The mean and the variance of five observations are 4 and 5.20, respectively.

Question

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

Accepted Answer

mean $$\overline x $$ = 4, $$\sigma $$2 = 5.2, n = 5, . x1 = 3 x2 = 4 = x3

$$\sum {{x_i}}  = 20$$

x4 + x5 = 9 . . . . . . (i)

$${{\sum {x_i^2} } \over x} - {\left( {\overline x } \right)^2} = \sigma  \Rightarrow \sum {x_i^2}  = 106$$

$x_4^2 + x_5^2 = 65$ . . . . . .(ii)

Using (i) and (ii) (x4 - x5)2 = 49

$$\left| {{x_4} - {x_5}} \right| = 7$$

Solutions · 1