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.
We will find the mean weight using step - deviation method, where A = Assumed mean and h = length of class interval.
Here, let A = 92 and h = 5
Since, the class intervals are inclusive type, we’ll first convert it into exclusive type by extending the class interval from both the ends.
WEIGHT(G) | MID - POINT(xi) | DEVIATION(di) di = xi – 92 | NUMBER OF EGGS(fi) | ui = di/h | fiui |
74.5 - 79.5 | 77 | - 15 | 4 | - 3 | - 12 |
79.5 - 84.5 | 82 | - 10 | 9 | - 2 | - 18 |
84.5 - 89.5 | 87 | - 5 | 13 | - 1 | - 13 |
89.5 - 94.5 | 92 = A | 0 | 17 | 0 | 0 |
94.5 - 99.5 | 97 | 5 | 12 | 1 | 12 |
99.5 - 104.5 | 102 | 10 | 3 | 2 | 6 |
104.5 - 109.5 | 107 | 15 | 2 | 3 | 6 |
TOTAL | 60 | - 19 |
We have got
A = 92, h = 5, Σfi = 60 & Σfiui = - 19
∵ mean is given by
⇒ 
⇒ 
Thus, mean weight is 90 g.