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Question

If the mean of the following data is $$20.6$$. Find the value of $$p$$.
$$x$$$$10$$$$15$$$$p$$$$25$$$$35$$
$$f$$$$3$$$$10$$$$25$$$$7$$$$5$$


Solution

Mean =$$ \dfrac {\sum x_{i} f_{i}} {\sum f_{i}} $$

$$\Rightarrow $$mean =$$\dfrac {(10\times 3)+(15\times 10)+(p \times 25)+(25 \times 7)+(35 \times 5)}{3+10+25+7+5}$$


$$\Rightarrow $$mean =$$\dfrac {30+150+25p+175+175}{3+10+25+7+5}=20.6$$

$$\Rightarrow 20.6=\dfrac {1030+25p}{50}$$

$$\Rightarrow 25p=500$$

$$\Rightarrow p=20$$

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