Answer

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**Hint:**There are two cases in finding the median one is when there are an odd number of values and second is when there is an even number of values. As we have to find the median of four numbers it means we have an even number of values. In this case we add two middle numbers and divide the sum by 2.

**Complete step by step solution:**

We have to explain how we can find the median of 4 numbers.

We know that median is the central element of a group of numbers arranged in the proper sequence according to their size. To find the median first we have to arrange the data according to their size. If we have an odd number of terms then the middle term is the median. If we have an even number of terms then we have to add two middle terms and then divide the sum by 2. The mean we get is the median.

Let us assume 4 numbers as 24,89,31,12

Let us arrange the numbers in ascending order then we will get

$\Rightarrow 12,24,31,89$

Now, as we have an even number of terms let us add two middle terms and divide the sum by 2. Then we will get

$\begin{align}

& \Rightarrow \dfrac{24+31}{2} \\

& \Rightarrow \dfrac{55}{2} \\

& \Rightarrow 27.5 \\

\end{align}$

Hence $27.5$ is the median.

**Note:**

Data is categorized into two types one is grouped data and second is ungrouped data. Above discussed procedure is for ungrouped data. For grouped data we will use the frequency distribution. First we need to calculate the cumulative frequency then we will use the following formula to calculate median:

$Median=l+\left( \dfrac{h}{f} \right)\left( \dfrac{n}{2}-c \right)$

Where, l = lower class interval

h = class interval size

f = median class’s frequency

n = total frequency

c = cumulative frequency of preceding class.

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