Question

the mean of 4 observations is 5 and the mean of 6 observation is 3 then find the mean of total 10 observations​

Answer 1

$\textbf{Given:}$

$\textsf{Mean of 4 observations is 5}$

$\textsf{Mean of 6 observations is 3}$

$\textbf{To find:}$

$\textsf{Mean of total 10 obserrvations}$

$\textbf{Solution:}$

$\underline{\textsf{Formula used:}}$

$\mathsf{Combined\;average=\dfrac{n_1\,x_1+n_2\,x_2}{n_1+n_2}}$

$\mathsf{Here,\;n_1=4,\;n_2=6,\;x_1=5\;and\;x_2=3}$

$\mathsf{Using\;Combined\;average\;formula}$

$\mathsf{Combined\;average=\dfrac{4(5)+6(3)}{4+6}}$

$\mathsf{Combined\;average=\dfrac{20+18}{10}}$

$\mathsf{Combined\;average=\dfrac{38}{10}}$

$\implies\boxed{\mathsf{Combined\;average=3.8}}$

$\textbf{Find more:}$

The average salary of 150 workers is Rs. 75 per week . Out of these 150 workers 60 are female with average salary equal to Rs. 70 per week .Find out Average salary of male workers.

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Answer 2

SOLUTION

GIVEN

The mean of 4 observations is 5 and the mean of 6 observation is 3

TO DETERMINE

The mean of total 10 observations

EVALUATION

Here it is given that the mean of 4 observations is 5

So sum of 4 observations

= 4 × 5

= 20

Again it is also given that the mean of 6 observation is 3

So sum of 6 observations

= 6 × 3

= 18

So total number of observations

= 4 + 6

= 10

Sum of the observations

= 20 + 18

= 38

Hence the mean of total 10 observations

$\displaystyle \sf{ = \frac{Sum \: of \: the \: observations }{Total \: number \: of \: observations } }$

$\displaystyle \sf{ = \frac{38}{10} }$

$\sf{= 3.8}$

FINAL ANSWER

The mean of total 10 observations = 3.8

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