Data Handling, Mean, Median, Mode and Chance: Class 7 Study Guide
Data helps us understand the world, from sports scores to rainfall. Class 7 learns to summarise and read it.
Data is information collected from observation or surveys. It can be organised in a frequency table using tally marks and shown in bar graphs, pictographs or double bar graphs. Three measures summarise a set of values: the mean (the average), the median (the middle value when ordered) and the mode (the most frequent). The range is the highest minus the lowest.
Probability measures chance. If all outcomes are equally likely, P(event) = number of favourable outcomes ÷ total outcomes, between 0 (impossible) and 1 (certain).
Average measures
For the marks 12, 15, 15, 18, 20: mean = (12 + 15 + 15 + 18 + 20) ÷ 5 = 16, median = 15 (the middle), mode = 15 and range = 8. If there is an even number of values, the median is the mean of the two middle values: for 4, 6, 8, 10 it is 7.
| Measure | How | Marks 12, 15, 15, 18, 20 |
|---|---|---|
| Mean | sum ÷ number of values | 16 |
| Median | middle of ordered list | 15 |
| Mode | most frequent | 15 |
| Range | highest − lowest | 8 |
Reading graphs
A bar graph uses bars of equal width, and the height shows the value. A double bar graph compares two sets, such as boys' and girls' marks in each subject. Always check the title, the labels and the scale. A broken scale can exaggerate differences.
What is measured?
What does each step mean?
Compare.
Use numbers.
Chance
Tossing a fair coin: P(head) = 1/2. Rolling a die: P(a number greater than 4) = 2/6 = 1/3. A bag with 3 red and 7 blue balls: P(red) = 3/10. P(not red) = 1 − 3/10 = 7/10. Chance experiments show that outcomes vary in the short run, but proportions settle down over many trials.
Worked examples and common mistakes
Example: The mean of 5 numbers is 12. Their total is 60. If a sixth number is 18, the new mean is 78 ÷ 6 = 13. Common mistakes: finding the median without ordering the data, mixing up the mean and the mode and thinking an unlikely event is impossible. Always sort data first.
Check your understanding: model answers
1. 3, 5, 7, 9, 11, so the median is 7. 2. 8. 3. 3/6 = 1/2.
✨ Key Takeaways
- Mean = total ÷ count.
- Order the data before finding the median.
- Mode is the most frequent value.
- Probability is between 0 and 1.
💬 Questions for Discussion & Reflection
- Find the median of 7, 3, 9, 5, 11.
- Find the mean of 4, 8, 12.
- Find P(odd number) on a die.
Print graph paper for bar graphs →