Chapter 4 exercise answers: Data Handling and Presentation

Open NCERT p. 75One way to think about it

1. Go through the list of 31 classmates one at a time.
2. Make a tally mark for each student against the game they named.
3. Add up the tally marks to get a count (frequency) for every game.
4. Compare the six counts — the game with the highest count is the most popular one.

In shortCount how many students chose each game using tally marks, then see which game has the highest count.

Watch this explained “Counting it: 8, 6, 6, 5, 4, 2 — and they total 31”, 4:09 into Turning an argument into a question you can settle with data · हिंदी में देखें

Open NCERT p. 75Matches NCERT’s answer

1. Put a tally mark next to each of the 31 names for the game they chose.
2. Count the tally marks for each game: Kabaddi 6, Hockey 8, Satoliya (Pittu) 5, Cricket 6, Badminton 2, Football 4.
3. 6 + 8 + 5 + 6 + 2 + 4 = 31, which matches the number of classmates, so nothing was missed.
4. Hockey has the highest count, 8, so hockey is the most popular game.

AnswerHockey — it was chosen by 8 of the 31 classmates, the highest count.

Watch this explained “Counting it: 8, 6, 6, 5, 4, 2 — and they total 31”, 4:09 into Turning an argument into a question you can settle with data · हिंदी में देखें

Open NCERT p. 75One way to think about it

1. Decide the exact question to ask ("What is your favourite game?") and the group to ask (every classmate, each asked once).
2. Ask each classmate and write down their name and their answer as you go, like Navya did.
3. Make a tally mark for each answer against that game, then add up the tally marks for each game.
4. Add all the counts together: the total must equal the number of classmates you asked, so you know nobody was missed or counted twice.
5. The game with the highest count is the most popular game in your class.
6. Example (your class will give different numbers): in a class of 30, suppose the counts are Cricket 11, Kabaddi 7, Football 5, Kho-kho 4, Badminton 3. Check: 11 + 7 + 5 + 4 + 3 = 30. The highest count is 11, so cricket is the most popular game in that class.

In shortSurvey every classmate, tally each one's favourite game, check the counts add up to the class size, and pick the game with the highest count. The answer depends on your own class, so there is no single correct answer; in the example above it is cricket (11 of 30).

Watch this explained “Settle the group and the record before you collect”, 2:07 into Turning an argument into a question you can settle with data · हिंदी में देखें

Open NCERT p. 75Matches NCERT’s answer

(a) What is the most popular TV show among her classmates?

1. A favourite TV show is a personal choice that differs from student to student.
2. There is no existing record of this — Pari must ask her classmates herself.

AnswerYes, she needs to collect data.

(b) When did India get independence?

1. India's independence date is one fixed historical fact (15 August 1947).
2. It is already written down in books, so nothing new needs to be gathered.

AnswerNo, she does not need to collect data.

(c) How much water is getting wasted in her locality?

1. The amount of water wasted changes by place and by time, and nobody has already measured it for her locality.
2. So she would have to observe or measure it herself — that is data collection.

AnswerYes, she needs to collect data.

(d) What is the capital of India?

1. The capital of India is one fixed, well-known fact (New Delhi).
2. It is already recorded, so no new data collection is needed.

AnswerNo, she does not need to collect data.

Watch this explained “Pari's four questions: which need collecting?”, 5:39 into Turning an argument into a question you can settle with data · हिंदी में देखें

Open NCERT p. 76Matches NCERT’s answer

(a) How many students chose jalebi?

1. The tally for jalebi is a full group of 5 plus 1 more stroke.
2. 5 + 1 = 6.

Answer6 students

(b) Barfi was chosen by ___ students?

1. The tally for barfi is 3 single strokes.
2. That is simply 3.

Answer3 students

(c) How many students chose gujiya?

1. The tally for gujiya is two full groups of 5 plus 3 more strokes.
2. 5 + 5 + 3 = 13.

Answer13 students

(d) Rasgulla was chosen by ___ students?

1. The tally for rasgulla is a full group of 5 plus 2 more strokes.
2. 5 + 2 = 7.

Answer7 students

(e) How many students chose gulab jamun?

