The find the value of X if the median of the following data arranged in ascending order is 19.5
3 7 8 11 15 X X +327 28 39 45 51
Answers
Step-by-step explanation:
Given:-
the median of the following data arranged in ascending order is 19.5 . The data is 3 ,7, 8, 11, 15, X ,X +3,27 28, 39, 45 51.
To find:-
Find the value of x?
Solution:-
Given observations of the data is
3 ,7, 8, 11, 15, X ,X +3,27 28, 39, 45 51.
Number of observations = 12
12 is an even number
we know that
the median of the data of "n" observations an even number is the average of (n/2)th and (n/2)+1 th observations.
we have n =12
n/2 = 12/2 = 6th observation
6th observation = X
(n/2)+1 = 6+1=7th observation
7th observation = X+3
Median of the data = Average of 6th and 7th observations
=>Median = (X+X+3)/2
=>Median =(2X+3)/2
According to the given problem
Median = 19.5
=>(2X+3)/2=19.5
=>2X+3=19.5×2
=>2X+3 = 39
=>2X=39-3
=>2X=36
=>X=36/2
=>X=18
The value of X = 18
Answer:-
The value of X for the given problem = 18
Used formula:-
the median of the data of "n"observations an even number is the average of (n/2)th and (n/2)+1 th observations.