The table below gives the percentage of girls in higher secondary science stream of rural areas of various states of India. Find the mean percentage of girls by step-deviation method:

This is a grouped frequency distribution.

In step deviation, we need to mark the assumed mean in x_i. Step deviation also calculates deviation of each x_i values from the assumed mean using a formula.

The assumed mean is the value from x_i closest to the central value.

So, assumed mean is

A = 50

Here, class interval is given by

h = 10 (∵ 25 – 15 = 35 – 25 = … = 85 – 75 = 10)

We need to represent it in tabular form:

So now, we have

∑f_iu_i = -29 and ∑f_i = 35.

Also, assumed mean, A = 50 and class interval, h = 10.

Mean by step-deviation is given by

⇒ [using the values from the table]

⇒

⇒ Mean = 50 – 8.29

⇒ Mean = 41.71

Thus, mean is 41.71.