Find the median of following data:-
5, 19, 42, 11, 50, 30, 21, 0, 56, 36, 27

Question

Find the median of following data:- 
5, 19, 42, 11, 50, 30, 21, 0, 56, 36, 27

Accepted Answer

The correct option is 2:
To find the median of a given set of data, we first need to arrange the data in ascending order (from smallest to largest). The median is the middle value in a sorted list of numbers.

Given data set:
$5, 19, 42, 11, 50, 30, 21, 0, 56, 36, 27$

Step 1: Arrange the data in ascending order.
$0, 5, 11, 19, 21, 27, 30, 36, 42, 50, 56$

Step 2: Count the number of observations ($n$) in the data set.
In this data set, there are 11 numbers. So, $n = 11$.

Step 3: Determine the position of the median.
Since the number of observations ($n$) is odd, the median is the value at the $\left(\frac{n+1}{2}\right)^{th}$ position.
Median position = $\left(\frac{11+1}{2}\right)^{th} = \left(\frac{12}{2}\right)^{th} = 6^{th}$ position.

Step 4: Identify the median value.
Looking at the sorted data, the number at the $6^{th}$ position is 27.
Sorted data: $0, 5, 11, 19, 21, \textbf{27}, 30, 36, 42, 50, 56$
Therefore, the median of the data is 27.

The incorrect option is 1 (21): This would be the median if the data set was different or if there was a miscalculation in ordering or finding the middle term. It is the 5th term in the sorted list.
The incorrect option is 3 (30): This is the 7th term in the sorted list, not the middle term.
The incorrect option is 4 (36): This is the 8th term in the sorted list and is not the median.