Question

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.

Answer 1

We may prepare the table as shown:

(i) Direct method
We know that mean,
$$\begin{gathered} =\frac{3620}{140} \\ =25.857 \end{gathered}$$

Hence, the mean is 25.857.

(ii) Short-cut method

Let the assumed mean A = 25.

We know that mean,

Hence, the mean is 25.857.

(iii) Step deviation method

Let the assumed mean A = 25 and h = 10.

We know that mean,

Hence, the mean is 25.857.