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Class 10 Statistics: cheat sheet
CBSE Mathematics. Mean, median and mode of grouped data (class intervals with frequencies).
Key ideas
- For grouped data, use the class mark (the middle of each class) as the value of the class.
- The mean can be found directly, by the assumed-mean method, or by step deviation; all give the same answer.
- The modal class is the class with the highest frequency.
- The median class is the class whose cumulative frequency first reaches n/2 or more.
- In the median formula, cf is the cumulative frequency of the class just before the median class.
- h is the class width; l is the lower limit of the modal or median class.
Remember
| Class mark | (lower limit + upper limit) ÷ 2 |
| Mean (direct) | x̄ = Σfᵢxᵢ ÷ Σfᵢ |
| Mean (assumed mean a) | x̄ = a + Σfᵢdᵢ ÷ Σfᵢ, where dᵢ = xᵢ − a |
| Mode | l + [(f₁ − f₀) ÷ (2f₁ − f₀ − f₂)] × h |
| Median | l + [(n/2 − cf) ÷ f] × h |
Watch out
- Using the class limits instead of the class mark for the mean.
- Taking cf of the median class itself instead of the class before it.
- Choosing the class with the largest values as the modal class (it is the largest frequency).
Worked example
Find the median of 59, 44, 64, 78, 63, 20, 59, 49.
Working: in order: 20, 44, 49, 59, 59, 63, 64, 78; the mean of the two middle values
Answer: 59
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