Chapter 14 of 14
Chapter 14: Data Handling
Pictographs, Bar Graphs, Tally Tables & Frequency Distribution | CBSE Session 2026ā27
Core Pedagogical Competencies & Concepts
- Representing information using pictographs with a defined scale key (e.g., 1 icon = 5 students).
- Drawing and reading vertical and horizontal bar graphs with labeled axes.
- Finding maximum, minimum, and difference values from graphical data.
- Drawing valid conclusions and inferences from statistical representations.
All Textbook Exercises & In-Text Tasks (15 Questions)
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Q1
Pictograph & Scale Interpretation
In a pictograph, the symbol š represents 6 library books borrowed. Look at the data: Class 4A has 5 symbols; Class 4B has 4 symbols; Class 4C has 6 symbols; Class 4D has 3 and a half symbols. (a) How many books were borrowed by each class? (b) What is the total number of books borrowed?
[3 Marks]
ā
Step-by-Step Solution & Working
Scale: 1 symbol š = 6 books.
Half symbol = 6 Ć· 2 = 3 books.
(a) Books borrowed by each section:
ā¢ Class 4A: 5 Ć 6 = 30 books.
ā¢ Class 4B: 4 Ć 6 = 24 books.
ā¢ Class 4C: 6 Ć 6 = 36 books.
ā¢ Class 4D: (3 Ć 6) + 3 = 18 + 3 = 21 books.
(b) Total books borrowed:
Total = 30 + 24 + 36 + 21 = 111 books.
Half symbol = 6 Ć· 2 = 3 books.
(a) Books borrowed by each section:
ā¢ Class 4A: 5 Ć 6 = 30 books.
ā¢ Class 4B: 4 Ć 6 = 24 books.
ā¢ Class 4C: 6 Ć 6 = 36 books.
ā¢ Class 4D: (3 Ć 6) + 3 = 18 + 3 = 21 books.
(b) Total books borrowed:
Total = 30 + 24 + 36 + 21 = 111 books.
CBSE Step-by-Step Marking Scheme
Correct calculation for all 4 sections with half-symbol logic
2.0 M
Accurate sum of 111 books
1.0 M
Q2
Data Handling ā¢ Pictograph Interpretation
In a school library pictograph, one symbol š represents 10 books. The records show:
ā¢ Science: š š š š
ā¢ Maths: š š š š š š
ā¢ Storybooks: š š š š š š š š
(a) How many Maths books are there? (b) How many more Storybooks are there than Science books?
[3 Marks]
ā¢ Science: š š š š
ā¢ Maths: š š š š š š
ā¢ Storybooks: š š š š š š š š
(a) How many Maths books are there? (b) How many more Storybooks are there than Science books?
ā
Step-by-Step Solution & Working
Pictograph Reading (Key: š = 10 books):
ā¢ Science = 4 symbols Ć 10 = 40 books.
ā¢ Maths = 6 symbols Ć 10 = 60 books.
ā¢ Storybooks = 8 symbols Ć 10 = 80 books.
1. (a) Number of Maths books: 60 books.
2. (b) Difference between Storybooks and Science:
80 - 40 = 40 more Storybooks.
ā¢ Science = 4 symbols Ć 10 = 40 books.
ā¢ Maths = 6 symbols Ć 10 = 60 books.
ā¢ Storybooks = 8 symbols Ć 10 = 80 books.
1. (a) Number of Maths books: 60 books.
2. (b) Difference between Storybooks and Science:
80 - 40 = 40 more Storybooks.
CBSE Step-by-Step Marking Scheme
Using key scale of 10 books accurately
1.0 M
Maths books count = 60
1.0 M
Difference = 40 books
1.0 M
Q3
Data Visualization ā¢ Chapati (Pie) Chart
A survey of 40 children about their favourite sport revealed: 20 like Cricket, 10 like Football, and 10 like Badminton. Represent this data as fractions on a circular Chapati Chart.
[3 Marks]
ā
Step-by-Step Solution & Working
Circular Chart Representation (Total = 40 children):
ā¢ Cricket: 20 out of 40 = 20/40 = 1/2 (Half of the circle).
