What this chapter is about
Every day we meet numbers that tell us something useful. How many students were absent this week? Which fruit is most popular in your class? How much rain fell each month during the monsoon? These numbers are called data — pieces of information we collect to answer a question.
This chapter teaches you how to collect data, organise it neatly, and show it using pictures like bar graphs and pictographs. When data is presented well, patterns jump out and comparisons become easy. You will also learn to read graphs that others have made and answer questions from them.
After studying this chapter, you should be able to gather information, arrange it in tables, draw simple graphs, and make sense of data you see in newspapers, books or on television.
Key ideas
- Data means facts or numbers collected to answer a question. Example: the heights of all students in your class.
- Tally marks are short strokes used to count items quickly. Every fifth mark crosses the first four, making groups of five that are easy to add.
- A frequency is the number of times a particular item or value appears in your data.
- A frequency table lists each item along with its frequency, helping you see totals at a glance.
- A pictograph uses small pictures or symbols to show data. A key tells you what one picture stands for (for example, one ball picture = 5 runs).
- A bar graph uses rectangular bars of equal width. The height of each bar shows the frequency or value it represents.
- Choosing a suitable scale is important: if one symbol stands for too few items, your pictograph becomes crowded; if it stands for too many, you cannot show small differences.
- Graphs make it easy to compare groups and spot the highest, lowest or most common item quickly.
Formulas and facts to remember
- Tally mark groups: |||| with a slanted stroke through them equals 5.
- Frequency = count of how many times an item appears.
- In a pictograph, total for a category = number of symbols × value of one symbol.
- In a bar graph, all bars must have the same width and start from a common base line.
- The scale on the vertical axis must have equal gaps (for example, 0, 10, 20, 30…).
Worked examples
Example 1 – Making a frequency table
Riya asked 12 friends their favourite colour. The answers were: Red, Blue, Green, Blue, Red, Red, Green, Blue, Blue, Red, Green, Blue.
Step 1: List the colours and use tally marks.
- Colour: Red · Tally: |||| · Frequency: 4
- Colour: Blue · Tally: |||| | · Frequency: 5
- Colour: Green · Tally: ||| · Frequency: 3
Step 2: Check the total: 4 + 5 + 3 = 12. Correct!
Blue is the most popular colour.
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Example 2 – Reading a pictograph
A pictograph shows books read by four students. Each book symbol = 2 books.
- Student: Amit · Symbols: 📖📖📖
- Student: Priya · Symbols: 📖📖📖📖
- Student: Kiran · Symbols: 📖📖
How many books did Priya read?
Priya has 4 symbols. Each symbol = 2 books. Total = 4 × 2 = 8 books.
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Example 3 – Drawing a bar graph
Runs scored by four friends in a gully-cricket match: Sana 15, Mohit 25, Leela 20, Arjun 10.
Step 1: Draw a horizontal line (base). Mark the names: Sana, Mohit, Leela, Arjun with equal spacing. Step 2: Draw a vertical line (height axis). Choose a scale: let 1 cm = 5 runs. Mark 0, 5, 10, 15, 20, 25. Step 3: Draw bars of equal width. Sana's bar goes up to 15, Mohit's to 25, Leela's to 20, Arjun's to 10. Step 4: Give your graph a title: "Runs scored in the match".
From the graph you can see Mohit scored the most and Arjun scored the least.
Common mistakes
- Forgetting to cross every fifth tally mark → always bundle tallies in fives to avoid counting errors.
- Making bars of different widths → keep all bars equally wide; only the height should change.
- Ignoring the key in a pictograph → always check what one symbol stands for before calculating.
- Using unequal gaps on the scale → the axis must go up by the same amount each step (5, 10, 15… not 5, 10, 20).
- Adding frequencies that do not match the total data count → always verify your sum equals the number of items you collected.
Quick revision
- Data is information collected to answer a question.
- Tally marks help you count quickly; every fifth mark crosses the first four.
- A frequency table shows each item and how often it appears.
- A pictograph uses symbols; multiply the number of symbols by the key value.
- A bar graph uses bars of equal width; height shows frequency.
- Always label your graph and include a title.