Measures of Central Tendency and Variability

The one idea: A single number for the "center" of your data (mean, median, or mode) tells you where the data tends to sit — it says nothing about how far the data wanders from there. Two datasets can share an identical mean and describe completely different businesses; you only find out which one you have by also reporting spread.

⚠️ The trap: "Average daily sales: $500" sounds like a complete sentence. It isn't. A store that sells almost exactly $500 every day and a store that swings from $100 to $900 both average $500 — and they need opposite operational responses (the second one needs a cash and staffing buffer the first one doesn't). Reporting the mean alone hides the exact fact a decision-maker needs.

Central tendency answers "where's the middle?" Variability answers "how far does the data spread out from there?" You need both, always, together — a center without a spread is a rumor about the data, not a description of it.

The three measures of center

Mean — the arithmetic average. Population: μ = ΣX / N. Sample: x̄ = Σx / n. The mean uses every value in its calculation, which is exactly why it's sensitive to extreme values: one huge number pulls it hard in that direction.

Median — the middle value once the data is sorted. Find its position first: (n + 1) / 2. If n is odd, that position lands on a real value. If n is even, it lands between two values — average them. Twelve monthly salaries sorted (3310, 3355, 3450, 3480, 3480, 3490, 3520, 3540, 3550, 3650, 3730, 3925) have their median at position (12+1)/2…