Question

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.

Answer 1

Hint: We will first recreate the table using the data given above in the table with adding one more column or row of data with multiplication of both f and x. Then, we will use the formula for mean and thus get the answer.

Complete step-by-step solution:
Let us first of all recreate the table using the data given in the table above and adding one more column with the multiplication of both the data given to us already in the question.
So, then we will get the following table with us:-

No. of children (x)	No. of families (f)	(f.x)
0	10	0
1	21	21
2	55	110
3	42	126
4	15	60
5	7	35
TOTAL	150	352

Now, we know that we have a formula for mean which is given by:-
\[ \Rightarrow \bar x = \dfrac{{\sum {fx} }}{{\sum f }}\]
Now, since we calculated in the table that $\sum {f = 150} $ (Because 10 + 21 + 55 + 42 + 15 + 7 = 150) and $\sum {fx = 352} $ (Because 0 + 21 + 110 + 126 + 60 + 35 = 352). Therefore, let us put these values in the formula mentioned above. We will get the following expression:-
\[ \Rightarrow \bar x = \dfrac{{352}}{{150}}\]
Simplifying the RHS of the above expression, we will get:-
\[ \Rightarrow \bar x = 2.35\]
So, the average number of children per family is 2.35.

$\therefore $ The required mean is 2.35

Note: The students must know that mean refers to the average. Like if we take the example of the given question, if we pick out a random family, the average number of children the family will have is 2.35.
The students must note that we did not use any different method than regular in this question because we did not require it, that would have complicated the problem more than making it easy.