Math Through Sports
Middle and spread: mean, median, mode, range
7 min · Four numbers describe a set — and one strange game can pull one of them badly.
- Mean, median, mode, range
- Trends and outliers
- Graphs and charts
The stat
Four numbers describe a set — and one strange game can pull one of them badly.
His average says eighteen. He scored twelve or fewer in four games out of five.
- 1. Watch
- 2. Try it
- 3. Predict
- 4. Explain
- 5. Get feedback
- 6. Master
Video slot · not yet filmed
The episode for this lesson is in production. Everything it teaches is below — the storyboard, the full script, and the same questions the video pauses on. Nothing here is blocked while we film.
What happens, and when
- 0:00HookA graphic says "18.0 PPG". Four of five games were 12 or fewer
- 0:20ConceptMean, median, mode and range on one bar chart
- 0:55Sports example8, 10, 12, 10, 50 — the 50 towers over the rest
- 1:35Interactive questionVideo pauses: which number describes him better?
- 1:55ExplanationOne outlier drags the mean and barely moves the median
- 2:30ChallengeSpot the outlier in a second chart
- 2:52Mastery checkBack to the lesson questions
Try it
These are the questions the video stops on. They are answerable here whether or not you watch — and they are what counts toward mastery. Watching alone does not.
Try it · paused at 1:35
Games of 8, 10, 12, 10 and 50. Which better describes a typical night?
The video is paused until you answer. Answering here counts toward mastery.
Try it · paused at 2:30
What makes the 50-point game an outlier?
The video is paused until you answer. Answering here counts toward mastery.
Learn the number
The mean is the average: add everything, divide by how many. The median is the middle value once you put them in order. The mode is the value that appears most. The range is the largest minus the smallest.
An outlier is a value far away from the rest. One 50-point explosion can drag the mean upward while the median barely moves.
On a bar chart, the outlier is the bar that towers over the others. On a line graph, it is the spike.
Read the stat
A player scores 8, 10, 12, 10 and 50 points across five games.
- Mean: 8 + 10 + 12 + 10 + 50 = 90, and 90 ÷ 5 = 18.
- Median: in order they are 8, 10, 10, 12, 50 — the middle value is 10.
- Mode: 10 appears twice, more than anything else.
- Range: 50 − 8 = 42.
Mean 18, median 10, mode 10, range 42. The mean is nearly double the median.
Your turn
Find the median and the range of 14, 9, 21, 9 and 17.
Explain what it means
When the mean is far above the median, one or two big values are doing the work. Saying "he averages 18" hides that he scored 12 or fewer in four of five games.
Make a prediction
Look at a player's last five games. Predict their next score — and decide first whether the mean or the median is the more honest starting point.
Review what happened
Was the next game closer to the mean or the median? With one big outlier in the set, the median usually wins.
Check your understanding
0 of 4 correct
Every question has to be right for this lesson to count as complete. Miss one and you can try it again.