Data Handling — Line Graphs, Pie Charts

Mathematics

Class 5 | CBSE, NCERT & ICSE

Learning Objectives

Collect, organise, and represent data using tally marks and frequency tables
Read and interpret pictographs with a key/legend
Read, interpret, and draw bar graphs (horizontal and vertical)
Read, interpret, and plot line graphs showing change over time
Read and interpret pie charts (circle graphs) showing parts of a whole
Choose the correct type of graph for different kinds of data
Find the range of a given data set
Solve word problems based on data interpretation

Introduction — Data is Everywhere!

Every day, we come across information in the form of numbers. The marks you score in tests, the temperature outside your house each morning, the runs scored by India in each over of a cricket match, the number of students absent in your class every day — all of this is data.

But raw numbers alone can be confusing. Imagine your teacher lists the marks of 40 students in one long row — it would be hard to make sense of it! That is why we organise data into tables, and then represent it using graphs and charts. Graphs turn numbers into pictures, making it easy to compare, spot trends, and draw conclusions at a glance.

In Class 5, we will learn four types of data representation: Pictographs, Bar Graphs, Line Graphs, and Pie Charts. You will also learn when to use each type and how to read them like a pro!

What is Data?

Data is a collection of facts, numbers, or information gathered for a specific purpose. Data can be about anything — heights of students, favourite colours, number of cars passing a road, temperatures over a week, pocket money received, etc.

Raw Data vs Organised Data

Raw data is the information as it is collected, without any arrangement. For example, the marks of 10 students written randomly:

Raw data (marks out of 50): 45, 32, 38, 45, 50, 32, 40, 38, 45, 50

This is hard to read. We need to organise it.

Frequency Table (Tally Marks)

A frequency table shows how many times each value appears. We use tally marks to count: each stroke (|) = 1, and every 5th stroke crosses the previous four (||||).

Marks	Tally Marks	Frequency
32	\|\|	2
38	\|\|	2
40	\|	1
45	\|\|\|	3
50	\|\|	2

Now we can clearly see that 45 marks appeared most often (3 times). The frequency tells us how many times a particular value occurs in the data.

Think About It: Why do we cross every 5th tally mark? It makes counting easier! Instead of counting individual strokes, we can count in groups of 5.

Pictograph — Pictures Tell a Story

A pictograph uses pictures or symbols to represent data. Each picture stands for a certain number of items. This number is called the key or legend.

How to Read a Pictograph

Look at the key — it tells you what each picture represents (e.g., 🍎 = 5 students)
Count the pictures in each row or column
Multiply the number of pictures by the key value
A half picture means half the key value

Example: The pictograph below shows the favourite fruits of students in Class 5-A.
Key: 🍎 = 4 students

Fruit	Number of Students	Total
Mango	🍎🍎🍎🍎	4 × 4 = 16
Apple	🍎🍎🍎	3 × 4 = 12
Banana	🍎🍎	2 × 4 = 8
Guava	🍎🍎½	2½ × 4 = 10
Orange	🍎🍎🍎½	3½ × 4 = 14

Questions:

Which fruit is liked by the most students? → Mango (16 students)
How many more students like Mango than Banana? → 16 − 8 = 8 students
Total students surveyed? → 16 + 12 + 8 + 10 + 14 = 60 students

Image needed: A colourful pictograph showing favourite fruits (Mango, Apple, Banana, Guava, Orange) using fruit icons. Key shows 1 fruit icon = 4 students. Labels clear and child-friendly. Title: "Favourite Fruits of Class 5-A".
Style: Flat illustration, bright colours, grid layout, clear legend at bottom
Size: 700×400px

Example 2 (Indian Context): A pictograph shows vehicles passing a school gate in one hour.
Key: 🚗 = 10 vehicles

Vehicle	Symbols	Number
Auto-rickshaw	🚗🚗🚗🚗🚗	50
Car	🚗🚗🚗	30
Two-wheeler	🚗🚗🚗🚗🚗🚗🚗	70
Bus	🚗🚗	20
Bicycle	🚗🚗🚗🚗	40

Total vehicles: 50 + 30 + 70 + 20 + 40 = 210 vehicles

Bar Graph — Comparing with Bars

A bar graph uses rectangular bars of equal width to represent data. The length (or height) of each bar shows the value it represents. Bars can be drawn vertically (standing up) or horizontally (lying flat).

