Statistics and Probability
Mean, median and mode
Find the mean, median, mode and range of a small set of numbers.
An average is one number that stands in for a whole set of them. There are three worth knowing, and they answer three different questions, so the interesting part is not the arithmetic but choosing which one to use.
The three averages
The mean shares the total out equally. The median is the value sitting in the middle once you have put them in order. The mode is the one that turns up most often. The range is not an average at all — it just tells you how spread out the numbers are.
Worked example
Find the mean of 4, 8, 6, 10 and 2.
Add them all up: 4 + 8 + 6 + 10 + 2 = 30.
The mean pretends everyone got the same, so first you need the whole pile.
Try it together
Now find the median of 12, 5, 9, 3 and 7.
The median is the middle value, but 'middle' only means anything once the numbers are lined up in order. That first step is the one people skip.
1.Put them in order, smallest first. What is the smallest of the five?
When there is no single middle
With an even count, two numbers share the middle, so the median is halfway between them. For 2, 4, 6, 8 the middle pair is 4 and 6, so the median is 5.
Have a go
Have a go on your own: find the median of 10, 2 and 6.
Hint: In order they are 2, 6, 10.
Ready to practice?
Eight questions on what you have just read. Nothing is timed, and you can play as many times as you like.