# The mean of the numbers a, b, 8, 5, 10 is 6 and the variance is 6.80. Then, find the values of a and b?

## Solution :

According to given condition,

6.80 = $$(6-a)^2 + (6-b)^2 + (6-8)^2 + (6-5)^2 + (6-10)^2\over 5$$

$$\implies$$  34 = $$(6-a)^2 + (6-b)^2$$ + 4 + 1 + 16

$$\implies$$  $$(6-a)^2 + (6-b)^2$$ = 13

$$\implies$$  $$(6-a)^2 + (6-b)^2$$ = 13 = $$3^2$$ + $$2^2$$

$$\implies$$  a = 3 and b = 4

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