Parts of a Bar Graph

Title: Tells what the graph is about
X-axis (horizontal): Shows the categories (e.g., subjects, months, items)
Y-axis (vertical): Shows the values/numbers with a scale
Scale: The number each unit on the axis represents (e.g., 1 unit = 5 students)
Bars: Rectangles of equal width, with height showing the value
Gap: Equal spacing between bars

Example 1: Marks scored by Arjun in different subjects (out of 100):

Subject	Marks
Maths	85
Science	78
English	92
Hindi	70
Social Studies	65

To draw a vertical bar graph:

X-axis: Subject names
Y-axis: Marks (scale: 1 unit = 10 marks, going from 0 to 100)
Draw bars of height 85, 78, 92, 70, and 65 for each subject

From the graph we can tell:

Arjun scored highest in English (92)
He scored lowest in Social Studies (65)
Difference between highest and lowest = 92 − 65 = 27 marks

Image needed: A vertical bar graph titled "Marks Scored by Arjun" with X-axis showing subjects (Maths, Science, English, Hindi, Social Studies) and Y-axis showing marks 0-100. Bars coloured differently. Grid lines visible. Scale clearly labelled.
Style: Clean flat illustration, colourful bars (one colour per subject), grid background, child-friendly
Size: 700×450px

Example 2 (Horizontal Bar Graph): Favourite sports of students in Class 5-B:

Sport	Number of Students
Cricket	18
Football	12
Badminton	8
Kabaddi	6
Swimming	4
Hockey	7

In a horizontal bar graph, the categories go on the Y-axis and the values go on the X-axis. The bars extend to the right.

How to Draw a Bar Graph (Step by Step)

Steps to Draw a Bar Graph

Step 1: Draw two perpendicular lines (axes) — the X-axis and Y-axis
Step 2: Choose a suitable scale (e.g., 1 cm = 5 students)
Step 3: Write category names on one axis and number scale on the other
Step 4: Draw bars of equal width with proper height according to the data
Step 5: Keep equal gaps between bars
Step 6: Give your graph a title and label both axes

Think About It: Why do bar graphs need equal gaps between bars? Because the gaps make it clear that each bar represents a separate category. Without gaps, it would look like the bars are connected — which is what a histogram does (a topic for higher classes)!

Line Graph — Showing Change Over Time

A line graph uses points connected by straight lines to show how data changes over time. It is the best graph to use when you want to see trends — whether something is increasing, decreasing, or staying the same.

When to Use a Line Graph

When data changes over time (hours, days, weeks, months, years)
When you want to see if values are going up or down
Examples: temperature over a week, plant height over days, cricket score over overs, COVID cases over months

Parts of a Line Graph

Title: What the graph shows
X-axis: Shows time (days, months, overs, etc.)
Y-axis: Shows the measured values (temperature, height, runs, etc.)
Points: Dots plotted at the correct positions
Lines: Straight lines connecting one point to the next

Example 1: Temperature in Delhi over one week (in °C):

Day	Mon	Tue	Wed	Thu	Fri	Sat	Sun
Temp (°C)	32	34	35	33	30	28	31

To draw this line graph:

X-axis: Days of the week (Mon to Sun)
Y-axis: Temperature in °C (scale: start from 25, go up to 40; 1 unit = 1°C)
Plot a point above each day at the correct temperature
Connect the points with straight lines

What the graph tells us:

Temperature was highest on Wednesday (35°C)
Temperature was lowest on Saturday (28°C)
Temperature rose from Monday to Wednesday, then fell till Saturday, and rose again on Sunday
Range = 35 − 28 = 7°C

Image needed: A line graph titled "Temperature in Delhi (One Week)" with X-axis showing days Mon-Sun and Y-axis showing temperature 25°C-40°C. Points plotted at 32, 34, 35, 33, 30, 28, 31 and connected with lines. Grid lines visible. Rise and fall clearly shown.
Style: Clean flat illustration, blue/red line on white grid, dot markers at each point, child-friendly labels
Size: 700×450px

Example 2: Height of a plant (in cm) measured every 5 days:

Day	Day 5	Day 10	Day 15	Day 20	Day 25	Day 30
Height (cm)	3	6	10	15	18	20

Observations from the line graph:

The plant grew continuously — the line goes up throughout
The plant grew fastest between Day 10 and Day 20 (steepest part of the line)
Growth slowed down after Day 25 (line becomes flatter)
Total growth = 20 − 3 = 17 cm in 25 days

Example 3 (Cricket): India's score in a T20 match (runs scored in each over):

Over	1	2	3	4	5	6	7	8	9	10
Total Runs	8	15	28	35	42	55	60	72	85	98

A line graph of this data shows how India's total score built up over the innings. A steep upward line means a lot of runs were scored in that over. A flat section would mean few runs.

