Question

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

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

Answer 1

The given series is an inclusive series. Firstly, make it an exclusive series.

Class Interval	Mid-Value(xi)	Frequency(fi)	$$\begin{gathered} d_i=x_i-A \\ =x_i-57 \end{gathered}$$	$u_i=\frac{d_i}{h}=\frac{d_i}{3}$	$f_i{u}_i$
49.5$-$52.5	51	15	−6	−2	−30
52.5$-$55.5	54	110	−3	−1	−110
55.5$-$58.5	57	135	0	0	0
58.5$-$61.5	60	115	3	1	115
61.5$-$64.5	63	25	6	2	50
		$\sum _{}^{}{f}_i=400$			$\sum _{}^{}{f}_i{u}_i=25$

Let the assumed mean be A = 57 and h = 3.

We know that mean,

Now, we have.

Putting the values in the above formula, we have

Hence, the mean is approximately 57.19.