If the mean of the following data is 18.75, find the value of p .Whex i & 10 & 15 & p & 25 & 30 Nlhlinef i & 5 & 10 & 7 & 8 & 2 Whhe end array [4 MARKS]

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Mean of Raw Data

If the mean o...

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Solution

We may prepare th frequency table as given below:

$∴ m e a n = \frac{\sum (f_{i} \times x_{i})}{\sum f_{i}} = \frac{10 \times 5 + 15 \times 10 + p \times 7 + 25 \times 8 + 30 \times 2}{5 + 10 + 7 + 8 + 2} = \frac{460 + 7 p}{32}$
But, mean = 18.75 (given)

$∴ \frac{460 + 7 p}{32} = 18.75 \Rightarrow 460 + 7 p = (18.75 \times 32)$

$\Rightarrow (460 + 7 p) = 600$

$\Rightarrow 7 p = 140 \Rightarrow p = 20$

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\begin{matrix} x_{i} & 10 & 15 & p & 25 & 30 f_{i} & 5 & 10 & 7 & 8 & 2 \end{matrix}

18.75

p

$x_{i}$ :	$10$	$15$	$p$	$25$	$30$
$f_{i}$ :	$5$	$10$	$7$	$8$	$2$

18.75

p

Class mark $(x_{i})$	$10$	$15$	$p$	$25$	$30$
Frequency $(f_{i})$	$5$	$10$	$7$	$8$	$2$

If the mean of the following data is 18.75, then the value of P is

x_i:	10	15	p	25	30
f_i:	5	10	7	8	2

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