How to Plot a Line Graph (Step by Step)

Steps to Draw a Line Graph

Step 1: Draw the X-axis (horizontal) and Y-axis (vertical)
Step 2: Write the time values on the X-axis (days, months, etc.)
Step 3: Choose a scale for the Y-axis and mark the values
Step 4: Plot each data point as a dot at the intersection of its X and Y values
Step 5: Connect the dots with straight lines (left to right)
Step 6: Give a title and label both axes

Think About It: A line going upward means the value is increasing. A line going downward means it is decreasing. A flat (horizontal) line means no change. The steeper the line, the faster the change!

Pie Chart (Circle Graph) — Parts of a Whole

A pie chart (also called a circle graph) is a circular diagram divided into slices. Each slice represents a part of the whole. The whole circle = 100% (or the total of all data). Pie charts are best for showing how a total is divided into different parts.

Key Facts About Pie Charts

The whole circle represents the total (100%)
Each slice shows a fraction or percentage of the total
Bigger slices mean larger portions of the total
All slices together must add up to 100%
Pie charts are good for showing how something is divided or shared

Example 1: How Meena spends her day (24 hours):

Activity	Hours	Percentage
Sleeping	8	33%
School	7	29%
Homework/Study	3	13%
Playing	2	8%
Eating + Getting Ready	2	8%
TV/Screen Time	1	4%
Other Activities	1	4%
Total	24	~100%

In the pie chart, the "Sleeping" slice would be the largest (33%), and "TV/Screen Time" and "Other" would be the smallest slices (4% each).

Image needed: A pie chart titled "How Meena Spends Her Day" with colourful slices for Sleeping (33%, blue), School (29%, green), Homework (13%, yellow), Playing (8%, orange), Eating (8%, pink), TV (4%, purple), Other (4%, grey). Each slice labelled with activity name and percentage. Legend shown.
Style: Bright flat colours, clean labels, child-friendly, clear legend
Size: 600×500px

Example 2: Monthly family budget of Ravi's family (₹40,000 total):

Expense	Amount (₹)	Percentage
Food & Groceries	12,000	30%
Rent	10,000	25%
Education	6,000	15%
Transport	4,000	10%
Medical	2,000	5%
Savings	4,000	10%
Entertainment & Other	2,000	5%
Total	₹40,000	100%

Reading the pie chart:

Which is the largest expense? → Food & Groceries (30%)
What fraction of the budget goes to education? → 15% = 15/100 = 3/20
How much is spent on rent and transport combined? → ₹10,000 + ₹4,000 = ₹14,000 (35%)

Calculating Values from a Pie Chart

If you know the percentage and the total, you can find the actual value:

Formula

Value = (Percentage ÷ 100) × Total
Example: 25% of ₹40,000 = (25 ÷ 100) × 40,000 = ₹10,000

Example 3: A pie chart shows that in a school of 500 students:

40% like Cricket → (40/100) × 500 = 200 students
25% like Football → (25/100) × 500 = 125 students
15% like Badminton → (15/100) × 500 = 75 students
10% like Kabaddi → (10/100) × 500 = 50 students
10% like other sports → (10/100) × 500 = 50 students

Check: 200 + 125 + 75 + 50 + 50 = 500 ✓

Choosing the Right Graph

Different graphs are best for different types of data. Choosing the right graph helps communicate information clearly.

