The following observations have been arranged in ascending order. If the median of the data is 63, find the value of x.
29, 32, 48, 50, x, x + 2, 72, 78, 84, 95

Options

A. 26
B. 62
C. 27
D. 72

Answer

B

Explanation

Number of observations, n = 10 which is even
`:.` Median
`= (((n)/(2))" th observation" + ((n)/(2) +1) " th observation")/(2)`
`= (((10)/(2)) "th observation" + ((10)/(2) + 1) " th observation")/(2)`
`("5 th observation + 6th observation")/(2)`
`= ( x + ( x + 2))/( 2) = x + 1 `
According to the questions, median = 63
` :. x + 1 = 63 rArr x = 63 - 1 = 62`
Hence, the value of x is 62