Question

Find the mean age from the following frequency distribution:
$\begin{array}{cccccccc}\text{Age (in years)}& 25-29& 30-34& 35-39& 40-44& 45-49& 50-54& 55-59\\ \text{Number of persons}& 4& 14& 22& 16& 6& 5& 3\end{array}$

Answer 1

Solution:

Converting the series into exclusive form, we get:

Class	Frequency (fi)	Mid values (xi)	ui = (xi−A) /h=(xi−42) /5	fiui
24.5 - 29.5	4	27	-3	-12
29.5 - 34.5	14	32	-2	-28
34.5 - 39.5	22	37	-1	-22
39.5 - 44.5	16	42 = A	0	0
44.5 - 49.5	6	47	1	6
49.5 - 54.5	5	52	2	10
54.5 - 59.5	3	57	3	9
Total	∑fi=70			∑(fi×ui)=−37

Now, A = 42, h = 5,
∑fi=70 and ∑(fi×ui)=−37

Therefore,
Mean, $\overline{x}$=A+{h×∑(fiui)/∑fi}

= 42 + {5×(−37)/70}

= 42- 2.64

= 39.36

Therefore, $\overline{x}$ = 39.36.

Therefore, Mean age = 39.36 years.