ā¢ Football: 10 out of 40 = 10/40 = 1/4 (One-fourth / quarter of the circle).
ā¢ Badminton: 10 out of 40 = 10/40 = 1/4 (One-fourth / quarter of the circle).
On the circular chart, draw a straight diameter dividing the circle into two halves; label one half 'Cricket (1/2)'. Divide the other half into two equal quarters; label one 'Football (1/4)' and the other 'Badminton (1/4)'.
ā¢ Cricket: 20 out of 40 = 20/40 = 1/2 (Half of the circle).
ā¢ Football: 10 out of 40 = 10/40 = 1/4 (One-fourth / quarter of the circle).
ā¢ Badminton: 10 out of 40 = 10/40 = 1/4 (One-fourth / quarter of the circle).
On the circular chart, draw a straight diameter dividing the circle into two halves; label one half 'Cricket (1/2)'. Divide the other half into two equal quarters; label one 'Football (1/4)' and the other 'Badminton (1/4)'.
CBSE Step-by-Step Marking Scheme
Calculating correct fractional share (1/2, 1/4, 1/4)
1.5 M
Describing accurate geometric sector partition of circle
1.5 M
Q4
Tally Marks ā¢ Organizing Raw Data
Represent the number 18 using standard 5-bar tally marks.
[2 Marks]
ā
Step-by-Step Solution & Working
Tally Marks for 18:
Standard tally marks group in clusters of five (four vertical bars crossed by a diagonal fifth bar||||):
ā¢ 18 = 5 + 5 + 5 + 3
ā¢|||| |||| |||| |||
(Three groups of five plus three individual tally bars).
Standard tally marks group in clusters of five (four vertical bars crossed by a diagonal fifth bar
ā¢ 18 = 5 + 5 + 5 + 3
ā¢
(Three groups of five plus three individual tally bars).
CBSE Step-by-Step Marking Scheme
Three groups of 5 tallies plus 3 singles correctly written
2.0 M
Q5
Textbook Exercise ā¢ Real-World Context
In Chapter 14 ('Data Handling'), a classroom project investigates real-world mathematics: If a school bus travels 48 kilometres on 4 litres of diesel, what is the mileage (kilometres per litre) of the bus? How much diesel is needed for a 120-kilometre journey?
[3 Marks]
ā
Step-by-Step Solution & Working
Step-by-Step Solution:
1. Mileage calculation:
ā¢ Distance = 48 km, Diesel used = 4 L.
ā¢ Mileage = 48 Ć· 4 = 12 km per litre.
2. Diesel for 120 km:
ā¢ Required diesel = Total distance Ć· Mileage = 120 Ć· 12 = 10 litres.
1. Mileage calculation:
ā¢ Distance = 48 km, Diesel used = 4 L.
ā¢ Mileage = 48 Ć· 4 = 12 km per litre.
2. Diesel for 120 km:
ā¢ Required diesel = Total distance Ć· Mileage = 120 Ć· 12 = 10 litres.
CBSE Step-by-Step Marking Scheme
Mileage = 12 km/L
1.5 M
Diesel needed = 10 L
1.5 M
Q6
Practice Time ā¢ Measurement & Conversions
Convert the following measurements into standard units:
(a) 4 metres 65 centimetres into centimetres.
(b) 3500 millilitres into litres and millilitres.
(c) 2 kilograms 750 grams into grams.
[3 Marks]
(a) 4 metres 65 centimetres into centimetres.
(b) 3500 millilitres into litres and millilitres.
(c) 2 kilograms 750 grams into grams.
ā
Step-by-Step Solution & Working
Conversions:
ā¢ (a) 1 m = 100 cm ā (4 Ć 100) + 65 = 465 cm.
ā¢ (b) 1000 mL = 1 L ā 3500 mL = 3 L 500 mL.
ā¢ (c) 1 kg = 1000 g ā (2 Ć 1000) + 750 = 2750 g.
ā¢ (a) 1 m = 100 cm ā (4 Ć 100) + 65 = 465 cm.
ā¢ (b) 1000 mL = 1 L ā 3500 mL = 3 L 500 mL.
