What is the difference between mean and median?

The mean is the arithmetic average of all values, while the median is the middle value when the data is sorted. The median resists outliers, so it can describe a skewed data set better than the mean.

Can a data set have more than one mode?

Yes. If two or more values are tied for the highest frequency, the data set is multimodal and the calculator lists every value that shares that top count, sorted in ascending order.

How is the median found when there is an even number of values?

With an even count there is no single middle value, so the median is the average of the two central values after sorting. With an odd count it is simply the single middle value.

What does the range tell me?

The range is the difference between the largest and smallest values, giving a quick measure of total spread. A large range signals widely scattered data, but it only reflects the two extremes, not the distribution in between.

Mean Median Mode Range Calculator

Dataset (comma-separated)

Mean5.0000

Median4.5000

Mode4

Range7.0000

This calculator reports four key descriptive statistics for a list of numbers in one pass: the mean (arithmetic average), the median (middle value), the mode (most frequent value or values), and the range (spread from lowest to highest). Together they summarize where a data set centers and how widely it is spread, making them a go-to first step in any statistics assignment or quick data check.

Formula

mean = (sum of values) / n; range = max - min; median = middle of sorted values

n: The number of values in the data set
mean: Sum of all values divided by n (the average)
median: The middle value of the sorted list, or the average of the two middle values
mode: The value(s) that occur most often
range: The largest value minus the smallest value

How it works

Enter your data set as a list of numbers. The calculator accepts any real values and processes them all together.
It sums the values and divides by the count for the mean, sorts them to find the middle value for the median, counts frequencies to find the mode (returning every value tied for most frequent), and subtracts the minimum from the maximum for the range.
All four statistics are displayed at once. When the count is even, the median is the average of the two middle values; when several values tie for most frequent, all of them are listed as modes.

Worked example

Analyze the data set 4, 8, 15, 16, 16, 23, 42.

Mean: (4 + 8 + 15 + 16 + 16 + 23 + 42) / 7 = 124 / 7, about 17.714.
Median: the middle of seven sorted values is the 4th, which is 16.
Mode: 16 appears twice, more than any other value; range: 42 - 4 = 38.

Mean about 17.71, median 16, mode 16, and range 38.

Frequently asked questions

What is the difference between mean and median?: The mean is the arithmetic average of all values, while the median is the middle value when the data is sorted. The median resists outliers, so it can describe a skewed data set better than the mean.
Can a data set have more than one mode?: Yes. If two or more values are tied for the highest frequency, the data set is multimodal and the calculator lists every value that shares that top count, sorted in ascending order.
How is the median found when there is an even number of values?: With an even count there is no single middle value, so the median is the average of the two central values after sorting. With an odd count it is simply the single middle value.
What does the range tell me?: The range is the difference between the largest and smallest values, giving a quick measure of total spread. A large range signals widely scattered data, but it only reflects the two extremes, not the distribution in between.

Related calculators

Average Calculator Fibonacci Calculator Number Sequence Calculator