How to Find the Median

The median is a metric used to describe the central tendency of a set of numbers. It is often preferred over the mean (average) when dealing with skewed distributions or when the data set contains outliers. In this article, we will learn how to find the median of a given set of numbers.

What is the Median?

The median is the middle value in a set of numbers when they are arranged in order from smallest to largest. It is also known as the second quartile (Q2). When there is an even number of observations, the median is the average of the two middle values.

Steps to Find the Median:

1. Arrange the data in order: Begin by arranging the numbers in the data set in order from smallest to largest.
2. Identify the middle value: If the data set has an odd number of observations, the middle value is the median. If the data set has an even number of observations, there are two middle values.
3. Find the median: If the data set has an odd number of observations, the median is the middle value. If the data set has an even number of observations, the median is the average of the two middle values.

Example:

Let’s say we have the following set of exam scores: 60, 70, 80, 90, 100.

1. Arrange the data in order: 60, 70, 80, 90, 100
2. Identify the middle value: The middle value is 80, which is the third value in the ordered data set.
3. Find the median: Since there are an odd number of observations, the median is simply the middle value, which is 80.

What to Do When There Are Tied Values:

When there are tied values in the data set, it is generally best to treat them as a single value for the purposes of finding the median. This means that if there are two or more values that are the same, they are considered as one value when identifying the middle value.

What to Do When There Are Outliers:

Outliers are values that are significantly higher or lower than the majority of the data set. When dealing with outliers, it is often best to consider only the main body of the data (excluding the outliers) when finding the median.

Conclusion:

Finding the median is a simple process that involves arranging the data in order, identifying the middle value, and averaging the two middle values if there are an even number of observations. Remember to treat tied values as a single value and exclude outliers when necessary. With practice, you will become proficient in finding the median and using it to describe the central tendency of a data set.