ā¢ (c) 1 kg = 1000 g ā (2 Ć 1000) + 750 = 2750 g.
CBSE Step-by-Step Marking Scheme
465 cm
1 M
3 L 500 mL
1 M
2750 g
1 M
Q7
Try These ā¢ Geometry and Shapes
Look at a solid brick:
(a) How many faces does a brick have?
(b) What is the shape of each face?
(c) How many straight edges and how many corners (vertices) does a brick have?
[3 Marks]
(a) How many faces does a brick have?
(b) What is the shape of each face?
(c) How many straight edges and how many corners (vertices) does a brick have?
ā
Step-by-Step Solution & Working
Properties of a Brick (Cuboid):
ā¢ (a) Faces: A brick has 6 flat faces.
ā¢ (b) Shape of faces: Each face is a rectangle.
ā¢ (c) Edges and Corners: It has 12 straight edges and 8 corners (vertices).
ā¢ (a) Faces: A brick has 6 flat faces.
ā¢ (b) Shape of faces: Each face is a rectangle.
ā¢ (c) Edges and Corners: It has 12 straight edges and 8 corners (vertices).
CBSE Step-by-Step Marking Scheme
6 faces
1 M
Rectangular faces
1 M
12 edges and 8 corners
1 M
Q8
Money & Accounts ā¢ Rate List Calculation
At a recycling shop, the rate list shows: Waste paper = ā¹12 per kg, Plastic = ā¹18 per kg, Iron = ā¹25 per kg.
Ramesh sells 10 kg of waste paper, 5 kg of plastic, and 4 kg of iron.
(a) Find the cost of each item sold.
(b) What is the total money Ramesh earns?
[3 Marks]
Ramesh sells 10 kg of waste paper, 5 kg of plastic, and 4 kg of iron.
(a) Find the cost of each item sold.
(b) What is the total money Ramesh earns?
ā
Step-by-Step Solution & Working
Calculations:
ā¢ Waste paper: 10 Ć ā¹12 = ā¹120.
ā¢ Plastic: 5 Ć ā¹18 = ā¹90.
ā¢ Iron: 4 Ć ā¹25 = ā¹100.
ā¢ Total Earnings: ā¹120 + ā¹90 + ā¹100 = ā¹310.
ā¢ Waste paper: 10 Ć ā¹12 = ā¹120.
ā¢ Plastic: 5 Ć ā¹18 = ā¹90.
ā¢ Iron: 4 Ć ā¹25 = ā¹100.
ā¢ Total Earnings: ā¹120 + ā¹90 + ā¹100 = ā¹310.
CBSE Step-by-Step Marking Scheme
Individual costs (ā¹120, ā¹90, ā¹100)
1.5 M
Total = ā¹310
1.5 M
Q9
Fractions Exploration ā¢ Parts of a Whole
A rectangular chocolate bar has 16 equal pieces. Reena gives 1/4 of the chocolate to her brother and 1/2 of it to her friend.
(a) How many pieces does her brother receive?
(b) How many pieces does her friend receive?
(c) How many pieces are left for Reena?
[3 Marks]
(a) How many pieces does her brother receive?
(b) How many pieces does her friend receive?
(c) How many pieces are left for Reena?
ā
Step-by-Step Solution & Working
Fractional Breakdown:
ā¢ Total pieces = 16.
ā¢ Brother's share (1/4): 16 Ć· 4 = 4 pieces.
ā¢ Friend's share (1/2): 16 Ć· 2 = 8 pieces.
ā¢ Remaining for Reena: 16 - (4 + 8) = 16 - 12 = 4 pieces (which is 1/4 of the bar).
ā¢ Total pieces = 16.
ā¢ Brother's share (1/4): 16 Ć· 4 = 4 pieces.
ā¢ Friend's share (1/2): 16 Ć· 2 = 8 pieces.
ā¢ Remaining for Reena: 16 - (4 + 8) = 16 - 12 = 4 pieces (which is 1/4 of the bar).
