Question:
If the mean of the following data is 20.2, find the value of p.
Solution:
We know that,
Mean $=\frac{\sum x_{i} f_{i}}{\sum f_{i}}$
For the following data:
Mean $=\frac{(10 \times 6)+(15 \times 8)+(20 \times p)+(25 \times 10)+(30 \times 6)}{6+8+p+10+6}$
$\Rightarrow 20.2=\frac{60+120+20 p+250+180}{30+p}$
$\Rightarrow 20.2(30+p)=610+20 p$
$\Rightarrow 606+20.2 p=610+20 p$
$\Rightarrow 20.2 p-20 p=610-606$
$\Rightarrow 0.2 p=4$
$\Rightarrow p=\frac{4}{0.2}$
$\Rightarrow p=\frac{40}{2}$
$\Rightarrow p=20$
Hence, the value of p is 20.
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