The mean, median and mode are three kinds of average. The mean is the sum of the numbers divided by how many there are. The median is the middle value when they are sorted. The mode is the value that appears most often. The average calculator gives all three at once, along with the range and standard deviation.
Here is how to find each one.
The mean
Add up all the numbers, then divide by how many there are. For 2, 4, 4, 4, 5, 5, 7, 9 the sum is 40 and there are 8 values, so the mean is 40 ÷ 8 = 5.
The mean uses every value, which makes it sensitive to extremes. A single very large or very small number pulls it up or down, so it best describes data without big outliers.
The median
Sort the numbers from smallest to largest, then take the middle one. With an odd count there is a single middle value. With an even count, average the two middle values.
For 2, 4, 4, 4, 5, 5, 7, 9 there are eight values, so the median is the average of the fourth and fifth: (4 + 5) ÷ 2 = 4.5. Because the median only cares about position, not size, it is barely moved by an outlier, which makes it a good average for skewed data like incomes or house prices.
The mode
The mode is the value that appears most often. For 2, 4, 4, 4, 5, 5, 7, 9 the value 4 appears three times, more than any other, so the mode is 4.
A set can have more than one mode if values tie for the most appearances, and no mode at all if every value is unique. The mode is the only average that works for non-numeric data, such as the most common shoe size sold.
Which average to use
The three can differ, and the right one depends on the data:
- Mean when the values are fairly even and you want every number to count.
- Median when there are outliers, so a few extreme values do not distort the result.
- Mode when you want the most typical or most frequent value.
The range and spread
Two more figures describe how spread out the numbers are. The range is the largest value minus the smallest, so for 2 to 9 the range is 7. The standard deviation measures the typical distance of values from the mean. The average calculator reports both, along with the sum and count, so you get a full summary from one paste of numbers.
Where this comes up
These averages turn up wherever a set of numbers needs summarising:
- Grades, for an average mark and the middle result in a class.
- Reporting, for a quick summary of a column without a spreadsheet.
- Measurements, for an average reading and how much the readings vary.
Open the average calculator to paste your own numbers and see all of these at once.