1. The tally for gulab jamun is a full group of 5 plus 4 more strokes.
2. 5 + 4 = 9.

Answer9 students

Watch this explained “Filling the three blanks: 13, 3 and 7”, 2:50 into Tally marks and frequency: organising data so it can be read · हिंदी में देखें

Open NCERT p. 77Matches NCERT’s answer

1. The table only records how many students chose each sweet — it has no column with student names.
2. So Shri Nilesh knows how many of each sweet to buy, but not which named student wanted which sweet.
3. To hand out the correct sweet to the correct child, he needs the original list pairing each student's name with their choice.

AnswerNo, the table is not sufficient — it only gives totals, not which student chose which sweet. The alternative is to keep (or go back to) the name-by-name list of each student's sweet choice.

Watch this explained “13 want ice cream. The table cannot say which 13”, 4:57 into Tally marks and frequency: organising data so it can be read · हिंदी में देखें

Open NCERT p. 77Matches NCERT’s answer

(a) The largest shoe size in the class is ________.

1. In the sorted (ascending) list, the largest value is the very last number.
2. The last number in the sorted list is 7.

Answer7

(b) The smallest shoe size in the class is ________.

1. In the sorted (ascending) list, the smallest value is the very first number.
2. The first number in the sorted list is 3.

Answer3

(c) There are ________ students who wear shoe size 5.

1. In the sorted list, all the 5s sit together in one run.
2. Counting that run of equal numbers gives 10 students.

Answer10 students

(d) There are ________ students who wear shoe sizes larger than 4.

1. Sizes larger than 4 are 5, 6 and 7.
2. Counting these from the sorted list: 10 fives + 4 sixes + 1 seven = 15.

Answer15 students

Watch this explained “Sorted: smallest, largest, ten fives, fifteen above four”, 6:23 into Tally marks and frequency: organising data so it can be read · हिंदी में देखें

Open NCERT p. 77One way to think about it

1. Once sorted, the smallest and largest sizes are simply the first and last numbers — no need to scan the whole list.
2. Equal sizes end up next to each other, so counting how many students wear a given size just means counting a run of matching numbers.
3. Sizes above (or below) a value all land together at one end, so they can be counted in one sweep instead of checking every entry.

In shortSorting grouped equal sizes together and put the extreme values at the two ends, so the smallest, largest, and any size-based count could be read off directly instead of scanning the jumbled original list each time.

Watch this explained “Sorted: smallest, largest, ten fives, fifteen above four”, 6:23 into Tally marks and frequency: organising data so it can be read · हिंदी में देखें

Open NCERT p. 77Matches NCERT’s answer

1. Ascending order is only one way of organising the same 27 numbers.
2. The same data could be listed in descending order instead, or grouped into a tally/frequency table showing each distinct size once with its count.

AnswerYes — for example, the sizes could be arranged in descending order, or organised as a tally/frequency table (like the sweets table) that lists each size once alongside how many students wear it.

Watch this explained “Two organisings, two different things given up”, 7:14 into Tally marks and frequency: organising data so it can be read · हिंदी में देखें

Open NCERT p. 78One way to think about it

(a) Which tree was found in the greatest number?

1. Walk from home to school and make a tally mark against a tree's name each time you pass that kind of tree. Then count the tally marks and fill in the table.
2. Example (your walk will give different numbers): Peepal 4, Neem 7, Mango 3, Banyan 1, Gulmohar 3.
3. The tree with the highest count is the answer. In the example, Neem has the highest count, 7.

In shortThe tree with the highest count in your own table. In the example, Neem (7).

(b) Which tree was found in the smallest number?

1. Look at the same table of counts.
2. The tree with the lowest count is the answer. In the example, Banyan has the lowest count, 1.

In shortThe tree with the lowest count in your own table. In the example, Banyan (1).

(c) Were there any two trees found in the same numbers?

1. Compare the counts of every pair of trees in your table.
2. If two trees have exactly the same count, they were found in the same numbers. In the example, Mango and Gulmohar both have 3.

