Mean, Median, Mode and Standard Deviation Explained (With a Free Calculator)
Five numbers can describe almost any data set. This guide explains what each one means and when to use it.
What is the Statistics Calculator?
Paste a comma-separated list of numbers and the tool summarises the whole set. It finds the mean, the middle value, the most frequent value, the spread from smallest to largest, and the population standard deviation, which measures how far the numbers typically sit from the mean.
How to use it
- Type your numbers separated by commas.
- Check that every entry is a number.
- Calculate to see the full summary of your data set.
Worked example
2, 4, 4, 4, 5, 5, 7, 9 gives mean 5, median 4.5, mode 4, range 7, population standard deviation 2 and count 8.
What is the median of 2, 4, 4, 4, 5, 5, 7, 9?
Sort the numbers, then take the middle value. With eight numbers there are two middle values, 4 and 5, so the median is their average, 4.5. The mean of the same set is 5, the mode is 4, the range is 7 and the population standard deviation is 2.
Frequently asked questions
What is the difference between mean and median?
The mean is the total divided by the count, while the median is the middle value when the numbers are sorted. The median is less affected by one very large or very small value.
What does standard deviation tell me?
It tells you how spread out the numbers are. A small value means the numbers cluster near the mean; a large value means they are more scattered.