# 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.

### Key Takeaways

• The median is the middle number in a sorted list of numbers and can be more descriptive of that data set than the average.
• The median is sometimes used as opposed to the mean when there are outliers in the sequence that might skew the average of the values.
• 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.

## 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.

The median is sometimes used as opposed to the mean when there are outliers in the sequence that might skew the average of the values. The median of a sequence can be less affected by outliers than the mean.

## Median vs. Mean

As noted above, it's important not to confuse the terms median and mean. The two may sound the same (which is a common misconception) 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 or (5 + 7) ÷ 2. That's because there's an even number of data points, which we add together and divide by 2 to get the result.

The median is closely associated with quartiles, or dividing up observed data into four equal parts. The median would be the center point, with the first two quartiles falling below it and the second two above it. Other ways of bucketing data include quintiles (in five sections) and deciles (in 10 sections).

## 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.

## How Do You Calculate the Median?

The median is the middle value in a set of data. First, organize and order the data from smallest to largest. To find the midpoint value, divide the number of observations by two. If there are an odd number of observations, round that number up, and the value in that position is the median. If the number of observations is even, take the average of the values found above and below that position.

## Where Is the Median in a Normal Distribution?

In the normal distribution or bell curve the median, mean, and mode are all the same value and fall at the highest point in the center of the curve.

## When Is the Mean and Median Different?

In a skewed data set, the mean and median will typically be different. The mean is calculated by adding up all of the values in the data and dividing by the number of observations. If there are sizable outliers, or if the data clumps around certain values, the mean (average) will not be the midpoint of the data.

For instance, in a set of data {0, 0, 0, 1, 1, 2, 10, 10} the average would be 24/8 = 3. The median, however, would be 1 (the midpoint value).

This is why many economists favor the median for reporting a nation's income or wealth, since it is more representative of the actual income distribution.

## 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.

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