Question

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

Answer 1

Answer:

Step-by-step explanation:

Given data = 15, 17, x - 1 , x + 5 , 31 ,36 and

Median of the data = 22

Number of observations = 6 (∵ It iis an even number )

∴ Median is ( n / 2 ) th observation and ( n/ 2 + 1)th observation.

So , Median = [ ( n/ 2 ) + ( n/2 + 1 ) ] / 2

⇒ 22 = ( x - 1 + x + 5 ) / 2

⇒ 22 × 2 = 2x + 4

⇒ 44 = 2x + 4

⇒ 2x = 44 - 4

⇒ 2x = 40

⇒ x = 40 / 2

⇒ x = 20 is the answer.

∴ Mean = ( Sum of the observations ) / Number of observations)

= ( 15 + 17 + ( 20 - 1 ) + ( 20 + 5 ) + 31 + 36 ) / 6

= ( 15 + 17 + 19 + 25 + 31 + 36 ) / 6

= ( 143 ) / 6

= 23 .84 is the answer.