Question

If the median of the data:15,17,x-1,x+5,31,36 is 22 then find mean​

Answer 1

Answer:

median = 6/2 th term +( 6/2 +1)term

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2

median = 3rd term + 4th term /2

median = (x-1 + x+5)/2 = 22

2x +4 = 44

x= 20

the terms are 15, 17 , 19 , 25, 31 , 36

mean = 15+17+19+25+31+36/6

= 143/6 = 23.83

Step-by-step explanation:

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Answer 2

Given:

The median of the data: 15, 17, x-1, x+5, 31, 36 is 22.

To find:

The mean.

Solution:

The mean of the given data is 23.83

To answer this question, we will follow the following steps:

As we know if there is an odd number (n) of observations in a data, then its median is obtained by:

$( \frac{n + 1}{2} )th \: observation$

Also,

if there is an even number (n) of observations in a data, then median is obtained by:

$\frac{ (\frac{n}{2})th \: observation \: + (\frac{n}{2} + 1)th \: observation }{2}$

Now,

as given, we have,

A data

15, 17, x-1, x+5, 31, 36

As we can see, there are 6 observations in the given data set.

So,

n = 6, which is even

Also,

The median of given data = 22

So,

$\frac{n}{2} th \: observation \: = \frac{6}{2} = 3rd \: observation$

3rd observation

$= x - 1$

Also,

$(\frac{n}{2} + 1)th \: observation \: = \:( 3 + 1)th \: observation \: = \: 4th \: observation$

4th observation

$= x + 5$

So,

$\frac{(x - 1) + (x + 5)}{2} = 22$

$2x + 4 = 44$

$2x = 40$

$x = 20$

So,

3rd observation = x - 1 = 20 - 1 = 19

4th observation = x + 5 = 20 + 5 = 25

The data is

15, 17, 19, 25, 31, 36

So,

The mean is

$= \frac{sum \: of \: observations}{number \: of \: observations}$

$= \frac{15 + 17 + 19 + 25 + 31 + 36}{6}$

$= \frac{143}{6}$

$= 23.83$

Hence, the mean of the data is 23.83.