Correct Answer - Option 2 : 5
Concept:
To determine the Median the following formulas are used,
Case 1: If the number of observation (n) is even
Median = \(\rm {value of (\frac{n}{2} )^{th} observation\; + \;value of (\frac{n}{2} \;+\;1)^{th} observation}\over2\)
Case 2: If the number of observation (n) is odd
Median = \(\rm value\ of (\frac{n\;+\;1}{2})^{th} observation \)
Calculation:
The given set of numbers is,
4, 5, 5, 8, 4, 2, 7, 9 which can be arranged in increasing order as,
2, 4, 4, 5, 5, 7, 8, 9
So, the total number in the set is n = 8 which is an odd number so, the median will be the average of \(\rm n\over 2\)th and (\(\rm n\over 2\) + 1)th
Since n = 8, \(\rm n\over 2\) = 4 and (\(\rm n\over 2\) + 1) = 5
The numbers corresponding to \(\rm n\over 2\) and (\(\rm n\over 2\) + 1) are 5 and 5 respectively.
The average of 5 and 5 is 5
So, the median of the given set of numbers is 5.
