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 (xi) for each interval, the following relation is used.  

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

\(x_i\) and \(f_ix_i\) can be calculated as follows. 
 

Number of plants	Number of houses (\(\bf{f_i}\))	\(\bf{x_i}\)	\(\bf{f_ix_i}\)
0-2	1	1	1 x 1 =1
2-4	2	3	2 x 3 = 6
4-6	1	5	2 x 3 = 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

From the table, it can be observed that  

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

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

Therefore, mean number of plants per house is 8.1.

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