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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? 


Solution

 No. of plants No. of houses $$(f_i)$$ Mid point $$(X_i)$$ $$f_ix_i$$
 $$0-2$$  $$1$$  $$1$$   $$1$$
 $$2-4$$  $$2$$  $$3$$  $$6$$
 $$4-6$$  $$1$$  $$5$$  $$5$$
 $$6-8$$  $$5$$  $$7$$  $$35$$
 $$8-10$$  $$6$$  $$9$$  $$54$$
 $$10-12$$  $$2$$  $$11$$  $$22$$
 $$12-14$$  $$3$$  $$13$$  $$39$$
 Total  $$20$$    $$162$$
Calculating mean, we get
Mean, $$\bar x = \dfrac1n\sum f_ix_i$$
Here, $$n = 20, \sum f_ix_i = 162$$

Therefore, Mean, $$\bar x = \dfrac{162}{20} = 8.1$$ plants

We have used direct method because numerical values of $$f$$ and $$x$$ are small.

Mathematics
RS Agarwal
Standard X

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