What is the difference between sample and population standard deviation?

Sample standard deviation (s) divides by n-1 (Bessel's correction) and is used when data is a sample from a larger population. Population standard deviation (sigma) divides by n and is used when data represents the entire population.

What is the standard error of the mean (SEM)?

SEM = s / sqrt(n). It estimates how far the sample mean is likely to be from the true population mean. Smaller SEM indicates more precise estimates.

Can I input data as a frequency table?

Yes. Switch to 'Frequency Table' mode to enter values and their frequencies, which is convenient for grouped or repeated data.

What are quartiles and IQR?

Q1 (25th percentile) and Q3 (75th percentile) divide data into quarters. IQR = Q3 - Q1 and measures the spread of the middle 50% of data, useful for identifying outliers.

Standard Deviation Calculator

Calculate standard deviation, variance, mean, median, mode, and other descriptive statistics from a data set.

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Disclaimer: This tool provides estimates for informational and educational purposes only. It does not constitute professional financial, medical, or legal advice. Please consult with a qualified professional before making any significant decisions based on these estimations.

Common Use Cases

double-checking day-to-day calculations
sanity-checking numbers before sharing them
fast answers on mobile without a spreadsheet

What is Standard Deviation Calculator?

The Standard Deviation Calculator computes both sample and population standard deviation along with a full suite of descriptive statistics: mean, median, mode, range, variance, standard error of the mean, quartiles (Q1, Q3), and interquartile range (IQR). You can enter data as a comma-separated list or via a frequency table. It is an essential tool for students, researchers, data analysts, and anyone performing statistical analysis.

How to Use This Tool

1Enter your numbers separated by commas, spaces, or use the frequency table
2View calculated statistics including standard deviation, variance, and quartiles
3Copy all results for use in reports or assignments

Example

Input

2, 4, 4, 4, 5, 5, 7, 9

Output

Mean: 5, Std Dev (s): 2.138, Median: 4.5

Before You Rely on This Result

UtilityNest keeps tools in this category focused on transparency: short instructions, a worked example, and plain-language guidance so you can review the result before you depend on it.

Check that the inputs reflect your real situation before you rely on the estimate.
Rules, rates, health needs, and legal requirements may vary by country, state, insurer, or provider.
Use this result as a starting point, then confirm important decisions with official sources or a qualified professional.

Frequently Asked Questions

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