-fourth of 3400 = 850; 800 < 850 → Yes.

✅ Answer: (1) Food, then house rent (2) Yes (3) Yes

📖 Page 93Figure it Out · Q1

Help Samantha prepare a bar graph: mites 6, caterpillars 10, beetles 5, butterflies 3, grasshoppers 2.

1Scale: 1 unit = 1 insect (largest value 10 fits easily).

2Mark 0 to 10 on the vertical axis.

3Bars of equal width: 6, 10, 5, 3, 2.

✅ Answer: See the bar graph.

📖 Textbook Page 94

📖 Page 94Figure it Out · Q2

Pooja’s ticket graph was partly erased (Vidisha 24, Jabalpur 20, Seoni 16, Indore 28, Sagar 16). (a)–(b) Write 24 and 20 above the bars. (c) Vidisha’s bar is 6 units, Jabalpur’s 5 units. What is the scale? (d) Draw Sagar’s bar. (e) Number the vertical axis. (f) Are Seoni’s and Indore’s bars correct?

1(c) 24 ÷ 6 = 4 and 20 ÷ 5 = 4 → 1 unit = 4 tickets.

2(e) Axis: 0, 4, 8, 12, 16, 20, 24, 28, 32.

3(d) Sagar: 16 ÷ 4 = 4 units.

4(f) Seoni’s bar is 4 units = 16 ✔ correct.

5Indore’s bar is only about 4½ units (≈ 18), but 28 ÷ 4 = 7 units → wrong; draw it 7 units high.

✅ Answer: (c) 1 unit = 4 tickets (d) Sagar 4 units (f) Seoni correct; Indore wrong — it should be 7 units (28).

📖 Page 94Figure it Out · Q3

Chinu listed the vehicles passing his house from 9 to 10 a.m. (a) Make a frequency table. (b) Which means of transport was used most? (c) How would you collect such data?

1(a) Tally each vehicle: bike 13, scooter 9, auto rickshaw 8, bicycle 8, car 6, bus 4, bullock cart 2 (total 50).

2(b) Bike (13).

3(c) Sit at a safe place near the road with a notebook and a watch; make a column for each type; put a tally mark for every vehicle from 9:00 to 10:00; count at the end.

✅ Answer: (b) Bike — 13 times out of 50.

📖 Textbook Page 95

📖 Page 95Figure it Out · Q4

Roll a die 30 times, make a tally table and find the number that appeared (a) the least (b) the most (c) numbers that appeared equally often.

1Roll 30 times and put a tally against the number each time.

2Example result: 1 → 4, 2 → 6, 3 → 5, 4 → 3, 5 → 6, 6 → 6 (total 30).

3(a) least: 4 (3 times) (b) most: 2, 5 and 6 (6 times each) (c) 2, 5 and 6 appeared equally.

✅ Answer: Your answers depend on your rolls — see the example.

📖 Page 95Figure it Out · Q5

Faiz’s table: wickets taken by Bumrah in 30 matches. (a) What does it tell? (b) A title? (c) What catches your attention? (d) In how many matches did he take 4 wickets? (e) Can Mayank find total wickets by adding 0 + 1 + … + 7? (f) How do we find the total?

Wickets taken	Number of matches
0	2
1	4
2	6
3	8
4	3
5	5
6	1
7	1

1(a) For each number of wickets (0 to 7), the number of matches in which he took that many.

2(b) ‘Wickets taken by Jaspreet Bumrah in his last 30 matches’.

3(c) He most often took 3 wickets (8 matches); only 2 matches with no wicket.

4(d) 3 matches.

5(e) No — 0 + 1 + … + 7 = 28 ignores how many matches each happened in.

6(f) Multiply wickets × matches and add: 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.

✅ Answer: (d) 3 (e) No (f) 90 wickets in all.

⚠️ Common mistake: Adding only 0 to 7. Each wicket number must be multiplied by how many matches it happened in.

📖 Textbook Page 96

📖 Page 96Figure it Out · Q6

Tractors in five villages (one symbol = 1 tractor). (a) Smallest number? (b) Most? (c) How many more in C than B? (d) Komal: ‘D has half as many as E.’ Is she right?

1Read: A 6, B 5, C 8, D 3, E 6.

2(a) Village D (3).

3(b) Village C (8).

4(c) 8 − 5 = 3.

5(d) Half of 6 = 3 = D → Yes.

✅ Answer: (a) D (b) C (c) 3 more (d) Yes

📖 Textbook Page 97

📖 Page 97Figure it Out · Q7

Girl students in each class (one symbol = 4 girls). (a) Least girls? (b) Difference between Classes 5 and 6? (c) If 2 more girls join Class 2, how does the graph change? (d) Girls in Class 7?

1Girls = symbols × 4: 24, 18, 20, 14, 10, 16, 12, 6.

2(a) Class 8 (6 girls).

3(b) Class 6: 16, Class 5: 10 → difference 6.

4(c) Class 2: 18 + 2 = 20 → the half symbol becomes a full one: 5 full symbols.

5(d) Class 7: 3 × 4 = 12.

✅ Answer: (a) Class 8 (b) 6 (c) Class 2 gets 5 full symbols (d) 12

📖 Textbook Page 98

📖 Page 98Figure it Out · Q8

Mudhol hounds: A 18, B 36, C 12, D 48, E 18, F 24. Make a pictograph. (a) A useful key? (b) Symbols for Village B? (c) Kamini says B and D together have more dogs than the other 4 villages together. Is she right?

1(a) All numbers are multiples of 6 → one symbol = 6 dogs (no part symbols needed).

2(b) 36 ÷ 6 = 6 symbols.