In shortYes, if any two counts in your table match. In the example, Mango and Gulmohar (3 each).

Watch this explained “One stroke per answer — and every fifth one crossed”, 1:26 into Tally marks and frequency: organising data so it can be read · हिंदी में देखें

Open NCERT p. 78One way to think about it

(a) The letter found the most number of times is ______.

1. Paste a news item on your paper. Go through it word by word and make a tally mark each time you see 'c', 'e', 'i', 'r' or 'x'. Then count the tally marks and fill in the table.
2. Example: a 57-word news item, "The village school opened a new library room on Monday. Students from every class came to see the shelves, and the teachers read stories aloud. The principal said that more books will arrive next month, and children may borrow two books each week. Parents were invited to visit the room during the first exhibition of student artwork."
3. Counting gives c = 7, e = 35, i = 18, r = 22, x = 2.
4. The largest count is 35, for 'e'.

In shortThe letter with the highest count in your own article. In the example it is 'e' (35 times).

(b) The letter found the least number of times is ______.

1. Look at the same five counts.
2. The smallest count in the example is 2, for 'x'.

In shortThe letter with the lowest count in your own article. In the example it is 'x' (2 times).

(c) List the five letters … in ascending order of frequency.

1. Arrange the letters from the lowest count to the highest. In the example: x (2), c (7), i (18), r (22), e (35).
2. The book says almost everyone gets x, c, r, i, e. The example is nearly the same: only 'i' and 'r' have swapped places, because their counts are close.
3. This happens because the letters are not used equally in English. 'e' is one of the most used letters and 'x' is one of the rarest, so almost any article shows the same pattern.

In shortYour order depends on your article; the example gives x, c, i, r, e, nearly the same as x, c, r, i, e. The orders match because some letters (like e) are used far more often in English words than others (like x), whatever the article is about.

Watch this explained “Three to go and do — including the letter count”, 7:08 into Turning an argument into a question you can settle with data · हिंदी में देखें

Open NCERT p. 83Matches NCERT’s answer

(a) On which day were the minimum number of books borrowed?

1. The key says 1 book symbol = 1 book, so just count the symbols in each row: Mon 5, Tue 4, Wed 2, Thu 0, Fri 5, Sat 8.
2. Thursday's row has no symbols at all, the lowest of all six days.

AnswerThursday

(b) What was the total number of books borrowed during the week?

1. Add the books borrowed on all six days: 5 + 4 + 2 + 0 + 5 + 8.
2. 5 + 4 + 2 + 0 + 5 + 8 = 24.

Answer24 books

(c) On which day were the maximum number of books borrowed?

1. Saturday's row has 8 symbols, the highest of all six days.
2. A possible reason: Saturday may have had no regular classes, so students had more free time to read and borrow books.

AnswerSaturday (8 books) — possibly because it is a day with more free time for students, such as a holiday from regular classes.

Watch this explained “Books borrowed: biggest instantly, total slowly”, 8:10 into Pictographs, and why the scale has to be stated · हिंदी में देखें

Open NCERT p. 84Matches NCERT’s answer

(a) How many symbols represent the kites that Rani purchased?

1. First draw the pictograph. 1 symbol = 100 kites, so each shopkeeper needs (kites ÷ 100) symbols: Chaman 250 ÷ 100 = 2½, Rani 300 ÷ 100 = 3, Rukhsana 100 ÷ 100 = 1, Jasmeet 450 ÷ 100 = 4½, Jetha Lal 250 ÷ 100 = 2½, Poonam Ben 700 ÷ 100 = 7. A half symbol stands for 50 kites.
2. Rani purchased 300 kites, so 300 ÷ 100 = 3 symbols.

Answer3 symbols

(b) Who purchased the maximum number of kites?

1. Compare all six totals: Chaman 250, Rani 300, Rukhsana 100, Jasmeet 450, Jetha Lal 250, Poonam Ben 700.
2. 700 is the highest (the longest row, 7 symbols), and it belongs to Poonam Ben.

AnswerPoonam Ben (700 kites)

(c) Who purchased more kites, Jasmeet or Chaman?

