Question

99. If the mean of 20 prices is $10.39,and 5 of the items with a mean of $10.99 are sampled, what is the mean of the other 15 prices?

Answer 1

Here

Grand mean $\bar{x} = 10.39$

Total sample size $n = 20$

and

5 of the items with a mean of $10.99 that implies $\bar{x_1} = 10.99,n_1 = 5$

According to the formula,

$\frac{n_1\bar{x_1}+n_2\bar{x_2}}{n_1+n_2} = \bar{x}$

$\Rightarrow \frac{(5*10.99)+(15*\bar{x_2})}{20} = 10.39$

$\Rightarrow (5*10.99)+(15*\bar{x_2})= 10.39*20$

$\Rightarrow (15*\bar{x_2})= (10.39*20) - (5*10.99)}$

$\Rightarrow \bar{x_2}= \frac{(10.39*20) - (5*10.99)}{15}$

$\Rightarrow \bar{x_2}= 10.19$

ans-> The mean of the other 15 prices is $10.19