Type of Graph	Best For	Examples
Pictograph	Showing data with pictures; simple comparisons for younger audiences	Favourite fruits, number of books read, vehicles on road
Bar Graph	Comparing quantities across different categories	Marks in subjects, population of cities, favourite sports
Line Graph	Showing change over time (trends, rise and fall)	Temperature over a week, plant growth, stock prices, COVID cases
Pie Chart	Showing parts of a whole (how a total is divided)	Budget breakdown, how you spend your day, exam score distribution

Image needed: A visual guide showing 4 mini-examples side by side — a small pictograph, a small bar graph, a small line graph, and a small pie chart. Under each, a short label: "Pictograph: Compare with pictures", "Bar Graph: Compare categories", "Line Graph: Change over time", "Pie Chart: Parts of a whole".
Style: Clean infographic style, 4-column layout, colourful icons/mini-graphs, child-friendly
Size: 800×350px

Quick Quiz — Which graph would you use?

To show how Mumbai's temperature changed in January → Line Graph
To show how many students like each subject → Bar Graph
To show how Arjun divides his pocket money → Pie Chart
To show how many birds of each type were seen in a park → Pictograph or Bar Graph
To show India's GDP growth over 10 years → Line Graph

Finding the Range

The range of a data set tells us how spread out the values are. It is the difference between the highest (maximum) value and the lowest (minimum) value.

Formula

Range = Highest Value − Lowest Value

Example 1: Marks of 8 students: 45, 72, 58, 90, 63, 81, 55, 68
Highest = 90, Lowest = 45
Range = 90 − 45 = 45

Example 2: Temperature in Jaipur over 5 days: 38°C, 42°C, 35°C, 40°C, 37°C
Highest = 42°C, Lowest = 35°C
Range = 42 − 35 = 7°C

Example 3: Runs scored by Virat Kohli in 6 IPL matches: 32, 85, 14, 63, 101, 48
Highest = 101, Lowest = 14
Range = 101 − 14 = 87 runs
(A large range means the performance varied a lot!)

Think About It: If the range is very small (like 3 or 4), it means all values are close together. If the range is very large, it means the values are spread out widely. For example, if all students scored between 75 and 80, the range is only 5 — very consistent! But if scores are from 25 to 98, the range is 73 — very spread out.

Word Problems — Data in Real Life

Problem 1: The bar graph shows the number of students in 5 sections of Class 5:

Section	5-A	5-B	5-C	5-D	5-E
Students	42	38	45	40	35

Questions:

Which section has the most students? → 5-C (45)
Which section has the fewest? → 5-E (35)
Total students in Class 5? → 42 + 38 + 45 + 40 + 35 = 200
How many more students does 5-A have than 5-B? → 42 − 38 = 4
Range of students across sections? → 45 − 35 = 10

Problem 2: Akriti recorded the maximum temperature of her city for 6 months:

Month	Jan	Feb	Mar	Apr	May	Jun
Max Temp (°C)	22	25	32	38	43	40

Questions:

Which graph type is best to show this data? → Line Graph (shows change over time)
In which month was the temperature highest? → May (43°C)
Between which two months did temperature rise the most? → March to April (32→38, rise of 6°C)
Did the temperature always increase? → No, it dropped from May (43°C) to June (40°C)
Range = 43 − 22 = 21°C

Problem 3: A pie chart shows how 60 students of Class 5 travel to school:

School bus: 40%
Walking: 25%
Auto-rickshaw: 20%
Bicycle: 10%
Car: 5%

Questions:

How many students come by school bus? → (40/100) × 60 = 24 students
How many walk to school? → (25/100) × 60 = 15 students
How many come by bicycle? → (10/100) × 60 = 6 students
How many more students use the bus than walk? → 24 − 15 = 9 students
What fraction of students come by car? → 5% = 5/100 = 1/20

Problem 4 (IPL): The line graph shows India's score over the first 10 overs of a T20 match:

After Over	1	2	3	4	5	6	7	8	9	10
Total Score	7	18	25	38	52	58	65	78	90	105

Questions:

In which over were the most runs scored? → Over 5 (score went from 38 to 52, i.e., 14 runs)
In which over were the fewest runs scored? → Over 6 (score went from 52 to 58, i.e., 6 runs)
What was the total score after 10 overs? → 105 runs
What was the run rate (average runs per over)? → 105 ÷ 10 = 10.5 runs per over

