When averages mislead
Change the group sizes and watch the overall winner change.
Reverse the overall winner
1 question · No time limit
Example
Example
Team A has the higher mean in both groups. Can you make Team B lead overall by at least 2 points?
Each slider sets that team’s percentage in Group 1, from 10% to 90% in whole percentages. The rest belongs to Group 2. Means for Group 1, then Group 2, stay fixed: A = 79, 33; B = 73, 27.
1. Predict
| Group 1 | Group 2 | |
|---|---|---|
| Team A | 79 | 33 |
| Team B | 73 | 27 |
Team A
Team B
Group 1Group 2
Combined mean
Make a prediction first. It is not scored.
2. Test your idea
Try the controls, then check your solution.
Why?
One solution puts 32% of A and 50% of B in Group 1. The overall means are 47.72 for A and 50 for B, so they differ by 2.28.
For each team, overall mean = Group 1 share × Group 1 mean + Group 2 share × Group 2 mean, with shares written as fractions of 1.
The group sizes supply the weights. Comparing each group separately can therefore tell a different story from comparing the overall means.
Revisit your prediction
The starting overall means are 56 for A and 50 for B. These use the starting weights, before any slider changes.
Keep exploring the experiment.
3. Change the rules
A linked challenge. This answer is not scored.
Continue your unfinished round
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- Answered
- 0 / 1
- Active time
- 0:00
Round complete.
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How this data is usedHelp
Try the controls, then check your solution.
Your first checked solution is recorded. You can keep experimenting afterwards.
About this practice
Learn a method
Weight the groupsChange the group sizes and watch the overall winner change.
For a broader mix of practices, explore the statistics practice test. Membership is required to start a test.
Report a problem
Optional and off by default. Share starts, completions, replays and error categories. For visits from ChatGPT, starts and completions can also include the first QuickenBrain page and broad country. No answers, drawings or names.
How this data is used