Exam score consistency
Use standard deviation to see whether a class performed consistently or whether scores were widely spread around the average. After that, compare center values with the Mean Calculator or Median Calculator for more context.
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Standard Deviation Calculator
Calculate population and sample standard deviation instantly from any numeric dataset. Review variance, mean absolute deviation, coefficient of variation, and spread interpretation for statistics, education, QA, research, and finance workflows.
Standard Deviation Calculator
Use this free standard deviation calculator to measure how spread out a dataset is around its mean. Paste values, switch between population and sample formulas, and instantly see variance, mean absolute deviation, coefficient of variation, and a plain-English interpretation. If you also need central tendency, continue with the Mean Calculator, compare middle values with the Median Calculator, or explore more tools in Math & Statistics Calculators.
Calculate dataset spread instantly
Enter comma, space, or line-break separated numbers to compute population and sample standard deviation side by side.
Best for
Spread and consistency checks
Useful for scores, measurements, finance, QA, and research summaries.
8 numeric values parsed.
Formula selection
Switch between population and sample interpretation depending on whether your dataset is complete or only a subset.
population standard deviation
6.936092
This is the typical distance each value sits from the mean for the selected formula.
Variance
48.109375
Mean
84.875
Count
8
Range
22
Spread summary
Low variability
The data is tightly clustered around the mean. A 6.936092 standard deviation indicates fairly consistent values.
Population std dev
6.936092
Sample std dev
7.414994
MAD
5.90625
Coefficient of variation
8.172126%
Calculation steps
- 1Count the values in the dataset: n = 8
- 2Find the mean: sum 679.0000 / 8 = 84.8750
- 3Subtract the mean from each value to get its deviation.
- 4Square each deviation and add them together.
- 5Population variance = squared deviations / n = 48.109375
- 6Sample variance = squared deviations / (n - 1) = 54.982143
- 7Population standard deviation = sqrt(variance) = 6.936092
- 8Sample standard deviation = sqrt(variance) = 7.414994
Sorted dataset
7278818588909194
What this tool does
This standard deviation calculator shows how tightly or loosely your numbers cluster around the mean. It helps you quickly understand consistency in test scores, manufacturing measurements, revenue data, survey responses, and many other numeric datasets.
How it works
The calculator finds the mean, measures each value's deviation from that mean, squares those deviations, averages them into variance, and then takes the square root to produce standard deviation. It shows both population and sample results so you can use the right formula for your context.
Standard deviation formulas
Population standard deviation
σ = √(Σ(x - μ)^2 / N)
Sample standard deviation
s = √(Σ(x - x̄)^2 / (n - 1))
σ
Population standard deviation.
s
Sample standard deviation.
μ / x̄
Population mean or sample mean.
N / n
Number of observations in the full set or sample.
Standard deviation examples
Manufacturing tolerance
In quality control, lower standard deviation often means production is more stable. That makes this tool useful for checking whether measurements stay tightly clustered around a target size or weight.
Business and finance data
Revenue, returns, and operational metrics can look similar on average but behave very differently in terms of volatility. Standard deviation helps reveal that variability quickly.
If you are analyzing a dataset from scratch, start here for spread, then move to the Mean Calculator for average comparisons, the Mode Calculator for peak frequency detection, or the Random Number Generator when you need sample datasets for testing and demonstrations.
Why standard deviation matters
Two datasets can share the same mean but differ dramatically in consistency. Standard deviation helps you see that hidden difference by quantifying how far values tend to sit from the average.
Population vs sample
The population formula describes the complete set you have. The sample formula adjusts with n - 1 so the spread estimate is less biased when you are using a subset to represent a larger group.
Useful next links
Stay inside Math & Statistics Calculators if you are building a basic descriptive statistics workflow. Pair standard deviation with mean, median, and mode to get a fuller picture of center and spread.
Related tools
Frequently asked questions
It measures how spread out your numbers are around the mean. A lower standard deviation means the values stay closer to the average, while a higher standard deviation means the data is more dispersed.
Explore This Tool in Context
Standard Deviation Calculator is part of the Math & Statistics Calculators collection. If you want a broader view of similar workflows, open the Math & Statistics Calculators category page or browse all QuickTools categories.
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