Note on Median

What is the Median?

The median is the value in the middle of a list that is ranked from smallest to largest.

Finding the Median

The median is the point in a dataset where half of the data points are more minor and half are more significant than the median.

To find the median:

1. Sort the data points in ascending order from smallest to greatest.
2. The median is the data point in the center of the list if the number of data points is odd.
3. The median is the average of the two middle data points in the list when the number of data points is even.

Example 1 (with formula) – 

Find the median of the following data:

1, 4, 5, 2, 9

Step 1: Arrange the data in ascending order.

1, 2, 4, 5, 9

As we can see above that, there is an odd number of data points, so the median will be the middle data point, that is, 

1, 2, 4, 5, 9

Hence, the median is 4

Example 2 (with formula)

Find the median of the following data:

40, 20, 60, 80

So, according to the rule, we have to arrange the above data in ascending order, that is, 

20, 40, 60, 80

Now, as we can see that there is an even number of data points; hence, the median is the average of the middle two data points, that is, 

20, 40, 60, 80

Median = 40+60/2 = 100/2 = 50

Hence, the median is 50. 

Function or Role of Median

The median indicates where a data set’s center is located. It’s employed in various real-life scenarios, such as bankruptcy legislation, which stipulates that you can only file for bankruptcy if your income is below the state’s median.

A word of caution when using the median formula: depending on whether your data set has an even or odd number of numbers, the steps alter slightly.

Importance of Median

In statistics, the median is one of the methods for determining the data’s center value. The median is the value in the data set that is in the middle. The median is a position in a numerical data set where an equal number of data values are above and below it. The median value is significant because it conveys information about the data’s distribution. The dataset is uniformly distributed from the smallest to the most significant values if the mean and median of the data set are the same.

Merits of Median

1. It is simple to calculate and comprehend.
2. It is well established what an ideal average is.
3. In the case of a frequency distribution with open-ended classes, it can also be computed.
4. It is unaffected by extreme values and is reliant on the data’s range or dispersion.
5. It is possible to calculate it graphically.
6. It is a correct average for qualitative data that is scored rather than measured.
7. It’s only appropriate to use an average when the data is qualitative and it’s conceivable to rank items based on qualitative features.
8. It is simple to calculate simply by looking at the data.
9. In some circumstances, the median performs better than the mean.

Demerits of Median

1. Data must be sorted in ascending or descending order to compute the median.
2. It is not based on all of the data’s observations.
3. Further algebraic treatment is not possible.
4. The variability of sampling has an impact on it.
5. When the data is small, it is not accurate.
6. In certain circumstances, the median is roughly computed as the midpoint of two observations, although this is not the case with the mean.

Conclusion

Thus, in this article, you learn about the median and its formulas. There are two different formulas for calculating the median in the case of odd number data set and an even number data set. As the steps alter in both sets, special care should be taken to carefully observe and follow the procedure of calculation so as to avoid unnecessary mistakes. The importance of median with its merits and demerits has also been explained above for a better understanding of this topic.