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`

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}=(\sum a_1)/(n_1)\\\\\Rightarrow \sum a_1=\bar{x_1}* n_1\\\\\Rightarrow \sum a_1=198\quad \ldots(1)`

Similarly,

`\therefore \bar{x_2}=(\sum a_2)/(n_2)\\\\\Rightarrow \sum a_2=\bar{x_2}* n_2\\\\\Rightarrow \sum a_2=279\quad \ldots(2)`

Mean of 27 measurements

`\Rightarrow \bar{x_3}=(\sum a_1+\sum a_2)/(n_1+n_2)\\\\\Rightarrow \bar{x_3}=(198+279)/(12+15)\\\\\Rightarrow \bar{x_3}=(477)/(27)\\\\\Rightarrow \bar{x_3}=17.67`