Mean vs. Median: Formula, Examples and Key Differences
By Indeed Editorial Team
Updated July 21, 2022 | Published May 17, 2021
Updated July 21, 2022
Published May 17, 2021
The Indeed Editorial Team comprises a diverse and talented team of writers, researchers and subject matter experts equipped with Indeed's data and insights to deliver useful tips to help guide your career journey.
When you work in accounting, finance, statistics or any other profession that involves data and numbers, it’s important to know how and when to apply various mathematical concepts. Two common values you might encounter include mean, which is the average of a data set, and median, which is the middle value. Understanding the differences between these terms can help you better analyze sets of values in your profession or field of academia.
In this article, we explain mean compared to median by discussing formulas, examples and key differences between the two.
What is mean?
The mean is the average of a set of numbers. You can calculate this number by adding a set of values together and dividing the total by the number of values. Note that many people use the terms “mean” and “average” interchangeably.
Mean formula and example
The formula to calculate the mean for a set of values is:
Mean = (total of values) / number of values
For example, you might want to calculate the mean of these numbers: 1, 2 and 3. To get the mean, plug the numbers into the formula as follows: (1 + 2 + 3) / 3 = 2. In this case, the mean is 2. The mean doesn't necessarily have to be a whole number. It may be a decimal or a fraction. For example, you might want to calculate the mean of these numbers: 1, 3, 4 and 10. Using the formula above, the mean equals (1 + 3 + 4 + 10) / 4 = 4.5.
What is median?
The median is the numeric value that separates the higher half of a set of numbers from its lower half. Although a median is also a type of average, it doesn't have the same formula as a mean. To calculate the median of a group of figures, scan the list of numbers and find the value in the middle. In order for this method to work correctly, you have to write or type the numbers from smallest to largest.
Because the median isn't technically a calculation, it doesn't have a formula. If the list of values is short, you can simply count them manually to determine the median. For longer lists of numbers, you can use a simple formula for finding the location of the median.
Median formula and example
The formula to calculate the median for a set of values is:
Median location = ([number of data points] + 1) / 2
For example, you might want to find the median of 1, 2 and 3. Use the formula as follows: (3 +1) / 2 = 2. The median is the second number in the series, which is 2. In some cases, the median can also be a decimal. For example, you might want to know the median of 1, 3, 4 and 10. Using the median location formula generates this result: (4 + 1) / 2 = 2.5. That means the median is between the second and third values. 3.5 is in between three and four, making 3.5 the median of this set.
Mean vs. median
Here are some key similarities and differences between mean and median:
Consideration of a set’s values
Depending on the set of numbers, which is also known as a vector, the mean and the median may be the same or completely different values. In either case, the mean always takes into account every value in the vector since the formula requires you to add them all. In contrast, the median only considers some values, as it disregards all the numbers aside from the most central one.
In many cases, it's helpful to use both methods and calculate the mean and the median. Then you can determine which is a more accurate representation of your data set. However, in certain situations, one is much more useful than the other. For instance, consider the following student test scores: 10, 15, 20, 25 and 100. The mean is 34, but it’s a misleading average because the majority of scores were below 34. It may be more useful to use the median of 20 to evaluate student performance, as it’s closer to the majority of scores.
Relevance in theoretical problems
A clear mean formula makes it simple to calculate the average in theoretical problems. You simply add the values together and divide the total by the number of values. The lack of a median formula requires you to order the values chronologically and determine the value in the middle. You may use the location formula to determine the position of the median, but it’s up to you to find the average if the location is a decimal.
Generally speaking, there is only one type of median which describes the value in the middle of a data set. The most common type of mean is the arithmetic mean that describes a data set’s average value. However, there’s also the geometric mean that describes the nth root of the product of n numbers. Other types of means include harmonic and Pythagorean.
Related: How To Find Outliers
Why is it important to know the differences between mean and median?
Anyone who works with data should understand how mean and median differ and when to use one concept rather than the other. Some professional roles that often use these calculations include:
Market research analysts
Related: How Do You Find the Mean?
How and where to use mean
When you need to determine the average of a set of numbers, using the mean formula is often a good choice. However, you should only use this formula if the vector doesn't include significant outliers, as they can skew the results. For example, if the vector includes the numbers 1, 5 and 10, using the mean formula makes sense. If the vector includes the numbers 1, 5 and 1,000, the largest number is too much of an outlier and would significantly skew the calculation.
As a general rule, use mean when you want to calculate the average of a set of numbers that are relatively consistent. For example, say five medical students take the same patient's pulse, resulting in this data set: 72, 74, 80, 76 and 78 beats per minute. These numbers are all relatively close, and there are no major outliers. By using the mean formula, you can accurately determine that the patient's heart rate is about 76 beats per minute.
How and where to use median
Finding the median can also help you determine the average of a set of values, especially if the data set includes significant outliers. For example, the median of the vector 1, 5 and 1,000 is 5, which offers a much better sense of the values of the data set. As a general rule, use median when you want to get the average of a vector that includes a more erratic data set. For example, say five medical students take the same patient's pulse, resulting in this data set: 72, 74, 80, 76 and 96. Although most of these numbers are similar, 96 is an outlier.
If you were to use the mean formula, the outlier would skew the results and indicate an average of 79.6 beats per minute. However, the median of this data set is 76 beats per minute, which is a more accurate representation of the average. It effectively eliminates the outlier, which is likely to be a mistake in the data set.
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