NCERT Solutions Class 5 Maths Chapter 15 Data Through Pictures

F R E E S T U D Y M AT E R I A L F O R E V E R Y S T U D E N T

C L A S S 5 · M AT H S

NCERT Solutions

Chapter 15: Data Through
Pictures

NCERT Textbook — Math Mela

BOOK PAGES SECTIONS QUESTIONS MEDIUM

179 – 190 8 46 English

Solutions, notes, sample papers & more at 48 pages

Class 5 Maths Chapter 15 Data Through Pictures AglaSem · NCERT Solutions

CLASS 5 · MATHS · MATH MELA

NCERT Solutions — Chapter 15: Data Through Pictures
Chapter 15 of Math Mela is the last chapter of the book. It is about data — the facts and numbers we collect
— and about two neat ways to show data as a picture: a pictograph, where a small drawing stands for a
number of things, and a bar graph, where a tall bar stands for a big number and a short bar for a small one.
Samaira and Kabir count TV hours, Joseph Uncle counts the toys in his shop, Deepti counts scooters on the
road, Raman and Sheela record a whole day, and Rani looks at how much food her school throws away.

TEXTBOOK BOOK PAGES

Math Mela (Class 5) 179 – 190

SECTIONS QUESTIONS

8 46

MEDIUM

English

Child TV Reporter — Pages 179–180

Page 1 of 48

Class 5 Maths Chapter 15 Data Through Pictures AglaSem · NCERT Solutions

Samaira and Kabir collect data from 35 friends

CHILD TV REPORTER

Q1 They collected data from 35 friends and recorded it in a notebook as shown below.

1 hr 1½ hr 1 hr 2 hr ½ hr 2½ hr 1½ hr

1 hr ½ hr 1 hr ½ hr 2 hr ½ hr 1 hr

1½ hr 1½ hr ½ hr 1 hr 1½ hr 1 hr ½ hr

1 hr 1 hr 1 hr 2 hr 2½ hr 1 hr 2½ hr

½ hr 1 hr ½ hr 1½ hr 1 hr 1½ hr ½ hr

Page 179 — the notebook page. Each speech bubble is one friend’s answer. There are 35
bubbles in all.

Fill in the table.

NO. OF HOURS SPENT WATCHING TV NO. OF CHILDREN

½ hour

1 hour

1½ hour

2 hours

More than 2 hours

Page 180 — the table to fill in.

Go through the notebook one speech bubble at a time and put a mark against the right row.
Here is the finished table.

Page 2 of 48

Class 5 Maths Chapter 15 Data Through Pictures AglaSem · NCERT Solutions

NO. OF HOURS SPENT WATCHING TV NO. OF CHILDREN

1/2 hour 9

1 hour 13

1 1/2 hour 7

2 hours 3

More than 2 hours 3

Total 35

Do it like this, step by step.

1. Make five rows first — one for each answer that appears: 1/2 hour, 1 hour, 1 1/2 hour, 2
hours, more than 2 hours.
2. Start at the first bubble on the top left and read it. It says 1 hr. Put one mark in the "1
hour" row.
3. Move to the next bubble and do the same. Work left to right, row by row, so you never miss
a face or count one twice.
4. Count the marks in each row and write the number.
5. Add up the five numbers. They must come to 35, because 35 friends were asked.

9 + 13 + 7 + 3 + 3

= 22 + 7 + 3 + 3

= 29 + 3 + 3

= 32 + 3

= 35 ✓

The bubbles saying 2 1/2 hr belong in the last row, because 2 1/2 hours is more than 2 hours.

Page 3 of 48

as e
Class 5 Maths Chapter 15 Data Through Pictures
a g l AglaSem · NCERT Solutions

co m
m.
13
12 m as e
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a s em10
a gl 9
8 7
.com ag
6
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4 agl 3 3
2
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2 hr ag
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m . 1/2 hr 1 hr 1 1/2 hr more
ase
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than 2
Number of children (total 35)
The same table drawn as bars. The tallest bar tells you at once that 1 hour is the commonest answer.

m a s
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l a se
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Check it yourself: Count the bubbles that say 1 hr only. You should get 13 — more
a
than any other answer. That matches the tallest bar.

co m
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m as e
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How many children watch TV for more than half an hour?
a g l
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Q2

l a se
ag ANSWER

se m
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26 children.
o
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"More than half an hour" means every child

l a se 9 children watch for exactly half an hour, not more.
ag
1. Leave out the 1/2 hour row. Those
2. Add the four rows below it — 1 hour, 1 1/2 hour, 2 hours and more than 2 hours.

co m
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13 + 7 + 3 + 3
m as e
.=co20 + 3 + 3 a g l
se m
g l a
a
= 23 + 3
.c
= 26 children
s e m
m a
e m . co agl
g l as
a
Why it happens: 1 hour, 1 1/2 hours, 2 hours and 2 1/2 hours are all bigger than 1/2
hour. So every child in those four rows watches more than half an hour.

co m
m .
m ase
.co


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Class 5 Maths Chapter 15 Data Through Pictures AglaSem · NCERT Solutions

Check it yourself the short way: 35 children in all, and 9 of them watch exactly half
an hour. 35 − 9 = 26 ✓

Q3 How many children watch TV for less than two hours?

29 children.

1. Find the rows that are smaller than 2 hours. They are 1/2 hour, 1 hour and 1 1/2 hour.
2. Add those three counts.

9 + 13 + 7

= 22 + 7

= 29 children

Why it happens: "Less than two hours" does not include the children who watch for
exactly 2 hours. It also does not include the 2 1/2 hour children, because 2 1/2 is
more than 2.

Check it yourself: The children left out are the 3 who watch 2 hours and the 3 who
watch more than 2 hours. 29 + 3 + 3 = 35 ✓

Q4 The number of children who watch TV for more than two hours is ________.

The number of children who watch TV for more than two hours is 3.
In the notebook, three friends answered 2 1/2 hr. Two and a half hours is more than two hours,
so these three children go in the last row of the table.

Children who said 2 1/2 hr = 3

Page 5 of 48

Class 5 Maths Chapter 15 Data Through Pictures AglaSem · NCERT Solutions

Careful: Do not put the three children who said exactly 2 hr in this row. Two hours is
not more than two hours.

Q5 More children watch TV for two hours than half an hour. (True/False)

False.

1. Read the two rows. Two hours → 3 children. Half an hour → 9 children.
2. Compare. 3 is smaller than 9.

Children who watch for 2 hours = 3

Children who watch for 1/2 hour = 9

3 < 9, so the statement is False

Why it happens: The statement claims the 2-hour group is the bigger one. It is
actually the smaller one. Six fewer children watch for two hours than for half an hour
(9 − 3 = 6).

Tip: For a True/False question about data, always find the two numbers first and
write them down. Then compare. Never guess from the look of the picture.

Q6 Can watching TV for a long time be harmful to the eyes?

Yes, it can. Watching a screen for a long time without a break tires the eyes.
Here is what happens and what helps.

When we stare at a screen we blink less. Blinking spreads water over the eye, so blinking
less makes the eyes feel dry and itchy.
The eyes stay focused at one distance for a long time. The tiny muscles inside the eye get
tired, and the head may start to ache.
Watching in a dark room or sitting very close makes it worse.

