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Why can a higher average prize still feel like a worse deal?

Imagine one fictional game awards 10 points for certain. Another awards 30 points half the time and zero otherwise. The second has the higher average, but its possible outcomes include disappointment. Expected value summarizes a distribution; it does not tell you which outcome will occur or how much uncertainty a person is willing to accept.

3–5 min

Questions you could explore

  • Why is the second game’s average of 15 points an outcome that no single play actually awards?

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Maths and statistics

When one long wait changes the average

An average wait can sound straightforward until one person waits much longer than everyone else. The mean and median offer two ways to summarize that same group. Their different responses to an unusually large value raise a practical question: what do we want an average to tell us?

5–7 min

When one long wait changes the average

Maths and statistics5–7 minAn average wait can sound straightforward until one person waits much longer than everyone else. The mean and median offer two ways to summarize that same group. Their different responses to an unusually large value raise a practical question: what do we want an average to tell us?

Maths and statistics

How is random sampling different from random assignment?

A study can choose people at random, assign them to groups at random, do both, or do neither. Those choices answer different problems: who the findings may describe, and how fairly the study compares conditions.

3–5 min

How is random sampling different from random assignment?

Maths and statistics3–5 minA study can choose people at random, assign them to groups at random, do both, or do neither. Those choices answer different problems: who the findings may describe, and how fairly the study compares conditions.

Why does the Gregorian calendar sometimes skip a leap year?

Maths and statistics2–3 minThe familiar 'every four years' rule has exceptions. The Gregorian calendar treated 1900 and 2000 differently because its century rules refine how calendar years track the solar year.

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