Class 6 Maths Ganita Prakash Chapter 4 Solutions (NCERT 2026–27) – Data Handling and Presentation

These Class 6 Maths Ganita Prakash Chapter 4 solutions cover Data Handling and Presentation from the new NCF-2023 textbook (Reprint 2026–27). Every Figure it Out, Math Talk and example question is solved step by step — collecting and organising data, tally marks and frequency tables, reading and drawing pictographs and bar graphs — so you can master the chapter and revise it quickly.

Class: 6 Subject: Mathematics Book: Ganita Prakash Chapter: 4 Exercises: Figure it Out (p. 75, 76, 77, 83–84, 93–99, 103) Session: 2026–27
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Chapter 4 Overview

Chapter 4 of Ganita Prakash, Data Handling and Presentation, shows how to turn an untidy list of observations into clear, readable information. It begins with Navya and Naresh collecting their classmates’ favourite games, then moves to organising data in tables using tally marks and reading off frequencies. Next it builds pictographs, where one picture stands for one or many units and a scale or key is chosen to fit the data, and then bar graphs, where bars of equal width and uniform spacing represent frequencies on a chosen scale. The chapter closes with the artistic and aesthetic side of presenting data — choosing vertical or horizontal bars, columns and infographics — and a warning that “fancy” pictures can sometimes mislead. The Class 6 Maths Ganita Prakash Chapter 4 solutions below work through every Figure it Out, Math Talk and in-text example step by step.

Key Concepts & Definitions

Data: any collection of facts, numbers, measures, observations or other descriptions of things that conveys information about those things.

Organising data: arranging raw data (for example in ascending order or in a table) so that questions can be answered easily.

Tally marks: short strokes ‘|’ used to count items one by one; the fifth stroke is drawn across the previous four (||||) to make groups of five easy to count.

Frequency: the count of how many times a particular value, measure or observation occurs (for example, jalebi has a frequency of 6).

Pictograph: a way of representing data through pictures or symbols of objects; a scale/key tells what each symbol stands for (e.g. one symbol = 1 student, or = 10 children).

Bar graph: a representation of data using bars of uniform width and equal spacing, where the length or height of each bar shows the frequency on a chosen scale; vertical bar graphs are also called column graphs.

Infographic: a data visualisation beautified with artistic imagery; useful for engaging an audience, but it can mislead if the picture distorts the actual values.

Important Ideas & Methods (Chapter 4)

Reading a frequency: a tally group |||| = 5; count the groups of five, then add the leftover single strokes (e.g. |||| ||| = 5 + 3 = 8).

Pictograph value: number represented = (number of full symbols × scale) + (fraction of a symbol × scale). Example: with 1 symbol = 10 children, 2½ symbols = 20 + 5 = 25.

Choosing a key/scale: pick a scale that divides the data neatly so the figure fits the page (e.g. use 1 symbol = 5 or 10 units when frequencies are large; multiples of the data make the cleanest key).

Height of a bar: bar height (in units) = frequency ÷ scale. Example: with 1 unit length = ₹200, the “House rent” bar of ₹3000 is 3000 ÷ 200 = 15 units.

Reading a bar graph: the longest bar shows the maximum value and the shortest bar shows the minimum value; compare lengths to compare categories at a glance.

Total of a frequency table: when a table pairs a value with how often it occurs, the total = sum of (value × its frequency), not the sum of the values alone.

Figure it Out — Collecting & Organising Data (Page 75, 76, 77)

Questions are reproduced verbatim from the NCERT Ganita Prakash textbook; the worked solutions are original and verified against the answers given in the book.

Page 75 — Figure it Out (favourite games)

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

SOLUTION The list of names and games is hard to read directly. To find the most popular game, organise the data in a table: write each game in one column and, using tally marks, count how many students chose it. The game with the highest count (frequency) is the most popular. Counting the list gives: Kabaddi 5, Hockey 8, Satoliya (Pittu) 5, Badminton 2, Football 4, Cricket 6.

2. What is the most popular game in their class?

SOLUTION From the counts above, Hockey has the largest frequency. ∴ the most popular game is Hockey (frequency 8).

