Question

The marks of a class test are given below:
$28,26,17,12,14,19,27,26,21,16,15$
Find the median.
A) $15$
B) $17$
C) $19$
D) $21$

Answer 1

Hint: First of all we must know what a median is. So, the median is the middle number in a sorted, ascending or descending, list of numbers and can be more descriptive of that data set than the average. In a list of numbers, the median can be calculated in two ways depending upon the number of terms in the list. If there are $n$ numbers in the list, then,
If $n$ is odd, the formula is,
$Median,M = \dfrac{{n + 1}}{2}th{\text{ term}}$
If $n$ is even, the formula is,
$Median,M = \dfrac{1}{2}\left( {\left( {\dfrac{n}{2}} \right)th{\text{ term}} + \left( {\dfrac{n}{2} + 1} \right)th{\text{ term}}} \right)$
We are going to use these formulas based on the given condition to find the median of the given data.

Complete step by step answer:
The given data is,
\[28,26,17,12,14,19,27,26,21,16,15\]
The given data in ascending order is,
$12,14,15,16,17,19,21,26,26,27,28$
The total number of terms in the list of numbers are, $n = 11$
Therefore, the total number of terms in the list is odd.
So, we are going to use the formula of median for odd numbers to find the median.
Therefore, $Median,M = \dfrac{{n + 1}}{2}th{\text{ term}}$
$ \Rightarrow M = \dfrac{{11 + 1}}{2}th{\text{ term}}$
[Since, total number of terms is $11$]
$ \Rightarrow M = 6th{\text{ term}}$
Now, from the ascending order of the list, we can see that the $6th$ term is $19$.
Therefore, $Median,M = 19$. So, option (C) is the correct option.

Note:
In statistics and probability theory, the median is the value separating the higher half from the lower half of a data sample, a population, or a probability distribution. The median is of central importance in statistics, having a breakdown point of $50\% $, so long a s no more than half the data are contaminated, the median is not an arbitrarily large or small result.