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
Here, `n=10` (even)
`therefore ” Median”=(((n)/(2))th” term” + ((n)/(2) +1)th ” term”)/(2)`
`rArr 63= (((10)/(2))th ” term” +((10)/(2)+1)th ” term”)/(2)`
`rArr 63 = (“5th term + 6th term”)/(2)`
`rArr (63)/(1) = (x+x+2)/(2)`
`rArr 63 xx 2 = 2x + 2`
`rArr 2x=126-2`
or `x = (124)/(2) = 62`
Hence, the value of x = 62.
Here, the total number of terms, `n =10`
So, Middle terms will be `(n/2 and n/2+1)^(th)` terms.
Here, Middle terms are `5^(th) and 6^(th)` terms.
So, Median `= (x+x+2)/2`
`=>63 = (2x+2)/2=>63 = x+1`
`=>x = 62`