Roll two dice. Once, record the sum. Next time, record the product. Do 50 of each. Plot both. The shapes are wildly different.
Try this
12
out of 36 equally-likely two-dice outcomes = 13
The experiment
- Roll two dice 50 times, recording the sum each time.
- Roll two dice 50 times more, recording the product.
- Plot both as bar charts side by side.
- Sums pile up around 7; products sprawl from 1 to 36.
The product distribution is right-skewed — a long tail on the high end. You see the same shape in incomes, city sizes and earthquake magnitudes.
Your turn
How many of the 36 dice-pairs give a product greater than 12?
Why?
Sums cluster around 7. Products spread out — most are below 12, but a few are 30 or 36. Multiplication blows numbers apart; addition keeps them tame.
The product distribution is right-skewed — heavy tail on the high end. You see this shape in incomes, city sizes, earthquake magnitudes.