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

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Solution

The given data in tabulated form is

We have to find the value of p using the information that the mean of the data is 20.

Prepare the following frequency table of which the first column consists of the values of the variate and the second column the corresponding frequencies. Multiply the frequency of each row with the corresponding values of variable to obtain the third column containing.

Find the sum of all entries in the second and third column to obtain N and respectively. Therefore,

The mean is

Hence, we have

If p is negative then the 4^th frequency becomes negative. But frequency can’t be negative. Hence the possible value of p is 1

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Similar questions

x:	8	12	15	p	20	25	30
f:	12	16	20	24	16	8	4

p

20

$x$ :	$15$	$17$	$19$	$20 + p$	$23$
$f$ :	$2$	$3$	$4$	$5 p$	$6$

p

20

$x$	15	17	19	20 + $p$	23
$f$	2	3	4	5 $p$	6

x:	15	17	19	20 + p	23
f:	2	3	4	5 p	6

p

16.6

$x$ :	$8$	$12$	$15$	$p$	$20$	$25$	$30$
$f$ :	$12$	$16$	$20$	$24$	$16$	$8$	$4$

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