1. Jasmeet purchased 450 kites and Chaman purchased 250 kites.
2. 450 is more than 250.

AnswerJasmeet (450 kites, against Chaman's 250)

(d) Rukhsana says Poonam Ben purchased more than double … Rani purchased.

1. Double Rani's 300 kites is 300 × 2 = 600.
2. Poonam Ben purchased 700 kites.
3. 700 is more than 600, so Rukhsana is correct.

AnswerYes, she is correct: double Rani's kites is 600, and Poonam Ben's 700 is more than 600.

Watch this explained “Choosing your own key — 100 kites, and six that divide”, 9:03 into Pictographs, and why the scale has to be stated · हिंदी में देखें

Open NCERT p. 88Matches NCERT’s answer

1. Read the number of vehicles for each hour off the bar graph, using 1 unit length = 100 vehicles: 6–7 about 150, 7–8 exactly 1200, 8–9 1000, 9–10 800, 10–11 about 700, 11–12 about 600.
2. Add all six hourly values together: 150 + 1200 + 1000 + 800 + 700 + 600.
3. 150 + 1200 + 1000 + 800 + 700 + 600 = 4450.

AnswerAbout 4450 vehicles.

Watch this explained “Two bars added, and the bar the book never states”, 6:27 into Reading a bar graph: what length is standing for · हिंदी में देखें

Open NCERT p. 88One way to think about it

1. 6–7 a.m. is very early — before schools, offices and most shops open for the day.
2. Very few people need to be travelling that early, so far fewer vehicles are on the road.
3. From 7 a.m. onwards, people start leaving home for work and school, so the traffic increases sharply.

In shortVery few people are out travelling that early because the day's regular activities — school, work, shopping — have not started yet, so the roads stay quiet until the morning rush begins around 7 a.m.

Watch this explained “Three readings, and the question each one forces”, 8:55 into Reading a bar graph: what length is standing for · हिंदी में देखें

Open NCERT p. 88One way to think about it

1. The longest bar is for 7–8 a.m.: 1200 vehicles passed then, more than in any other hour.
2. The graph shows WHEN the traffic was heaviest, not WHY — for that we think about who is on the road at that hour.
3. 7–8 a.m. is when most people set off for school, college, offices and shops, so many more vehicles pass the crossing then.

In shortMore than one sensible reason is possible. The most likely one: 7–8 a.m. is the morning rush hour, when most people are travelling to school, college or work, so the most vehicles (1200) crossed then.

Watch this explained “Three readings, and the question each one forces”, 8:55 into Reading a bar graph: what length is standing for · हिंदी में देखें

Open NCERT p. 88One way to think about it

1. Read the bars after 8 a.m.: 8–9 about 1000 vehicles, 9–10 about 800, 10–11 about 700 and 11–12 about 600 — each hour has fewer than the one before.
2. By 8 a.m. most people going to school, college or work have already made their journey.
3. So each later hour, fewer new journeys start, and the traffic keeps falling until noon.

In shortOther sensible reasons are possible. The most likely one: most people finish their morning journey to school, college or work by about 8–9 a.m., so fewer people travel in each later hour and the traffic falls from about 1000 to about 600 vehicles.

Watch this explained “Three readings, and the question each one forces”, 8:55 into Reading a bar graph: what length is standing for · हिंदी में देखें

Open NCERT p. 93One way to think about it

1. Draw a horizontal line and a vertical line meeting at a corner. Write the five names — Mites, Caterpillars, Beetles, Butterflies, Grasshoppers — equally spaced along the horizontal line.
2. Choose the scale from the smallest and largest counts, 2 and 10. A scale of 1 unit length = 1 insect fits well. (Other scales, such as 1 unit length = 2 insects, are also correct; we use 1 unit length = 1 insect.)
3. Number the vertical line 0, 1, 2, … up to 10, starting from 0, with equal spacing.
4. Draw one bar above each name, all the same width with equal gaps between them: Mites 6 units, Caterpillars 10 units, Beetles 5 units, Butterflies 3 units, Grasshoppers 2 units.
5. Label the axes (Insects and critters; Number seen), write the scale beside the graph, and give it a title such as "Insects and critters seen in the tea garden".

