Question:
If the mean of the following distribution is 27, find the value of p.
Solution:
Given: Mean = 27
Let the assumed mean A = 25 and h = 10.
We know that mean, $\bar{X}=A+h\left(\frac{1}{N} \sum f_{i} u_{i}\right)$
Now, we have $\sum f_{i}=43+p, \sum f_{i} u_{i}=17-p, h=10$ and $A=25$
Putting the values in the above formula, we have
$27=25+10\left(\frac{1}{43+p} \times(17-p)\right)$
$\frac{2}{10}=\left(\frac{(17-p)}{43+p}\right)$
$43+p=85-5 p$
$6 p=42$
$p=7$
Thus, the value of p is 7.
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