The median and average (mean) are two important measures of the central tendency in statistics. The median is the exact middle value, which separates lower and higher values into two groups. The average is the sum of all of the values, divided by the number of values. Here is a closer look at the median vs average, examples showing how you find them, and when you should use one over the other.
Average
Most people are familiar with the concept of “average” because it’s the most common method of calculating grades. The average is the mean of a set of numbers. It is the sum of a set of values divided by the number of values. For example, let’s find the average of a set of test scores:
64, 72, 88, 92, 100
Find the average by adding up the scores and dividing by the number of tests (5, in this case):
Average = (62 + 72 + 88 + 92 + 100) / 5 = 414 / 5 = 82.5
The average test score is 82.5.
The average gives the central tendency of a set of numbers. It provides a good picture of the data when it more or less follows a normal distribution. However, when the data set is skewed or there are outliers, the median is a better option.
Median
The median is the middle value of a data set. Find the median by listing values in numerical order. The middle of the sequence is the median.
For an odd number of values, finding the median is easy. For example, here is the list of test scores again:
64, 72, 88, 92, 100
The median value is 88.
If there are an even number of values, then two of them are in the middle. Here, find the median by taking the average of these values. For example, let’s find the median of this data set.
3, 9, 22, 4, 73, 15
First, order the data set:
3, 4, 9, 15, 22, 73
The two middle values are 9 and 15. Find the average of these numbers by adding them and dividing by the number of values (2).
average of 9 and 15 = (9 + 15)/2 = 12
The median of this data set is 12.
The median is helpful when a data set does not follow a normal distribution. For example, the median value of homes in real estate gives a better picture of home values than the average because outliers (homes in poor condition or exceptional ones) skew the data. Most of the time, the median trends toward the tail of the skew. So, the median is often higher than the average for positive-skewed data and lower than the average for negative-skewed data. However, there are exceptions, so this is not a hard-and-fast rule.
Median vs Average – Summary
Use the average when the data set is fairly uniform. If it is skewed or there are outliers, the median helps find the central value.
| Median | Average | |
|---|---|---|
| Definition | The median is the middle value that separates the lower and higher halves of a number set. | The average is the arithmetic mean of a number set. |
| Uses | The median finds the central tendency of a skewed distribution. | The average finds the central tendency of a normal distribution. |
| Calculation | List the numbers in order and find the number in the middle. | Add up all the values and divide the sum by the total number of values. |
| Example: Normal distribution | 2, 3, 3, 5, 8, 10, 11 median = 5 | 2, 3, 3, 5, 8, 10, 11 (2+3+3+5+8+10+11)/7 = 6 |
| Example: Skewed distribution | 2, 2, 3, 3, 5, 7, 8, 130 (3+5)/2 = 4 | 2, 2, 3, 3, 5, 7, 8, 130 (2+2+3+3+5+7+8+130)/8 = 20 |
References
- Maindonald, John; Braun, W. John (2010). Data Analysis and Graphics Using R: An Example-Based Approach. Cambridge University Press. ISBN 978-1-139-48667-5.
- Sheskin, David J. (2003). Handbook of Parametric and Nonparametric Statistical Procedures (3rd ed.). CRC Press. ISBN 978-1-4200-3626-8.
- Underhill, L.G.; Bradfield, D. (1998). Introstat. Juta and Company Ltd. ISBN 0-7021-3838-X.
- von Hippel, Paul T. (2005). “Mean, Median, and Skew: Correcting a Textbook Rule”. Journal of Statistics Education. 13 (2). doi:10.1080/10691898.2005.11910556