Key Words

Term	Meaning
Data	A collection of facts or numbers gathered for a purpose
Frequency	The number of times a value appears in the data
Tally Marks	Strokes used to count frequency; every 5th stroke crosses the previous four
Pictograph	A graph that uses pictures/symbols to represent data
Key (Legend)	Tells what each symbol in a pictograph represents
Bar Graph	A graph that uses rectangular bars to compare data
Scale	The number each unit on an axis represents
Line Graph	A graph that uses points connected by lines to show change over time
Pie Chart	A circular graph divided into slices showing parts of a whole
Range	Highest value minus lowest value in a data set
X-axis	The horizontal axis of a graph (usually categories or time)
Y-axis	The vertical axis of a graph (usually values/numbers)
Trend	The general direction of change (up, down, or flat)
Percentage	A number out of 100 (used in pie charts)

Key Points to Remember

Data is information collected for a purpose. It must be organised before it can be represented.
A pictograph uses pictures with a key. Half a picture = half the key value.
A bar graph uses bars of equal width. Bar height/length = data value. Bars have equal gaps between them.
A line graph shows change over time. Points are connected by straight lines. Upward line = increase, downward = decrease.
A pie chart shows parts of a whole. The full circle = 100%. All slices must add up to 100%.
Use a bar graph to compare categories. Use a line graph to show trends over time. Use a pie chart to show how a total is split.
Range = Highest value − Lowest value. It tells how spread out the data is.
Every graph needs a title, labelled axes, and a proper scale.
To find a value from a pie chart: Value = (Percentage ÷ 100) × Total

Finished learning? Now test what you know!

🎯 Quick Quiz — Test Yourself!

Answer these questions right here. You get instant feedback — no paper needed!

Score: 0 / 8

1. A graph that uses pictures or symbols to show data is called a:

A pictograph uses pictures/symbols, each standing for a number of items.

2. Which graph is best for showing how temperature changes over a week?

A line graph is best for showing change over time.

3. In a pictograph, 1 symbol = 5 students. How many students do 4 symbols show?

4 symbols × 5 = 20 students.

4. A whole pie chart (circle) represents:

The full circle of a pie chart is the whole data set = 100%.

5. In a pictograph, 1 apple symbol = 6 apples. How many apples do 5 symbols show?

5 × 6 = 30 apples.

6. Meena read these many books over 4 months: 20, 30, 25, 25. What is the average per month?

(20 + 30 + 25 + 25) ÷ 4 = 100 ÷ 4 = 25.

7. A graph that uses rectangular bars of different heights to compare amounts is a ______.

A bar graph uses bars to compare quantities across categories.

8. A bar for "Cricket" reaches 35 on the scale. How many children like cricket?

Read the bar's height on the scale: 35 children.

Practice Questions

A. Read the Pictograph and Answer:

The pictograph below shows the number of books read by students in one month.
Key: 📖 = 5 books

Student	Books
Arya	📖📖📖
Dhruv	📖📖📖📖
Sita	📖📖
Ravi	📖📖📖📖📖
Meena	📖📖📖½

1. How many books did Ravi read?

2. How many books did Meena read?

3. Who read the fewest books?

4. How many more books did Dhruv read than Sita?

5. Total books read by all students =

B. Read the Bar Graph and Answer:

A bar graph shows the number of students who chose each activity for Sports Day:

Activity	Students
Running	25
Relay Race	20
Long Jump	15
Tug of War	30
Lemon & Spoon	10

1. Which activity was chosen by the most students?

2. Which activity was least popular?

3. How many students participated in total?

4. How many more chose Tug of War than Long Jump?

5. What is the range?

C. Read the Line Graph and Answer:

The line graph shows the number of visitors to a park over 6 days:

Day	Mon	Tue	Wed	Thu	Fri	Sat
Visitors	120	150	130	160	180	250

1. On which day did the park have the most visitors?

2. On which day did visitors decrease compared to the previous day?

3. Between which two consecutive days did visitors increase the most?

4. What is the range of visitors?

5. What is the total number of visitors over 6 days?

D. Read the Pie Chart and Answer:

A pie chart shows how 200 students travel to school:

School Bus: 35%
Walking: 20%
Auto-rickshaw: 25%
Bicycle: 10%
Car: 10%

1. How many students come by school bus?

2. How many students walk?

3. How many students come by auto-rickshaw?

4. How many more students use the bus than a bicycle?

5. What fraction of students come by car?

E. Draw a Bar Graph:

The table shows the number of trees planted by different classes during Van Mahotsav:

Class	Trees Planted
Class 3	15
Class 4	25
Class 5	35
Class 6	30
Class 7	20

Draw a vertical bar graph using Scale: 1 cm = 5 trees. X-axis: Classes. Y-axis: Number of trees.

