In a retail market, fruit vendor were-selling mangoes kept in packing boxes. Number of mangoes: 50 - 52, 53 - 55, 56 - 58, 59 - 61, 62 - 64

Question

In a retail market, fruit vendor 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

We may observe that the class intervals are not continuous. There is a gap between two class intervals so we have to add \(\frac{1}{2}\) from lower class limit of each interval.

Class size (h) of this data = 3

Now taking 57 as assumed mean, 

we can calculate as follows:

Class interval	fi	xi	di = xi - 57	ui = \(\frac{xi-57}{h}\)	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	6	1	115
61.5 - 64.5	25	63	3	2	50
	N = 400				\(\sum\)fiui = 25

Mean = A + \(\frac{\sum f_iu_i}{N}\times h\) 

\(=57+\frac{25}{400}\times3\)

\(57+\frac{3}{16}\)

\(=57+0.1875=57.1875\)

\(=57.16\) 

Number of mangoes kept in packing box is 57.19