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Question

Calculate the mean of the following frequency distribution.
Class$$90-100$$$$100-110$$$$110-120$$$$120-130$$$$130-140$$
Frequency$$18$$$$78$$$$80$$$$100$$$$72$$


Solution

$$Class$$ $$Frequency$$
$$f_i$$ 
$$x_i$$ $$f_ix_i$$ 
$$90-100$$ $$18$$ $$95$$ $$1710$$ 
$$100-110$$ $$78$$ $$105$$ $$8190$$ 
$$110-120$$ $$80$$ $$115$$ $$9200$$ 
$$120-130$$ $$100$$ $$125$$ $$12500$$ 
$$130-140$$ $$72$$ $$135$$ $$9720$$ 
 $$\sum f_i=348$$  $$\sum f_ix_i=41320$$ 
$$\Rightarrow$$  $$Mean(\overline{x})=\dfrac{\sum f_ix_i}{\sum f_i}=\dfrac{41320}{348}=118.73$$

Mathematics

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