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

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

It can be observed that class intervals are not continuous. There is a gap of 1 between two class intervals. Therefore, has to be added to the upper class limit and has to be subtracted from the lower class limit of each interval.

Class mark (x_i) can be obtained by using the following relation.

Class size (h) of this data = 3

Taking 57 as assumed mean (a), d_i, u_i, f_iu_i are calculated as follows.

Class interval	fi	xi	di = xi − 57		fiui
49.5 − 52.5	15	51	− 6	− 2	− 30
52.5 − 55.5	110	54	− 3	− 1	− 110
55.5 − 58.5	135	57	0	0	0
58.5 − 61.5	115	60	3	1	115
61.5 − 64.5	25	63	6	2	50
Total	400				25

It can be observed that

Mean number of mangoes kept in a packing box is 57.19.

Step deviation method is used here as the values of f_i, d_i are big and also, there is a common multiple between all d_i.