What is the difference between mean and median?

The mean is the arithmetic average, found by adding all values and dividing by the count. The median is the middle value when the data is sorted in order. In a symmetrical data set they are close together, but in a skewed set the median is usually the better measure of centre because it is not pulled by extreme values the way the mean is.

What does it mean when there is no mode?

If every value in the data set appears exactly once, there is no mode because no value occurs more frequently than any other. Some data sets have more than one mode (bimodal or multimodal) when two or more values share the highest frequency.

How is the range calculated?

The range is the difference between the largest and smallest values in the data set. It is the simplest measure of spread but is sensitive to outliers because a single extreme value can make the range much larger than the typical spread of the data.

Mean Median Mode Range Calculator

This calculator computes all the core descriptive statistics for a data set in one step: the mean, median, mode, range and count. Descriptive statistics summarise a collection of numbers so you can understand the typical value, the spread, and the most common result without having to process every figure individually. The mean is the arithmetic average and gives you the balancing point of the data; the median is the middle value after the data is sorted and is more resistant to extreme values; the mode is the value that appears most often and is especially useful with categorical or repeated data; and the range measures the total spread from the smallest to the largest value. To use the calculator, type or paste your numbers into the input box separated by commas. You can include decimals and negative numbers. The calculator parses the list, sorts it, and computes all four statistics simultaneously. The hero figure shown is the mean, with the median, mode, range and count shown below it. If a data set has no repeated values, the mode will show as none; if two or more values tie for highest frequency, all of them are listed. This tool is useful for students working through statistics assignments, teachers demonstrating central tendency, researchers doing a quick sanity check on a data set, and anyone comparing results across a group of numbers. Results are descriptive only and do not account for sampling method or data quality.

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Data set (comma-separated numbers)

5.17

mean (average)

Median5

Mode8

Range6

Count6

How it works

The calculator splits your input on commas, converts each token to a number, and ignores any blank or non-numeric entries. It then sorts the values in ascending order. The mean is the sum divided by the count. The median is the middle value for an odd count, or the average of the two middle values for an even count. The mode is found by tallying how often each value appears and returning the value or values with the highest frequency; if all values appear only once, there is no mode. The range is the maximum value minus the minimum value.

Worked example

Using the default data set 4, 8, 6, 8, 3, 2: sorted it becomes 2, 3, 4, 6, 8, 8. The sum is 31, so the mean is 31 divided by 6 = 5.17. The median of six values is the average of the 3rd and 4th values: (4 + 6) / 2 = 5. The value 8 appears twice (more than any other), so the mode is 8. The range is 8 minus 2 = 6. The count is 6.

Related calculators

Variance Calculator: compute population or sample variance and standard deviation from your data set.
Z-Score Calculator: find how many standard deviations a value sits from the mean.
Normal Distribution Calculator: find cumulative probabilities using the standard normal curve.
Percent Error Calculator: measure how far a result deviates from an accepted value.

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