Question

Find the mean of each of the following frequency distributions :

Classes:	25−29	30−34	35−39	40−44	45−49	50−54	55−59
Frequency:	14	22	16	6	5	3	4

Answer 1

The given series is an inclusive series. Firstly, make it an exclusive series.

Class Interval	Mid-Value(xi)	Frequency(fi)	$$\begin{gathered} d_{\mathit{i}}=x_i-A \\ =x_i-42 \end{gathered}$$	$u_i=\frac{d_i}{h}=\frac{d_i}{5}$	$f_i{u}_i$
24.5$-$29.5	27	14	−15	−3	−42
29.5$-$34.5	32	22	−10	−2	−44
34.5$-$39.5	37	16	−5	−1	−16
39.5$-$44.5	A = 42	6	0	0	0
44.5$-$49.5	47	5	5	1	5
49.5$-$54.5	52	3	10	2	6
54.5$-$59.5	57	4	15	3	12
		$\sum _{}^{}{f}_i=70$			$\sum _{}^{}{f}_i{u}_i=-79$

Let the assumed mean be A = 42 and h = 5.

We know that mean,

Now, we have.

Putting the values in the above formula, we have

Hence, the mean is 36.357.