Maths

Data Handling

Class 3

🎯 Learning Objectives

πŸ“– What is Data?

Data means information that we collect. When we ask questions and write down the answers, we are collecting data!

For example, if you ask all your classmates "What is your favourite fruit?" and write down their answers β€” that collection of answers is called data.

But a long list of answers is hard to understand. So we organise data using tally charts, pictographs, and bar graphs to make it easy to read.

Tally Marks

Tally marks are a quick way to count things. We draw one line for each item. After every 4 lines, the 5th line goes across them (like a gate). This makes counting in groups of 5 easy.

NumberTally MarksNumberTally Marks
1|6|||| |
2||7|||| ||
3|||8|||| |||
4||||9|||| ||||
5||||10|||| ||||
Think about it: Why do we cross the 5th line? Because it makes counting faster! Instead of counting one by one, we count in groups of 5.
Tally marks from 1 to 10 showing how to draw and count tallies

Tally Chart (Frequency Table)

A tally chart organises data into a table with tally marks and totals.

Example: Favourite Fruits of Class 3B (30 students)

Arjun asked his classmates about their favourite fruit. Here is the tally chart:

FruitTally MarksNumber of Students
Mango πŸ₯­|||| |||8
Banana 🍌|||| |6
Apple 🍎|||| ||||10
Grapes πŸ‡||||4
Orange 🍊||2

Questions we can answer from this chart:

  • Which fruit is most popular? β†’ Apple (10 students)
  • Which fruit is least popular? β†’ Orange (2 students)
  • How many more students like Mango than Grapes? β†’ 8 βˆ’ 4 = 4 more
  • Total students surveyed? β†’ 8 + 6 + 10 + 4 + 2 = 30

Pictograph

A pictograph uses pictures or symbols to show data. Each picture stands for a certain number of items.

Example: Books Read by Students in One Month

Key: Each πŸ“š = 2 books

StudentBooks (πŸ“š = 2 books)Total
SitaπŸ“šπŸ“šπŸ“š6
RaviπŸ“šπŸ“šπŸ“šπŸ“š8
MeenaπŸ“šπŸ“š4
ArjunπŸ“šπŸ“šπŸ“šπŸ“šπŸ“š10

Reading the pictograph:

  • Who read the most books? β†’ Arjun (10 books)
  • How many books did Sita read? β†’ 3 pictures Γ— 2 = 6 books
  • How many more books did Ravi read than Meena? β†’ 8 βˆ’ 4 = 4 more
Pictograph showing favourite sports β€” cricket, football, badminton and kabaddi

Bar Graph

A bar graph uses bars (rectangles) to show data. The taller the bar, the bigger the number. Bar graphs are easy to compare because you can see which bar is tallest at a glance.

Parts of a bar graph:

Example: Favourite Colours of Class 3A
ColourNumber of Students
Red7
Blue9
Green5
Yellow4
Pink6

In a bar graph, Blue would have the tallest bar (9) and Yellow the shortest (4).

Bar graph showing favourite colours with coloured bars

How to Draw a Bar Graph

Follow these steps:

  1. Step 1: Draw two lines β€” one horizontal (X-axis) and one vertical (Y-axis).
  2. Step 2: Write the categories on the X-axis (e.g., Red, Blue, Green...).
  3. Step 3: Write numbers on the Y-axis (0, 1, 2, 3... up to the highest value).
  4. Step 4: Draw bars for each category. The height of each bar = the number.
  5. Step 5: Give your graph a title.
Remember: All bars should have the same width. Leave equal gaps between bars. Always start the Y-axis from 0.

πŸ“ Key Words

WordMeaning
DataInformation collected by asking questions or observing
Tally MarksLines used to count items in groups of 5
Tally ChartA table showing data using tally marks
PictographA chart using pictures to represent data
Bar GraphA chart using bars (rectangles) to show data
KeyTells what each picture stands for in a pictograph
X-axisThe horizontal line in a graph (categories)
Y-axisThe vertical line in a graph (numbers)
⭐ Key Points to Remember

✏️ Practice Questions

A. Fill in the Blanks
1. Information collected by asking questions is called .
2. In tally marks, the 5th mark goes the first four.
3. A pictograph uses to show data.
4. In a bar graph, the taller the bar, the the number.
5. The horizontal line in a graph is called the .
6. |||| || in tally marks means .
7. The in a pictograph tells what each picture stands for.
8. A table that uses tally marks to show data is called a .
9. The vertical line in a graph is called the .
10. All bars in a bar graph should have the same .
B. Multiple Choice Questions
1. What does |||| |||| ||| mean in tally marks?
(a) 8(b) 13(c) 12(d) 15
2. In a pictograph, if 🍎 = 3 apples, then 🍎🍎🍎🍎 means:
(a) 4(b) 7(c) 12(d) 16
3. Which shows data using bars?
(a) Tally chart(b) Pictograph(c) Bar graph(d) Number line
4. In a bar graph, the Y-axis shows:
(a) Categories(b) Numbers(c) Pictures(d) Colours
5. How do you write 9 in tally marks?
(a) |||||||||(b) |||| ||||(c) |||| |(d) |||| ||||
C. Short Answer Questions
1. Meena surveyed her class about favourite sports. Cricket: 12, Football: 8, Kabaddi: 5, Badminton: 7. Which sport is most popular? Which is least popular?
2. In a pictograph, each ⭐ = 4 stars earned. Ravi has ⭐⭐⭐. How many stars did Ravi earn?
3. Draw tally marks for the number 14.
4. In a bar graph, Red bar = 6, Blue bar = 9. How many more students chose Blue than Red?
5. Why do we use graphs and charts instead of just writing a list of numbers?
D. True or False
1. Tally marks are counted in groups of 4.
2. A pictograph uses pictures to show data.
3. In a bar graph, all bars must be the same height.
4. The key in a pictograph tells what each picture means.
5. Data means information we collect.
E. Match the Following
Column AColumn B
1. Tally marksa. Uses bars to show data
2. Pictographb. Counting in groups of 5
3. Bar graphc. Horizontal line
4. X-axisd. Uses pictures to show data
5. Datae. Information collected
🎨 Fun Activity β€” Class Survey

