Question

How do you find the median of $6$ numbers?

Answer 1

Hint: To solve this question we need to know the concept of median. Median refers to the mid-term or the mid value in the given set of numbers. The formula used to find the median for $6$ numbers is $\text{median = }\dfrac{{{\left( \dfrac{\text{n}}{\text{2}} \right)}^{\text{th}}}+{{\left( \dfrac{n}{2}+1 \right)}^{\text{th}}}\text{observation}}{2}$. Here “n” is the total number of observations in a given set.

Complete step-by-step solution:
The question asks us to find the median for the six numbers. To do this we will follow certain steps. First of all we need to know what the median is. So median is a middle value in a set of given numbers. The first step in the calculation is to arrange the numbers given to us in a set. The numbers need to be arranged in such an order that it would be from lower to higher value.
The second step in the calculation is to count the number of observations that a given set contains.
The third step in this process will be to check whether the number of observations in a particular set is odd or even. Depending upon the number of observations in the set, we have two different formulas to find the median. you will use the formula any one of these odd number of observations the formula will be:
If the number of observations is an odd number then the sum of $1$ and number of observations is then divided by 2. We then get the position of median number. So mathematically the formula of median would be written as:
$\text{median = }{{\left( \dfrac{\text{n+1}}{\text{2}} \right)}^{\text{th}}}\text{observation}$
Now if the number of observations is even then the number of observations is divided by 2 then we need to average the number in that position with the number in the next higher position to get the median, mathematically represented as:
$\text{median = }\dfrac{{{\left( \dfrac{\text{n}}{\text{2}} \right)}^{\text{th}}}+{{\left( \dfrac{n}{2}+1 \right)}^{\text{th}}}\text{observation}}{2}$
Since in the given question the number of observation is $6$, an even number so the median will be
$\Rightarrow \text{median = }\dfrac{{{\left( \dfrac{6}{\text{2}} \right)}^{\text{th}}}+{{\left( \dfrac{6}{2}+1 \right)}^{\text{th}}}\text{observation}}{2}$
$\Rightarrow \text{median = }\dfrac{{{3}^{\text{th}}}+{{4}^{\text{th}}}\text{observation}}{2}$

Note: Check carefully whether the number in the set is even or odd. explain the concept of median, we will take an example. Consider a set having number $1,2,3,4,5,6$ so the median comes as
$\Rightarrow \text{median = }\dfrac{{{3}^{\text{th}}}+{{4}^{\text{th}}}\text{observation}}{2}$
$\Rightarrow \text{median = }\dfrac{3+4}{2}$
$\Rightarrow \text{median = }\dfrac{7}{2}$
$\Rightarrow \text{median = 3}\text{.5}$