A survey was conducted by a group of students as a part of their environment awareness program, 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. Which method did you use for finding the mean, and why?

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

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Solution

To find the mean value,
Let use the direct method because the numerical value of $f_{i}$ and $x_{i}$ are small.
Find the midpoint of the given interval using the formula.
$M i d p o i n t (x_{i}) = \frac{(u p p e r l i m i t + l o w e r l i m i t)}{2}$
No. of plants (Class interval) No. of houses Frequency (f_i) Mid-point (x_i) f_ix_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
Sum $f_{i} = 20$ Sum $f_{i} x_{i} = 162$
$M e a n = x̄ = \frac{\sum f_{i} x_{i}}{\sum f_{i}} = \frac{162}{20} = 8.1$
Hence, the number of plants per house is $8.1 .$

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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