Question

The median of the following observation arranged in the ascending order is 24. The observation are 14,18,x+2,x+4,30,34. Find the value of x+2,x+4. Find mean also.​

Answer 1

Answer:

23, 25 and 24.

Step-by-step explanation:

Here,

     Six numbers are given so their median should be the average of the terms ( 6 / 2 )th term and ( 6 / 2 ) + 1 th term.  

⇒ median = { ( x + 2 ) + ( x + 4 ) } / 2

⇒ 24 = ( x + 2 + x + 4 ) / 2

⇒ 24 x 2 = ( 2x + 6 )

⇒ 24 x 2 = 2( x + 3 )

⇒ 24 = x + 3

⇒ 24 -  3 = x

⇒ 21 = x

     thus,

     ⇒ x + 2 = 21 + 2 = 23

     ⇒ x + 4 = 21 + 4 = 25

We know, mean is ( sum of all observations ) / ( number of observations )

Here,

Sum of all observations is 14 + 18 + 23 + 25 + 30 + 34 = 144

Number of observations is 6.

Hence,

  mean is 144 / 6 = 24