Standard deviation tells you how spread out the numbers in a dataset are from the average (the mean).

Quick Scoop: Core idea

  • It measures how far, on average, each value is from the mean.
  • Low standard deviation ⇒ points are packed close to the mean (data is consistent).
  • High standard deviation ⇒ points are scattered far from the mean (data is variable).
  • It’s expressed in the same units as your data (dollars, centimeters, minutes, etc.), so it’s easy to interpret.

Think of test scores: if everyone scores around 80, standard deviation is small; if scores range from 10 to 100, it’s large.

A simple story example

Imagine you and four friends run a 100 m dash every day for a week and record times:

  • Group A times (in seconds): 11.9, 12.0, 12.1, 12.0, 12.0
    • Mean ≈ 12.0.
    • All times are very close to 12.0 ⇒ small standard deviation (you’re very consistent).
  • Group B times: 10.5, 11.8, 12.0, 13.4, 14.0
    • Mean might still be around 12.0.
    • Times are all over the place ⇒ large standard deviation (sometimes very fast, sometimes much slower).

Same mean, totally different “feel” to the data; standard deviation captures that “feel.”

How it’s defined (light math)

Conceptually, standard deviation is:

  1. Take each value’s distance from the mean (its deviation).
  2. Square those deviations and average them (that’s the variance).
  3. Take the square root of that average: that’s the standard deviation.

So if variance is the “average squared distance from the mean,” standard deviation is just its square root, bringing it back to the original units.

What does it mean in practice?

  • In many real‑world, roughly bell‑shaped (normal) datasets:
    • About 68% of values lie within 1 standard deviation of the mean.
    • About 95% lie within 2 standard deviations.

So if average monthly phone bill is 40 and the standard deviation is 10, most people are roughly between 30 and 50; very few are way outside that range.

Why people care about it

  • Science & medicine: shows how variable measurements are (e.g., blood pressure across patients).
  • Business & finance: used as a measure of risk or volatility (e.g., how much returns swing around the average).
  • Everyday stats: whenever you see “mean ± SD”, the “± SD” part tells you how tightly or loosely data clusters around that mean.

TL;DR: Standard deviation is “typical distance from the mean,” telling you whether your data is tightly clustered or widely scattered around the average.

Information gathered from public forums or data available on the internet and portrayed here.