Mean, Median, Mode Calculator

Find the mean, median, mode, and range of a data set along with other information such as the total sum, count, min, and max values.

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Summary Statistics:

Mean:
 
Median:
 
Mode:
 
Range:
 
Smallest:
 
Largest:
 
Sum:
 
Count:
 

Sorted Data:

 


How to Calculate Mean, Median, Mode, and Range

Mean, median, and mode are different ways to measure the center of a data set; this is referred to as the central tendency.[1]

The mean is the average of the data, the median is the middle, and the mode is the most commonly occurrences. The data represented on the graph below highlights the differences between these statistics.

Graph showing the mean, median, and mode of the data

The range describes the variance between the numbers in the set, or the difference between the largest and smallest number.

These summary statistics provide information on a data set. The minimum value, maximum value, sum, count, and standard deviation are other summary statistics for data sets.

Person working with statistics on a chart

How to Find the Mean

In statistics, the mean is the average value of a set of numbers. It’s also referred to as the arithmetic mean.

To find the mean, add up all of the numbers to find the sum, then divide the sum by the number of values in the set.

Example: Find the mean for the set [1,2,3,4,5,6,7,8]


sum = 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 = 36
mean = 36 ÷ 8 = 4.5

Learn more about how to find the mean.

How to Find the Median

The median is the middle number in an ordered set of numbers. If the count of numbers in the set is even, then the median is the average of the two middle numbers.

To find the median of a data set, start by sorting the set in ascending order, and then count the values.

If the count is odd, divide the count by 2, then round up to get the index of the median. The median is the value at that index in the set.

Example: Find the median for the set [1,3,5,7,15,22,29]


count ÷ 2 = 3.5
middle index = 3.5 rounded up = 4
median = number at 4th index = 7

If the count is even, then find the two middle numbers in the set. Divide the count by 2 to find the index of one of the middle numbers. Add 1 to the first index to get the index of the second middle number.

Find the values at those indexes, then add them together and divide by 2 to find the median.

Example: Find the median for a set of numbers [1,3,5,7,15,22,29,38]


count ÷ 2 = 4
lower middle index = 4
upper middle index = 4 + 1 = 5
number at 4th index = 7
number at 5th index = 15
median = (7 + 15) ÷ 2 = 11

Learn more about how to find the median.

How to Find the Mode

The mode is the number that occurs most frequently in a set of numbers. To find the mode, count the number of times each number in the set occurs. The number with the greatest count is the mode.

A set of data can have more than one mode if each of the modes occur the same number of times.

Example: Find the mode for a set of numbers [1,2,2,2,3,4,5,5,5,6,7,7]


1 occurs one time
2 occurs three times
3 occurs one time
4 occurs one time
5 occurs three times
6 occurs one time
7 occurs two times

modes = 2 & 5

Learn more about how to find the mode.

How to Find the Range

The range is the difference between the smallest and largest numbers in a set of numbers. To calculate the range, find the largest and smallest numbers in the set, then subtract the smallest number from the largest number.

Example: Find the range for a set of numbers [3,7,22,54]


smallest number = 3
largest number = 54
range = 54 – 3 = 51

Learn more about how to find the range.

References

  1. US National Library of Medicine | National Institutes of Health, Measures of central tendency: Median and mode, https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3157145/