Let us find the mean of the following data by assumed mean method.

We need to find the mean by assumed mean method.

For assumed-mean method, we assume a mean from the midpoints and calculate deviation from that assumed mean.

We can create a table showing frequencies, midpoints and deviations.

So, we have

∑f_ix_i = 2060

∑f_i = 40

Observe that, we have taken assumed mean as 50. Assumed mean is a mid-value usually from the x_i’s.

Here, d_i is the deviation from the mean.

Using x_i’s and A, we have found d_i and further have found out f_id_i.

We have the following formula to calculate arithmetic mean using assumed-mean method,

Substituting all the values from the table into the formula, we get

⇒

⇒

⇒ Mean = 101.5

Thus, the mean of the data is 101.5.