3(c) B + D = 36 + 48 = 84; A + C + E + F = 18 + 12 + 18 + 24 = 72.

484 > 72 → Yes, Kamini is right.

✅ Answer: (a) 1 symbol = 6 dogs (b) 6 (c) Yes — 84 > 72.

💡 Tip: Choose a key that divides all the numbers exactly — then no broken symbols are needed.

📖 Page 98Figure it Out · Q9

Draw a bar graph of activities (playing 45, reading story books 30, TV 20, music 10, painting 15) using 1 unit = 5 students. Which activity is liked most after playing?

1Heights: 45 ÷ 5 = 9, 30 ÷ 5 = 6, 20 ÷ 5 = 4, 10 ÷ 5 = 2, 15 ÷ 5 = 3 units.

2Check: 45 + 30 + 20 + 10 + 15 = 120 ✔

3After playing, the tallest bar is reading story books.

✅ Answer: Reading story books (30 students).

📖 Textbook Page 99

📖 Page 99Figure it Out · Q10

Saplings planted in a week (bar graph). (a) Wednesday + Thursday? (b) Whole week? (c) Most and least on which days? Why?

1Read the bars: Mon 52, Tue 40, Wed 30, Thu 40, Fri 50, Sat 60, Sun 40.

2(a) 30 + 40 = 70.

3(b) 52 + 40 + 30 + 40 + 50 + 60 + 40 = 312.

4(c) Most: Saturday (60); least: Wednesday (30).

5Possible reasons: Saturday is a half day, so more time and more helpers; mid-week there are more classes/tests. We can check by asking the teachers or keeping a record of hours spent each day.

✅ Answer: (a) 70 (b) 312 (c) Saturday most, Wednesday least.

💡 Tip: Monday’s bar is a little above 50 — about 52.

📖 Textbook Page 100

📖 Page 100Figure it Out · Q11

Find and fix the mistakes in the bar graph of tigers in India (2006: 1400, 2010: 1700, 2014: 2200, 2018: 3000, 2022: 3700).

Year	Tigers (approx.)
2006	1400
2010	1700
2014	2200
2018	3000
2022	3700

1Compare each bar with the table (one grid gap = 1000).

22006 bar shows only about 800 — it should reach 1400.

32010 bar shows about 1500 — it should reach 1700.

4The 2014 and 2018 bars are swapped: 2014 shows about 2900 and 2018 about 2200.

52022 (≈ 3700) is correct. Redraw the four wrong bars.

Corrected: each bar now matches the table (scale: one grid gap = 1000 tigers).

✅ Answer: Mistakes: 2006 too short (should be 1400), 2010 too short (1700), 2014 and 2018 swapped. See the corrected graph.

📖 Textbook Page 101

📖 Page 101Think · Mountains

How much taller is Mount Everest than Mount Kosciuszko? Are Denali and Kilimanjaro very different in height?

18848 − 2228 = 6620 m.

2Denali 6194 m, Kilimanjaro 5895 m → difference 299 m only.

3A column graph makes this easy to see at a glance.

✅ Answer: Everest is 6,620 m taller. Denali and Kilimanjaro differ by only 299 m — nearly equal.

📖 Textbook Page 103

📖 Page 103Figure it Out · Q1

To show the heights of the tallest person in each class, would you use vertical or horizontal bars? Why?

1Heights are measured upward from the ground.

2Vertical bars (columns) grow upward like people standing.

✅ Answer: Vertical bars — they look like people standing, so heights are easy to compare.

📖 Page 103Figure it Out · Q2

For the longest river on each continent, would you use vertical or horizontal bars? Why? Which continents have the longest rivers?

1River lengths run along the ground, so horizontal bars suit them.

2Longest rivers (about): Nile 6650 km, Amazon 6400 km, Yangtze 6300 km, Mississippi–Missouri 6275 km, Murray–Darling 3672 km, Volga 3530 km (Antarctica has no big rivers).

3Africa and South America have the longest rivers.

✅ Answer: Horizontal bars. Africa (Nile) and South America (Amazon) have the longest rivers.

💡 Tip: Lengths are approximate; different books give slightly different values.

📖 Textbook Page 104

📖 Page 104Think · Infographics

In the triangle infographic, taller mountains are also wider. Is that a problem? Is the picture accurate?

1In a bar graph all bars have the same width, so only the heights are compared.

2In the infographic the taller triangles are also wider, so they look much ‘bigger’.

3Mountains are not always wider when they are taller, so the picture suggests wrong information.

Triangles of different WIDTHS: taller ones also look wider and ‘bigger’ — this can mislead.

✅ Answer: Yes — the extra width can mislead; only the heights carry the data.

📖 Textbook Page 105

📖 Page 105Think

In the mountain-range picture Everest looks twice as tall as Elbrus. What is 5642 × 2? Is the picture accurate?

15642 × 2 = 11,284 m.

2Everest is only 8848 m — much less than 11,284 m.

38848 ÷ 5642 ≈ 1.6, so Everest is about 1.6 times as tall as Elbrus, not twice.

✅ Answer: 5642 × 2 = 11,284. The picture is misleading — Everest is only about 1.6 times as tall as Elbrus.

🌍 Where do we use data?

Elections, census and population studies; weather reports; sports scores.
Shops track sales; doctors track health records; schools track attendance.
News and TV use bar graphs and infographics every day — read them carefully!

🚀 Link to higher classes

Class 7: Connecting the Dots — mean and median. Class 8: Tales by Dots and Lines — line graphs.

⬆ Top 🏠 Class 6 Hub

🌈⚡Key To Enjoy Learning Maths☘🌈