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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?

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