Find the mean of the following frequency distribution by step-deviation method:

This is a grouped frequency distribution.

In step deviation, we need to mark the assumed mean in x_i as similar to in assumed-mean method but the formula differs. In step deviation, we calculate the deviation of each value from the assumed mean value. This brings more accuracy when values are large.

Here, class interval is given by

h = 10 (∵ 50 – 40 = 60 – 50 = … = 100 – 90 = 10)

And let us assume mean as A = 65, which is the closest value to the centre-most value.

We need to represent it in tabular form:

So now, we have

∑f_iu_i = 7 and ∑f_i = 52

And assumed mean, A = 65

Mean by step-deviation is given by

⇒

⇒

⇒ Mean = 65 + 1.346

⇒ Mean = 66.346

Thus, mean is 66.346.