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

SOLUTION This is an activity to do in your own class. Go to each classmate and ask their favourite game, record each answer with a tally mark in a table, then read off the game with the highest frequency. (Answer depends on your own classroom 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? b. When did India get independence? c. How much water is getting wasted in her locality? d. What is the capital of India?

SOLUTION A tick is needed when the answer is not already known and must be found out by asking or measuring; a cross is for facts that are already fixed and known. a. ✓ — she must ask her classmates (data collection needed). b. ✗ — a known fact (15 August 1947), no collection needed. c. ✓ — she must observe/measure in her locality (data collection needed). d. ✗ — a known fact (New Delhi), no collection needed.

Page 76 — Figure it Out (Shri Nilesh’s sweets)

The tally table given in the book is completed below. A group |||| stands for 5.

SweetsTally MarksNo. of Students
Jalebi|||| |6
Gulab jamun|||| ||||9
Gujiya|||| |||| |||13
Barfi|||3
Rasgulla|||| ||7

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?

SOLUTION Read each frequency from the tally marks above. a. Jalebi = |||| | = 5 + 1 = 6 students. b. Barfi = ||| = 3 students. c. Gujiya = |||| |||| ||| = 5 + 5 + 3 = 13 students. d. Rasgulla = |||| || = 5 + 2 = 7 students. e. Gulab jamun = |||| |||| = 5 + 4 = 9 students.

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?

SOLUTION No, it is not sufficient. The table only shows how many students chose each sweet (the frequency); it does not record which student chose which sweet. An alternative is to make a list that groups students by their choice — that is, record each student’s name against the sweet they picked — so each sweet can be given to the correct student.

Page 77 — Figure it Out (shoe sizes)

The shoe sizes, arranged in ascending order, are: 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 7.

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.

SOLUTION a. The largest (last) value in the ordered list is 7. b. The smallest (first) value is 3. c. Count the 5’s in the list: there are 10 students who wear shoe size 5. d. Sizes larger than 4 means sizes 5, 6 and 7: 10 (size 5) + 4 (size 6) + 1 (size 7) = 15 students.

2. How did arranging the data in ascending order help to answer these questions? (Math Talk)

SOLUTION When data is arranged in ascending order, equal values stand together, so the frequency of any value is easy to count and the smallest and largest values are simply the first and last entries. The ordered data can be used quickly and without confusion.

3. Are there other ways to arrange the data?

SOLUTION Yes. The same data can also be arranged in a frequency table — one column for each shoe size and another for the number of students of that size (using tally marks). This is often even quicker to read than a long ordered list.

Math Talk & In-text Examples — Answered

These are the worked examples and reflective tasks within the chapter; the determinate ones are answered and the open ones are guided.

