A survey was conducted by a group of students as a part of their environment awareness programme. Number of plants: 0 - 2, 2 - 4, 4 - 6, 6 - 8,

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

Let us find class marks (x_i) for each interval by using the relation.

Class mark (x_i) = \(\frac{Upperclass\,limit\,+Lowerclass\,limit}{2}\)

Now we may compute x_i and f_ix_i as follows:

Number of plants	Number of house (fi)	xi	fixi
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
	N = 20		\(\sum\)fiui

From, 

the table we may observe that,

\(\sum\)f_i = 20

\(\sum\)f_ix_i = 162

Mean, x = \(\frac{\sum f_ix_i}{\sum f_i}\)

\(=\frac{162}{20}=8.1\)

So mean number of plants per house is 8.1

We have used for the direct method values x_i and f_i are very small.