In shortA bar graph with the scale 1 unit length = 1 insect and 5 bars of equal width and equal spacing: Mites 6, Caterpillars 10, Beetles 5, Butterflies 3, Grasshoppers 2.

Watch this explained “A table in, a picture out — four steps”, 0:00 into Drawing a bar graph, and choosing a scale that fits · हिंदी में देखें

Open NCERT p. 93Matches NCERT’s answer

(a) Write the number of tickets sold for Vidisha above the bar.

1. The table already says Vidisha sold 24 tickets — write 24 above its bar.

Answer24

(b) Write the number of tickets sold for Jabalpur above the bar.

1. The table says Jabalpur sold 20 tickets — write 20 above its bar.

Answer20

(c) What is the scale for this graph?

1. Vidisha's bar is 6 units tall and stands for 24 tickets, so 1 unit = 24 ÷ 6 = 4 tickets.
2. Check with Jabalpur: 5 units × 4 = 20 tickets, which matches — so the scale is confirmed.

Answer1 unit length = 4 tickets

(d) Draw the correct bar for Sagar.

1. Sagar sold 16 tickets, and 1 unit = 4 tickets, so the bar should be 16 ÷ 4 = 4 units tall.
2. Draw Sagar's bar the same width as the others, 4 unit lengths tall.

AnswerA bar 4 unit lengths tall (16 tickets ÷ 4 tickets per unit).

(e) Add the scale of the bar graph … on the vertical axis.

1. Mark the vertical axis 0, 4, 8, 12, 16, 20, 24, 28, … in steps of 4 (the scale found in (c)).

AnswerNumber the vertical axis 0, 4, 8, 12, 16, 20, 24, 28, …

(f) Are the bars for Seoni and Indore correct in this graph?

1. Seoni sold 16 tickets, so its correct height is 16 ÷ 4 = 4 units; the bar drawn for Seoni measures about 4 units — it is correct.
2. Indore sold 28 tickets, so its correct height is 28 ÷ 4 = 7 units; the bar drawn for Indore only reaches a little past 4 units — it is wrong, and much too short.
3. Redraw Indore's bar so it reaches 7 unit lengths.

AnswerSeoni's bar is correct (4 units). Indore's bar is wrong — it should be 7 units tall, not about 4.

Watch this explained “Recovering a lost scale from one surviving bar”, 6:11 into Drawing a bar graph, and choosing a scale that fits · हिंदी में देखें

Open NCERT p. 94Matches NCERT’s answer

(a) Prepare a frequency distribution table for the data.

1. Go through the list once, making one tally mark for each vehicle against its type.
2. Count the tally marks for each type.

3. Means of transport	Frequency
   Bike	13
   Car	6
   Bicycle	8
   Auto rickshaw	8
   Scooter	9
   Bus	4
   Bullock cart	2

4. Check the total: 13+6+8+8+9+4+2 = 50, which matches the number of entries in the list.

AnswerBike 13, Scooter 9, Bicycle 8, Auto rickshaw 8, Car 6, Bus 4, Bullock cart 2 (total 50).

(b) Which means of transport was used the most?

1. Look for the largest frequency in the table — that is bike, with 13.

AnswerBike

(c) If you were there … how could you do it?

1. Sit where you can clearly see the road for the whole hour, from 9 a.m. to 10 a.m.
2. List the types of transport you expect to see (bike, car, bicycle, and so on) as row headings before you start.
3. Each time a vehicle passes, put one tally mark against its type, without pausing to add up.
4. At the end of the hour, count the tally marks in each row to get the frequency table.

AnswerWatch the road for the full hour and make one tally mark per vehicle against its type as it passes; total the tally marks at the end to get the frequencies.