Simple rules that help:

Page 6 of 48

Class 5 Maths Chapter 15 Data Through Pictures AglaSem · NCERT Solutions

1. After every 20 minutes, look at something far away — a tree, the sky — for a slow count of
20.
2. Sit at least 3 metres away from a TV, about the length of a school bench and a half.
3. Keep a light on in the room. Do not watch in the dark.
4. Play outside every day. Looking at far-away things is rest for the eyes.

Look at our own data: 3 of the 35 friends watch TV for more than 2 hours a day.
That is a long time for a pair of eyes with no break. Those three friends could try the
20-minute rule.

Stock-Taking in a Shop — Pages 180–181
Joseph Uncle's pictograph, and what a scale does

STOCK-TAKING IN A SHOP

Q1 He notices that there are too many items of each kind in his shop and it is not easy
to make a picture for every item. “How can I show these with pictures?” Suggest
some ways to him.

Let one picture stand for many items instead of just one. That is the whole idea, and it is
called using a scale.
Here are ways Joseph Uncle can try.

1. Use one picture for 5 items. Draw one train for every 5 toys. 40 toys then need only 8 trains,
not 40.
2. Use one picture for 10 items if the numbers are very big. 40 toys would need only 4 trains.
3. Use half a picture for half the scale. If one train is 10 toys, half a train is 5 toys. So 45 toys =
4 trains and half a train.
4. Write the key on the chart. Somewhere on the page he must write one train = 5 toys, or
nobody can read his chart.
5. Use a different picture for each kind of item — a train for toys, a board for board games, a
racket for sports items. Then the three rows never get mixed up.
6. Draw bars instead of pictures. One tall bar for toys, one for board games, one for sports
items. That is a bar graph, and it is even quicker to draw.

Why it happens: A picture-chart is meant to be read at a glance. Forty little trains in
a row cannot be counted at a glance — you lose your place. Eight trains can.

Page 7 of 48

Class 5 Maths Chapter 15 Data Through Pictures AglaSem · NCERT Solutions

Q2 (1) How many toys does Joseph Uncle have? __________

40 toys.

Item Number of Items

Toys

Board games

Sports items

Key: one picture = 5 items
Dipesh's pictograph. Eight trains, ten boards, twelve rackets — each one worth 5 items.

1. Read the key first. It says one train = 5 toys.
2. Count the trains in the "Toys" row. There are 8.
3. Multiply. 8 groups of 5.

Number of trains = 8

Each train = 5 toys

Toys = 8 × 5 = 40 toys

Why it happens: Every picture is a bundle of 5. Eight bundles of 5 is the same as 5 +
5 + 5 + 5 + 5 + 5 + 5 + 5, and that is 40.

Check it yourself: Count in fives along the row — 5, 10, 15, 20, 25, 30, 35, 40. You
land on 40 at the eighth train ✓

Page 8 of 48

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Class 5 Maths Chapter 15 Data Through Pictures
a g l AglaSem · NCERT Solutions

co m
m.
(2) How many board games does Joseph Uncle have? __________
e
Q3

m l as
.co a g
a s em
50 g l games.
a board
1. Count the board pictures in the second row. There are 10.

com
2. Read the key. One board picture = 5 board games.
e m . ag
3. Multiply.
g l as
a
m
Number of board pictures = 10
co
Board games = 10 × 5 = 50 board games
em.
m l as
.co a g
a s em it yourself: Count in fives — 5, 10, 15, 20, 25, 30, 35, 40, 45, 50. Ten steps, and
a gl Check
you finish on 50 ✓

om a s
e
. c
m5 in each is ten fives. Ten fives make fifty, just like agl
s
Why it happens: Ten pictures with
ten 5-rupee coins make ₹50.gla
a

co m
m .
m as e
.co l
(3) How many total play items does Joseph Uncle have? __________
g
Q4

em a
a s
agl ANSWER

150 play items in all.
se m
com g l a
. a
First find the sports items, then add up all three rows.
m
ase
agl
1. Count the rackets. There are 12 rackets in the last row.
2. Multiply by the scale. 12 × 5 = 60 sports items.
3. Write down all three numbers. Toys 40, board games 50, sports items 60.

co m
4. Add them.
m .
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a c
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m a s e
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a

co m
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m ase
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a g l Page 9 of 48

Class 5 Maths Chapter 15 Data Through Pictures AglaSem · NCERT Solutions

Toys = 8 × 5 = 40

Board games = 10 × 5 = 50

Sports items = 12 × 5 = 60

Total = 40 + 50 + 60

= 90 + 60

= 150 play items

Check it yourself another way: Count all the pictures first. 8 + 10 + 12 = 30 pictures.
Each picture is 5 items. 30 × 5 = 150 ✓ The two ways agree, so the answer is right.

ITEM PICTURES SCALE NUMBER OF ITEMS

Toys 8 ×5 40

Board games 10 ×5 50

Sports items 12 ×5 60

Total 30 ×5 150

Q5 Is there any other scale that you can use to make the pictograph? Choose your
scale and show the same data using a pictograph in your notebook.

Yes. A scale of 10 works very well here. All three numbers — 40, 50 and 60 — divide by 10
exactly.

Toys: 40 ÷ 10 = 4 pictures

Board games: 50 ÷ 10 = 5 pictures
Sports items: 60 ÷ 10 = 6 pictures

Page 10 of 48

Class 5 Maths Chapter 15 Data Through Pictures AglaSem · NCERT Solutions

Toys

Board games

Sports items

Key: one picture = 10 items
Same data, half as many pictures to draw.
The same 150 items shown with a scale of 10 instead of 5. Only 15 pictures now, instead of 30.

Other scales you could pick:

SCALE TOYS BOARD GAMES SPORTS ITEMS GOOD OR NOT?
(40) (50) (60)

1 picture = 2 20 25 30 Too many pictures to draw

1 picture = 5 8 10 12 The book's choice — works
well

1 picture = 4 5 6 Best — few pictures, no
10 halves

1 picture = 2 2 1/2 3 Needs a half picture
20

Why it happens: A scale only works neatly if every number in the data divides by it.
40, 50 and 60 all divide by 10, so a scale of 10 gives whole pictures. They do not all
divide by 20, so a scale of 20 forces you to draw half a picture.

Rule to remember: Whatever scale you choose, write the key on your pictograph. A
pictograph without a key cannot be read by anybody.

Two-wheelers on the Road — Pages 181–182

Page 11 of 48

Class 5 Maths Chapter 15 Data Through Pictures AglaSem · NCERT Solutions

Deepti's pictograph, where one icon stands for 3

TWO-WHEELERS ON THE ROAD

Q1 Which day had the most two-wheelers passing her house? ________

Friday. On Friday 36 two-wheelers went past Deepti's house.

Day Number of Two-wheelers
one scooter = 3 two-wheelers

Monday 8 × 3 = 24

Wednesday 4 × 3 = 12

Friday

Friday: 12 × 3 = 36 — the longest row

Deepti's pictograph. Friday's row is the longest, so Friday had the most two-wheelers.

1. Look for the longest row of scooters. That is Friday, with 12 scooters.
2. Read the key — one scooter stands for 3 two-wheelers.
3. Multiply. 12 × 3 = 36.

Monday: 8 scooters = 8 × 3 = 24

Wednesday: 4 scooters = 4 × 3 = 12

Friday: 12 scooters = 12 × 3 = 36

36 is the biggest, so Friday had the most

Why it happens: Every scooter picture is worth the same, 3. So the row with the
most pictures must also stand for the biggest number. You can answer "which day"
just by looking, but you still need the key to say how many.