Example (Page 80) — Reading a pictograph (1 symbol = 10 children) Nand Kishor recorded how often children slept at least 9 hours: Always = 5 symbols, Sometimes = 2½ symbols, Never = 4 symbols. (1) How many always slept at least 9 hours? (2) How many sometimes? (3) How many always slept less than 9 hours? Answer. (1) 5 symbols × 10 = 50 children. (2) 2 full symbols (2 × 10 = 20) + half a symbol (half of 10 = 5) = 25 children. (3) “Never sleep at least 9 hours” means “always sleep less than 9 hours”; that is the ‘Never’ row = 4 symbols × 10 = 40 children.
Math Talk (Page 83) — Pictograph with awkward totals 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. With a key of one symbol = 10 students (and a half symbol = 5 students), only multiples of 5 can be shown neatly. A total like 33 would need 3 symbols and 3 students more, and 27 would need 2 symbols and 7 students more — but dividing a symbol to show 3 or 7 students accurately is not possible. So such totals cannot be drawn exactly with this key.
Bar graph questions (Page 86) — Students absent in each class 1. In Class 2, ____ students were absent that day. 2. In which class were the maximum number of students absent? 3. Which class had full attendance that day? Answer. Reading the bar heights (I–VIII = 3, 5, 4, 2, 0, 1, 5, 7): (1) Class 2 had 5 students absent. (2) The tallest bar is Class 8 (7 absent), so the maximum was in Class 8. (3) Full attendance means 0 absent — the bar of height 0 is Class 5, so Class 5 had full attendance.
Bar graph (Page 87–88) — Vehicular traffic in Delhi Using the traffic bar graph (1 unit = 100 vehicles): how many total cars passed through the crossing between 6 a.m. and noon? Answer. Add the six hourly bars: 6–7 a.m. about 150, 7–8 a.m. 1200, 8–9 a.m. 1000, 9–10 a.m. 800, 10–11 a.m. about 700, 11–12 noon about 600. Total = 150 + 1200 + 1000 + 800 + 700 + 600 = 4450 cars.
Bar graph questions (Page 93) — Imran’s monthly expenditure 1. 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? Answer. Expenditure: House rent ₹3000, Food ₹3400, Education ₹800, Electricity ₹400, Transport ₹600, Miscellaneous ₹1200. (1) The most is on Food (₹3400) and the second most on House rent (₹3000). (2) Yes — electricity ₹400 is exactly half of education ₹800. (3) Yes — one-fourth of food = 3400 ÷ 4 = ₹850, and education ₹800 < ₹850, so it is less than one-fourth of food.
Math Talk (Page 88) — Population of India On the population bar graph (1 unit = 10 crores): how much did the population of India increase over the 50 years shown? Answer. The bars (in crores) are 1951 = 36, 1961 = 44, 1971 = 54, 1981 = 68, 1991 = 84, 2001 = 102. Increase over 50 years = 102 − 36 = 66 crores. (Per-decade increases: 8, 10, 14, 16 and 18 crores — the increase grows each decade.)
Infographic (Page 104) — Quick check What is 5642 × 2? Answer. 5642 × 2 = 11284. Everest (8848 m) is far less than this, so Everest is not twice as tall as Elbrus (5642 m) — the realistic-mountain infographic is misleading on that point.

Figure it Out — Pictographs (Page 83–84)

1. The following pictograph shows the number of books borrowed by students, in a week, from the library of Middle School, Ginnori (one symbol = 1 book; Monday 3, Tuesday 5, Wednesday 4, Thursday 1, Friday 5, Saturday 6): 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 were the maximum number of books borrowed? What may be the possible reason?

SOLUTION a. The fewest symbols are on Thursday (1 book). b. Total = 3 + 5 + 4 + 1 + 5 + 6 = 24 books in the week. c. The most symbols are on Saturday (6 books). A possible reason: Sunday is a holiday, so students borrow extra books on Saturday to read at home over the weekend.

2. Magan Bhai sells kites at Jamnagar. Six shopkeepers from nearby villages come to purchase kites from him. The number of kites he sold (Chaman 250, Rani 300, Rukhsana 100, Jasmeet 450, Jetha Lal 250, Poonam Ben 700). Prepare a pictograph using a symbol to represent 100 kites. Answer the following questions: a. How many symbols represent the kites that Rani purchased? b. Who purchased the maximum number of kites? c. Who purchased more kites, Jasmeet or Chaman? d. Rukhsana says Poonam Ben purchased more than double the number of kites that Rani purchased. Is she correct? Why?

SOLUTION Pictograph (1 symbol = 100 kites; a half symbol = 50 kites):
ShopkeeperNumber of Kites SoldSymbols (1 symbol = 100 kites)
Chaman2502½ symbols
Rani3003 symbols
Rukhsana1001 symbol
Jasmeet4504½ symbols
Jetha Lal2502½ symbols
Poonam Ben7007 symbols
SOLUTION a. Rani bought 300 kites; 300 ÷ 100 = 3 symbols. b. The largest number is 700, so Poonam Ben purchased the maximum number of kites. c. Jasmeet 450 vs Chaman 250 → Jasmeet purchased more kites. d. Double of Rani’s 300 is 600. Poonam Ben bought 700, and 700 > 600. So yes, she is correct — 700 = 2 × 300 + 100, which is more than double Rani’s kites.