Watch this explained “One stroke per answer — and every fifth one crossed”, 1:26 into Tally marks and frequency: organising data so it can be read · हिंदी में देखें

Open NCERT p. 95One way to think about it

1. Every student's 30 rolls are different, so every student's table and answers are different. Here is one example.
2. Example rolls: 4, 2, 6, 1, 3, 4, 5, 2, 4, 3, 1, 5, 2, 4, 6, 3, 2, 5, 4, 1, 3, 2, 4, 5, 6, 3, 1, 2, 4, 5.
3. Make a row for each number 1 to 6. For each roll, draw one tally mark in that number's row; every fifth mark is drawn across the four before it. Then count the marks in each row.

4. Number on the die	Frequency
   1	4
   2	6
   3	5
   4	7
   5	5
   6	3

5. Check: 4 + 6 + 5 + 7 + 5 + 3 = 30 rolls.
6. (a) The smallest frequency is 3, for the number 6. (b) The largest frequency is 7, for the number 4. (c) The numbers 3 and 5 both appeared 5 times.

In shortAnswers depend on your own rolls. In this example: (a) 6 appeared the minimum number of times (3 times), (b) 4 appeared the maximum number of times (7 times), (c) 3 and 5 appeared an equal number of times (5 times each).

Watch this explained “Three to build — trees, letters, and thirty rolls of a die”, 7:59 into Tally marks and frequency: organising data so it can be read · हिंदी में देखें

Open NCERT p. 95Matches NCERT’s answer

(a) What information is this table giving?

1. The left column is a number of wickets (0 to 7). The right column says in how many of the 30 matches he took exactly that many wickets.

AnswerFor each number of wickets from 0 to 7, it shows in how many of Bumrah's last 30 matches he took exactly that many wickets.

(b) What may be the title of this table?

1. A good title says who, what is counted, and over how many matches. Other wordings are also fine.

AnswerOne suitable title: "Wickets taken by Jaspreet Bumrah in his last 30 matches".

(c) What caught your attention in this table?

1. Different students may notice different things; any true observation from the table is a good answer.
2. For example, the largest number in the matches column is 8, for 3 wickets, while 6 wickets and 7 wickets happened in only 1 match each.

AnswerAnswers can vary. One example: he most often took 3 wickets (in 8 of the 30 matches), and took 6 or 7 wickets only once each.

(d) In how many matches has Bumrah taken 4 wickets?

1. Read the row for 4 wickets: the number of matches is 3.

Answer3 matches

(e) Can Mayank get the total number of wickets taken in this way?

1. Mayank's sum is 0 + 1 + 2 + 3 + 4 + 5 + 6 + 7 = 28. It counts each number of wickets only once.
2. But each number of wickets happened in several matches. For example, 3 wickets were taken in 8 matches, which alone gives 3 × 8 = 24 wickets.
3. So 28 is not the total number of wickets.

AnswerNo. Adding 0 to 7 gives 28, which counts each number of wickets only once and ignores in how many matches it happened (3 wickets in 8 matches alone gives 3 × 8 = 24 wickets).

(f) How would you correctly figure out the total number of wickets taken …

1. Multiply each number of wickets by its number of matches: 0 × 2 = 0, 1 × 4 = 4, 2 × 6 = 12, 3 × 8 = 24, 4 × 3 = 12, 5 × 5 = 25, 6 × 1 = 6, 7 × 1 = 7.
2. Add the products: 0 + 4 + 12 + 24 + 12 + 25 + 6 + 7 = 90.

AnswerMultiply each number of wickets by its number of matches and add: 0 + 4 + 12 + 24 + 12 + 25 + 6 + 7 = 90 wickets.

Watch this explained “The best trap in the chapter: 28 against 90”, 7:56 into Drawing a bar graph, and choosing a scale that fits · हिंदी में देखें

Open NCERT p. 96Matches NCERT’s answer

(a) Which village has the smallest number of tractors?

1. Count the tractor pictures for each village: A=6, B=5, C=8, D=3, E=6.
2. The smallest count is 3, for Village D.

AnswerVillage D

(b) Which village has the most tractors?

1. The largest count is 8, for Village C.

AnswerVillage C

(c) How many more tractors does Village C have than Village B?

1. Village C has 8 tractors and Village B has 5.
2. 8 − 5 = 3.

Answer3 more tractors

(d) Village D has half the number of tractors as Village E.

