# Advantages And Disadvantages Of Median | Definition, Uses, Merits, De-merits, Pros and Cons

Advantages And Disadvantages Of Median: Whether you’re taking an introductory statistics class or not, everyone should be familiar with the terms average and median. An average is the sum of all numbers divided by the number of numbers in the set, while a median is any number in the middle when all of the numbers are lined up from smallest to largest, with half of the above and half below it. Although these terms are often used interchangeably, they aren’t interchangeable when it comes to considering your data set, especially regarding business use and scientific data sets.

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## What is Median And Where it is Used?

A median is a type of average that can be used to represent values in data sets. It is less commonly used than an average, but it’s particularly useful when you have outliers in your dataset that can skew a mean calculation or standard deviation.

Median values are calculated by finding where half your data is below and half your data is above. It’s called median because it represents the middle point in your dataset, which gives it certain statistical advantages over both averages and means.

The median value is used in data visualization and summary statistics to summarize distributional data. This includes visualizations like histograms, stemplots, boxplots, scatter plots and more.

When used with these types of visualizations, median values are plotted at either their exact centre point or where there is an odd number of data points. If you have an even number of data points, you’ll want to take a mean average instead.

First, it makes sense to talk about what the median is. In a set of numbers, the median marks out a middle value—the one with as many numbers below it as above it. For example, in [1, 4, 3], 3 is a median because there are two values smaller than 3 (1 and 2) while there are two values larger than 3 (4 and 5).  Since the median is a statistical measure, it has many advantages over other types of averages which are:

Easy And Simple:

• The median is easy to calculate as it does not require any difficult or complex calculations, unlike other types of averages.
• For example, when dealing with data that contain decimals, finding an average is easier said than done; however, calculating a median is effortless. Also, since it’s based on whole numbers only, it’s both simple and fast to arrive at a median value without having to go through any special procedures.

Unaffected By Extreme Values:-

• The median is not affected by extreme values. This means that even if a particular value is extremely high or low, it won’t affect your average.
• For example, in [1, 4, 3], 3 is a median because there are two values smaller than 3 (1 and 2) while there are two values larger than 3 (4 and 5). However, since we have only three numbers in our set here—and 4 is an extreme value—we can say that 4 doesn’t belong to our set at all.

Graphical Representation:

• The median is represented graphically by a line that divides a series of data points into two halves.
• For example, in [1, 4, 3], 3 is a median because there are two values smaller than 3 (1 and 2) while there are two values larger than 3 (4 and 5). You can see how easy it is to find out where exactly your median lies by simply drawing a line through your data points.

Suitable For Open End Distribution:

• The median is suitable for open-end distribution. This means that if your data has an infinite number of values, you can still find a median value using it.
• In other words, it doesn’t matter how many points are in your set; all you need to do is calculate their average and then find out which point lies exactly in between them.
• However, keep in mind that finding a median when dealing with continuous variables (such as age) isn’t possible since there’s no specific cut-off point where one ends and another begins.

Suitable For Qualitative Phenomenon:

• The median is suitable for the qualitative phenomenon. In other words, it’s great for data that can be categorized into different groups.
• For example, if you want to find out how many hours a week your employees work, you can simply group them into two categories—those who work more than 40 hours per week and those who work less than 40 hours per week—and then calculate their average.

As a non-parametric test, the median has no exact p-value. So, a low p-value doesn’t necessarily mean that there’s an outlier. Instead, it means that there might be one. If you want to know for sure if there’s an outlier in your data set, you can do a parametric test such as a t-test or ANOVA, on top of using the median. The disadvantages are as follows:

Tedious Process: The median is a tedious process to compute. To find out what number it is, you need to sort all your data sets in ascending order. This means that if you have N elements in your data set, it will take N-1 passes through your data to find out what number is the median.

Unsuitable For Even Observation: The median is not suitable for even observation. In other words, if you have an even number of observations in your data set, it will not be possible to find out what number is the median.

Unsuitable For Algebraic Treatment: The median is not suitable for algebraic treatment. This means that you cannot add, subtract, multiply or divide by 2.5 to get a new number that is closer to the median. A median is a number that can only be added to, subtracted from or multiplied by itself.

Unsuitable For Fraction And Percentage: It is unsuitable for fractional numbers and percentages. When you want to know what percent of your data is a certain number, it will be impossible to get that information if you take a median as an average. Because fractions are only available in integers, you won’t be able to determine what number is exactly in between two observations.

 Advantages Disadvantages Easy And Simple Tedious Process Unaffected By Extreme Values Unsuitable For Even Observation Graphical Representation Unsuitable For Algebraic Treatment Suitable For Open End Distribution Unsuitable For Fraction And Percentage Suitable For Qualitative Phenomenon

Question 1.
What is median used for?

By definition, a median value is one where half of all values are below it and half are above it.

Question 2.
Can you calculate the median for ordinal data?