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
Number 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 =} $\frac{x_i-92}{5}$.

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 = $\frac{{\mathbf{x}}_{\mathbf{i}}\mathbf{-}\mathbf{92}}{\mathbf{5}}$	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

$$\begin{gathered} \overline{x}=a+\left(\frac{{\displaystyle \sum _i}{f}_i{u}_i}{{\displaystyle \sum _i}{f}_i}\right)\times h \\ =92+\left(\frac{-19}{60}\right)\times 5 \\ =92-1.58 \\ =90.42 \\ \approx 90 \end{gathered}$$​

​Thus, the mean weight to the nearest gram is 90 g.