Variation is the signal

Beginners look only at averages. But the spread of the data, how much values vary, is just as important.

Why spread matters

ExampleTwo medicines lower blood pressure by 10 points on average. With medicine A, almost everyone drops by 8 to 12 points. With medicine B, some people drop by 30 points and others go up by 10. Same average, very different medicines.

Measuring spread

• Range: smallest to largest. Simple, but driven by extremes.
• Interquartile range (IQR): the middle 50% of values. Robust to outliers; pairs well with the median.
• Standard deviation (SD): roughly, the typical distance of values from the mean. Pairs with the mean.

Spread decides what you can detect

Whether a difference between two groups is "real" depends on the difference compared with the spread. A 2-point difference is huge if everyone's values are within 1 point of each other, and meaningless if values vary by 50.

This idea, signal compared with noise, is at the heart of almost every statistical test.

RememberAlways report spread next to the average. A difference only means something compared with how much the data varies.