CBSE Step-by-Step Marking Scheme
Brother = 4 pieces
1 M
Friend = 8 pieces
1 M
Reena = 4 pieces
1 M
Q10
Time & Clocks ā¢ Elapsed Time
A school cricket match began at 9:30 AM and concluded at 1:15 PM.
(a) Convert 1:15 PM into 24-hour railway clock time.
(b) How long did the cricket match last?
[3 Marks]
(a) Convert 1:15 PM into 24-hour railway clock time.
(b) How long did the cricket match last?
ā
Step-by-Step Solution & Working
Time Calculations:
ā¢ (a) 24-hour time: 1:15 PM = 12:00 + 1:15 = 13:15 hours.
ā¢ (b) Duration:
ā¢ From 9:30 AM to 12:30 PM = 3 hours.
ā¢ From 12:30 PM to 1:15 PM = 45 minutes.
ā¢ Total duration = 3 hours and 45 minutes.
ā¢ (a) 24-hour time: 1:15 PM = 12:00 + 1:15 = 13:15 hours.
ā¢ (b) Duration:
ā¢ From 9:30 AM to 12:30 PM = 3 hours.
ā¢ From 12:30 PM to 1:15 PM = 45 minutes.
ā¢ Total duration = 3 hours and 45 minutes.
CBSE Step-by-Step Marking Scheme
13:15 hours in 24-hr clock
1 M
Duration = 3 hours 45 minutes with steps
2 M
Q11
Perimeter & Area ā¢ Fencing a Field
A square vegetable garden has a side length of 15 metres.
(a) What is the total length of wire fence needed to go around the garden once?
(b) If fencing costs ā¹20 per metre, find the total cost of fencing.
[3 Marks]
(a) What is the total length of wire fence needed to go around the garden once?
(b) If fencing costs ā¹20 per metre, find the total cost of fencing.
ā
Step-by-Step Solution & Working
Perimeter & Cost:
ā¢ (a) Perimeter of square: 4 Ć Side = 4 Ć 15 m = 60 metres.
ā¢ (b) Total Cost: Perimeter Ć Rate = 60 m Ć ā¹20/m = ā¹1,200.
ā¢ (a) Perimeter of square: 4 Ć Side = 4 Ć 15 m = 60 metres.
ā¢ (b) Total Cost: Perimeter Ć Rate = 60 m Ć ā¹20/m = ā¹1,200.
CBSE Step-by-Step Marking Scheme
Perimeter = 60 m
1.5 M
Cost = ā¹1,200
1.5 M
Q12
Mental Math ā¢ Division and Multiplication
Solve mentally using number breakdown:
(a) 72 Ć· 6 = ?
(b) 15 Ć 8 = ?
(c) 25 Ć 40 = ?
(d) 96 Ć· 8 = ?
[2 Marks]
(a) 72 Ć· 6 = ?
(b) 15 Ć 8 = ?
(c) 25 Ć 40 = ?
(d) 96 Ć· 8 = ?
ā
Step-by-Step Solution & Working
Solutions:
ā¢ (a) 72 Ć· 6 = (60 Ć· 6) + (12 Ć· 6) = 10 + 2 = 12.
ā¢ (b) 15 Ć 8 = (10 Ć 8) + (5 Ć 8) = 80 + 40 = 120.
ā¢ (c) 25 Ć 40 = (25 Ć 4) Ć 10 = 100 Ć 10 = 1000.
ā¢ (d) 96 Ć· 8 = (80 Ć· 8) + (16 Ć· 8) = 10 + 2 = 12.
ā¢ (a) 72 Ć· 6 = (60 Ć· 6) + (12 Ć· 6) = 10 + 2 = 12.
ā¢ (b) 15 Ć 8 = (10 Ć 8) + (5 Ć 8) = 80 + 40 = 120.
ā¢ (c) 25 Ć 40 = (25 Ć 4) Ć 10 = 100 Ć 10 = 1000.
ā¢ (d) 96 Ć· 8 = (80 Ć· 8) + (16 Ć· 8) = 10 + 2 = 12.
CBSE Step-by-Step Marking Scheme
All 4 mental math facts correct
2 M
Q13
Patterns & Symmetries ā¢ Rotational Turns
Look at the letter 'H' and the letter 'N':
(a) What does each look like after a half-turn (180Ā° rotation)?
