Mean of 5 observations is 7. If four of these observations are 6, 7, 8, 10 and one is missing, then the variance of all the five observations is :

$$\text{Mean} (\bar{x}) = \frac{\sum x_i}{n}$$

$$7 = \frac{6 + 7 + 8 + 10 + x}{5}$$

$$x = 4$$

The complete set of five observations is $$\{4, 6, 7, 8, 10\}$$

$$\sigma^2 = \frac{\sum (x_i - \bar{x})^2}{n}$$

$$\sum (x_i - \bar{x})^2 = 9 + 1 + 0 + 1 + 9 = 20$$

$$\sigma^2 = \frac{20}{5} = 4$$

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