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

The class mark (xi) for each interval is calculated using the formula:

Class mark \((x_i)\) = \(\frac {\text{Upper \,limit + Lower \,limit}}{2}\)

\(x_i\) and \(f_ix_i\) are computed as presented below.

Number of plants	Number of houses (\(f_i\))	\(x_i\)	\(f_ix_i\)
0-2	1	1	1 x 1 =1
2-4	2	3	2 x 3 = 6
4-6	1	5	1 x 5 = 5
6-8	5	7	5 x 7 = 35
8-10	6	9	6 x 9 = 54
10-12	2	11	2 x 11 = 22
12-14	3	13	3 x 13 = 39
Total	20		162

The table shows:

\(\sum f_i = 20\)
\(\sum f_ix_i = 162\)

The mean (\(\overset{-}{x}\)) is calculated as:

\(\overset{-}{x} = \frac{\sum f_ix_i}{\sum f_i}\)
x = \(\frac{162 }{20}\)
x = 8.1

Consequently, the average number of plants per house is 8.1.

The direct method was employed due to the small values of class marks (\(x_i\)) and \(f_i\).