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

Question :

Number of Mangoes	50 – 52	53 – 55	56 – 58	59 – 61	62 – 64
Number of Boxes	15	110	135	115	25

Solution :

Here, the class intervals are formed by the exclusive method. If we make the data an inclusive one, the mid-values remain same. So there is no need to convert the data with the cation that while finding h, we should count both the limits of class interval. For example, for (53 – 55), both 53 and 55 should be counted and thus h = 3 and not (55 – 53) = 2.

Let A = 60

So, \(u_i\) = \(x_i – A\over h\) = \(x_i – 60\over 3\)

Calculation of Mean

Number of Mangoes	Mid – Values (\(x_i\))	Frequency (\(f_i\))	\(u_i\) = \(x_i – 60\over 3\)	\(f_iu_i\)
50 – 52	51	15	-3	-45
53 – 55	54	110	-2	-220
56 – 58	57	135	-1	-135
59 – 61	60	115	0	0
62 – 64	63	25	1	25
Total		\(\sum f_i\) = 400		\(\sum f_iu_i\) = -375

So, Mean = A + h\(\sum f_iu_i\over \sum f_i\) = 60 + 3 \(\times\) \(-375\over 400\)

= 60 – 2.81 = 57.19

Hence, mean number of mangoes per box is 57.19