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

To find the class mark (x_i) for each interval, the following relation is used.

Class mark (x_i)  = `("Upper class limit + Lower class limit")/2`

x_i and f_ix_i can be calculated as follows.

Number of plant	Number of houses (fi)	xi	fixi
0­ − 2	1	1	1 × 1 = 1
2­ − 4	2	3	2 × 3 = 6
4 − 6	1	5	1 × 5 = 5
6 − 8	5	7	5 × 7 = 35
8 − 10	6	9	6 × 9 = 54
10 − 12	2	11	2 ×11 = 22
12 − 14	3	13	3 × 13 = 39
Total	`bb(sumf_i = 20)`		`bb(sumf_ix_i = 162)`

From the table, it can be observed that

`sum f_i = 20`

`sumf_ix_i = 162`

Mean `barx = (sumf_ix_i)/(sumf_i)`

= `162/20 = 8.1`

Therefore, mean number of plants per house is 8.1.

Here, the direct method has been used as the values of class marks (x_i) and f_i are small.