Question

Some observations are arranged in the ascending order as 16, 17, x-2, x, 27 and
30. If the median of these observations is 26, then x=
D. 28
C. 27
B. 26
A. 25

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Answer 1

Answer:

27

Step-by-step explanation:

thera are total 6 observations

middle observation will be 3 and 4

now add 3 and 4 observation and divide by 2

x-2+x/2=26

hence=27

Answer 2

Given,

Series in ascending order :  16, 17, x-2, x, 27 and 30

Total observation  = 6

Median = 26

To Find,

Value of x =?

Solution,

We know that the median is the middle-most value of the series.

The series is already in ascending order and the total observations are 6 which is an even number. So, the median for an even number is

Median =$(n/2)^{th} observation+(n/2 +1)^{th} observation ) / 2$

Median = $(6/2)^{th} observation+(6/2 +1)^{th} observation ) / 2$

Median = $(3)^{rd} observation+(4)^{th} observation ) / 2$

Median = $((x - 2) + x )/2$

Median =$26 = ((x - 2) + x )/2$ [Median is given in question]

$26*2 = 2x -2 \\2x = 52 + 2\\2x = 54 \\x = 54/2\\x = 27$

Hence, the value of x is 27. Option(c) is the correct answer.