F. Draw a Line Graph:

Hridan measured the height of his sunflower plant every week:

Week	1	2	3	4	5	6
Height (cm)	4	9	15	22	28	32

Plot a line graph. X-axis: Week number. Y-axis: Height in cm (scale: 1 cm = 5 cm).

In which week did the plant grow the most?

What is the range of height?

G. Choose the Correct Answer (MCQ):

1. A pie chart shows data as:

a) Bars b) Lines c) Parts of a circle d) Pictures

2. Which graph is best to show temperature change over a week?

a) Pie chart b) Bar graph c) Line graph d) Pictograph

3. In a pictograph, if 🌟 = 8 students, then 🌟🌟½ means:

a) 16 students b) 20 students c) 24 students d) 12 students

4. The range of the data set 12, 45, 23, 67, 34 is:

a) 45 b) 55 c) 67 d) 34

5. In a bar graph, the bars must have:

a) Different widths b) Equal width and equal gaps c) No gaps d) Curved tops

6. If a pie chart shows 25%, what fraction is that?

a) 1/5 b) 1/4 c) 1/3 d) 1/2

H. Word Problems:

1. The marks scored by Bianca in 5 tests are: 82, 75, 90, 68, 95. Find the range. Which test did she perform best in?

2. A school has 400 students. A pie chart shows: 30% play cricket, 25% play football, 20% play badminton, 15% play kabaddi, 10% play other sports. How many students play each sport?

3. The temperature in Shimla over 5 days was: 12°C, 10°C, 8°C, 11°C, 14°C. Draw a line graph and answer: On which day was it coldest? Between which days did the temperature rise the most?

4. In a pictograph showing favourite ice cream flavours, 🍦 = 6 students. Chocolate has 5 symbols, Vanilla has 3½ symbols, Butterscotch has 4 symbols. How many students chose each flavour? Which is most popular?

5. Dhruv's family monthly expenses (₹50,000 total): Food 30%, Rent 25%, Education 20%, Transport 10%, Savings 15%. Find the amount spent on each category. How much more is spent on food than transport?

Visualising Different Graph Types

Here is a quick visual summary of all four types of graphs you've learned:

Image needed: A 2×2 grid showing all 4 graph types with a small sample of each. Top-left: Pictograph (fruits with icons). Top-right: Bar Graph (vertical bars showing marks). Bottom-left: Line Graph (temperature over days). Bottom-right: Pie Chart (how a student spends their day). Each clearly labelled.
Style: Clean flat illustration, 4 mini-graphs in a grid, colourful, child-friendly, labelled
Size: 750×550px

Activity — Class Survey!

Conduct a survey in your class. Ask all your classmates: "What is your favourite subject?"

Step 1: Collect the data. Use tally marks in the table below:

Subject	Tally Marks	Frequency
Maths
Science
English
Hindi
Social Studies
Computer
Art/Music

Step 2: Draw a bar graph on graph paper using the data above. Choose a suitable scale.

Step 3: Answer these questions:

Which subject is the most popular in your class?
Which subject is the least popular?
How many students did you survey in total?
What is the range?

Bonus: Can you also draw a pie chart? (Hint: Convert each frequency to a percentage first!)

Want to review the lesson again?

Mathematics

Data Handling — Line Graphs, Pie Charts

Class 5 | CBSE / NCERT / ICSE

Name: Class: Date:

Learning Objectives

Collect, organise, and represent data using tally marks and frequency tables
Read and interpret pictographs, bar graphs, line graphs, and pie charts
Draw bar graphs and line graphs from data tables
Choose the correct graph type for different data
Find the range of a data set
Solve word problems involving data interpretation

Introduction — Data is Everywhere!

Data is information collected for a purpose — marks, temperatures, runs, attendance, etc. Raw data is hard to read, so we organise it into tables and represent it using graphs. Graphs turn numbers into pictures for easy comparison and trend spotting.

In Class 5, we learn four types: Pictographs, Bar Graphs, Line Graphs, and Pie Charts.

