Question

Weight of 60 eggs were recorded as given below:

Weight (in grams)	75 – 79	80 – 84	85 – 89	90 – 94	95 – 99	100 - 104	105 - 109
No. of eggs	4	9	13	17	12	3	2

Calculate their mean weight to the nearest gram.

Answer 1

Let us choose a = 92, h = 5, then` d_i = x_i – 92 and u_i = (x_i− 92)/5`
Using step-deviation method, the given data is shown as follows:

Weight (in grams)	Number of eggs `(f_i)`	Class mark `(x_i)`	`d_i = x_i` – 92	`u_i =( x_i−92)/ 5`	`(f_i u_i)`
74.5 – 79.5	4	77	-15	-3	-12
79.5 – 84.5	9	82	-10	-2	-18
84.5 – 89.5	13	87	-5	-1	-13
89.5 – 94.5	17	92	0	0	0
94.5 – 99.5	12	97	5	1	12
99.5 – 104.5	3	102	10	2	6
104.5 – 109.5	2	107	15	3	6
Total	`Ʃ f_i` = 60				`Ʃ f_i u_i` = -19

The mean of the given data is given by,

x = a + `((Ʃ_i f_i u_i)/(Ʃ _i f_i)) xxh`

  =`92+((-19)/(60))xx5`

  = 92 – 1.58
 =90.42
 ≈ 90
Thus, the mean weight to the nearest gram is 90 g.