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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.
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 :


In order to find the mean value, we will use direct method because the numerical value of \(f_i \) and \( x_i \) are small.

The midpoint of the given interval is found by formula: \(Midpoint \ (x_i) \ = \ \frac{upper \ limit \ + \ lower \ limit}{2} \)

No. of plants (Class interval) No. of houses (Frequency \( (f_i) \) ) Mid-point \((x_i)\) \(f_i x_i \)
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
\( \sum \ f_i \ = \ 20 \) \( \sum \ f_i x_i \ = \ 162 \)

The formula to find the mean is:    \( \overline{x} \ = \ \frac{ \sum \ f_i x_i}{ \sum f_i} \)

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

\(\therefore \) The mean number of plants per house is 8.1

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