Question

28. 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
Number of eggs
4
9
13
17
12
3
2.
Calculate their mean weight to the nearest gram.​

Answer 1

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Answer 2

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Step-by-step explanation:

Let us choose a = 92, h = 5, then di = xi − 92 and ui = xi−925.

Using Step-deviation method, the given data is shown as follows:

Weight

(in grams) Number of eggs (fi) Class mark (xi) di = xi − 92 ui = xi−925 fiui

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 ∑ fi = 60 ∑ fiui = −19

The mean of given data is given by

x¯=a+⎛⎝∑ifiui∑ifi⎞⎠×h =92+(−1960)×5 =92−1.58 =90.42 ≈90 grams.