Page 12 of 48

Class 5 Maths Chapter 15 Data Through Pictures AglaSem · NCERT Solutions

Q2 How many total two-wheelers did she record over three days? ________

72 two-wheelers.

1. Work out each day. Monday 8 × 3 = 24. Wednesday 4 × 3 = 12. Friday 12 × 3 = 36.
2. Add the three days.

24 + 12 + 36

= 36 + 36
= 72 two-wheelers

Check it yourself another way: Count all the scooter pictures first. 8 + 4 + 12 = 24
pictures. Each is worth 3. 24 × 3 = 72 ✓ Both roads lead to 72, so the answer is right.

Why it happens: Multiplying each row and then adding gives the same answer as
adding all the pictures and then multiplying. The 3 is the same for every picture, so it
can be taken out and used once at the end.

Q3 How many fewer two-wheelers were seen on Wednesday than on Monday? ________

12 fewer.

1. Find Monday's number. 8 scooters × 3 = 24.
2. Find Wednesday's number. 4 scooters × 3 = 12.
3. Subtract the smaller from the bigger, because "how many fewer" asks for the gap
between them.

Monday = 24

Wednesday = 12

24 − 12 = 12 fewer two-wheelers

Page 13 of 48

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Class 5 Maths Chapter 15 Data Through Pictures
a g l AglaSem · NCERT Solutions

co m
m.
Check it yourself using pictures: Monday has 8 scooters, Wednesday has 4. The

m as e
l
gap is 8 − 4 = 4 pictures, and 4 × 3 = 12 ✓

m .co a g
l a se
a g
Q4 How many more two-wheelers were seen on Friday than on Wednesday? ___________

co m
e m . ag
l as

24 more. a g
m
1. Friday = 12 scooters × 3 = 36.
co
m.
2. Wednesday = 4 scooters × 3 = 12.

m as e
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3. Subtract. "How many more" also means find the gap.
a g l
a s em
a gl Friday = 36
s
Wednesday = 12
m a
m .co agl
se
36 − 12 = 24 more two-wheelers

g l a
a
Check it yourself using pictures: The gap is 12 − 4 = 8 pictures, and 8 × 3 = 24 ✓

co m
m .
o m l a se
g are usually busier on a
.c times as many two-wheelers — 36 instead of 12. Roads
Why it happens: Friday's row is three times as long as Wednesday's, so Friday had
m a
ase
three

agl
Friday than in the middle of the week.

se m
com g l a
m . a
ase
agl
Q5 Choose any other scale and represent the same data using a pictograph in your
notebook.

co m
.

em
m as
A scale of 6 works well here — 24, 12 and 36 all divide by 6.

.co a g l
se m
g l a
a
Monday: 24 ÷ 6 = 4 scooters

.c
Wednesday: 12 ÷ 6 = 2 scooters
s e m
m a
Friday: 36 ÷ 6 = 6 scooters
e m . co agl
g l as
a

com
m .
m ase
.co


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Class 5 Maths Chapter 15 Data Through Pictures AglaSem · NCERT Solutions

Monday 4 × 6 = 24

Wednesday 2 × 6 = 12

Friday

Key: one scooter = 6 two-wheelers
Half the pictures, exactly the same data.
The same three days drawn with a scale of 6. Friday's row is still the longest — the story does not
change.

Other scales that work:

SCALE MONDAY WEDNESDAY FRIDAY COMMENT
(24) (12) (36)

1 scooter = 8 4 12 The book's own scale
3

1 scooter = 6 3 9 Works, all whole
4

1 scooter = 4 2 6 Neatest — fewest pictures
6

1 scooter = 2 1 3 Very few pictures, but hard to see
12 the difference

1 scooter = 4 4/5 2 2/5 7 1/5 Do not use — the pictures do not
5 come out whole

Why it happens: A good scale must divide every number in the data. 3, 4, 6 and 12
all divide 24, 12 and 36. Five does not, so a scale of 5 would force you to draw
awkward part-pictures.

Remember: Changing the scale never changes the data. Friday is the busiest day
whichever scale you pick.

Page 15 of 48

Class 5 Maths Chapter 15 Data Through Pictures AglaSem · NCERT Solutions

Recording a Day — Pages 182–183

Page 16 of 48

Class 5 Maths Chapter 15 Data Through Pictures AglaSem · NCERT Solutions

Raman's table and Sheela's bar graph

RECORDING A DAY

Q1 Raman recorded his daily routine in the table below, using one square for one hour (
= 1 hour). Read his table and write the number of hours he spent on each activity.

ACTIVITIES NO. OF HOURS (□ = 1 HOUR)

Time spent sleeping

Time in school

Time spent studying

Time spent eating and playing

Other activities

Page 182 — Raman’s table. Each blue square stands for one hour.

Page 17 of 48

Class 5 Maths Chapter 15 Data Through Pictures AglaSem · NCERT Solutions

Count the blue squares in each row. One square is one hour.

ACTIVITY SQUARES COUNTED NO. OF HOURS

Time spent sleeping 9 squares 9 hours

Time in school 6 squares 6 hours

Time spent studying 2 squares 2 hours

Time spent eating and playing 6 squares 6 hours

Other activities 1 square 1 hour

Total 24 squares 24 hours

9+6+2+6+1

= 15 + 2 + 6 + 1

= 17 + 6 + 1

= 23 + 1
= 24 hours ✓

Why the check matters: A day has exactly 24 hours. If your squares add up to more
or less than 24, you have counted a row wrongly. Go back and count again.

Tip: When you count a long row, touch each square with your pencil tip as you say
the number. That way you never skip one.

Q2 How is Sheela’s recording different from Raman’s recording? Discuss in class.

Raman drew squares, one for each hour. Sheela drew one tall bar for each activity. Both
show the same kind of information, but in different ways.

Page 18 of 48

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Class 5 Maths Chapter 15 Data Through Pictures
a g l AglaSem · NCERT Solutions

co m
Raman: one square = 1 hour
em.
m l as
.co a g
Sleeping 9h

a s em
School 6h

a l
gStudying 2h
Eating, playing 6h

co m
. ag
Other 1h
m
as=e hours
agl
Sheela: the height of the bar
10
8
8 7

co m
m.
6
4
4 3
a se 2
. com2
ag l
m
ase
0

agl
Sleeping School Studying Eating, Other
playing
Both days add up to 24 hours.
m a s
.co agl
The same kind of information, drawn two ways. Raman counts squares; Sheela reads bar heights.

se m
g l a
RAMAN'S WAY a SHEELA'S WAY

co m
.
A pictograph — small squares in a row A bar graph — upright bars

e m
m l as
.co g
You must count the squares one by one You just read how high the bar reaches

m go across the page
eRows a
a s
gl
Bars stand up from a base line

a Only whole hours can be shown, one square A bar can also stop half-way, so half hours can be
se m
each
c o m shown
g l a
m . a
ase
agl
Long rows take a lot of space A tall bar takes very little space

Sample answer for the class discussion: "Raman made a pictograph. He drew one blue square
for every hour, so we have to count the squares to find the number of hours. Sheela made a bar
co m
m .
se
graph. She drew one bar for each activity and the height of the bar tells us the hours, so we can

o m l a
.c took the most time. Raman's way is easier to draw andagit shows each single hour clearly.
just read the number off the side line. Sheela's way is faster to read and it is easier to see which

se m
activity
a
agl
Both of them recorded the same 24 hours."

