The following table shows the marks scored by 140 students in an examination of a certain paper:

Marks:	0-10	10-20	20-30	30-40	40-50
Number of students:	20	24	40	36	20

Calculate the average marks by using all the three methods: direct method, assumed mean deviation and shortcut method.

Given:

The marks scored by 140 students in an examination of a certain paper

To do:

We have to calculate the average marks by using all the three methods: direct method, assumed mean deviation and shortcut method.

Solution:

Let the assumed mean be $A=25$.

Using direct method, we get,

 We know that,

Mean $=\frac{\sum{f_ix_i}}{\sum{f_i}}$    

Therefore,  

Mean $=\frac{3620}{140})$

$=25.857$

Using shortcut method, we get,

Mean $=A+\frac{\sum{f_id_i}}{\sum{f_i}}$    

Therefore,  

Mean $=25+\frac{120}{140}$

$=25+\frac{6}{7}$

$=25+0.857$

$=25.857$

Using assumed mean deviation method, we get,

Mean $=A+h \times \frac{\sum{f_iu_i}}{\sum{f_i}}$    

Therefore,  

Mean $=25+10 \times \frac{12}{140}$

$=25+\frac{120}{140}$

$=25+0.857$

$=25.857$

The average marks is $25.857$.