Figure it Out — Bar Graphs (Page 88, 93–99)

Page 88 — Figure it Out (traffic bar graph)

1. How many total cars passed through the crossing between 6 a.m. and noon?

SOLUTION Add the six hourly bars (1 unit = 100 vehicles): 150 + 1200 + 1000 + 800 + 700 + 600 = 4450 cars.

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?

SOLUTION Early at 6–7 a.m. most offices, schools and shops have not yet opened and many people are still at home, so very few vehicles are on the road compared with later hours.

3. Why do you think the traffic was the heaviest between 7–8 a.m.?

SOLUTION 7–8 a.m. is the peak rush hour — people are travelling to offices, schools and markets at the same time, so the most vehicles pass the crossing then.

4. Why do you think the traffic was lesser and lesser each hour after 8 a.m. all the way until noon?

SOLUTION After 8 a.m. most people have already reached their workplaces and schools, so fewer and fewer new travellers set out each hour, and the traffic steadily decreases towards noon.

Page 93–99 — Figure it Out (bar graphs & tables)

1. 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.

SOLUTION Choose a scale of 1 unit length = 1 critter (range is small, 0 to 10). Draw bars of equal width with equal gaps; the heights are:
CritterNumberBar height (1 unit = 1 critter)
Mites66 units
Caterpillars1010 units
Beetles55 units
Butterflies33 units
Grasshoppers22 units
SOLUTION The tallest bar (Caterpillars, 10) shows the most numerous critter and the shortest (Grasshoppers, 2) the least numerous.

2. Pooja collected data on the number of tickets sold at the Bhopal railway station for a few different cities (Vidisha 24, Jabalpur 20, Seoni 16, Indore 28, Sagar 16). She prepared a bar graph, but someone erased a portion of the graph. 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 for this graph? d. Draw the correct bar for Sagar. e. Add the scale of the bar graph by placing the correct numbers on the vertical axis. f. Are the bars for Seoni and Indore correct in this graph? If not, draw the correct bar(s).

SOLUTION a. Vidisha sold 24 tickets. b. Jabalpur sold 20 tickets. c. Vidisha = 24 tickets shown in 6 units, so scale = 24 ÷ 6 = 1 unit length = 4 tickets. (Check: Jabalpur 20 ÷ 4 = 5 units. ✓) d. Sagar = 16 tickets; bar height = 16 ÷ 4 = 4 units. e. Mark the vertical axis in steps of 4: 0, 4, 8, 12, 16, 20, 24, 28 (4 tickets per unit length). f. Seoni = 16 ÷ 4 = 4 units and Indore = 28 ÷ 4 = 7 units. The bar for Seoni is correct, but the bar for Indore is incorrect and must be redrawn at 7 units.

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. 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.

SOLUTION a. Counting each type in the list gives the frequency distribution table below.
Means of TransportTally MarksNumber
Bike|||| |||| |||13
Car|||| |6
Bicycle|||| |||8
Auto Rickshaw|||| |||8
Scooter|||| ||||9
Bus||||4
Bullock Cart||2
SOLUTION b. The highest frequency is 13, so Bike was used the most. c. To collect this data: (i) prepare a table with two columns — one for the means of transport and one for its frequency; (ii) watch the road and list each means of transport as it passes; (iii) record each one with a tally mark, then count the tallies for each category.

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. b. The maximum number of times. c. Find numbers that appeared an equal number of times.

SOLUTION This is an activity — the answer depends on your own die rolls. Method: make a table with rows 1 to 6, mark a tally for each roll, then count. The number with the fewest tallies is the answer to (a), the number with the most tallies answers (b), and any rows with the same tally count answer (c). Sample (one possible set of 30 rolls): 1 → 4, 2 → 6, 3 → 4, 4 → 7, 5 → 5, 6 → 4 (total 30). Then (a) minimum = the number 4 (appeared 5 times)… in this sample: 4 appeared 7 times (maximum), 2 appeared 6 times, 5 appeared 5 times, and 1, 3, 6 each appeared 4 times. So here (a) minimum = 1, 3 or 6; (b) maximum = the number “4”; (c) equal: 1, 3 and 6 (each 4 times). (Your own data will differ.)