What is Data? — Organising with Tally Marks

Raw data: 45, 32, 38, 45, 50, 32, 40, 38, 45, 50 (marks of 10 students)

Frequency table:

Marks	Tally	Frequency
32	\|\|	2
38	\|\|	2
40	\|	1
45	\|\|\|	3
50	\|\|	2

Frequency = how many times a value occurs. Tally: every 5th stroke crosses previous four.

Pictograph — Pictures Tell a Story

How to read: Check the key (e.g., 🍎 = 4 students). Count symbols. Multiply by key value. Half symbol = half value.

Example: Favourite fruits (Key: 🍎 = 4 students)
Mango: 🍎🍎🍎🍎 = 16 | Apple: 🍎🍎🍎 = 12 | Banana: 🍎🍎 = 8 | Guava: 🍎🍎½ = 10 | Orange: 🍎🍎🍎½ = 14
Most popular: Mango (16). Total: 60 students.

[Image: Colourful pictograph showing favourite fruits of Class 5-A with key: 1 icon = 4 students]

Bar Graph — Comparing with Bars

Parts: Title, X-axis (categories), Y-axis (values/scale), Bars (equal width), Gaps (equal spacing).

Example: Arjun's marks — Maths: 85, Science: 78, English: 92, Hindi: 70, Soc. St.: 65
Highest: English (92). Lowest: Social Studies (65). Range: 92 − 65 = 27.

[Image: Vertical bar graph showing Arjun's marks in 5 subjects, Y-axis 0-100, colourful bars]

Steps to draw: 1) Draw axes → 2) Choose scale → 3) Label categories → 4) Draw bars → 5) Equal gaps → 6) Title & labels

Line Graph — Showing Change Over Time

Best for: Data that changes over time. Shows trends (up/down/flat). Points connected by lines. Steeper = faster change.

Example: Temperature in Delhi over one week (°C):
Mon: 32 | Tue: 34 | Wed: 35 | Thu: 33 | Fri: 30 | Sat: 28 | Sun: 31
Highest: Wed (35°C). Lowest: Sat (28°C). Range: 35 − 28 = 7°C.
Rose Mon→Wed, fell Wed→Sat, rose Sat→Sun.

[Image: Line graph showing Delhi temperature Mon-Sun, points at 32,34,35,33,30,28,31 connected by lines]

Steps: 1) Draw axes → 2) Time on X-axis → 3) Scale on Y-axis → 4) Plot points → 5) Connect with lines → 6) Title

Reading tips: Upward line = increasing. Downward = decreasing. Flat = no change. Steeper = faster.

Pie Chart (Circle Graph) — Parts of a Whole

Key facts: Full circle = 100% (total). Each slice = one part. Bigger slice = larger portion. All slices add to 100%.

[Image: Pie chart showing "How Meena Spends Her Day" with colourful slices labelled with percentages]

Example 3: 500 students' favourite sports: Cricket 40% = 200 | Football 25% = 125 | Badminton 15% = 75 | Kabaddi 10% = 50 | Other 10% = 50. Check: 200+125+75+50+50 = 500 ✓

Choosing the Right Graph

Graph Type	Best For	Examples
Pictograph	Simple comparisons with pictures	Fruits, books, vehicles
Bar Graph	Comparing quantities across categories	Marks, populations, sports
Line Graph	Change over time (trends)	Temperature, growth, scores
Pie Chart	Parts of a whole (how total is split)	Budget, time use, percentages

[Image: 4 mini-graphs side by side — pictograph, bar graph, line graph, pie chart — with labels underneath]

Finding the Range

Range = Highest Value − Lowest Value
Small range = values are close together. Large range = values are spread out.

