Weights of 60 eggs were recorded as given below :
Weights (in gms) Number of eggs
75 – 79 4
80 – 84 9
85 – 89 13
90 – 94 17
95 – 99 12
100 – 104 3
105 – 109 2
Calculate their mean weight to the nearest gm.
Measures of Central Tendency
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Question

Weights of 60 eggs were recorded as given below :
Weights (in gms) Number of eggs
75 – 79 4
80 – 84 9
85 – 89 13
90 – 94 17
95 – 99 12
100 – 104 3
105 – 109 2
Calculate their mean weight to the nearest gm.

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KnowledgeBoat · Accepted Answer

Since, class are discontinuous we will first convert them into continuous class intervals.

Adjustment factor

= $\dfrac{\text{Lower limit of a class -Upper limit of previous class}}{2} = \dfrac{80 - 79}{2} = \dfrac{1}{2}$ = 0.5

Adding the adjustment factor to upper limit and subtracting from lower limit we get the continuous class intervals.

We construct the following table, taking assumed mean a = 92. Here, c (width of each class) = 5.

Weights (in gms)	Class interval	Number of eggs (f_i)	Class mark (y_i)	u_i = (y_i - a)/c	f_iu_i
75 – 79	74.5 - 79.5	4	77	-3	-12
80 – 84	79.5 - 84.5	9	82	-2	-18
85 – 89	84.5 - 89.5	13	87	-1	-13
90 – 94	89.5 - 94.5	17	a = 92	0	0
95 – 99	94.5 - 99.5	12	97	1	12
100 – 104	99.5 - 104.5	3	102	2	6
105 – 109	104.5 - 109.5	2	107	3	6
Total		∑ f_i= 60			∑ f_i u_i = -19

By formula,

$\text{Mean} = a + c \times \dfrac{\sum f$

Hence, mean weight of the eggs is 90 g.