SmartCalculators.ai
Home/Math/Standard Deviation Calculator

What is the standard deviation of my data?

Calculate mean, variance, and standard deviation for a set of numbers. Essential for statistical analysis.

What This Calculator Is

A standard deviation calculator measures the spread or variability in a dataset. Standard deviation tells you how much individual values typically differ from the average—low values mean data is clustered together, high values mean data is spread out. It's fundamental to statistics and data analysis.

Who This Calculator Is For

Students studying statistics, researchers analyzing data, quality control professionals measuring consistency, investors assessing volatility, and anyone working with data who needs to understand variability.

When to Use This Calculator

Use this calculator when analyzing data consistency, comparing variability between datasets, for statistics coursework, when measuring process consistency in quality control, or when you need to understand how spread out your data is.

Inputs

10
12
23
23
16

Results

Standard Deviation

5.419

Mean (Average)16.8
Variance29.36
Sum84

Results are for informational purposes. Verify calculations for critical applications.

Insights

Data spread

Your data has a mean of 16.80 with a standard deviation of 5.42, indicating moderate to high variability.

How Standard Deviation Is Calculated

The calculator finds the mean, then calculates how far each value is from the mean (variance), and takes the square root of the average variance to get standard deviation.

mean = sum(values)/n
variance = sum((v-mean)^2)/n
standardDeviation = sqrt(variance)
Where:
values = the 5 input numbers (value1..value5, each defaulting to 0 if blank); n = 5 (fixed count)
Assumptions:
Population standard deviation formula used (divides by n, not n-1 sample formula)
Always treats exactly 5 values, even if some default to 0
Results rounded to 4 decimal places

Key Takeaways

  • •In investing, higher standard deviation = higher volatility/risk
  • •68% of data falls within 1 standard deviation of the mean (normal distribution)
  • •95% falls within 2 standard deviations
  • •Sample standard deviation divides by (n-1); population by n
  • •Compare standard deviations only for data with similar means

Related Calculators

How do I calculate percentages?

Calculate percentages, percentage changes, and percentage differences. Find what percent one number is of another.

Math

How do I generate random numbers?

Generate random numbers within a specified range. Perfect for games, decisions, statistical sampling, and more.

Math