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:

• A. 60
• B. 55
• C. 50
• D. 45

Answer 1

Answer: (A)

60

Answer 2

The correct answer is (A) : 60
$∵ \overline{x}=6=\frac{(a+b+8+5+10)}{5}⇒a+b=7…(i)$
And
$σ^2=\frac{(a^2+b^2+8^2+5^2+10^2)}{5}−6^2=6.8$
⇒ a2 + b2 = 25 …(ii)
From (i) and (ii) (a, b) = (3, 4) or (4, 3)
Now mean deviation about mean
$M=\frac{1}{5}(3+2+2+1+4)=\frac{12}{5}$
⇒ 25M = 60.