Standard Deviation Calculator

Calculate standard deviation, variance, mean, and other descriptive statistics f...

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Standard Deviation Features

Complete statistical analysis

Sample & population
Variance calculation
Mean, median, mode
Range & count
Adjustable precision
Large data sets
Paste from Excel
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Mobile-friendly
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Step-by-step

Why Use Standard Deviation Calculator?

Complete Statistics

Get standard deviation, variance, mean, median, mode, range, sum, min, max, and count - all in one calculation.

Population & Sample

Choose between population standard deviation (when you have all data) or sample standard deviation (when working with a subset).

Step-by-Step

See the calculation steps and formula used, helping you understand how standard deviation is computed.

Instant Results

Enter your data and get results immediately. Handles large data sets with ease for quick analysis.

Common Use Cases

Statistics for every need

Statistics Homework

Check your statistics homework answers. Understand the calculation steps and verify your manual calculations are correct.

Data Analysis

Analyze variability in business data, research results, or survey responses. Understand how spread out your data is.

Scientific Research

Calculate measurement variability in experiments. Report standard deviation as error bars or uncertainty in your results.

Quality Control

Monitor process consistency in manufacturing or service delivery. Lower standard deviation means more consistent output.

How It Works

1

Enter Your Data

Type or paste your numbers separated by commas, spaces, or newlines. The calculator accepts any common format.

2

Choose Type

Select 'Sample' if your data is a subset of a larger population, or 'Population' if you have all possible values.

3

Set Precision

Choose how many decimal places you want in your results (2, 4, 6, or 8).

4

Get Statistics

Click calculate to see standard deviation, variance, mean, and other descriptive statistics for your data.

Pro Tips for Statistical Analysis

Watch for Outliers

Before interpreting standard deviation, check for outliers that might skew results. Consider removing extreme values or using median absolute deviation instead.

Use Coefficient of Variation

When comparing variability between data sets with different units or scales, use CV (std dev / mean × 100%) for meaningful comparison.

The 68-95-99.7 Rule

For normal distributions: ~68% of data falls within 1 std dev of the mean, ~95% within 2, and ~99.7% within 3 standard deviations.

Sample Size Matters

Larger samples give more reliable standard deviation estimates. With small samples (n < 30), be cautious about drawing conclusions.

Frequently Asked Questions

Standard deviation measures how spread out numbers are from the average (mean). A low standard deviation means numbers are close to the mean; a high standard deviation means they're spread out over a wider range.
Use population (σ) when you have data for the entire group. Use sample (s) when your data is a sample from a larger population. Sample standard deviation divides by (n-1) instead of n to account for estimation error.
Variance is the average of squared differences from the mean. Standard deviation is the square root of variance. Variance is in squared units, while standard deviation is in the same units as your data.
1) Find the mean of all values. 2) Subtract the mean from each value and square the result. 3) Find the average of these squared differences (variance). 4) Take the square root of the variance.
There's no universal 'good' value - it depends on context. A standard deviation of 5 is small for exam scores (0-100) but large for response times in milliseconds. Compare to the mean using coefficient of variation.
CV is standard deviation divided by mean, expressed as a percentage. It allows comparing variability between data sets with different units or scales. CV = (Standard Deviation / Mean) × 100%.
Yes! Copy your column of numbers from Excel and paste directly into the calculator. It handles various formats including tabs, newlines, and commas automatically.
Mean is the arithmetic average (sum divided by count). Median is the middle value when data is sorted. Median is less affected by outliers - use it when you have extreme values.
Outliers significantly increase standard deviation because the formula squares the difference from the mean. One extreme value can dramatically inflate the standard deviation.
Yes. All calculations happen in your browser. Your data is never uploaded to any server, stored, or shared. When you close the page, everything is gone.

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