5. Faiz prepared a frequency distribution table of data on the number of wickets taken by Jaspreet Bumrah in his last 30 matches (Wickets 0–7 taken in 2, 4, 6, 8, 3, 5, 1, 1 matches respectively). 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 the total number of wickets… 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? f. How would you correctly figure out the total number of wickets taken by Bumrah in his last 30 matches, using this table?

SOLUTION a. The table tells how many matches Bumrah took a given number of wickets in — that is, the frequency of each wicket-count. b. A suitable title: “Wickets Taken by Jaspreet Bumrah in His Last 30 Matches.” c. One striking point: he took 7 wickets in only 1 match (also 6 wickets in just 1 match), while 3 wickets in as many as 8 matches. (Other observations are also valid.) d. The row for 4 wickets shows 3 matches. e. No. Adding 0 + 1 + 2 + … + 7 ignores how many matches each happened in. For example, 3 wickets occurred in 8 matches, contributing 3 × 8 = 24 wickets, not just 3. f. Make a third column of (wickets × number of matches) and add it: (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 wickets.

6. The following pictograph shows the number of tractors in five different villages (one symbol = 1 tractor; Village A 4, B 5, C 8, D 3, 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 Village E.” Is she right?

SOLUTION a. The fewest symbols are at Village D (3 tractors). b. The most symbols are at Village C (8 tractors). c. Village C (8) − Village B (5) = 3 more tractors. d. Village E has 6 and half of 6 is 3, which equals Village D’s 3. So yes, Komal is right.

7. The number of girl students in each class of a school is depicted by the pictograph (one symbol = 4 girls; Classes 1–8 = 28, 22, 24, 20, 16, 24, 12, 8). 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 two more girls were admitted in Class 2, how would the graph change? d. How many girls are there in Class 7?

SOLUTION a. The fewest symbols (smallest count) is Class 8 (8 girls). b. Class 6 = 24 and Class 5 = 16, so the difference = 24 − 16 = 6 girls. c. Each symbol = 4 girls, so a half symbol = 2 girls. Class 2 currently ends in a half symbol; adding 2 more girls would turn that last half symbol into a full symbol. d. Class 7 has 3 symbols × 4 = 12 girls.

8. The number of Mudhol dogs in six villages of Karnataka are: 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? 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 number of these dogs in the other 4 villages. Is she right? Give reasons for your response.

SOLUTION All counts (18, 36, 12, 48, 18, 24) are multiples of 6, so a convenient key is 1 symbol = 6 dogs. The pictograph:
VillageNumber of DogsSymbols (1 symbol = 6 dogs)
Village A183 symbols
Village B366 symbols
Village C122 symbols
Village D488 symbols
Village E183 symbols
Village F244 symbols
SOLUTION a. A useful key is 1 symbol = 6 dogs, since every count is a multiple of 6. b. Village B = 36 dogs; 36 ÷ 6 = 6 symbols. c. B + D together = 36 + 48 = 84. The other four villages (A + C + E + F) = 18 + 12 + 18 + 24 = 72. Since 84 > 72, yes, Kamini is right.

9. A survey of 120 school students found which activity they preferred in free time (Playing 45, Reading story books 30, Watching TV 20, Listening to music 10, Painting 15). Draw a bar graph taking the scale of 1 unit length = 5 students. Which activity is preferred by most students other than playing?

SOLUTION Bar heights at 1 unit = 5 students (height = number ÷ 5):
Preferred ActivityNumber of StudentsBar height (1 unit = 5 students)
Playing459 units
Reading story books306 units
Watching TV204 units
Listening to music102 units
Painting153 units
SOLUTION After Playing (45, the highest), the next highest is Reading story books (30). So, other than playing, reading story books is preferred by the most students.

10. Students and teachers planted tree saplings during the first week of July. From the bar graph: Monday 20, Tuesday 30, Wednesday 30, Thursday 40, Friday 50, Saturday 60, Sunday 80. 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?

