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Standard Deviation

Overview

Measuring the spread.

What is it?

A number that tells you how spread out the data is from the mean.

History

Coined by Karl Pearson in 1893, replacing the older 'probable error' metric.

Key Idea

Low SD = Consistent (Reliable). High SD = Wild (Volatile).

Practice This Topic

Concept Guide

Plain English: The Mean tells you the center, but Standard Deviation (Sigma) tells you the risk. If two players average 10 points, but one scores 10 every game (Low SD) and the other scores 0 or 20 (High SD), they are very different players.

Real-world example: Investing. Stocks with high Standard Deviation are risky/volatile. Bonds have low Standard Deviation.

How to do it

  1. Find the Mean.
  2. Subtract the Mean from each data point.
  3. Square those results (to remove negatives).
  4. Find the Average of those squared numbers (Variance).
  5. Take the Square Root.
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Common Pitfall

Thinking a standard deviation of 0 is bad. It just means every single data point is exactly the same.

Word Problem
"Pizza delivery claims '30 mins average'. Driver A: 29, 30, 31. Driver B: 10, 30, 50. Both average 30. Who is more reliable?"
Reasoning: Driver A has a tiny spread (low SD). Driver B is wild (high SD). Driver A is more reliable.

Practice Examples

Formula
σ = √ ( Σ(x-μ)² / N )
Root of the Mean of the Square differences.