By Elimu Assistant Team 
TOPICS: Statistics
LEVEL: Form 4 Level
SOURCE: Kcse 1996
Paper 1, Question 10
MARKS: 4
Skills Tested:
- Statistics (mean, variance, standard deviation)
- Arithmetic (basic operations)
QUESTION
Five pupils A, B, C, D and E obtained the marks 53, 41, 60, 80 and 56 respectively. The table below shows part of the work to find the standard deviation.
(a) Complete the table (1 mark)
(b) Find the standard deviation (3 marks)
MARKING SCHEME
SOLUTION:
Question:
Five pupils A, B, C, D, and E obtained the marks 53, 41, 60, 80, and 56 respectively. The table below shows part of the work to find the standard deviation.
| Pupil | Mark x | x – x̄ | (x – x̄)² |
|---|---|---|---|
| A | 53 | -5 | 25 |
| B | 41 | -17 | 289 |
| C | 60 | 2 | 4 |
| D | 80 | 22 | 484 |
| E | 56 | -2 | 4 |
(a) Complete the table
The mean (average) of the marks is calculated as follows:
*** QuickLaTeX cannot compile formula:
\[ x̄ = \frac{53 + 41 + 60 + 80 + 56}{5} = \frac{290}{5} = 58 \]
*** Error message:
Unicode character ̄ (U+0304)
leading text: \[ x̄
Completed Table:
| Pupil | Mark x | x – x̄ | (x – x̄)² |
|---|---|---|---|
| A | 53 | -5 | 25 |
| B | 41 | -17 | 289 |
| C | 60 | 2 | 4 |
| D | 80 | 22 | 484 |
| E | 56 | -2 | 4 |
(b) Find the standard deviation
To calculate the variance:
*** QuickLaTeX cannot compile formula:
\[ \text{Variance} = \frac{\text{Sum of } (x - x̄)²}{N} = \frac{25 + 289 + 4 + 484 + 4}{5} = \frac{806}{5} = 161.2 \]
*** Error message:
Unicode character ̄ (U+0304)
leading text: ...nce} = \frac{\text{Sum of } (x - x̄)²}{N}
Now, we calculate the standard deviation:
*** QuickLaTeX cannot compile formula:
\[ σ = \sqrt{161.2} \approx 12.68 \]
*** Error message:
Unicode character σ (U+03C3)
leading text: \[ σ
Final Result:
The standard deviation of the marks is approximately
*** QuickLaTeX cannot compile formula: σ \approx 12.68 *** Error message: Unicode character σ (U+03C3) leading text: $σ.
