Blog

Standard deviation in use: how teachers curve grades, how labs report replicates, how traders read volatility, and what the spread of your commute tells you. Each article works through real numbers and links to the calculator that does the arithmetic.

Concepts

• Does Sample Size Change the Standard Deviation?

  A larger sample does not shrink the standard deviation: it settles toward σ while the standard error falls as 1/√n. Simulated samples show why. 4 min read.

• History of Standard Deviation: From Gauss to Pearson

  How the standard deviation came about: Gauss and the error curve, the probable error, Pearson naming it in 1893–94, and Fisher's variance in 1918. 5 min read.

• How Outliers Affect Standard Deviation (Worked Example)

  One extreme value can multiply the standard deviation many times over. A worked before-and-after example, robust alternatives, and when to keep an outlier. 5 min read.

• Standard Deviation of a Proportion: √(p(1 − p)) Explained

  Why yes/no data has a standard deviation of √(p(1 − p)), why it peaks at p = 0.5, and how it becomes the standard error and margin of error of a survey. 5 min read.

Education

• Common Standard Deviation Mistakes on Exams, With Fixes

  Seven standard deviation mistakes students make on tests, from n vs n − 1 to Sx vs σx, each shown as a wrong line and a right line on the same seven numbers. 5 min read.

• Grading on a Curve: How the Mean and SD Set Grades

  How teachers curve grades with the mean and standard deviation: z-score curves, flat adds and fixed percentages, worked on a class of ten scores. 5 min read.

Science & health

• How to Report Lab Replicates: Mean ± SD, %RSD and n

  Report replicate lab measurements properly: round the SD to 1–2 significant figures, match the mean to it, add %RSD and n. A worked eight-replicate example. 4 min read.

• Reference Ranges: Why Mean ± 2 SD Flags 1 in 20 Healthy People

  How lab reference ranges are built from the central 95% of healthy people: mean ± 1.96 SD, percentiles, log transforms for skewed tests, why 5% fall outside. 4 min read.

Business & finance

• Bollinger Bands: Rolling Standard Deviation, Worked

  How Bollinger Bands are built from a rolling mean and rolling SD, worked on a short price series, what a squeeze means, and why ±2 SD is not a 95% band. 5 min read.

• Six Sigma Explained: Sigma Levels, DPMO and the 1.5σ Shift

  What a sigma level means in quality control, how defects per million are worked out, where 3.4 DPMO comes from, and how sigma relates to Cp and Cpk. 5 min read.

• Tolerance Stack-Up: Worst Case vs RSS and Process SD

  Worst-case versus root-sum-square tolerance stack-up, how part SDs combine into an assembly SD, and the Cp and Cpk link, with a worked three-part assembly. 4 min read.

• Volatility and Diversification: SD of Returns Explained

  Volatility is the standard deviation of returns. How to annualise it with √252 or √12, and why a two-asset portfolio is less volatile than its parts. 5 min read.

Data & technology

• Reading Error Bars: SD vs SE vs 95% Confidence Interval

  SD, SE and 95% CI error bars look alike but can differ in width by 3× or more. A worked n = 10 example, and what overlapping bars do and do not tell you. 4 min read.

• Standard Deviation in A/B Testing: Sample Size and Duration

  Why the variance of your metric sets an A/B test's sample size and length, the SD of a conversion rate, and a full sample-size calculation worked by hand. 5 min read.

• Standard Deviation in Machine Learning: Feature Scaling

  How z-score standardisation uses the mean and SD to scale features, why models need it, how to avoid leakage, and what batch normalisation does. 5 min read.

• Standard Deviation of Likert Scale Data: Is It Meaningful?

  Is the standard deviation meaningful for 1–5 ratings? When it works, when to report the median, IQR or % agree, and two items with the same mean. 4 min read.

Everyday life

• Standard Deviation in Everyday Life: Plan for the Spread

  Commutes, grocery bills, sleep and phone battery: how knowing the spread as well as the average helps you plan, such as leaving mean + 1 SD early. 5 min read.

• Standard Deviation in Sports: Measuring Consistency

  How standard deviation measures an athlete's consistency, when a steady or streaky player is the better bet, and how the CV compares players across sports. 5 min read.

• Standard Deviation in Weather and Climate: Anomalies Explained

  Temperature anomalies in SD units: why a month 2 SD above normal is rare, and why daily temperatures vary far more than monthly averages. Worked examples. 4 min read.

• Variance in Gambling: Expected Value vs the Swings

  The SD of repeated bets grows as √n while the expected loss grows as n. Worked with a roulette bet, to show why short sessions mislead and long ones do not. 5 min read.

Start with the guides

• What is standard deviation?

  What the number means, its units, and how to read a high, low or zero SD.

• How to interpret standard deviation

  Judge a result against the mean, the range and a benchmark, then write it up.

• Standard deviation vs mean

  Centre and spread, mean ± SD vs ± SE, and what outliers do to each.

• Standard deviation and the normal distribution

  How σ sets the width of the bell, and how to check data for normality.

• Standard deviation in probability

  The SD of a random variable, for dice, sums, averages and named distributions.

• All learning pages

  The full reading order, from first principles to software guides.

Written and reviewed by our editorial team. Last updated September 27, 2026. Method and sources: how these numbers are computed.