Question

​The weights of tea in 70 packets are shown in the following table:

Weight (in grams)	200−201	201−202	202−203	203−204	204−205	205−206
Number of packets	13	27	18	10	1	1

Find the mean weight of packets using step-deviation method. [CBSE 2013]

Answer 1

​Let us choose a = 202.5, h = 1, then d_i = x_i − 202.5 and u_{i =} $\frac{x_i-202.5}{1}$.

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

Weight (in grams)	Number of packets (fi)	Class mark (xi)	di = xi − 202.5	ui = $\frac{{\mathit{x}}_{\mathit{i}}\mathbf{-}\mathbf{202}\mathbf{.}\mathbf{5}}{\mathbf{1}}$	fiui
200−201	13	200.5	−2	−2	−26
201−202	27	201.5	−1	−1	−27
202−203	18	202.5	0	0	0
203−204	10	203.5	1	1	10
204−205	1	204.5	2	2	2
205−206	1	205.5	3	3	3
Total	∑ fi = 70				∑ fiui = −38

The mean of given data is given by

$$\begin{gathered} \overline{x}=a+\left(\frac{{\displaystyle \sum _i}{f}_i{u}_i}{{\displaystyle \sum _i{f}_i}}\right)\times h \\ =202.5+\left(\frac{-38}{70}\right)\times 1 \\ =202.5-0.542 \\ =201.96 \end{gathered}$$

​Hence, the mean is 201.96 g.