Answer: [tex]17.67[/tex]
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 [tex]\bar{x_1},n_1[/tex] be the mean and no of measurements
and [tex]\bar{x_2},n_2[/tex] be the mean and no of measurements in second case
[tex]\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)[/tex]
Similarly,
[tex]\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)[/tex]
Mean of 27 measurements
[tex]\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[/tex]
