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	60-80	14
30-40	4	80-90	10
40-50	5	90-100	4
50-60	6

Mean, Median and Mode of the above data are respectively

• A. $64.33,68.33,76.33$
• B. $60,70,80$
• C. $66.11,71.11,79.11$
• D. none of these

Answer 1

The correct option is A $64.33,68.33,76.33$

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

Class $x_i$ $f_i$ c.f. $u_i=\frac{X_i-a}{10}$ $f_i{u}_i$

$\therefore$ The 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, $M=l+\frac{\frac{n}{2}-C}{f}\times c$

$=60+\frac{30-20}{12}\times 10$

$=60+\frac{100}{2}=60+8.333=68.333$

Using Empirical formula, we have,

$Mode=3Median-2Mean\Rightarrow$$3\left(68.333\right)-2\left(64.333\right)=204.999-128.666=76.333$