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Standard Deviation Calculator – Population & Sample SD

Calculate population and sample standard deviation, variance, mean, and coefficient of variation. See step-by-step statistics for your data set. Free tool for students and analysts.

Updated for 2026

By the GlobalCalqulate team, founded by Pavan Kusunuri · About our editorial standards

Data

Data Values (comma separated)

Enter numbers separated by commas.

Calculation Type

Standard Deviation

5.2372

Mean: 18.00 | n=8

Count (n)

Mean (Average)

18.0000

Variance

27.4286

Standard Deviation

5.2372

Coefficient of Variation

29.10%

Sum

144

Minimum

Maximum

Range

✓ Reviewed and updated for accuracy using current official rates and widely accepted formulas.

How to Use This Calculator

Enter Your Data

Type or paste your numbers, separated by commas. The calculator accepts whole numbers and decimals.

Choose Sample or Population

Sample (n-1) is for a subset of data and gives an unbiased estimate. Population (n) is for complete data sets where you have every value.

Review Statistics

See standard deviation, variance, mean, coefficient of variation, and range — a complete summary of your data set.

Understanding Your Results

Standard Deviation
A measure of how spread out numbers are from the mean. Low SD = data points cluster near the mean. High SD = data is widely scattered.
Sample vs Population
Sample divides by (n-1) using Bessel's correction for unbiased estimation from a subset. Population divides by n when you have all data points.
Coefficient of Variation
CV = (SD ÷ Mean) × 100%. Measures relative variability — useful for comparing data sets with different units or means.
Variance
The average of squared differences from the mean. SD is the square root of variance. Both measure spread, but SD is in the original units.

Help & FAQs

Frequently Asked Questions

Clear answers to common questions to help you use this calculator confidently.

What is standard deviation?

Tap to view the answer

Standard deviation measures how spread out numbers are from the mean. A low SD means numbers are close to the mean.

What's the difference between population and sample SD?

Tap to view the answer

Population SD divides by n (all data). Sample SD divides by n-1 (Bessel's correction) for unbiased estimation.

What is variance?

Tap to view the answer

Variance is the average of squared differences from the mean. SD is the square root of variance.

What is coefficient of variation?

Tap to view the answer

CV = (SD / Mean) × 100%. It measures relative variability independent of the unit of measurement.

How do I interpret SD?

Tap to view the answer

In normal distributions, ~68% of data falls within 1 SD of mean, ~95% within 2 SD, ~99.7% within 3 SD.

Can I use decimal values?

Tap to view the answer

Yes, the calculator accepts decimal numbers. Separate values with commas.

Need more help? Contact support or email support@globalcalqulate.com

We typically reply within 24–48 hours.

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How to Use This Calculator

Enter Your Data

Type or paste your numbers, separated by commas. The calculator accepts whole numbers and decimals.

Choose Sample or Population

Sample (n-1) is for a subset of data and gives an unbiased estimate. Population (n) is for complete data sets where you have every value.

Review Statistics

See standard deviation, variance, mean, coefficient of variation, and range — a complete summary of your data set.

Understanding Your Results

Standard Deviation
A measure of how spread out numbers are from the mean. Low SD = data points cluster near the mean. High SD = data is widely scattered.
Sample vs Population
Sample divides by (n-1) using Bessel's correction for unbiased estimation from a subset. Population divides by n when you have all data points.
Coefficient of Variation
CV = (SD ÷ Mean) × 100%. Measures relative variability — useful for comparing data sets with different units or means.
Variance
The average of squared differences from the mean. SD is the square root of variance. Both measure spread, but SD is in the original units.

Key Tips

✓
Use sample (n-1) when working with a subset of a larger population — this gives an unbiased estimate.
✓
Use population (n) only when you have every possible data point.
✓
In a normal distribution: ~68% within 1 SD, ~95% within 2 SD, ~99.7% within 3 SD of the mean.
✓
CV is useful for comparing variability across different data sets — a CV under 10% indicates low relative variability.

How Standard Deviation Works

What Standard Deviation Tells You

Standard deviation answers: how typical is the average? In a class where all students score 70-75 on a test, the SD is small (~2). In a class where scores range from 40 to 100, the SD is large (~20). The larger the SD, the less representative the mean is of any individual data point. Financial analysts use SD to measure investment volatility. Quality control engineers use it to monitor manufacturing consistency.

Sample vs Population — Why n-1 Matters

When you calculate SD from a sample (not the entire population), dividing by n underestimates the true population SD. Bessel's correction (dividing by n-1) compensates for this bias. The difference matters most with small samples. With n=5, sample SD uses n-1=4 (25% difference). With n=100, the correction is only 1%. Use population SD when you have census data; use sample SD when you have survey data.

Coefficient of Variation — Comparing Apples to Oranges

CV = (SD ÷ Mean) × 100%. It expresses variability relative to the mean, making it unit-independent. You can compare the variability of heights (inches) to weights (pounds), or stock A ($50 mean, $5 SD) to stock B ($500 mean, $50 SD). Both have CV=10% — they're equally volatile relative to their price. CV is widely used in finance, quality control, and laboratory testing.

Standard Deviation Calculator – Population & Sample SD

Data

How to Use This Calculator

Understanding Your Results

Frequently Asked Questions

What is standard deviation?

What's the difference between population and sample SD?

What is variance?

What is coefficient of variation?

How do I interpret SD?

Can I use decimal values?

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Data

How to Use This Calculator

Understanding Your Results

Key Tips

How Standard Deviation Works

What Standard Deviation Tells You

Sample vs Population — Why n-1 Matters

Coefficient of Variation — Comparing Apples to Oranges

Example: 8 Data Points

Key Tips

How Standard Deviation Works

What Standard Deviation Tells You

Sample vs Population — Why n-1 Matters

Coefficient of Variation — Comparing Apples to Oranges

Example: 8 Data Points

Data

How to Use This Calculator

Understanding Your Results

What is standard deviation?

What's the difference between population and sample SD?

What is variance?

What is coefficient of variation?

How do I interpret SD?

Can I use decimal values?

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Age Calculator

Password Generator

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Data

How to Use This Calculator

Understanding Your Results

Key Tips

How Standard Deviation Works

What Standard Deviation Tells You

Sample vs Population — Why n-1 Matters

Coefficient of Variation — Comparing Apples to Oranges

Example: 8 Data Points

Key Tips

How Standard Deviation Works

What Standard Deviation Tells You

Sample vs Population — Why n-1 Matters

Coefficient of Variation — Comparing Apples to Oranges

Example: 8 Data Points