The following table gives the number of children of 150 families in a village
| No. of children ($x$): | 0 | 1 | 2 | 3 | 4 | 5 |
| No. of families ($f$): | 10 | 21 | 55 | 42 | 15 | 7 |
Find the average number of children per family.
Given:
The number of children of 150 families in a village.
To do:
We have to find the average number of children per family.
Solution:
Let the assumed mean be $A=3$
| Number of children ($x_i$) | Number of families ($f_i$) | $d_i = x_i -A$ $A =3$ | $f_i \times\ d_i$ |
| 0 | 10 | $-3$ | $-30$ |
| 1 | 21 | $-2$ | $-42$ |
| 2 | 55 | $-1$ | $-55$ |
| 3 - $A$ | 42 | 0 | 0 |
| 4 | 15 | 1 | 15 |
| 5 | 7 | 2 | 14 |
| Total | $\sum{f_i}=150$
| | $\sum{f_id_i}=-98$
|
We know that,
Mean $=A+\frac{\sum{f_id_i}}{\sum{f_i}}$
Therefore,
Mean $=3+\frac{-98}{150}$
$=3-0.65$
$=2.35$
The number of children per family is $2.35$.
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