The mean of five observations is 5 and their variance is 9.20.

Question

The mean of five observations is 5 and their variance is 9.20. If three of the given five observations are 1, 3 and 8, then a ratio of other two observations is -

Accepted Answer

Let two observations are x1  \& x2

mean = $${{\sum {{x_i}} } \over 5} = 5 $$

$$\Rightarrow 1 + 3 + 8 + {x_1} + {x_2} = 25$$

$$ \Rightarrow {x_1} + {x_2} = 13$$      . . . . (1)

variance $$\left( {{\sigma ^2}} \right)$$ = $${{\sum {x_i^2} } \over 5} - 25 = 9.20$$

$$ \Rightarrow $$  $${\sum {x_i^2 = 171} }$$

$$ \Rightarrow $$  $x_1^2 + x_2^2 = 97$      . . . . . (2)

$$ \Rightarrow (x1 + x2)2 - 2x1x2 = 97

\[ \Rightarrow $$ 169 - 2x1x2 = 97

or   x1x2 = 36

$$ \therefore $$  x1 : x2 = 4 : 9

Solutions · 1