Question

The frequency distribution table is given here.

Class	30 - 40	40 - 50	50 - 60	60 - 70	70 - 80	80 - 90	90 - 100
Frequency	3	7	12	15	8	3	2

Find the mean

• A. $62$
• B. $64$
• C. $65$
• D. $63$

Answer 1

Answer: (A)

From the given data, we construct the following table:

Class	Frequency$f_i$	Mid point$(x_i)$	$f_i{x}_i$	$(x_i-\bar{x}{)}^2$	$f_i(x_i-\bar{x}{)}^2$
30 - 40	3	35	105	729	2187
40 - 50	7	45	315	289	2023
50 - 60	12	55	660	49	588
60 - 70	15	65	975	9	135
70 - 80	8	75	600	169	1352
80 - 90	3	85	255	529	1587
90 - 100	2	95	190	1089	2178
Total	50		3100		10050

Thus Mean $\bar{x}=\frac{1}{N}\sum _{i=1}^7{f}_i{x}_i$
$=\frac{3100}{50}=62$,