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# Find the standard deviation of 2, 5, 9, 2, 7 (correct to 2 decimal places)

### Question

Find the standard deviation of 2, 5, 9, 2, 7 (correct to 2 decimal places)

A) 5.80

B) 3.41

C) 2.76

D) 1.80

### Explanation:

$$(\bar{x}) = \cfrac{2 + 5 + 9 + 2 + 7}{5} = \cfrac{25}{5}$$
Variance = $$\sum \cfrac{(x - \bar{x})^2}{N}$$
$$= \cfrac{(2-5)^2 + (5-5)^2 + (9-5)^2 + (2-5)^2 + (7-5)}{5}$$
$$= \cfrac{9 + 0 + 16 + 9 + 4}{5} = \cfrac{38}{5} = 7.6$$
$$\text{Standard deviation} = \sqrt{\text{Variance}}$$
Variance is referred to as the mean-squared deviation, while standard deviation is the the root mean-squared deviation.
$$= \sqrt{7.6} = 2.76$$ (to 2 d.p)

## Dicussion (1)

• $$(\bar{x}) = \cfrac{2 + 5 + 9 + 2 + 7}{5} = \cfrac{25}{5}$$
Variance = $$\sum \cfrac{(x - \bar{x})^2}{N}$$
$$= \cfrac{(2-5)^2 + (5-5)^2 + (9-5)^2 + (2-5)^2 + (7-5)}{5}$$
$$= \cfrac{9 + 0 + 16 + 9 + 4}{5} = \cfrac{38}{5} = 7.6$$
$$\text{Standard deviation} = \sqrt{\text{Variance}}$$
Variance is referred to as the mean-squared deviation, while standard deviation is the the root mean-squared deviation.
$$= \sqrt{7.6} = 2.76$$ (to 2 d.p)