(b) What does each look like after a quarter-turn (90Ā° rotation)?
[2 Marks]
(a) What does each look like after a half-turn (180Ā° rotation)?
(b) What does each look like after a quarter-turn (90Ā° rotation)?
ā
Step-by-Step Solution & Working
Rotational Symmetry:
ā¢ (a) Half-turn (180Ā°): Both 'H' and 'N' look exactly the same after a half-turn.
ā¢ (b) Quarter-turn (90Ā°): 'H' rotates to look like 'I' with sleeping bars, and 'N' rotates to look like 'Z'.
ā¢ (a) Half-turn (180Ā°): Both 'H' and 'N' look exactly the same after a half-turn.
ā¢ (b) Quarter-turn (90Ā°): 'H' rotates to look like 'I' with sleeping bars, and 'N' rotates to look like 'Z'.
CBSE Step-by-Step Marking Scheme
Half-turn explanation (same)
1 M
Quarter-turn explanation
1 M
Q14
Smart Charts ā¢ Data Interpretation
In a Class 4 survey of 40 children, 20 like Cricket, 10 like Football, and 10 like Badminton.
(a) What fraction of children like Cricket?
(b) Draw a simple circular pie chart (Chapati Chart) representing this data.
[3 Marks]
(a) What fraction of children like Cricket?
(b) Draw a simple circular pie chart (Chapati Chart) representing this data.
ā
Step-by-Step Solution & Working
Data & Chapati Chart:
ā¢ (a) Fraction: 20 out of 40 = 20/40 = 1/2 (half of the class).
ā¢ (b) Chapati Chart: A circle divided in half represents Cricket (1/2). The other half is split equally into two quarters (1/4 for Football and 1/4 for Badminton).
ā¢ (a) Fraction: 20 out of 40 = 20/40 = 1/2 (half of the class).
ā¢ (b) Chapati Chart: A circle divided in half represents Cricket (1/2). The other half is split equally into two quarters (1/4 for Football and 1/4 for Badminton).
CBSE Step-by-Step Marking Scheme
Fraction = 1/2 for cricket
1.5 M
Pie chart sectors explained (1/2, 1/4, 1/4)
1.5 M
Q15
Chapter Review ā¢ True or False
State True or False:
(a) A circle has no corners and no straight edges.
(b) 1 litre is equal to 100 millilitres.
(c) The perimeter of any rectangle is 2 Ć (Length + Breadth).
[3 Marks]
(a) A circle has no corners and no straight edges.
(b) 1 litre is equal to 100 millilitres.
(c) The perimeter of any rectangle is 2 Ć (Length + Breadth).
ā
Step-by-Step Solution & Working
Answers:
ā¢ (a) True: A circle is a smooth curve with 0 corners.
ā¢ (b) False: 1 Litre is equal to 1000 millilitres.
ā¢ (c) True: Perimeter = 2 Ć (L + B).
ā¢ (a) True: A circle is a smooth curve with 0 corners.
ā¢ (b) False: 1 Litre is equal to 1000 millilitres.
ā¢ (c) True: Perimeter = 2 Ć (L + B).
CBSE Step-by-Step Marking Scheme
True, False, True with explanations
3 M
š NEP 2020 Competency-Based Case Study
School Canteen Drink Preferences
A bar graph shows fruit juice sales: Lemonade = 45 glasses, Apple Juice = 30 glasses, Orange Juice = 55 glasses, and Coconut Water = 70 glasses.
Analytical Task: Which drink is the most popular, and how many more glasses of coconut water were sold than apple juice?
Evaluation & Model Answer:
Analysis:
ā¢ Most popular drink = Coconut Water (70 glasses).
ā¢ Difference between coconut water and apple juice = 70 - 30 = 40 glasses.
ā¢ Most popular drink = Coconut Water (70 glasses).
ā¢ Difference between coconut water and apple juice = 70 - 30 = 40 glasses.
Rubric: 1 Mark for identifying coconut water; 1 Mark for 40 glasses difference.