Ask 10 friends: "What is your favourite ice cream flavour?" (Choose from: Chocolate, Vanilla, Strawberry, Mango, Butterscotch)

1. Write their answers in a tally chart.

2. Draw a pictograph using 🍦 where each 🍦 = 1 student.

3. Which flavour is most popular in your group?

4. Which flavour is least popular?

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Mathematics

Data Handling

Class 3 | CBSE / NCERT / ICSE
Name: Class: Date:
What is Data?

Data = information collected by asking questions or observing. We organise data using tally charts, pictographs, and bar graphs to make it easy to understand.

Tally Marks

Tally marks count items in groups of 5. The 5th mark crosses the first 4.

NumberTallyNumberTally
1|6|||| |
2||7|||| ||
3|||8|||| |||
4||||9|||| ||||
5||||ΜΈ10||||ΜΈ ||||ΜΈ
Tally marks 1 to 10
Tally Chart Example

Favourite Fruits of Class 3B (30 students):

FruitTally MarksStudents
Mango||||ΜΈ |||8
Banana||||ΜΈ |6
Apple||||ΜΈ ||||ΜΈ10
Grapes||||4
Orange||2

Most popular: Apple (10). Least popular: Orange (2).

Pictograph

A pictograph uses pictures to show data. Always check the key.

Books Read in One Month (Key: πŸ“š = 2 books)

StudentBooksTotal
SitaπŸ“šπŸ“šπŸ“š6
RaviπŸ“šπŸ“šπŸ“šπŸ“š8
MeenaπŸ“šπŸ“š4
ArjunπŸ“šπŸ“šπŸ“šπŸ“šπŸ“š10
Pictograph of favourite sports
Bar Graph

A bar graph uses bars to show data. Taller bar = bigger number.

Parts: Title, X-axis (categories), Y-axis (numbers), Bars

Favourite Colours: Red=7, Blue=9, Green=5, Yellow=4, Pink=6

Blue has the tallest bar (9). Yellow has the shortest (4).

Bar graph of favourite colours
How to Draw a Bar Graph
  1. Draw X-axis (horizontal) and Y-axis (vertical).
  2. Write categories on X-axis.
  3. Write numbers on Y-axis (start from 0).
  4. Draw bars β€” height = the number.
  5. Give your graph a title.
  • Data = information collected.
  • Tally marks: every 5th mark crosses the first 4.
  • Pictograph: uses pictures (check the key!).
  • Bar graph: uses bars (taller = bigger number).
  • Always label axes and give a title.
Mathematics

Data Handling β€” Practice Questions

Class 3 | CBSE / NCERT / ICSE
A. Fill in the Blanks
1. Information collected by asking questions is called .
2. In tally marks, the 5th mark goes the first four.
3. A pictograph uses to show data.
4. In a bar graph, the taller the bar, the the number.
5. The horizontal line in a graph is called the .
6. ||||ΜΈ || in tally marks means .
7. The in a pictograph tells what each picture stands for.
8. A table that uses tally marks is called a .
9. The vertical line in a graph is called the .
10. All bars in a bar graph should have the same .
B. Multiple Choice Questions
1. What does ||||ΜΈ ||||ΜΈ ||| mean in tally marks?
(a) 8(b) 13(c) 12(d) 15
2. If 🍎 = 3 apples, then 🍎🍎🍎🍎 means:
(a) 4(b) 7(c) 12(d) 16
3. Which shows data using bars?
(a) Tally chart(b) Pictograph(c) Bar graph(d) Number line
4. In a bar graph, the Y-axis shows:
(a) Categories(b) Numbers(c) Pictures(d) Colours
5. How do you write 9 in tally marks?
(a) |||||||||(b) ||||ΜΈ ||||(c) ||||ΜΈ |(d) |||| ||||
C. Short Answer Questions
1. Cricket: 12, Football: 8, Kabaddi: 5, Badminton: 7. Which sport is most popular? Least popular?
2. In a pictograph, each ⭐ = 4 stars. Ravi has ⭐⭐⭐. How many stars did Ravi earn?
3. Draw tally marks for the number 14.
4. In a bar graph, Red bar = 6, Blue bar = 9. How many more chose Blue than Red?
5. Why do we use graphs and charts instead of just writing a list?
D. True or False
1. Tally marks are counted in groups of 4.
2. A pictograph uses pictures to show data.
3. In a bar graph, all bars must be the same height.
4. The key in a pictograph tells what each picture means.
5. Data means information we collect.
E. Match the Following
Column AColumn B
1. Tally marksa. Uses bars to show data
2. Pictographb. Counting in groups of 5
3. Bar graphc. Horizontal line
4. X-axisd. Uses pictures to show data
5. Datae. Information collected
🎨 Fun Activity β€” Class Survey

Ask 10 friends their favourite ice cream flavour (Chocolate, Vanilla, Strawberry, Mango, Butterscotch).

1. Make a tally chart. 2. Draw a pictograph. 3. Which is most popular? 4. Which is least popular?

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