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A distribution consists of three components with frequencies 45 ,40 and 15 having their means 2,2.5 and 2 respectively . find combined mean

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Solution: A distribution consists of three components with frequencies 45 ,40 and 15 having their means 2,2.5 and 2 respectively . find combined mean

Answer: Let
\bar{x_(1)} be the mean of first component and
n_(1) be the frequency of first component

Let
\bar{x_(2)} be the mean of second component and
n_(2) be the frequency of second component

Let
\bar{x_(3)} be the mean of third component and
n_(3) be the frequency of third component

Then we have:


\bar{x_(1)} = 2, n_(1) = 45


\bar{x_(2)} = 2.5, n_(2) = 40


\bar{x_(3)} = 2, n_(3) = 15

Now the combined mean is:

Combined mean
=\frac{\bar{x_(1)} * n_(1)+\bar{x_(2)} * n_(2)+\bar{x_(3)} * n_(3)}{n_(1) +n_(2) +n_(3)}


=(2 * 45 +2.5 * 40 +2 * 15)/(45+40+15)


=(90 + 100 + 30)/(100)


=(220)/(100)=2.2

Therefore, the combined mean is 2.2

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