If the mean of the following data is 20.6. Find the value of p.
Given:
Also, mean $=20.6$
First of all prepare the frequency table in such a way that its first column consist of the values of the variate $\left(x_{i}\right)$ and the second column the corresponding frequencies $\left(f_{i}\right)$.
Thereafter multiply the frequency of each row with corresponding values of variable to obtain third column containing $\left(f_{i} x_{i}\right)$.
Then, sum of all entries in the column second and denoted by $\sum f_{i}$ and in the third column to obtain $\sum f_{i} x_{i}$.
We know that mean, $\bar{X}=\frac{\sum f_{i} x_{i}}{\sum f_{i}}$
$20.6=\frac{530+25 p}{50}$
By using cross multiplication method,
$530+25 p=20.6 \times 50$
$25 p=1030-530$
$p=\frac{500}{25}$
$=20$
Hence, $p=20$
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