Question

Question 4
The weights of tea in 70 packets are shown in the following table
$\begin{array}{cc}\text{Weight(in~g) \& Number of packets}& \\ 200-201& 13\\ 201-202& 27\\ 202-203& 18\\ 203-204& 10\\ 204-205& 1\\ 205-206& 1\end{array}$
Find the mean weight of packets.

Answer 1

First, we find the class marks of the given data as follows.
$\begin{array}{ccccc}\text{weight(in~ g) \& Number of packets}\left(f_i\right)& \text{Class marks}\left(x_i\right)& \text{deviation}(d_i=x_i-a)& f_i{d}_i& \\ 200-201& 13& 200.5& -3& -39\\ 201-202& 27& 201.5& -2& -54\\ 202-203& 18& 202.5& -1& -18\\ 203-204& 10& a=203.5& 0& 0\\ 204-205& 1& 204.5& 1& 1\\ 205-206& 1& 205.5& 2& 2\\ & N=\sum f_i=70& & & \sum f_i{d}_i=-108\end{array}$
Here, (assumed mean) a=203.5
and (class width) h=1
By assumed mean method,
Mean $\left(\overline{x}\right)=a+\frac{\sum f_i{d}_i}{\sum f_i}=203.5-\frac{108}{70}=203.5-1.54=201.96$
Hence, the required mean weight is 201.96 g.