Question

A survey was conducted by a group of students as a part of their environment awareness programme, in which they collected the following data regarding the number of plants in 20 houses in a locality. Find the mean number of plants per house.

$\begin{array}{cccccccc}\text{Number of plants}& 0-2& 2-4& 4-6& 6-8& 8-10& 10-12& 12-14\\ \text{Number of Houses}& 1& 2& 1& 5& 6& 2& 3\end{array}$

Which method did you use for finding the mean, and why?

Answer 1

Let us find class marks $\left(x_i\right)$ for each interval by using the relation:

$\text{Class Mark (x\_i)}=\frac{\text{Upper class limit + lower class limit}}{2}$

Now we may compute $x_{i}and{f}_i{x}_i$ as following

$\begin{array}{cccc}\text{Number of plants}& \text{Number of Houses}\left(f_i\right)& x_i& f_i{x}_i\\ 0-2& 1& 1& 1\times 1=1\\ 2-4& 2& 3& 2\times 3=6\\ 4-6& 1& 5& 1\times 5=5\\ 6-8& 5& 7& 5\times 7=35\\ 8-10& 6& 9& 6\times 9=54\\ 10-12& 2& 11& 2\times 11=22\\ 12-14& 3& 13& 3\times 13=39\\ Total& 20& & 162\end{array}$

From the table we may observe that:

$Mean\left(\overline{x}\right)=\frac{\sum f_i{x}_i}{\sum f_i}=\frac{162}{20}=8.1$

So, mean number of plants per house is 8.1.

We have used the direct method as values of class marks $\left(x_i\right)and{f}_i$ are small.