Percentiles & z-Scores

How unusual is a value?

An interactive lesson with 7 steps, about 6 minutes: you predict, drag and solve, with instant feedback on every answer. It runs in your browser and needs JavaScript.

What you’ll learn

• z-score: $z = (x - \mu)/\sigma$, the number of standard deviations from the mean.
• For normal data, z determines the percentile (z = 1.28 is the 90th).
• Quartiles, IQR and the 1.5 × IQR rule describe any data and flag outliers.

Steps

1. Standard units
2. An IQ score
3. The top ten percent
4. An IQ cut-off
5. Box plots
6. An outlier?
7. Who did better?