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Standard Deviation

The Hook

Measuring the spread.

What is it?

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

Time Travel (History)

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

Cheat Code

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

Practice This Now!

The Field Guide

In 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.

In The Real World: 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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Booby Trap!

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

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

Training Drills

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