If the mean of the following distribution is $27$ , find the value of $p$ .
Class: 0-10 10-20 20-30 30-40 40-50
Frequency: $8$ $p$ $12$ $13$ $10$

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Solution

Answer:-
Marks No. of
students
$f_{i}$ $x_{i}$ $f_{i} x_{i}$
0-10 8 5 40
10-20 $p$ 15 15 $p$
20-30 12 25 300
30-40 13 35 455
40-50 10 45 450
$Σ f_{i} = 43 + p$ $Σ f_{i} x_{i} = 1245 + 15 p$
$m e a n = \frac{Σ f_{i} x_{i}}{Σ f_{i}} = 27 \Rightarrow (g i v e n)$

$∴ \frac{1245 + 15 p}{43 + p} = 27$

$\Rightarrow 1245 + 15 p = 27 (43 + p)$
$\Rightarrow 1245 + 15 p = 1161 + 27 p$
$\Rightarrow 1245 - 1161 = 27 p - 15 p$
$\Rightarrow 12 p = 84$

$\Rightarrow p = 7$

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