Calculate the mean of the distribution given below using the shortcut method.
marks 11-20 21-30 31-40 41-50 51-60 61-70 71-80
number of students 2 6 10 12 9 7 4

Open in App

Solution

$M a r k s$ $C l a s s - M a r k$
$x_{i}$ $N o . o f s t u d e n t s$
$f_{i}$ $f_{i} x_{i}$
$10.5 - 20.5$ $15.5$ $2$ $31$
$20.5 - 30.5$ $25.5$ $6$ $153$
$30.5 - 40.5$ $35.5$ $10$ $355$
$40.5 - 50.5$ $45.5$ $12$ $546$
$50.5 - 60.5$ $55.5$ $9$ $499.5$
$60.5 - 70.5$ $65.5$ $7$ $458.5$
$70.5 - 80.5$ $75.5$ $4$ $302$
$\sum f_{i} = 50$ $\sum f_{i} x_{i} = 2345$
$\Rightarrow$ $M e a n (¯ ¯ ¯ x) = \frac{\sum f_{i} x_{i}}{\sum f_{i}} = \frac{2345}{50} = 46.9$

Suggest Corrections

Marks	1 - 10	11 - 20	21 - 30	31 - 40	41 - 50	51 - 60	61 - 70	71 - 80
Frequency	3	8	12	14	10	6	5	2

Area in hectare	11 - 20	21 - 30	31 - 40	41 - 50	51 - 60	61 - 70	71 - 80
No. of farmers	58	103	208	392	112	34	12

Class-interval:	31-35	36-40	41-45	46-50	51-55	56-60	61-65	66-70
Frequency:	2	3	8	12	16	5	2	3

Weight (in mg)	11 - 20	21 - 30	31 - 40	41 - 50	51 - 60
No. of seeds	18	22	30	16	4

marks	11-20	21-30	31-40	41-50	51-60	61-70	71-80
number of students	2	6	10	12	9	7	4