Mean, Median, Mode & Range
When you have a whole list of numbers, it helps to sum it up in just one number. What's a typical value? How spread out are the numbers? The mean, median, and mode each describe the middle of a data set in a different way, and the range tells you how spread out it is. Learn all four, then practice with three activities.
Describing a Data Set
A data set is a list of numbers you collected. Here's one: the points a basketball player scored in her last 7 games.
It's hard to answer "How many points does she usually score?" just by looking at seven numbers. So we use four measures:
| Measure | What it tells you | For this data set |
|---|---|---|
| Mean | The fair share: what each game would be if the points were evened out. | 12 |
| Median | The middle number when the data is put in order. | 11 |
| Mode | The number that shows up most often. | 8 |
| Range | How spread out the data is: the greatest number minus the least. | 12 |
The mean, median, and mode each describe the center of the data (a typical value). The range describes the spread. The rest of this lesson shows how to find each one.
Mean: The Fair Share
The mean (often called the average) is what each value would be if everything were shared out evenly. Picture each number as a stack of cubes. Move cubes from the tall stacks to the short stacks until every stack is the same height. That height is the mean.
You don't need cubes to find the mean. Add up all the numbers to get the total, then share the total equally by dividing by how many numbers there are.
Median: The Middle
The median is the number in the middle. To find it, first put the numbers in order from least to greatest. Then cross off one number from each end, over and over, until you reach the middle.
Mode: The Most Often
The mode is the number that appears most often. A dot plot makes it easy to spot: each dot is one value, so the mode has the tallest column of dots.
Range: The Spread
The range tells how spread out the data is. Subtract the least number from the greatest number. It's the distance from one end of the data to the other on a number line.
Practice
Three ways to practice: level out stacks to find the mean, find any of the four measures, and build a data set that hits a target.
Level It Out
Tap a stack to pick up its top cube, then tap another stack to drop it there. Make every stack the same height to find the mean. Try to use as few moves as you can!
Find It!
Find the mean, median, mode, or range of each data set. Scratch paper helps!
Build a Data Set
Use the + and − buttons to change the five numbers until your data set hits every target. The chart below updates as you go.