.c
s e m
m a
co agl
New word: Sheela's way of recording the data is called a bar graph.

m .
as e
a g l

co m
m .
m as e
.co


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Class 5 Maths Chapter 15 Data Through Pictures AglaSem · NCERT Solutions

Q3 Whose daily routine shows more time spent on sleeping? _____________________

Raman. He sleeps for 9 hours; Sheela sleeps for 8 hours.

1. Count Raman's sleeping squares. There are 9, so 9 hours.
2. Read Sheela's sleeping bar. It reaches the line marked 8, so 8 hours.
3. Compare. 9 is more than 8.

Raman sleeps 9 hours

Sheela sleeps 8 hours

9 > 8, so Raman sleeps more

He sleeps 9 − 8 = 1 hour more

Did you know? Children of your age need about 9 to 11 hours of sleep every night.
Both Raman and Sheela are close to that.

Q4 Who spends more hours in the school? _____________________

Sheela. She spends 7 hours in school; Raman spends 6 hours.

1. Raman's school row has 6 squares → 6 hours.
2. Sheela's school bar reaches 7 → 7 hours.
3. Compare. 7 is more than 6.

Sheela = 7 hours

Raman = 6 hours

7 − 6 = 1 hour more for Sheela

Why it happens: Different schools have different timings. Sheela's school day is one
hour longer than Raman's, or she stays back for an extra activity.

Page 20 of 48

Class 5 Maths Chapter 15 Data Through Pictures AglaSem · NCERT Solutions

Q5 How many more hours does Sheela spend studying compared to Raman?
______________________

2 hours more.

1. Sheela's studying bar reaches 4, so 4 hours.
2. Raman's studying row has 2 squares, so 2 hours.
3. Subtract to find how many more.

Sheela = 4 hours

Raman = 2 hours

4 − 2 = 2 hours more

Another way to say it: Sheela studies twice as long as Raman, because 2 × 2 = 4.

Q6 Is there any activity on which they spend the same amount of time? If yes, name
the activity _________________________

No. There is no activity on which they spend the same amount of time.
Put the two routines side by side and check every row.

ACTIVITY RAMAN SHEELA SAME?

Sleeping 9h 8h No

Time in school 6h 7h No

Studying 2h 4h No

Eating and playing 6h 3h No

Other activities 1h 2h No

Total 24 h 24 h Yes — the whole day

Page 21 of 48

Class 5 Maths Chapter 15 Data Through Pictures AglaSem · NCERT Solutions

9≠8·6≠7·2≠4·6≠3·1≠2

Not one pair matches → answer is No

Why it happens: Two people can both have a 24-hour day and still spend it
completely differently. The one thing that is the same for both is the total: 24 hours.

Tip: Make the two-column table first, then read across each row. That way you
cannot miss a match, and you cannot invent one either.

Q7 Based on their data, whose routine do you think is more balanced? Why?
___________________________________

Sheela's routine is the more balanced one. This is an opinion question, so you must give a
reason from the data.
Look at what each child does with the day.

ACTIVITY RAMAN SHEELA

Sleeping 9h 8h

Time in school 6h 7h

Studying at home 2h 4h

Eating and playing 6h 3h

Other activities 1h 2h

Sample answer: "I think Sheela's routine is more balanced. She gets 8 hours of sleep, spends 7
hours in school and still studies for 4 hours at home, and she keeps 3 hours for eating and
playing. Every part of her day gets a fair share. Raman studies for only 2 hours but spends 6
hours eating and playing. His day leans too much towards play and not enough towards study."

The other side is also worth saying: Raman gets 9 hours of sleep and 6 hours of
play, and both sleep and play are important for health. A friend who says "Raman's
routine is more balanced because he rests and plays enough" is not wrong either —
as long as the reason comes from the data. In an opinion question the reason
matters more than the choice.

Page 22 of 48

Class 5 Maths Chapter 15 Data Through Pictures AglaSem · NCERT Solutions

What "balanced" means here: A balanced day gives enough time to each
important thing — sleep, school, study, food, play and rest — instead of giving one
of them far too much and another far too little.

Day in My Life — Pages 183–184
Record your own 24 hours and draw your own bar graph

DAY IN MY LIFE

Q1 Record your daily routine (24 hours) in hours and minutes, as necessary. Note the
time spent on activities like sleeping, studying, playing, eating, and others. Fill the
table.

ACTIVITY NO. OF HOURS

Sleeping

Time in school

Studying

Eating

Page 184 — the blank table to fill in with your own day.

This is about your own day, so your table will be your own. Here is how to make it, and a filled
sample you can copy the shape of.

1. Start from the time you wake up and go through the whole day in order until you fall
asleep again.
2. Write the start time and end time of each block — for example, school from 8:00 a.m. to
2:00 p.m.
3. Work out the hours in each block. From 8 to 2 is 6 hours.
4. Put small bits together. Breakfast 30 minutes + lunch 30 minutes + dinner 30 minutes = 1
hour 30 minutes for eating.

Page 23 of 48

as e
Class 5 Maths Chapter 15 Data Through Pictures
a g l AglaSem · NCERT Solutions

5. Add up all the hours at the end. The total must be exactly 24 hours. If it is not, some time is
co m
missing — find it and add a row.
em.
m l as
Sample answer:
.co a g
a s em
gl
aACTIVITY NO. OF HOURS

m
.co
Sleeping 9 hours

ag
asem
agl
Time in school 6 hours

Studying (homework at home) 2 hours

co m
m.
Eating 1 hour 30 minutes

m as e
Playing
.co
2 hours
a g l
se m
g l a
a
Travel, bath, helping at home, TV 3 hours 30 minutes

s
Total 24 hours

m a
m .co agl
l a se
ag
9 + 6 + 2 = 17 hours

1 h 30 min + 2 h + 3 h 30 min = 7 hours

co m
17 + 7 = 24 hours ✓
m .
m as e
.co a g l
s m for the two empty rows: The book leaves two rows blank on purpose. Use them
eTip
a
gl for the things that are special to your day — cycling to school, cricket practice,
a
helping in the shop, prayers, music class.
se m
com g l a
m . a
ase
Q2 agl
Make a bar graph of the time you spend on different activities in the space given

m
below.

. co
se m
o m
l a
g from the last question drawn
m .c each row of your table into one bar. Here is the sample table
a
se
Turn
a
agl
as a bar graph.

.c
s e m
m a
e m . co agl
g l as
a

co m
m .
m ase
.co


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Class 5 Maths Chapter 15 Data Through Pictures AglaSem · NCERT Solutions

9
9
8
7
6
6
Number of Hours

5
4 3 1/2
3
2 2
2 1 1/2
1
0
Sleeping School Studying Eating Playing Other

Activities

Sample bar graph of one child's day. All six bars together stand for 24 hours.

How to draw yours, step by step:

1. Write the activity names in the boxes along the bottom line — one name per box.
2. Use the numbers already printed up the side. The book's graph is marked 0 to 9, which is
enough, because no single activity except sleep takes more than 9 hours.
3. For each activity, find its number on the side line and make a small pencil dot at that
height above its box.
4. Draw the bar from the bottom line up to that dot. Keep every bar the same width and leave
the same gap between bars.
5. Colour the bars the same colour, so that only the height tells the story.
6. Write the number on top of each bar so a reader does not have to guess.

