Question

The mean of 5 observations is 15 and the

variance is 9. If two more observations

having values – 3 and 10 are combined

with these 5 observations, what will be the

variance of the

7 observations ?

Answer 1

for 5 observations:

$\sum x_i=\mu n=15\cdot5=75$

for 7 observations:

$\sum x_i=75-3+10=82$

then, the new mean is

$\mu_1=82/7$

variance for 5 observations:

$\sigma^2=\sum x_i^2/5-\mu^2=\sum x_i^2/5-15^2=9$

then

$\sum x_i^2=5\cdot(9+15^2)=1170$

for 7 observations:

$\sum x_i^2=1170+3^2+10^2=1279$

new variance:

$\sigma_1^2=1279/7-\mu_1^2=1279/7-82^2/7^2=45.49$