Question

the following observations arranged in ascending order :6, 9,12,13,x, x+2, 20,25,32,43.if the median if 15 find x
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Answer 1

Given :-

The observations are 6,9,12,13,X, X+2, 20,25,32,43

To find :-

The value of X

Solution :-

Given observations are : 6,9,12,13,X, X+2, 20,25,32,43

Number of observations = 10

n = 10

We know that

If the number of all observations is n, an even number then the median is the average of

(n/2)th and [(n/2)+1]th observations.

n/2th observation = 10/2 = 5th observation

5th observation = X

(n/2)+1 th observation = 6th observation

6th observation = X+2

The average of 5th and 6th observations

= (X+X+2)/2

= (2X+2)/2

=> 2(X+1)/2

=> X+1

The Median = X+1

According to the given problem

The Median = 15

Therefore, X+1 = 15

=> X = 15-1

=> X = 14

Therefore, X = 14

Answer :-

The value of X is 14

Used formulae:-

♦ If the number of all observations is n, an even number then the median is the average of

If the number of all observations is n, an even number then the median is the average of (n/2)th and [(n/2)+1]th observations.

Points to know:-

♦ The middle term of the observations in a data when it is arranged in either ascending order or descending order is called its Median.

♦ Median is denoted by M.

♦ If the number of all observations is n, an odd number then the median is (n+1)/2 th observation.

Answer 2

Answer:

x = 14

Justification :

Given that ;

Observations in Ascending Order ;

6 , 9 , 12 , 13 , x , x + 2 , 20 , 25 , 32 , 43

We Know That ,

Median = 15

Number of Observations = 10

Even ,

Median = x or x + 2

Median of even number of Observations ,

n + 1 / 2

10 + 1 / 2

11 / 2

5.5

5th observation = x

5.5 observation is 15,

6th observation = x + 2

So;

x is the preceding number of 15

Hence ,

x = 14

x + 2 = 16