Data Handling - Class 7 Mathematics (CBSE)
Based on the 2025-26 NCERT syllabus for Class 7 Mathematics. This chapter introduces students to collecting, organising, and interpreting data using measures of central tendency and basic probability.
1. Why this chapter matters
Data handling is one of the most practical mathematics topics. From cricket batting averages to weather reports to opinion polls, the ability to interpret data is a life skill. In CBSE exams, this chapter contributes 6-8 marks through averages, graphs, and simple probability questions.
2. Mean, median, and mode
Mean (average)
Mean = Sum of all observations / Total number of observations
Example: Marks of 5 students are 12, 15, 18, 20, 25. Mean = (12 + 15 + 18 + 20 + 25) / 5 = 90/5 = 18
Median
The median is the middle value when data is arranged in ascending or descending order.
For odd number of observations: median = (n+1)/2 th observation. For even number of observations: median = average of (n/2)th and (n/2 + 1)th observations.
Example (odd): 5, 7, 12, 15, 20. Middle = 12. Example (even): 5, 7, 12, 15. Median = (7 + 12)/2 = 9.5
Mode
The mode is the value that appears most frequently in a dataset.
Example: 2, 3, 5, 3, 7, 3, 8, 9. Mode = 3 (appears 3 times).
A dataset can have no mode, one mode, or multiple modes.
3. Comparison of mean, median, and mode
| Measure | Best used when | Limitation |
|---|---|---|
| Mean | Data has no extreme outliers | Affected by very high/low values |
| Median | Data has outliers | Ignores most values |
| Mode | Data has frequently repeated values | May not exist or be unique |
4. Bar graphs
Double bar graph
A double bar graph shows two sets of data side by side for comparison.
Example: Compare the number of boys and girls in different classes using adjacent bars.
Drawing a bar graph
Steps:
- Choose a scale (e.g., 1 unit = 5 students).
- Draw X-axis (categories) and Y-axis (frequency).
- Draw bars of equal width with equal gaps.
- For double bar graphs, use different colours/patterns with a key.
5. Chance and probability
Random experiment
An experiment whose outcome cannot be predicted with certainty.
Equally likely outcomes
All outcomes have the same chance of occurring. Example: Tossing a fair coin gives Heads or Tails with equal probability.
Probability of an event
Probability = Number of favourable outcomes / Total number of possible outcomes
Range of probability
Probability always lies between 0 and 1.
- Probability 0 = impossible event.
- Probability 1 = certain event.
Simple events
Example 1: Probability of getting a head when a coin is tossed = 1/2. Example 2: Probability of rolling a 4 on a die = 1/6. Example 3: Probability of getting an even number on a die = 3/6 = 1/2.
6. Worked examples
Example 1: Find mean, median, and mode of 4, 7, 4, 9, 10, 4, 7
Mean = (4 + 7 + 4 + 9 + 10 + 4 + 7) / 7 = 45/7 = 6.43 Arrange in order: 4, 4, 4, 7, 7, 9, 10. Median = 7 (4th value). Mode = 4.
Example 2: A die is rolled. What is the probability of getting a number greater than 4?
Favourable outcomes: 5, 6 (2 outcomes). Total outcomes: 6. Probability = 2/6 = 1/3.
Example 3: A bag has 3 red balls and 5 blue balls. Find probability of picking a blue ball.
Total balls = 8. Favourable (blue) = 5. Probability = 5/8.
7. Common mistakes and how to fix them
| Mistake | Fix |
|---|---|
| Forgetting to arrange data for median | Always sort data in ascending or descending order first |
| Calculating mean when data has extreme outliers | Consider if median might be more appropriate |
| Saying probability can be 2 | Probability is always between 0 and 1 inclusive |
| Unequal bar widths in graphs | All bars must have same width |
| Writing 'mode' without checking frequency | Count the frequency of each value carefully |
8. CBSE exam focus
| Question type | Marks | Frequency |
|---|---|---|
| Mean, median, mode calculation | 2-3 marks | 1-2 questions |
| Double bar graph drawing | 3 marks | 1 question |
| Probability of simple events | 2 marks | 1 question |
| Data interpretation from graph | 2 marks | 1 question |
| Application-based probability | 3 marks | Occasional |
9. Self-test
- Find the mean of first five natural numbers.
- Find the median of: 12, 7, 15, 9, 11, 8, 14.
- Find the mode of: 2, 4, 2, 6, 8, 2, 4, 10, 4.
- A coin is tossed 50 times and heads appear 28 times. What is the experimental probability of getting heads?
- In a class of 40 students, 18 are girls. A student is selected at random. What is the probability of selecting a boy?
- Draw a double bar graph for the following data: Class 7A has 15 boys and 20 girls; Class 7B has 18 boys and 17 girls.
10. Answer key
- First five natural numbers: 1, 2, 3, 4, 5. Mean = 15/5 = 3.
- Sorted: 7, 8, 9, 11, 12, 14, 15. Median = 11.
- 2 appears 3 times, 4 appears 3 times. Mode = 2 and 4 (bimodal).
- Experimental probability = 28/50 = 14/25.
- Boys = 40 - 18 = 22. Probability = 22/40 = 11/20.
- Draw X-axis with '7A' and '7B'. For each, draw adjacent bars for boys and girls using scale 1 unit = 5 students.
11. Quick revision
- Mean = sum of observations / number of observations.
- Median = middle value of sorted data.
- Mode = most frequent value.
- Probability = favourable / total outcomes.
- Probability is always between 0 and 1.
- Bar graphs need equal bar widths and appropriate scale.
