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

By Akhilesh Ganti
Updated September 03, 2024
Reviewed by Charles Potters
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Median Median

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What Is the Median?

Median refers to a metric used in statistics. It's the middle number in a sorted ascending or descending list of numbers and can be more descriptive of the data set than the average. It's the point above and below which 50% of the observed data falls so it represents the midpoint of the data.

The median is often compared with other descriptive statistics such as the mean which means 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 rather than 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 that allows researchers to make inferences or determinations about a certain topic. The analysis of quantitative data can be used to study anything from demographics and populations to investments.

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

  • 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 it isn't to be confused with the actual mean.

The median is sometimes used rather than 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

Median and mean may sound the same but they're very different. A median is a number that falls in the middle of a group. This is accomplished by ordering the numbers from smallest to largest and locating the one that falls in the middle.

A mean is the average of a data set. It's also called the arithmetic mean. It's the average of the sum of the numbers in a group. You must take the sum of the numbers and divide it by the total number of data points to calculate the mean.

Let's say a data set consists of the numbers 3, 5, 7, and 19:

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

The mean is 8.5 in this case. The median would be 6 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 = 6.

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

Find the number that's in the middle with an equal amount of numbers on either side of the median to find the median value in a list with an odd amount of numbers. First arrange the numbers in order, usually from lowest to highest.

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

Determine the middle pair, add them, and divide by two to find the median value in a list with an even amount of numbers. Again, arrange the numbers in order from lowest to highest. The sorted order becomes 2, 3, 11, 13, 17, 27, 34, 47 in a data set of 3, 13, 2, 34, 11, 17, 27, 47. The median is the average of the two numbers in the middle of 2, 3, 11, 13, 17, 26 34, 47 which is 15 or (13 + 17) ÷ 2 = 15 in this case.

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. Divide the number of observations by two to find the midpoint value. Round the number up if there's an odd number of observations and the value in that position is the median. Take the average of the values found above and below that position if the number of observations is even.

Where Is the Median in a Normal Distribution?

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

When Are the Mean and Median Different?

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

The average would be 24/8 = 3 in a set of data 0, 0, 0, 1, 1, 2, 10, 10. The median would be 1 or the midpoint value, however.

The Bottom Line

The median is the number that lies in the middle of an ordered dataset that goes from lowest to highest. It shouldn't be confused with the mean that's 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. Many economists favor the median for reporting a nation's income or wealth because it's more representative of the actual income distribution.

Article Sources
Investopedia requires writers to use primary sources to support their work. These include white papers, government data, original reporting, and interviews with industry experts. We also reference original research from other reputable publishers where appropriate. You can learn more about the standards we follow in producing accurate, unbiased content in our editorial policy.

  1. National Library of Medicine. “Median.”

  2. CFI Education. "Mean."

  3. National Cancer Institute. “Learn More About Normal Distribution.”

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