R Variance and Standard Deviation

How it works

Variance averages squared deviations using a specified denominator. R’s var and sd use the sample denominator n-1. Standard deviation returns to the original measurement units. A population-style calculation for the observed finite list instead divides by n. State which interpretation a report uses and avoid estimating a sample variance from one observation.

Run this R example

These examples run locally with R, not PHP, Python or JavaScript. The reviewed baseline is R 4.5.2 on Windows x64/UCRT, using only packages shipped with R. This is a tested version, not a newest-release claim. Install your own R from the official R project; an IDE is optional. Save the complete source as variance.R in a separate learning folder and run Rscript --vanilla variance.R. Keep code and fictional fixtures separate from a real project.

Bhylu has no R browser runner. There is no Try in playground link because the existing Python and JavaScript editors do not execute R. No package installation, account, network dataset, Apache, MySQL or PHP setting is needed to run these base-R sources.

The complete download uses a local scope, restores its temporary options and treats unexpected warnings as errors. Examples that handle an expected warning do so narrowly. Random examples change only their R process’s RNG state. File examples own their temporary output; figure examples leave their named PNG in the current learning folder and refuse to overwrite it. Use a new empty folder to rerun a figure.

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For the optional collection downloader, save download-examples.mjs in an empty folder and run node download-examples.mjs. Local preview before publishing uses node download-examples.mjs http://127.0.0.1:8000/examples/r/. It refuses an existing bhylu-r-examples folder and does not install or execute R.

Example

local({
  previous_options <- options(warn = 2, digits = 8, stringsAsFactors = FALSE)
  on.exit(options(previous_options), add = TRUE)
  visits <- c(8, 10, 12)
  population_variance <- mean((visits - mean(visits))^2)
  cat("sample variance:", var(visits), "\n")
  cat("sample sd:", sd(visits), "\n")
  cat("population calculation:", sprintf("%.3f", population_variance), "\n")
  invisible(NULL)
})

visits <- c(8, 10, 12)
population_variance <- mean((visits - mean(visits))^2)
cat("sample variance:", var(visits), "\n")
cat("sample sd:", sd(visits), "\n")
cat("population calculation:", sprintf("%.3f", population_variance), "\n")

Expected result

sample variance: 4
sample sd: 2
population calculation: 2.667

The three observations have squared deviations four, zero and four. Dividing their sum by two gives the sample variance four. A larger number does not explain why sessions differed; investigate the data and context rather than treating variability as a cause.