Standard Deviation Calculator
Title: Standard Deviation Calculator Find SD & