Question

The marks obtained by 60 students in a certain test are given below :

Marks	No. of students	Marks	No. of students
10 - 20	2	60 - 70	12
20 - 30	3	70 - 80	14
30 - 40	4	80 - 90	10
40 - 50	5	90 - 100	4
50 - 60	6

Mean and Median of the above data are respectively

• A. 64.33, 68.33
• B. 60, 70
• C. 66.11, 71.11,
• D. none of these

Answer 1

Answer: (A)

We construct the following table taking assumed mean a = 55 (step deviation method).

Class	$x_i$	$f_i$	c.f.	$u_i-\frac{x_i-a}{10}$	$f_i{u}_i$
10 - 20	15	2	2	-4	-8
20 - 30	25	3	5	-3	-9
30 - 40	35	4	9	-2	-8
40 - 50	45	5	14	-1	-5
50 - 60	55	6	20	0	0
60 - 70	65	12	32	1	12
70 - 80	75	14	46	2	28
80 - 90	85	10	56	3	30
90 - 100	95	4	60	4	16
Total		60			56

$\therefore$ Mean = $a+\frac{\sum f_i{u}_i}{\sum f_i}\times c$
$=55+\frac{56}{60}\times 10=55+\frac{56}{6}=64.333$
Here $n=60\Rightarrow \frac{n}{2}=30$ , therefore, 60-70 is the median class
Using the formula :
$M=l+\frac{\frac{n}{2}-C}{f}\times c=60+\frac{30-20}{12}\times 10$
$=60+\frac{100}{12}=60+8.333=68.333$