Question

The mean and the variance of five observation are 4 and $5.20$, respectively. If three of the observations are $3, 4$ and 4; then then absolute value of the difference of the other two observations, is :

• A. 1
• B. 3
• C. 7
• D. 5

Answer 1

Answer: (C)

$mean \, \bar{x} \, = \, 4 , \sigma^2 \, =5.2 , n=5,. x_1 = 3,\, x_2 \, = \, 4 \, = \, x_3 $
$\sum x_i \, = \, 20$
$x_4 \, + \, x_5 \, = \, 9 \, \, \, \, \, \, \, \, \, $.....(i)
$\frac{\sum x_i^2}{x} - (\bar{x})^2 \, \sigma^2 \, \, \Rightarrow \, \sum x_i^2 \, = 106$
$x_4^2 + x_5^2 \, = 65$......(ii)
Using (i) and (ii) (x$_4 - x_5)^2 = 49$
$ \, \, \, \, \, \, \, \, \, \, \, \, | x_4 - x_5| = 7$