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.

Number of plants	$0-2$	$2-4$	$4-6$	$6-8$	$8-10$	$10-12$	$12-14$
Number of houses	$1$	$2$	$1$	$5$	$6$	$2$	$3$

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

Answer 1

No. of plants	No. of houses $\left(f_i\right)$	Mid point $\left(X_i\right)$	$f_i{x}_i$
$0-2$	$1$	$1$	$1$
$2-4$	$2$	$3$	$6$
$4-6$	$1$	$5$	$5$
$6-8$	$5$	$7$	$35$
$8-10$	$6$	$9$	$54$
$10-12$	$2$	$11$	$22$
$12-14$	$3$	$13$	$39$
Total	$20$		$162$

Calculating mean, we get

Mean, $\overline{x}=\frac{1}{n}\sum f_i{x}_i$

Here, $n=20,\sum f_i{x}_i=162$

Therefore, Mean, $\overline{x}=\frac{162}{20}=8.1$ plants

We have used direct method because numerical values of $f$ and $x$ are small.