In a retail market, fruit vendors were selling mangoes kept in packing boxes. These boxes contained varying number of mangoes. The following was the distribution of mangoes according to the number of boxes.

Number of mangoes	Number of boxes
50 - 52	15
53 - 55	110
56 - 58	135
59 - 61	115
62 - 64	25

Find the mean number of mangoes kept in a packing box. Which method of finding the mean did you choose ?

Here the given data is discontinuous.

Adjustment factor = (Lower limit of one class - Upper limit of previous class) / 2

= $\dfrac{53 - 52}{2} = \dfrac{1}{2}$ = 0.5

∴ 0.5 has to be added to the upper-class limit and 0.5 has to be subtracted from the lower-class limit of each interval.

We will use step deviation method to find the mean.

In the following table a is the assumed mean and h is the class size.

Here, h = 3.

By formula,

Class mark = $\dfrac{\text{Upper limit + Lower limit}}{2}$

By formula,

Mean = a + $\dfrac{Σf$iui}{Σf_i} \times h

Substituting values we get :

$\text{Mean } = 57 + \dfrac{25}{400} \times 3 \\[1em] = 57 + \dfrac{3}{16} \\[1em] = 57 + 0.19 \\[1em] = 57.19$

Hence, mean number of mangoes = 57.19