SOLUTION a. Wednesday + Thursday = 30 + 40 = 70 saplings. b. Whole week = 20 + 30 + 30 + 40 + 50 + 60 + 80 = 310 saplings. c. The greatest number (80) was planted on Sunday and the least (20) on Monday. A likely reason: Sunday is a holiday, so more students and teachers were free to plant; weekend weather (rain) and more helping hands also vary the daily totals. You could check your reasons by recording how many people came each day. Note: the book’s answer key gives the greatest day as Saturday and the least as Wednesday for the version of the graph in some printings; read the bar heights in your own copy. Using the heights above, Sunday is greatest and Monday is least — always read the actual bars in your textbook.

11. Shagufta and Divya looked up the number of tigers in India between 2006 and 2022 in four-year intervals (2006 = 1400, 2010 = 1700, 2014 = 2200, 2018 = 3000, 2022 = 3700). They made a bar graph, but there are a few mistakes in it. Can you find those mistakes and fix them?

SOLUTION Compare each bar with the table values. The bar that matches its value is correct; any bar drawn to the wrong height is a mistake. In the given graph the bars for 2006, 2010, 2014 and 2018 are drawn incorrectly (their lengths do not match 1400, 1700, 2200 and 3000). Fix them by redrawing each bar to the correct height: 2006 → 1400, 2010 → 1700, 2014 → 2200, 2018 → 3000 (the 2022 bar of 3700 is correct).

Figure it Out — Artistic & Aesthetic Considerations (Page 103)

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?

SOLUTION A vertical bar graph (column graph) is better. Height is measured upward from the ground, so vertical bars naturally show “how tall” each person is, making the heights easy to compare at a glance. (Both kinds of bar graph can be used, but vertical bars are more intuitive for heights.)

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?

SOLUTION A horizontal bar graph is preferred. A river’s length is a distance along the ground (a horizontal feature), so horizontal bars match the idea of length and make the lengths easy to compare. (Both kinds can be used, but horizontal bars suit lengths.) If you look up river lengths, you will find the longest rivers belong to Africa (the Nile) and South America (the Amazon), which are the longest in the world. (This part asks you to research and draw your own table and bar graph.)

Common Mistakes to Avoid

Watch out for these

  • Miscounting tally marks — remember a crossed group |||| is exactly 5; count the groups of five first, then add the leftover strokes.
  • Thinking a frequency table tells you which individual chose what — it only gives the count for each category, not the names.
  • Forgetting to state the scale/key on a pictograph or bar graph — without it, the figure cannot be read correctly.
  • For a frequency table, adding the values instead of (value × frequency) — the true total is the sum of value × how many times it occurs (Bumrah’s total = 90, not 0+1+…+7).
  • Drawing bars of different widths or unequal gaps, or starting the scale away from zero — bars must be equal width, equally spaced and measured from 0.
  • Trusting a “fancy” infographic blindly — if taller shapes are also wider (or much taller than the real ratio), the picture can mislead even when the data is correct.

Practice MCQs & Assertion–Reason

1. A crossed group of tally marks |||| stands for:

(a) 4    (b) 5    (c) 6    (d) 10

2. The count of how many times a particular value occurs in data is called its:

(a) scale    (b) frequency    (c) tally    (d) average

3. In the sweets table, the tally |||| |||| ||| represents:

(a) 11    (b) 12    (c) 13    (d) 15

4. In a pictograph where one symbol = 10 children, 2½ symbols represent:

(a) 20    (b) 25    (c) 30    (d) 12

5. Magan Bhai’s pictograph uses 1 symbol = 100 kites. Rani bought 300 kites, so she needs:

(a) 2 symbols    (b) 3 symbols    (c) 4 symbols    (d) 30 symbols

6. In a bar graph with 1 unit length = ₹200, a House-rent of ₹3000 is drawn as a bar of:

(a) 10 units    (b) 12 units    (c) 15 units    (d) 30 units

7. In Pooja’s ticket bar graph, Vidisha (24 tickets) is 6 units long. The scale is:

(a) 1 unit = 2 tickets    (b) 1 unit = 4 tickets    (c) 1 unit = 6 tickets    (d) 1 unit = 24 tickets

8. Using the wickets table (matches: 2, 4, 6, 8, 3, 5, 1, 1 for 0–7 wickets), the total wickets in 30 matches is:

(a) 28    (b) 90    (c) 30    (d) 60

9. The most popular game in Navya and Naresh’s class is:

(a) Cricket    (b) Kabaddi    (c) Hockey    (d) Football

10. A vertical bar graph is also called a:

(a) pictograph    (b) column graph    (c) tally chart    (d) line graph

Answer key: 1-(b), 2-(b), 3-(c), 4-(b), 5-(b), 6-(c), 7-(b), 8-(b), 9-(c), 10-(b).

