Question

the following observations have been arranged in ascending order the median of that data is 63 find the value of x. 29,32,4850,x,x+2,72,78,84,91,95.

Answer 1

Given Median of Data = 63

Given terms => 29,32,48,50,x,x+2,72,78,84,91,95

Total number of terms = 11

As, 11 is odd so median of the given data will be

$= > \: median \: = ( \frac{n + 1}{2} )th \: term$

Here total no. of terms or n = 11

Therefore,

$median \: = \frac{11 + 1}{2} th \: term \\ \\ 63 = \frac{11 + 1}{2} \\ \\ 63 = \frac{12}{2} th \: term \\ \\ 63 = 6th \: term \\ \\ 6th \: term \: is \: x +2 \\ \\ 63 = x + 2 \\ \\ 63 - 2 = x \\ \\ 61 = x \: \\ \\ or \: x \: = 61 \\ \\ therefore \: x = 61 \: and \: x + 2 = 63$

So we get the middle value (x+2) = 63

Which is the given median.