In a retail market, a fruit vendor was selling apples kept in packed boxes. These boxes contained varying number of apples. The following was the distribution of apples according to the number of boxes. Find the mean by the assumed mean number of apples kept in the box.

Number of apples	50-53	53-56	56-59	59-62	62-65
Number of boxes	20	150	115	95	20

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 = 57.5 (a value quite centrally placed).

So now, we have

∑f_id_i = -165 and ∑f_i = 400.

And we have assumed mean as, A = 57.5

Mean is given by

⇒

⇒ Mean = 57.5 – 0.4125

⇒ Mean = 57.0875

Thus, mean number of apples in a box is 57.0875.