For half hours: One box on the graph paper is half an hour. So 1 1/2 hours means
the bar stops half a square above the line marked 1.

Why bars are drawn the same width: If one bar were fatter than another, a small
number could look big. Keeping the width the same means only the height carries
the information, and the graph tells the truth.

Whose Index Finger is Longer? — Pages 184–185

Page 25 of 48

Class 5 Maths Chapter 15 Data Through Pictures AglaSem · NCERT Solutions

A bar graph made from paper strips

WHOSE INDEX FINGER IS LONGER?

Q1 Cut long paper strips from waste paper. Give one strip (each of the same width) to
each of your friends. Now, put the paper strip on your index finger and tear off the
extra strip extending above your fingers. Paste these paper strips along the
horizontal line in the given bar graph.

Paste the strips in the space given below.

10
9
8
7
6
5
4
3
2
1
1 cm

Mine ________ ________ ________ ________

Page 185 — the blank bar graph. The scale is 1 cm for each unit on the upright line.

This activity turns real fingers into a real bar graph. The strips are the bars.

1. Cut the strips first. Cut five or six strips from an old newspaper, all of the same width —
about 1 cm wide is good.
2. Give one strip to each friend. Take one for yourself.
3. Lay the strip along your index finger. The bottom end of the strip sits where the finger
joins the palm, at the lowest knuckle line.
4. Tear off the extra. Tear the strip exactly at your fingertip. What is left is as long as your
index finger.
5. Write the name on each strip at once, or you will forget whose is whose.
6. Paste the strips standing up on the base line of the graph, one in each labelled box. Put the
bottom edge of every strip exactly on the line — otherwise the heights cannot be compared.

Page 26 of 48

Class 5 Maths Chapter 15 Data Through Pictures AglaSem · NCERT Solutions

7. Read each strip against the numbers up the side. On this graph one step is 1 cm.

10
9
8
7
6
Length in cm

6
5
5
4
4 3 1/2
3
3
2
1
0
Mine Asha Imran Divya Ravi

Imran's strip is the tallest; Ravi's is the shortest.

Sample answer: five pasted strips make a bar graph of index-finger lengths. Your own graph will have
your friends' names and lengths.

Why the strips must be the same width: A bar graph compares only heights. If
one strip were twice as wide, it would look bigger even if the finger were shorter, and
the graph would tell a lie.

Tip: Paste the strips in any order you like, but keep the same gap between them.
Neat gaps make the graph easy to read.

Q2 Whose index finger is the longest? ________ .

The answer comes from your own graph — it is the friend whose strip reaches highest.

1. Look across the tops of all the strips.
2. Find the one that reaches highest up the side line.
3. Read the name written under that strip. That is your answer.

Page 27 of 48

Class 5 Maths Chapter 15 Data Through Pictures AglaSem · NCERT Solutions

Sample answer: In the graph above, Imran has the longest index finger. His strip reaches the
line marked 6.

If two strips look the same: Hold a ruler flat across their tops. If the ruler touches
both, the two fingers are equal — then write both names.

Q3 The length of the longest index finger is _________ cm.

Read the number where the tallest strip stops.

1. Put your finger on the top of the tallest strip.
2. Slide it straight left until you reach the numbers on the side line.
3. Read the number. Remember the label on this graph: one step is 1 cm.

Sample answer: The longest index finger is 6 cm long.

Check it yourself: Take the strip off the page and measure it with your ruler. The
ruler should show the same number the graph shows. If it does not, the strip was
not pasted with its bottom edge on the base line.

Q4 The smallest index finger is ___________ cm long.

Now find the shortest strip and read its height in the same way.

1. Find the strip that stops lowest.
2. Slide left to the side line and read the number.

Sample answer: The smallest index finger is 3 cm long.

Longest = 6 cm

Shortest = 3 cm

Difference = 6 − 3 = 3 cm

Page 28 of 48

as e
Class 5 Maths Chapter 15 Data Through Pictures
a g l AglaSem · NCERT Solutions

co m
m.
Extra question you can ask yourself: How much longer is the longest finger than

m as e
l
the shortest? Subtract the two numbers, as shown above.

m .co a g
l a se
a g
Q5 It belongs to __________.

co m
m . ag
l a se
ag the shortest strip.
Read the name written in the box under
Sample answer: The smallest index finger, 3 cm long, belongs to Ravi.

co m
se m.
m l a
Why this activity works: Nobody measured a single finger with a ruler at the start.
o g side by side on one
m .c strips carried the lengths for us. Once the strips stand
The paper a
l a se line, the eye can compare them instantly — and that is exactly what a bar graph
g
base
a does with numbers.

m a s
e
. c o
m finger and paste those strips next to the first agl
s
Try this: Do the same with your middle

a g la index finger also the one with the longest middle
set. Is the friend with the longest
finger?

co m
m .
o m l a se
.c a g
m
Food Wastage in the School Canteen — Pages 185–186
se dining hall notice board and the food wastage bar graph
l a
ag
Rani's

se m
FOOD WASTAGE IN THE SCHOOL CANTEEN

com g l a
m . a
ase
Rani stays in a residential school. Her school’s dining hall displays the amount of
gl
Q1

a
food wasted and the number of children the food could have fed. Read the notice
board — what does it say?

co m
m .
as e

m l
m .co
The notice board in the dining hall says:
a g
l a se
ag
.c
s e m
m a
em . co agl
g l as
a

com
m .
m ase
.co


a g l Page 29 of 48

Class 5 Maths Chapter 15 Data Through Pictures AglaSem · NCERT Solutions

NOTICE BOARD
Take all you can eat.
Eat all you take.
Yesterday’s food wastage was
13 kg,
which could have fed 25 people.

The dining hall notice board. It turns wasted food into the number of people it could have fed.

Take all you can eat. Eat all you take. — the rule of the dining hall.
Yesterday's food wastage was 13 kg, which could have fed 25 people.

13 kg of food thrown away

13 kg would have fed 25 people

So roughly 1 kg feeds about 2 people at a full meal

Why the board shows people and not only kilograms: "13 kg" is just a weight; it is
easy to walk past. "25 people" is a picture in the mind — twenty-five hungry people
who could have eaten. Data speaks louder when it is written in a way people can
feel.

Notice this: The board is updated every day. That makes it live data — the children
can see whether today is better than yesterday.

Page 30 of 48

Class 5 Maths Chapter 15 Data Through Pictures AglaSem · NCERT Solutions

Q2 Rani was shocked to see the data. What do you think about food wastage? How can
we reduce the wastage of food? What can we do with the leftover food?

Wasting food wastes much more than food. It wastes the farmer's work, the water in the
field, the fuel that cooked it, and the money that paid for it — and someone nearby may have
gone hungry.
How we can reduce wastage — six things a child can actually do:

1. Take a small helping first. You can always go back for more. A plate you cannot finish is
waste; a second helping is not.
2. Say no politely to a dish you know you will not eat, instead of taking it and leaving it.
3. Finish what is on your plate before you get up.
4. Tell the cook the true number. If ten children are away on a school trip, the kitchen should
cook for ten fewer.
5. Keep a wastage board like Rani's school, and check it every day. What gets measured gets
better.
6. Never throw food in the dustbin without first asking if someone or something can use it.

