Marks obtained by 140 students of class X out of 50 in mathematics are given in the following distribution. Find the mean by method of assumed mean method:

We have grouped frequency distribution and we need to find mean by assumed-mean method.

Assumed-mean method is given such name because in this method, we actually assume a mean from x_I (usually a centre value) and the formula of mean is also based on that particular assumed mean.

By using assumed-mean method, we can avoid the risk of miscalculation. Also, by using assumed mean method, we’ll be able to solve the question with ease and more accuracy.

So, let us assume mean from the midpoints. Let assumed mean, A = 25 (a value quite centrally placed).

So now, we have

∑f_id_i = 120 and ∑f_i = 140.

And we have assumed mean as, A = 25

Mean is given by

⇒

⇒ Mean = 25 + 0.86

⇒ Mean = 25.86

Thus, mean is 25.86.