1. Village E has 6 tractors, so half of that is 6 ÷ 2 = 3.
2. Village D has 3 tractors, which is exactly this half.

AnswerYes, Komal is right — Village D (3) has exactly half of Village E's 6 tractors.

Watch this explained “Longest row, shortest row — answered without arithmetic”, 1:18 into Pictographs, and why the scale has to be stated · हिंदी में देखें

Open NCERT p. 97Matches NCERT’s answer

(a) Which class has the least number of girl students?

1. Each full symbol is 4 girls and a half symbol is 2 girls, so: Class 1=24, 2=18, 3=20, 4=14, 5=10, 6=16, 7=12, 8=6.
2. The smallest of these is 6, for Class 8.

AnswerClass 8

(b) What is the difference … in Classes 5 and 6?

1. Class 5 has 10 girls and Class 6 has 16 girls.
2. 16 − 10 = 6.

Answer6 girls

(c) If two more girls were admitted … how would the graph change?

1. Class 2 currently has 18 girls, shown as 4 full symbols and 1 half symbol (4×4 + 2 = 18).
2. Adding 2 more girls makes 20, and 20 ÷ 4 = 5 exactly.
3. So the half symbol disappears and Class 2's row becomes 5 full symbols, with no half symbol left over.

AnswerThe row would change from 4 full symbols and a half symbol to exactly 5 full symbols (20 girls), with no half symbol needed.

(d) How many girls are there in Class 7?

1. Class 7's row shows 3 full symbols: 3 × 4 = 12.

Answer12 girls

Watch this explained “The half tile is half of the key — 20 + 5 = 25”, 2:42 into Pictographs, and why the scale has to be stated · हिंदी में देखें

Open NCERT p. 98Matches NCERT’s answer

(a) What will be a useful scale or key to draw this pictograph?

1. The counts are 18, 36, 12, 48, 18 and 24.
2. A key is useful if every count can be drawn with whole symbols without very long rows. The numbers that divide all six counts are 1, 2, 3 and 6.
3. The largest of these, 6, needs the fewest symbols: A 3, B 6, C 2, D 8, E 3 and F 4 symbols.
4. Other keys can also work, for example 1 symbol = 12 dogs with half symbols (18 dogs = 1½ symbols). Below we use 1 symbol = 6 dogs.

Answer1 symbol = 6 dogs (other keys, such as 1 symbol = 12 dogs with half symbols, are possible; with 6, no half symbols are needed).

(b) How many symbols will you use to represent the dogs … Village B?

1. Village B has 36 dogs, and 36 ÷ 6 = 6.

Answer6 symbols (with the key 1 symbol = 6 dogs)

(c) Is she right? Give reasons for your response.

1. Villages B and D together: 36 + 48 = 84 dogs.
2. The other four villages, A, C, E and F: 18 + 12 + 18 + 24 = 72 dogs.
3. 84 is more than 72. On the pictograph, B and D have 6 + 8 = 14 symbols, and the other four have 3 + 2 + 3 + 4 = 12 symbols.

AnswerYes, Kamini is right: Villages B and D together have 84 dogs, which is more than the 72 dogs in the other 4 villages.

Watch this explained “Choosing your own key — 100 kites, and six that divide”, 9:03 into Pictographs, and why the scale has to be stated · हिंदी में देखें

Open NCERT p. 98Matches NCERT’s answer

1. Check the total: 45 + 30 + 20 + 10 + 15 = 120 students.
2. With 1 unit length = 5 students, each bar's height is the number of students ÷ 5: Playing 45 ÷ 5 = 9 units, Reading story books 30 ÷ 5 = 6 units, Watching TV 20 ÷ 5 = 4 units, Listening to music 10 ÷ 5 = 2 units, Painting 15 ÷ 5 = 3 units.
3. Write the activities along the horizontal line and number the vertical line 0, 5, 10, … 45. Draw 5 bars of equal width with equal gaps, to these heights.
4. Leaving out Playing, the tallest bar is Reading story books: 6 units, which is 30 students.

AnswerReading story books, preferred by 30 students (a bar 6 units tall).