What we can do with leftover food:

Food that has not been served and is still fresh can be packed and given the same day to
people who need it, or sent to a shelter.
Food from plates should never be given to people. Give clean vegetable peels and leftover
rice or roti to cows, dogs or birds.
Make compost. Peels, stalks and spoiled food buried in a pit turn into rich black soil in a few
weeks. That soil grows the next crop of vegetables.
Cook it again. Leftover rice becomes fried rice; leftover dal becomes parathas; stale roti
becomes churma. Every Indian kitchen knows these tricks.

Sample answer: "I think food wastage is a serious problem. Rani's school threw away 13 kg of
food in one day, and that food could have fed 25 people. We can reduce it by taking small
helpings, going back for more only if we are still hungry, and telling the kitchen exactly how
many children will eat. Fresh untouched food can be given away the same day, and food scraps
can go to animals or into a compost pit instead of the dustbin."

Something to think about: If Rani's school wastes 13 kg every day, that is 13 × 7 =
91 kg in one week — nearly a whole quintal.

Page 31 of 48

Class 5 Maths Chapter 15 Data Through Pictures AglaSem · NCERT Solutions

Q3 Which food item had the highest amount of wastage? _____________

Khichdi, on Wednesday. 8 kg of khichdi was wasted.

Food Wastage (kg)
9
8
8
7
7
6
6
5
5
4
4
3
2
1
0
Sandwich Paratha Khichdi Puri-Sabzi Idli-Sambar
Monday Tuesday Wednesday Thursday Friday

Red = the most wasted. Green = the least wasted.

Rani's canteen graph. Five weekdays, five food items, five bars.

1. Look for the tallest bar. It is the third one, over Khichdi / Wednesday.
2. Slide left from the top of that bar to the numbers on the side.
3. Read the number. It stops exactly on 8.

Sandwich (Monday) = 5 kg

Paratha (Tuesday) = 6 kg

Khichdi (Wednesday) = 8 kg ← highest

Puri-Sabzi (Thursday) = 7 kg

Idli-Sambar (Friday) = 4 kg

Tip: Before answering any question on a bar graph, write out all five values in a list
as above. Then every question becomes easy and you never have to squint at the
picture twice.

Page 32 of 48

Class 5 Maths Chapter 15 Data Through Pictures AglaSem · NCERT Solutions

Q4 Which food item had the least amount of wastage? _______________

Idli-Sambar, on Friday. Only 4 kg was wasted.

1. Look for the shortest bar. It is the last one, over Idli-Sambar / Friday.
2. Read its height against the side line. It stops on 4.

The five amounts in order, smallest first:

4 kg (Idli-Sambar) < 5 kg (Sandwich) < 6 kg (Paratha) < 7 kg (Puri-Sabzi) < 8 kg (Khichdi)

Least = Idli-Sambar, 4 kg

What this might mean: The children probably like idli-sambar the most, so they
finish it. Khichdi is left the most, so many children do not enjoy it. A canteen can use
this to plan the menu.

Q5 How much total food wastage was recorded in these days? _________________

30 kg in the five days.

1. Write down the five bar heights. 5, 6, 8, 7 and 4.
2. Add them one at a time, keeping the running total in your head or on paper.

5 + 6 = 11

11 + 8 = 19
19 + 7 = 26

26 + 4 = 30 kg

Check it yourself by pairing: 6 + 4 = 10 and 8 + 7 = 15. Then 10 + 15 = 25, and 25 + 5
= 30 ✓ Same answer by a different route, so 30 kg is right.

Page 33 of 48

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Class 5 Maths Chapter 15 Data Through Pictures
a g l AglaSem · NCERT Solutions

co m
m.
Think about the size of it: 30 kg is about the weight of a big sack of rice, or about

m as e
l
as heavy as a Class 5 child. That much food went into the bin in one school week.

m .co a g
l a se
a g
Q6 If 1 kg of food waste can feed 3 children, how many children could have been fed

co m
ag
with the total food wasted? ________________

m .
as e
a g l
90 children.

co m
m.
1. Find the total wastage first. From the last question, it is 30 kg.

mbecause every single kilogram feeds 3 more children. glas
2. Read what one kilogram can do. 1 kg feeds 3 children. e
. c o a
m
3. Multiply,
s e
a gla Total food wasted = 30 kg

m a s
.co agl
1 kg feeds 3 children

se m
30 kg feeds 30 × 3
g l a
= 90 children a

co m
m .
m
Check it yourself day by day:
o l a se
m .c 5 × 3 = 15 · Tuesday 6 × 3 = 18 · Wednesday 8 × 3 a=g24 · Thursday 7 × 3 = 21 ·
Monday

aseFriday 4 × 3 = 12
agl 15 + 18 + 24 + 21 + 12 = 90 ✓

se m
com g l a
m . a
e
Why this number matters: Ninety children is about three full classrooms. In one
as enough food to give three classrooms of children a
week, Rani's school threw laway
g
meal. a

co m
m .
m_______ day had less food wastage than _______ day. glas e
. c o a
e m
Q7

a s
agl c
.

s e m
m a
co agl
Many pairs of days make this sentence true. Pick any two days and put the smaller one first.

m .
e
Sample answers:

g l as
a
Friday day had less food wastage than Wednesday day. (4 kg < 8 kg)
Monday day had less food wastage than Thursday day. (5 kg < 7 kg)

com
m .
m ase
.co


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Class 5 Maths Chapter 15 Data Through Pictures AglaSem · NCERT Solutions

Tuesday day had less food wastage than Wednesday day. (6 kg < 8 kg)

Here are all five days in order, from least wasted to most wasted. Any day in this list had less
wastage than every day to its right.

ORDER DAY FOOD ITEM WASTAGE

Least Friday Idli-Sambar 4 kg

2nd Monday Sandwich 5 kg

3rd Tuesday Paratha 6 kg

4th Thursday Puri-Sabzi 7 kg

Most Wednesday Khichdi 8 kg

Careful: The sentence must be true. Wednesday had less wastage than Friday would
be wrong, because 8 kg is more than 4 kg. Always check the two numbers before
you fill the blanks.

Q8 If the same food items are to be repeated next week, can you predict which food
item is likely to be wasted the most?

Yes — khichdi is likely to be wasted the most again.

1. Look at this week's data. Khichdi had the highest wastage, 8 kg.
2. Ask why. The most likely reason is that fewer children enjoy khichdi than the other dishes.
3. Think about next week. The same children and the same cooking will probably give the
same result. So khichdi will most likely top the list again.

Khichdi wastage this week = 8 kg (the highest)

Same children + same dish → khichdi is likely to be wasted most again

What "predict" means: To predict is to say what will probably happen, using the
data you already have. A prediction is a good guess, not a certainty. If the cook
changes the recipe, or if the children are told about the wastage board, next week's
numbers could be quite different.

Page 35 of 48

Class 5 Maths Chapter 15 Data Through Pictures AglaSem · NCERT Solutions

What the school can do with this prediction: Cook a smaller quantity of khichdi
next Wednesday, or serve it with something the children like, or ask the children
what they would rather eat. That is data being used to make a decision — which is
the whole point of collecting it.

