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?

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 getMean, $$\bar x = \dfrac1n\sum f_ix_i$$Here, $$n = 20, \sum f_ix_i = 162$$Therefore, Mean, $$\bar x = \dfrac{162}{20} = 8.1$$ plantsWe have used direct method because numerical values of $$f$$ and $$x$$ are small.MathematicsRS AgarwalStandard X

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