How to Find Mean, Median, Mode, and Range
Mean, median, mode, and range are the four building blocks of descriptive statistics. This guide walks through each calculation step by step with real examples so you can analyze any data set with confidence.
Step 1 – Collect and Arrange Your Numbers
Before calculating anything, write down all the numbers in your data set and sort them from smallest to largest. Sorting is not needed for finding the mean, but it is essential for finding the median and mode, and it helps you spot the minimum and maximum values you need for the range.
For example, suppose a teacher recorded the following quiz scores for seven students: 72, 85, 90, 85, 68, 91, 77. Arranged in order, the list becomes: 68, 72, 77, 85, 85, 90, 91. This sorted list is the foundation for every calculation in this guide.
If your data set has duplicate values, keep all copies. Removing duplicates changes the mode and may affect the median. Every data point in the original set should appear in your sorted list.
Step 2 – Calculate the Mean
The mean is the arithmetic average. Add all the values together, then divide by how many values there are. Using the quiz scores: 68 plus 72 plus 77 plus 85 plus 85 plus 90 plus 91 equals 568. There are 7 values, so divide 568 by 7 to get a mean of approximately 81.1.
The mean is sensitive to outliers, meaning one very high or very low value can pull the average significantly in that direction. If one student scored a 10 instead of a 68, the mean would drop dramatically even though six of the seven scores were unchanged. This is why the mean alone does not always tell the full story of a data set.
The mean is widely used for calculating grade point averages, batting averages, average monthly expenses, and other everyday metrics where you want a single representative value for a collection of numbers.
Step 3 – Find the Median
The median is the middle value when the data is sorted in order. With 7 values, the middle position is the 4th value (since there are 3 values below and 3 above it). Counting through the sorted list: 68, 72, 77, 85, the 4th value is 85. The median is 85.
When your data set has an even number of values, there is no single middle position. In that case, find the two middle values and calculate their average. If the scores were 68, 72, 77, 85, 90, 91, the two middle values are 77 and 85. Their average is (77 plus 85) divided by 2, which equals 81.
The median is more resistant to outliers than the mean. This is why median household income is often reported instead of mean household income; a small number of extremely high earners would inflate the mean and make it unrepresentative of most households.
Step 4 – Identify the Mode
The mode is the value that appears most frequently in the data set. Scan through the sorted list and look for repeats. In the quiz score example, the value 85 appears twice while all other values appear once. The mode is 85.
A data set can have more than one mode if two or more values tie for most frequent. A set with two modes is called bimodal. A set with three or more modes is called multimodal. If every value appears exactly once, the data set has no mode.
The mode is most useful for categorical data where you want to know the most common response. A clothing retailer tracking which shoe size sells most frequently, or a restaurant analyzing which menu item is ordered most often, would rely on the mode rather than the mean or median.
Step 5 – Calculate the Range
The range measures the spread of the data by finding the difference between the largest and smallest values. Subtract the minimum from the maximum. In the quiz score example, the maximum is 91 and the minimum is 68. The range is 91 minus 68, which equals 23.
A large range indicates that the data values are spread out widely, while a small range means the values cluster closely together. A class where quiz scores range from 40 to 98 has much more variation than a class where scores range from 78 to 92, even if both classes have similar means.
The range is easy to calculate but can be distorted by a single extreme outlier. More advanced measures of spread, like standard deviation and interquartile range, are used in statistics when a more complete picture of variability is needed. For everyday analysis, however, the range gives a quick and intuitive sense of how diverse the data is.