Question

A sample of 12 measurements has a mean of 16.5, and a sample of 15 measurements has a mean of 18.6. Find the mean of all 27 measurements

Answer 1

Answer: $17.67$

Step-by-step explanation:

Given

Sample  of 12 measurements has a mean of 16.5 and

a sample of 15 measurements has a mean of 18.6

Take $\bar{x_1},n_1$ be the mean and no of measurements

and $\bar{x_2},n_2$ be the mean and no of measurements in second case

$\therefore \bar{x_1}=\dfrac{\sum a_1}{n_1}\\\\\Rightarrow \sum a_1=\bar{x_1}\times n_1\\\\\Rightarrow \sum a_1=198\quad \ldots(1)$

Similarly,

$\therefore \bar{x_2}=\dfrac{\sum a_2}{n_2}\\\\\Rightarrow \sum a_2=\bar{x_2}\times n_2\\\\\Rightarrow \sum a_2=279\quad \ldots(2)$

Mean of 27 measurements

$\Rightarrow \bar{x_3}=\dfrac{\sum a_1+\sum a_2}{n_1+n_2}\\\\\Rightarrow \bar{x_3}=\dfrac{198+279}{12+15}\\\\\Rightarrow \bar{x_3}=\dfrac{477}{27}\\\\\Rightarrow \bar{x_3}=17.67$