Watch this explained “Six divisions by 200 — the column that is the graph”, 4:03 into Drawing a bar graph, and choosing a scale that fits · हिंदी में देखें

Open NCERT p. 99Checked by computer

(a) The total number of saplings planted on Wednesday and Thursday is ____.

1. From the graph: Wednesday 30, Thursday 40.
2. 30 + 40 = 70.

Answer70

(b) The total number of saplings planted during the whole week is ____.

1. Read each bar: Monday 50, Tuesday 40, Wednesday 30, Thursday 40, Friday 50, Saturday 60, Sunday 40.
2. Total = 50 + 40 + 30 + 40 + 50 + 60 + 40 = 310. NCERT's answer key gives 310, reading Monday's bar as 50.
3. Look closely at the print: Monday's bar goes a little above the 50 line and is taller than Friday's bar, which sits on 50. It measures about 52. Read that way the total is 52 + 40 + 30 + 40 + 50 + 60 + 40 = 312.

Answer310 (NCERT's key, with Monday read as 50). Reading Monday's bar as drawn, about 52, the total is 312.

(c) The greatest number of saplings were planted on ____ …

1. The tallest bar is Saturday (60) and the shortest is Wednesday (30).
2. Possible reasons: Saturday may be a half day or holiday, so more students, teachers and villagers were free to help. On Wednesday there may have been heavy rain (July is the rainy season), a test, or fewer students present.
3. To check your ideas: ask the teachers and students, look at the attendance register and the school timetable for that week, and find out what the weather was on each day.

AnswerGreatest on Saturday; least on Wednesday. Reasons will vary, for example rain, attendance or the school timetable; check them with attendance records, the timetable and the weather for that week.

Watch this explained “Two bars added, and the bar the book never states”, 6:27 into Reading a bar graph: what length is standing for · हिंदी में देखें

Open NCERT p. 99Matches NCERT’s answer

1. The scale has grid lines at 0, 1000, 2000, 3000 and 4000 tigers. Read where each bar ends, then compare it with the table.

2. Year	Table says	Bar is drawn to about	Correct?
   2006	1400	800	No
   2010	1700	1500	No
   2014	2200	2900	No
   2018	3000	2200	No
   2022	3700	3700	Yes

3. A quick clue: in the table the number of tigers goes up every time, so each year's bar should be longer than the year before. But the 2014 bar is longer than the 2018 bar.
4. To fix the graph, redraw the bars to end at 1400 (2006), 1700 (2010), 2200 (2014) and 3000 (2018). The 2022 bar can stay.

AnswerThe bars for 2006, 2010, 2014 and 2018 are drawn wrongly; only the 2022 bar is right. Correct them to 1400 (2006), 1700 (2010), 2200 (2014) and 3000 (2018).

Watch this explained “The bar that is wrong and the bar that is missing”, 7:03 into Drawing a bar graph, and choosing a scale that fits · हिंदी में देखें

Open NCERT p. 103Matches NCERT’s answer

1. Height is measured upward from the ground.
2. A bar that also runs upward matches the direction of the thing it represents, so a taller person is simply shown as a taller bar.

AnswerVertical bars — because height is measured upward, and an upward bar reads the same way as the quantity it stands for.

Watch this explained “Two to try, both settled by the same rule”, 7:59 into What makes a data picture clear and worth looking at · हिंदी में देखें

Open NCERT p. 103Matches NCERT’s answer

1. A river's length runs along the ground, not upward. A flat (horizontal) bar runs the same way as the quantity it shows, so horizontal bars are the better choice.
2. To finish the activity, look up the longest river on each continent in an atlas, write them in a table, and draw one horizontal bar per continent with a scale such as 1 unit length = 1000 km. Different books give slightly different lengths.
3. The two longest are the Nile in Africa (about 6,650 km) and the Amazon in South America (about 6,400 km).

AnswerHorizontal bars, because the length of a river lies along the ground. Africa (the Nile) and South America (the Amazon) have the longest rivers.

Watch this explained “Two to try, both settled by the same rule”, 7:59 into What makes a data picture clear and worth looking at · हिंदी में देखें