The median of the following observation arranged in ascending order is 24 . Find x. 14, 18 , x+2, x+4 , 30, 34 . Using the the value of x . find the mean of the above data.

Thanks it was a great help@jaideepsingh

Median of the observations 11 ,12 ,14, 18, x+2, x+4, 30, 32, 35 and 41 which are arranged in the ascending order is 24.
Number of observations of the data is 10 which is an even number.
Therefore, median of the data = Average of the 5 th and the 6 th observations.
= (x + 2) + (x + 4) / 2
⇒ (x + 2) + (x + 4) / 2 = 24
⇒ (x + 2) + (x + 4) = 48
⇒ 2x + 6 = 48
⇒ 2x  = 42
⇒ x  = 21.

Median = 24 (given) Total no.of observations n = 6 Median = avg of the middle numbers ( since n is even ) Median = x + 2 + x + 4 ÷ 2 24 =2x + 6 / 2 24 =x + 3 24 - 3 = x X = 21