The mean of the numbers a, b, 8, 5, 10 is 6 and their variance is 6.8.

Question

The mean of the numbers a, b, 8, 5, 10 is 6 and their variance is 6.8. If M is the mean deviation of the numbers about the mean, then 25 M is equal to :

Accepted Answer

$$\because$$ $$\overline x  = 6 = {{a + b + 8 + 5 + 10} \over 5} \Rightarrow a + b = 7$$ ...... (i)

And $${\sigma ^2} = {{{a^2} + {b^2} + {8^2} + {5^2} + {{10}^2}} \over 5} - {6^2} = 6.8$$

$$ \Rightarrow {a^2} + {b^2} = 25$$ ..... (ii)

From (i) and (ii) (a, b) = (3, 4) or (4, 3)

Now mean deviation about mean

$$M = {1 \over 5}(3 + 2 + 2 + 1 + 4) = {{12} \over 5}$$

$$ \Rightarrow 25M = 60$$

Solutions · 1