Question

The mean of five observations is 4 and their variance is 5.2 . If three of them are 1, 2, 6, then other two are

• A. 2, 9
• B. 4, 7
• C. 5, 6
• D. 2, 10

Answer 1

Answer: (B)

4, 7

Number of observations $=5$
Mean $\overline{x}=4$ and $x=1,2,6,a,b$
$\therefore$ ${\sigma }^2=\frac{\sum {(x_i-\overline{x})}^2}{N}(N=5)$
$\therefore$ $\frac{\sum {(x_i-\overline{x})}^2}{5}=5.2$ or $\sum {(x_i-\overline{x})}^2=26$ (i)
$\therefore$ ${(1-4)}^2+{(2-4)}^2+{(6-4)}^2+{(a-4)}^2+{(b-4)}^2=26$
${(a-4)}^2+{(b-4)}^2=9$ (*)
(Here a, b are unknown quantities)
By cross check we find only the number 4 and 7 satisfies the equation (*)