Question

Ten observations 6,14, 15,17, x+1, 2x-13, 30, 32,34 and 43 are written in an ascending order. The median of the data is 24. Find the value of x.

Answer 1

Given observations are 6,14,15,17,x+1,2x-13, 30,32,34,43
Here, total number of given observations, n=10 (even)
Since, n is even, so we use the formula for median,
Median =`((n/2)th "Observation" + (n/2+1)"observation")/(2)`
`=((10/2)"observation"+(10/2+1)"observation")/(2)` [put n=10]
`=(5th observation + 6th observation)/(2)` [put n=10]
`rArr 24=((x+1)+(2x-13))/(2)` (given)
`rArr 3x-12=48 rArr 3x=60 rArr x=20`
Hence, the value of x is 20.