True or False — Page 187
Reading data straight from a picture of a group of children

TRUE OR FALSE

Q1 Observe the picture carefully.

Back row

Front row

Page 187 — the group of children, redrawn. Back row: 9 children. Front row: 8 children.
Girls wear a blue pinafore with a skirt; boys wear a cream shirt with shorts.

True or False: All girls are wearing glasses.

False. Only 3 of the 8 girls are wearing glasses.
Before answering any of these eight statements, count the picture once, carefully, and write the
counts down. Here is the full count.

Page 36 of 48

Class 5 Maths Chapter 15 Data Through Pictures AglaSem · NCERT Solutions

WHAT TO COUNT HOW MANY

Children in all 17

Boys 9

Girls 8

Children wearing caps 10

Children wearing glasses 7

Boys wearing glasses 4

Girls wearing glasses 3

Children holding books 14

Boys holding books 7

Girls holding books 7

Children with backpacks 4

1. Count the girls. The girls wear a blue pinafore over the cream shirt, or have a plait or
ponytail. There are 8 of them.
2. Count how many of those 8 wear glasses. Only 3 do.
3. Compare. 3 is not the same as 8, so "all girls" is wrong.

Girls = 8

Girls wearing glasses = 3

3 ≠ 8, so the statement is False

How to count a crowded picture without mistakes: Work in two rows. Count the
back row from left to right, then the front row from left to right. Touch each face with
your pencil. Say the number aloud. If you get a different total the second time, count
once more before deciding.

Page 37 of 48

Class 5 Maths Chapter 15 Data Through Pictures AglaSem · NCERT Solutions

Q2

Back row

Front row

Page 187 — the group of children, redrawn. Back row: 9 children. Front row: 8 children.
Girls wear a blue pinafore with a skirt; boys wear a cream shirt with shorts.

True or False: 10 children are wearing caps on their heads.

True. Exactly 10 children are wearing red caps.

1. Count the caps in the back row. There are 5 red caps.
2. Count the caps in the front row. There are 5 red caps.
3. Add.

Back row caps = 5

Front row caps = 5

5 + 5 = 10 caps

The statement says 10, so it is True

Tip: A cap is much easier to spot than a pair of glasses, because the red colour
stands out. Count the easy things first — it builds your confidence for the harder
counts.

Page 38 of 48

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Class 5 Maths Chapter 15 Data Through Pictures
a g l AglaSem · NCERT Solutions

co m
m.
Also worth noticing: 10 of the 17 children wear caps, so 17 − 10 = 7 children do not.

m as e
.co a g l
se m
l a
aQ3g
Back row

co m
e m . ag
g l as
a

co m
em.
m l as
m .co Front row
a g
l a se
a g
m a s
m .co agl
l a se
ag
Page 187 — the group of children, redrawn. Back row: 9 children. Front row: 8 children.

co m
.
Girls wear a blue pinafore with a skirt; boys wear a cream shirt with shorts.

e m
m l as
m .coTrue or False: More boys are holding books than girls.
a g
l a se
ag ANSWER

se m
com a
False. The same number of boys and girls are holding books — 7 each.

. a g l
m
ase
1. Count the boys holding books. In the back row, 6 boys hold books. In the front row, 1 boy

agl
holds a book. 6 + 1 = 7.
2. Count the girls holding books. In the back row, 3 girls hold books. In the front row, 4 girls

m
hold books. 3 + 4 = 7.

. co
m
3. Compare. 7 and 7 are equal — neither group has more.

m as e
.co a g l
a s em Boys holding books = 7

agl
.c
Girls holding books = 7

s e m
m a
agl
7 = 7, so "more boys than girls" is False
. c o
s e
The correct sentence is: as many m boys as girls are holding books
a
agl

co m
m .
m ase
.co


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Class 5 Maths Chapter 15 Data Through Pictures AglaSem · NCERT Solutions

Why it happens: There are 9 boys but only 7 of them hold books — two boys have
their hands free. There are 8 girls and 7 of them hold books — only one girl has her
hands free. So even though there are more boys in the picture, the book-holders
come out equal.

Careful: "More than" means strictly bigger. If two counts are equal, a "more than"
statement is false. Count both sides before you answer, never one.

Q4

Back row

Front row

Page 187 — the group of children, redrawn. Back row: 9 children. Front row: 8 children.
Girls wear a blue pinafore with a skirt; boys wear a cream shirt with shorts.

True or False: More than half of the children are wearing glasses.

False. 7 of the 17 children wear glasses, and 7 is less than half of 17.

1. Count all the children. 9 in the back row + 8 in the front row = 17.
2. Count the children with glasses. 4 in the back row + 3 in the front row = 7.
3. Find half of the total. Half of 17 is 8 1/2.
4. Compare. 7 is smaller than 8 1/2.

Page 40 of 48

Class 5 Maths Chapter 15 Data Through Pictures AglaSem · NCERT Solutions

Total children = 17

Children with glasses = 7

Half of 17 = 17 ÷ 2 = 8 1/2

7 < 8 1/2, so less than half wear glasses → False

An easier way to see it: Children with glasses = 7. Children without glasses = 17 − 7
= 10. Since 10 is more than 7, the "without glasses" group is the bigger one. So the
glasses group cannot be more than half.

Q5

Back row

Front row

Page 187 — the group of children, redrawn. Back row: 9 children. Front row: 8 children.
Girls wear a blue pinafore with a skirt; boys wear a cream shirt with shorts.

True or False: The number of children holding books is greater than the number of
children wearing caps.

True. 14 children are holding books and only 10 are wearing caps.

1. Count the children holding books. 9 in the back row (every child there holds a book) + 5 in
the front row = 14.
2. Count the children wearing caps. 10, as found in Q2.
3. Compare. 14 is bigger than 10.

Page 41 of 48

Class 5 Maths Chapter 15 Data Through Pictures AglaSem · NCERT Solutions

Children holding books = 14

Children wearing caps = 10

14 > 10, so the statement is True
There are 14 − 10 = 4 more book-holders than cap-wearers

Why it happens: Every one of the 9 children in the back row is carrying a book. Only
5 of the 8 children in the front row are — the rest are waving or shaking hands. Caps
are spread more evenly, 5 in each row.

Q6

Back row

Front row

Page 187 — the group of children, redrawn. Back row: 9 children. Front row: 8 children.
Girls wear a blue pinafore with a skirt; boys wear a cream shirt with shorts.

True or False: The number of boys wearing glasses is greater than the number of
girls wearing glasses.

True. 4 boys wear glasses and 3 girls wear glasses.

1. Count the children with glasses. There are 7 in all.
2. Sort them into boys and girls. Boys wear a cream shirt with shorts; girls wear a blue
pinafore with a skirt.
3. Compare the two counts.

Page 42 of 48

Class 5 Maths Chapter 15 Data Through Pictures AglaSem · NCERT Solutions

BOYS WEARING GLASSES GIRLS WEARING GLASSES

Back row: 3 boys Back row: 1 girl

Front row: 1 boy Front row: 2 girls

Total 4 Total 3

Boys with glasses = 4

Girls with glasses = 3

4 > 3, so the statement is True

Check it yourself: 4 + 3 = 7, and 7 is the total number of children wearing glasses ✓
If your two counts do not add up to 7, one of them is wrong.