Examples:
Marks: 45, 72, 58, 90, 63, 81, 55, 68 → Range = 90 − 45 = 45
Temperature: 38, 42, 35, 40, 37 → Range = 42 − 35 = 7°C
Kohli's runs: 32, 85, 14, 63, 101, 48 → Range = 101 − 14 = 87 runs

Key Words

Term	Meaning
Data	Collection of facts/numbers for a purpose
Frequency	How many times a value occurs
Pictograph	Uses pictures/symbols with a key
Bar Graph	Uses rectangular bars to compare
Line Graph	Points connected by lines (change over time)
Pie Chart	Circle divided into slices (parts of whole)
Range	Highest − Lowest value
Scale	What each unit on axis represents
Trend	General direction of change

Key Points to Remember:
• Pictograph: pictures + key. Half picture = half value.
• Bar graph: equal-width bars, equal gaps, title + labelled axes.
• Line graph: shows change over time. Up = increase. Down = decrease. Steep = fast change.
• Pie chart: full circle = 100%. Value = (% ÷ 100) × Total. All slices must add to 100%.
• Range = Highest − Lowest.
• Bar graph for comparing. Line graph for trends. Pie chart for parts of whole.

Practice Questions

A. Read the Pictograph and Answer:

Books read in one month. Key: 📖 = 5 books
Arya: 📖📖📖 | Dhruv: 📖📖📖📖 | Sita: 📖📖 | Ravi: 📖📖📖📖📖 | Meena: 📖📖📖½

1. How many books did Ravi read?

2. How many books did Meena read?

3. Who read the fewest books?

4. How many more books did Dhruv read than Sita?

5. Total books read by all =

B. Read the Bar Graph and Answer:

Sports Day activities: Running: 25, Relay: 20, Long Jump: 15, Tug of War: 30, Lemon & Spoon: 10

1. Most popular activity?

2. Least popular?

3. Total participants?

4. How many more chose Tug of War than Long Jump?

5. Range =

C. Read the Line Graph and Answer:

Park visitors: Mon: 120, Tue: 150, Wed: 130, Thu: 160, Fri: 180, Sat: 250

1. Day with most visitors?

2. Day visitors decreased from previous day?

3. Biggest increase between consecutive days?

4. Range of visitors?

5. Total visitors over 6 days?

D. Read the Pie Chart and Answer:

200 students travel to school: Bus 35%, Walk 20%, Auto 25%, Bicycle 10%, Car 10%

1. Students by bus?

2. Students walking?

3. Students by auto?

4. More by bus than bicycle?

5. Fraction by car?

E. Draw a Bar Graph:

Trees planted during Van Mahotsav: Class 3: 15, Class 4: 25, Class 5: 35, Class 6: 30, Class 7: 20. Scale: 1 cm = 5 trees.

Draw the bar graph in the space below:

F. Draw a Line Graph:

Sunflower height: Week 1: 4 cm, Week 2: 9 cm, Week 3: 15 cm, Week 4: 22 cm, Week 5: 28 cm, Week 6: 32 cm.

Plot the line graph below (X: Weeks, Y: Height, Scale: 1 cm = 5 cm):

Week with most growth? Range of height?

G. Choose the Correct Answer (MCQ):

1. A pie chart shows data as:

a) Bars b) Lines c) Parts of a circle d) Pictures

2. Best graph for temperature change over a week:

a) Pie chart b) Bar graph c) Line graph d) Pictograph

3. If 🌟 = 8 students, then 🌟🌟½ means:

a) 16 b) 20 c) 24 d) 12

4. Range of 12, 45, 23, 67, 34:

a) 45 b) 55 c) 67 d) 34

5. Bars in a bar graph must have:

a) Different widths b) Equal width & gaps c) No gaps d) Curved tops

6. 25% as a fraction is:

a) 1/5 b) 1/4 c) 1/3 d) 1/2

H. Word Problems:

1. Bianca's marks in 5 tests: 82, 75, 90, 68, 95. Find the range. Best test?

2. School of 400: Cricket 30%, Football 25%, Badminton 20%, Kabaddi 15%, Other 10%. Find numbers.

3. Shimla temp (5 days): 12°C, 10°C, 8°C, 11°C, 14°C. Coldest day? Biggest rise between which days?

4. Pictograph (🍦 = 6): Chocolate 5 symbols, Vanilla 3½, Butterscotch 4. How many each? Most popular?

5. Dhruv's family (₹50,000): Food 30%, Rent 25%, Education 20%, Transport 10%, Savings 15%. Amounts? How much more food than transport?

Activity — Class Survey!

Ask classmates: "Favourite subject?" Record using tally marks, then draw a bar graph.

Subject	Tally	Frequency
Maths
Science
English
Hindi
Social Studies
Computer

Most popular: | Least popular: | Total surveyed: | Range:

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