Compute the mean by short cut method of the following frequency distribution
Marks obtained $10 - 20$ $20 - 30$ $30 - 40$ $40 - 50$ $50 - 60$ $60 - 70$
Number of Students $6$ $8$ $13$ $7$ $4$ $2$

Open in App

Solution

Marks obtained No. of
Students
$f$ Mid-value
$x$ $u = \frac{x - a}{10}$
$f u$
$10 - 20$ $6$ $15$ $- 2$ $- 12$
$20 - 30$ $8$ $25$ $- 1$ $- 8$
$30 - 40$ $13$ $35$ $0$ $0$
$40 - 50$ $7$ $45$ $1$ $7$
$50 - 60$ $4$ $55$ $2$ $8$
$60 - 70$ $2$ $65$ $3$ $6$
$\sum f = 40$
$\sum f u = 1$

$a = 35, h = 10$

$¯ ¯ ¯ x = a + \frac{\sum f u}{\sum f} \times h$

$= 35 + \frac{1}{40} \times 10$

$= 35 + \frac{1}{4} = 35 + 0.25 = 35.25$

Arithmetic Mean $= 35.25$

Suggest Corrections

Similar questions

Marks	$10 - 20$	$20 - 30$	$30 - 40$	$40 - 50$	$50 - 60$	$60 - 70$	$70 - 80$
Frequency	$3$	$7$	$10$	$6$	$8$	$2$	$4$

80, 10, 30, 70, 60, 50, 50, 40, 40, 20, 40, 90, 50, 30, 70, 10, 60, 50, 20, 70, 70, 30, 80, 40, 20, 80, 90,

50, 80, 60, 70, 40, 50, 60, 90, 60, 40, 40, 60

60

80, 10, 30, 70, 60, 50, 50, 40, 40, 20, 40, 90, 50, 30, 70, 10, 60, 50, 20, 70, 70, 30, 80, 40, 20, 80,

90, 50, 80, 60, 70, 40, 50, 60, 90, 60, 40, 40, 60

60

40

Marks	10-20	20-30	30-40	40-50	50-60
Frequency	4	10	20	40	50

124

Join BYJU'S Learning Program