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Find the value of $p$, if the mean of the following distribution is 20.
$x$ | 15 | 17 | 19 | $20+p$ | 23 |
$f$ | 2 | 3 | 4 | $5p$ | 6 |
Given:
The arithmetic mean of the given data is 20.
To do:
We have to find the value of $p$.
Solution:
$x$ | $f$ | $f \times\ x$ |
15 | 2 | 30 |
17 | 3 | 51 |
19 | 4 | 76 |
$20+p$ | $5p$ | $100p+5p^2$ |
23 | 6 | 138 |
Total | $15+5p$ | $295+100p+5p^2$ |
We know that,
Mean$=\frac{\sum fx}{\sum f}$
Mean $20=\frac{295+100p+5p^2}{15+5p}$
$20(15+5p)=295+100p+5p^2$
$5p^2+100p+295=100p+300$
$5p^2=300-295$
$5p^2=5$
$p^2=1$
$p=1$
The value of $p$ is $1$.
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