Question

The median of the observation 8 11 13 15 (x+1) (x+3) 30 35 40 43 arrange in the ascending order is 22.find the value of x.

Answer 1

Middle terms are x+1 and x+3

(X+1+x+3)/2= 22

2x+4 = 44

2x = 40

X = 20

Answer 2

The value of x is 20.

Given:

• 8, 11, 13, 15, (x+1), (x+3), 30, 35, 40, 43
• Median of data is 22.

To find:

• Find the value of x.

Solution:

If given data is even (n=even) in number, then median is mean of n/2th and (n/2+1)th data.

Step 1:

Total numbers are 10.

n= 10; even number

Step 2:

n/2th data is 10/2= 5th number

5th number is (x+1)

(n/2+1)th data is (10/2)+1= 6th number

6th number is (x+3)

Step 3:

Put values in formula.

$22 = \frac{(x + 1) + (x + 3)}{2}$

or

$(x + 1) + (x + 3) = 44$

or

$2x + 4 = 44$

or

$2x = 44 - 4$

or

$x = 20$

Thus,

Value of x is 20.

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