Question

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 1

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