A survey conducted by a student of B.B.A. for daily income of 600 families is as follows, find the mean income of a family:

This is a grouped frequency distribution.

We can find the mean of this type of distribution by either direct method, assumed-mean method or step deviation method.

But let us try doing it by assumed-mean method since it assures accuracy of the answer when data given is large.

Also, notice given data is inclusive-type of data. We need to convert the inclusive type of data into exclusive type by subtracting 0.5 from lower limit of each class and adding 0.5 to upper limit of each class.

Let us assume mean by taking a value from x_i’s closest from the central value.

Let assumed mean, A = 549.5

So, we have

So now, we have

∑f_id_i = 18500 and ∑f_i = 600

Mean is given by

⇒

⇒ Mean = 549.5 + 30.83

⇒ Mean = 580.33

Thus, mean is 580.33.