If the mean of five observations


If the mean of five observations x, x + 2, x + 4, x + 6, x + 8 is 13, find the value of and hence find the mean of the last three observations.


We know that,

Mean $=\frac{\text { Sum of observa tions }}{\text { Number of observations }}$

The first five observations are x, x + 2, x + 4, x + 6 and x + 8.

Mean of these numbers $=\frac{x+(x+2)+(x+4)+(x+6)+(x+8)}{5}$

$\Rightarrow 13=\frac{5 x+20}{5}$

$\Rightarrow 13 \times 5=5 x+20$

$\Rightarrow 65=5 x+20$

$\Rightarrow 5 x=65-20$

$\Rightarrow 5 x=45$

$\Rightarrow x=\frac{45}{5}$

$\Rightarrow x=9$

Hence, the value of is 9.

Now, the last three observations are 13, 15 and 17.

Mean of these observations $=\frac{13+15+17}{3}$



Hence, the mean of the last three observations is 15.


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