Median: What It Is and How To Calculate It, With Examples

What Is the Median?

The term median refers to a metric used in statistics. It is the middle number in a sorted ascending or descending list of numbers and can be more descriptive of that data set than the average. It is the point above and below which half (50%) of the observed data falls, and so represents the midpoint of the data. The median is often compared with other descriptive statistics such as the mean (average), mode, and standard deviation.

Understanding the Median

Statistics is a branch of mathematics. It involves the collection and study of data, which allows researchers to make inferences or determinations about a certain topic. The analysis of quantitative data can be used to study anything from demographics, populations, and investments among other things.

A median is the middle number in a sorted list of numbers (either ascending or descending) used in statistical studies. To determine the median value in a sequence of numbers, the numbers must first be sorted or arranged in value order from lowest to highest or highest to lowest.

• If there is an odd amount of numbers, the median value is the number that is in the middle, with the same amount of numbers below and above.
• If there is an even amount of numbers in the list, the middle pair must be determined, added together, and divided by two to find the median value.

The median can be used to determine an approximate average, or mean, but is not to be confused with the actual mean.

Median vs. Mean

As noted above, it's important not to confuse the terms median and mean. The two may sound the same, but they are very different. A median is a number that falls in the middle of a group. Remember, this is done by ordering the numbers from smallest to largest and locating the one that falls in the middle.

A mean, on the other hand, is the average of a data set. Also called the arithmetic mean, it is the average of the sum of the numbers in a group. In order to figure out the mean, you must take the sum of the numbers in the group and divide the sum by the total number of data points. For instance, let's say a data set consists of the numbers 3, 5, 7, and 19. To figure out the mean:

1. Add the numbers together: 3 + 5 + 7 + 19 = 34
2. Divide the sum by the number of data points: 34 ÷ 4 = 8.5

In this case, the mean is 8.5. The median, on the other hand, would be 6. That's because there's an even number of data points, the middle two of which we add together and divide by 2 to get the result: (5 + 7) ÷ 2.

Example of a Median

To find the median value in a list with an odd amount of numbers, one would find the number that is in the middle with an equal amount of numbers on either side of the median. To find the median, first arrange the numbers in order, usually from lowest to highest.

For example, in a data set of {3, 13, 2, 34, 11, 26, 47}, the sorted order becomes {2, 3, 11, 13, 26, 34, 47}. The median is the number in the middle {2, 3, 11, 13, 26, 34, 47}, which in this instance is 13 since there are three numbers on either side.

To find the median value in a list with an even amount of numbers, one must determine the middle pair, add them, and divide by two. Again, arrange the numbers in order from lowest to highest.

For example, in a data set of {3, 13, 2, 34, 11, 17, 27, 47}, the sorted order becomes {2, 3, 11, 13, 17, 27, 34, 47}. The median is the average of the two numbers in the middle {2, 3, 11, 13, 17, 26 34, 47}, which in this case is 15 or (13 + 17) ÷ 2 = 15.

The Bottom Line

The median is the number that lies in the middle of an ordered dataset that goes from lowest to highest. It should not be confused with the mean, which is determined by adding the numbers in a set together and dividing by the total number of data points. Many experts prefer using the median over the mean because it often provides a more accurate representation of the distribution in a data set.