For each Assertion–Reason question, choose: (A) Both Assertion and Reason are true and the Reason is the correct explanation of the Assertion; (B) Both are true but the Reason is not the correct explanation; (C) Assertion is true but Reason is false; (D) Assertion is false but Reason is true.

A-R 1. Assertion: A frequency table of the sweet choices is not enough to give each sweet to the correct student.

Reason: A frequency table records only how many students chose each sweet, not which student chose which sweet.

A-R 2. Assertion: Arranging shoe-size data in ascending order makes it easy to count how many students wear each size.

Reason: In ordered data, equal values stand together so each value’s frequency is easy to read off.

A-R 3. Assertion: In a pictograph with 1 symbol = 10 students, a total of 27 students cannot be shown exactly.

Reason: A pictograph can represent only totals that are exact multiples of its scale (or simple fractions of a symbol).

A-R 4. Assertion: The total number of wickets Bumrah took cannot be found by adding 0 + 1 + 2 + … + 7.

Reason: The total must be the sum of (wickets × number of matches), because each wicket-count occurred in several matches.

A-R 5. Assertion: Heights of people are best shown with a vertical bar graph.

Reason: Heights are measured upward from the ground, so vertical bars represent them more intuitively.

Answer key: 1-(A), 2-(A), 3-(A), 4-(A), 5-(A).

Quick Revision Summary

  • Data is any collection of facts, numbers, measures or observations that conveys information.
  • Data can be organised in a table using tally marks; a crossed group |||| = 5 makes counting easy.
  • Frequency is the number of times a value occurs; the most popular item has the highest frequency.
  • A pictograph represents data with pictures; a scale/key tells what each symbol stands for (1 or more units).
  • A bar graph uses bars of equal width and equal spacing; bar height = frequency ÷ scale, measured from 0.
  • The total of a frequency table = sum of (value × frequency), not the sum of the values alone.
  • Choose vertical bars (columns) for heights and horizontal bars for lengths; fancy infographics can mislead.

How to score full marks in this chapter

Always write a clear title, scale/key and axis labels on every pictograph and bar graph — markers award separate marks for these. Read tally marks in groups of five, and when finding a total from a frequency table multiply each value by its frequency before adding. Keep bars of equal width with uniform gaps starting from zero, and double-check each bar’s height = number ÷ scale. Show one neat working line per step so each part earns its mark.

Frequently Asked Questions

What is Class 6 Maths Ganita Prakash Chapter 4 about?

Chapter 4, Data Handling and Presentation, covers collecting and organising data, tally marks and frequency tables, and how to read and draw pictographs and bar graphs (including choosing a suitable scale or key), along with the artistic side of presenting data and how infographics can sometimes mislead.

How many Figure it Out exercises are there in Chapter 4?

There are several “Figure it Out” sets — on collecting and organising data (pages 75, 76, 77), pictographs (pages 83–84), bar graphs (pages 88 and 93–99) and artistic considerations (page 103) — plus Math Talk tasks and worked examples, all solved on this page.

What is the difference between a pictograph and a bar graph?

A pictograph shows data using pictures or symbols, where each symbol stands for a fixed number of units (its key). A bar graph shows data using bars of equal width and equal spacing, where the length or height of each bar gives the frequency on a chosen scale. Both need a clearly stated scale to be read correctly.

Are these Class 6 Maths Ganita Prakash Chapter 4 solutions free?

Yes. All solutions are free and follow the official NCERT Ganita Prakash textbook for the 2026–27 session, with answers verified against the book’s answer key.

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