What does the Standard Deviation Calculator do?

The Standard Deviation Calculator takes your data and returns the test statistic, degrees of freedom, p-value and effect size with a plain-English interpretation. Paste numbers or summary stats and get a result in seconds on DataTistics.

What data do I need to paste?

You can paste raw values (one per line or comma-separated) or summary statistics (mean, SD, n) depending on the calculator. The page shows the exact input format above the form.

How do I interpret the p-value and effect size?

If p < 0.05 the result is statistically significant. Check the effect size (Cohen's d, eta-squared, Cramer's V etc.) for practical importance: small ~0.2, medium ~0.5, large ~0.8, and the confidence interval for plausible values.

Standard Deviation Calculator

Q: How do I interpret the p-value and effect size?

If p < 0.05 the result is statistically significant. Check the effect size (Cohen's d, eta-squared, Cramer's V etc.) for practical importance: small ~0.2, medium ~0.5, large ~0.8, and the confidence interval for plausible values.

The formula

Sample standard deviation:

s = √( Σ(xᵢ − x̄)² ÷ (n − 1) )

The n − 1 (Bessel’s correction) makes s an unbiased estimate of the population SD when you only have a sample. Divide by n instead for the population SD.

How the calculation works

Find the mean (x̄) of your values.
Subtract the mean from every value and square each difference.
Sum the squared differences.
Divide by n − 1 (sample) or n (population).
Take the square root.

Assumptions to check

The values should be at least roughly symmetric, SD describes spread best for bell-shaped data.
Outliers inflate the SD dramatically; report median/IQR alongside if present.

The calculator runs the test regardless, but the result is only trustworthy if the assumptions hold. DataTistics checks these automatically on full datasets.

Worked example

Ten delivery times in minutes: 10, 12, 11, 14, 13, 15, 12, 11, 13, 12.

Mean = 12.3, sample SD ≈ 1.49. Most deliveries fall within roughly 12.3 ± 1.49 minutes, the ±1 SD range.

How to interpret the result

The SD is the typical distance of a value from the mean. For bell-shaped data, about 68% of values lie within ±1 SD and 95% within ±2 SD. Compare SD with the mean for context: a SD of 5 is large for a mean of 20 but tiny for a mean of 2,000.

Sample vs population SD, SD vs IQR

The sample SD divides by n − 1 to estimate the population spread; the population SD divides by n and describes a complete dataset. For skewed data, the IQR (quartiles) describes spread more honestly than the SD.

Frequently asked questions

Why divide by n − 1?

Using n underestimates the population SD because the sample mean is already the best fit to the sample. Bessel’s correction (n − 1) fixes that bias.

What is a 'good' standard deviation?

It depends on the scale. Always judge the SD relative to the mean, a common rule of thumb is the coefficient of variation (SD ÷ mean).

SD vs IQR?

SD for symmetric data without outliers. IQR for skewed data or when outliers are present, it ignores the extremes.

Related calculators

Z-Score

Free z-score calculator: convert a raw value into a z-score and percentile, with the standard normal curve and two-tailed p-value.

Confidence Interval

Free confidence interval calculator for a mean or proportion: 90/95/99% intervals with the t-distribution (mean) and Wilson method (proportion), plus a CI plot.

One-Sample t-Test

Free one-sample t-test calculator: paste your numbers, compare against a target value, and get the t statistic, p-value, Cohen’s d and a plain-English interpretation.

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