Q7

Back row

Front row

Page 187 — the group of children, redrawn. Back row: 9 children. Front row: 8 children.
Girls wear a blue pinafore with a skirt; boys wear a cream shirt with shorts.

True or False: Some children are wearing both glasses and caps.

True. Six children are wearing a cap and glasses at the same time.

Page 43 of 48

as e
Class 5 Maths Chapter 15 Data Through Pictures
a g l AglaSem · NCERT Solutions

1. Look only at the 7 children wearing glasses.
co m
2. Of those, count how many also have a red cap on. Three in the back row and three in the
e m.
m l as
.co g
front row.

em a
a s
gl
aChildren with glasses = 7

m
Of these, children who also wear a cap = 3 + 3 = 6
. co ag
e m
as
6 is more than zero, so "some" is True

a g l
Why the word "some" matters: "Some" only means "at least one". Even a single
co m
m.
child with both a cap and glasses would make this statement true. Here there are

m as e
.co l
six, so it is comfortably true.
a g
a s em
a gl Follow-up you can work out: 7 children wear glasses and 6 of them also wear caps.
So only 1 child wears glasses without a cap.
m a s
m .co agl
l a se
ag

co m
m .
m as e
.co a g l
se m
g l a
a
se m
com g l a
m . a
ase
agl

co m
m .
m as e
.co a g l
se m
g l a
a c
m .
m a s e
e m . co agl
g l as
a

co m
m .
m ase
.co


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Class 5 Maths Chapter 15 Data Through Pictures AglaSem · NCERT Solutions

Q8

Back row

Front row

Page 187 — the group of children, redrawn. Back row: 9 children. Front row: 8 children.
Girls wear a blue pinafore with a skirt; boys wear a cream shirt with shorts.

True or False: There is no child who has all three items — a cap, a book and a
backpack.

False. There is such a child — the girl standing at the far left of the back row.

1. Find the children with backpacks first, because there are only 4 of them. Grey shoulder
straps make them easy to spot.
2. Check each of those 4 for a cap.
3. Check each of those for a book.

CHILD WITH A BACKPACK CAP? BOOK? ALL THREE?

Girl at the far left, back row (with a plait) Yes Yes Yes

Girl at the far left, front row (waving) Yes No No

Boy in the front row shaking hands Yes No No

Boy at the far right, front row No No No

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Class 5 Maths Chapter 15 Data Through Pictures AglaSem · NCERT Solutions

At least one child has a cap and a book and a backpack

So the sentence "there is no child…" is False

How to disprove a "there is no…" statement: You do not have to check every child.
You only have to find one child who has all three. One example is enough to make
such a statement false.

Tip: When a question mentions three things at once, start with the rarest of the
three. Backpacks are rarest here (only 4 children), so checking those 4 is much
quicker than checking all 17.

Chapter at a glance
Data means the facts we collect. Samaira and Kabir asked 35 friends one question: How
many hours a day do you spend watching TV? Every answer they wrote down is one piece of
data. A pile of 35 answers is hard to read. So the first job is always to sort the answers into
groups and count each group. Nine friends said half an hour, thirteen said one hour, seven
said one and a half hours, three said two hours and three said two and a half hours. 9 + 13 +
7 + 3 + 3 = 35. The count is complete.
A table is the first picture of data. A table has two columns: what you counted on the left,
how many on the right. Once the 35 answers sit in a table you can read anything off it in a
second — which group is biggest, which is smallest, how many in two groups together.
A pictograph shows data with small drawings. Joseph Uncle has hundreds of toys in his
shop. Drawing one toy for each toy would take all day. So his helper Dipesh drew one train
picture for every 5 toys. Eight train pictures then mean 8 × 5 = 40 toys. The little line that
says one picture = 5 toys is called the key, and the number 5 in it is called the scale.
Always read the key first. This is the one rule that matters most. In Joseph Uncle's
pictograph one picture stands for 5. In Deepti's pictograph of two-wheelers one scooter
stands for 3. Same-looking rows of pictures, completely different answers. Count the
pictures, then multiply by the number in the key: 12 scooters × 3 = 36 two-wheelers.
You may choose your own scale. The same data can be drawn with one picture = 5, or 10,
or 2. A bigger scale means fewer pictures to draw but half-pictures may be needed. Joseph
Uncle's 40 toys, 50 board games and 60 sports items can be drawn as 4, 5 and 6 pictures if
one picture = 10.
A bar graph shows data with bars. Sheela drew her day as five upright bars. The line
going up the side is marked 0, 1, 2, 3 … and shows the number of hours. The line along the

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Class 5 Maths Chapter 15 Data Through Pictures AglaSem · NCERT Solutions

bottom carries the names of the activities. A bar that reaches 8 means 8 hours. Reading a
bar graph is just reading how high the bar goes.
The bar graph and the pictograph tell the same story. Raman used one blue square for
each hour, Sheela used a bar for each hour. Raman's day was 9 + 6 + 2 + 6 + 1 = 24 hours;
Sheela's day was 8 + 7 + 4 + 3 + 2 = 24 hours. Two different pictures, one full day each.
Data helps us decide and predict. Rani's canteen graph shows khichdi wasted most (8 kg)
and idli-sambar wasted least (4 kg). From that we can guess that khichdi will probably be
wasted most next week too, and the school can cook less khichdi. That is what data is for —
not just to look at, but to act on.
About the pages after this chapter: the chapter itself ends on page 190. After it come the
Learning Material Sheets — cut-out sheets to be used with earlier chapters, not questions.
They are: the Fractions Kit of circle pieces (for Chapter 2, Fractions), the Tessellation and
Shapes sheet with a rhombus, a tangram square, pentagons, hexagons, squares, triangles
and circles (for Chapter 7 Shapes and Patterns, Chapter 10 Symmetrical Designs and
Chapter 11 Grandmother's Quilt), the Number Tokens of 10,000, 1,000, 100, 10 and 1 (for
Chapter 1 and Chapter 4, We the Travellers), the nets of an icosahedron and a
dodecahedron (for Chapter 7), and plain dot paper and square grid paper for drawing.

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Class 5 Maths Chapter 15 Data Through Pictures AglaSem · NCERT Solutions

Quick revision

WORD WHAT IT MEANS WHERE IT EXAMPLE
APPEARS

Data The facts and numbers we collect Chapter title, page The TV hours of 35
179 friends

Table A box with columns, one for the thing and Page 180 1 hour → 13 children
one for how many

Pictograph A picture-chart in which a small drawing Stock-Taking in a 8 train pictures = 40 toys
stands for a number of things Shop, page 181

Icon (symbol) The one small drawing used again and Page 181 One train, one scooter
again in a pictograph

Key The line that tells you what one icon Page 181 and page One train = 5 toys
stands for 182

Scale The number in the key — how many Page 181 Scale of 5; scale of 3
things one icon stands for

Bar graph A chart in which the height of a bar shows Page 183 A bar up to 8 means 8
the number hours

Bar One upright block of the bar graph Page 183 Sheela's sleeping bar

Horizontal The line along the bottom that carries the Page 183 Sleeping, Studying,
base names Eating…

Vertical line The line going up the side that carries the Page 183 0, 1, 2, 3 … 10 hours
numbers

Highest / The tallest bar and the shortest bar Page 186 Khichdi 8 kg is highest
lowest

Predict To say what will probably happen next, Page 186 Khichdi will likely be
using the data you have wasted most again

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