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 mangoe	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
50 − 52	15
53 − 55	110
56 − 58	135
59 − 61	115
62 − 64	25

Let the assumes mean a = 57

∴ d_i = x_i - 57

Now, we have the following table: 

Number of mangoes	fi	xi	di = xi − 57	fiui
50 - 52	15	51	− 6	− 6
53 − 55	110	54	− 3	− 330
56 − 58	135	57	0	0
59 − 61	115	60	3	345
62 − 64	23	63	6	150
Total	400			75

It can be observed that

`sumf_i = 400`

`sumf_iu_i = 75`

∴ `barx = a + 1/N sumf_id_iu_i`

= `57 + 75/400`

= 57 + 0.1875 

= 57.1875 ≈ 57.19

Thus, the average number of mangoes per box = 57.19, we choose the assumed mean method.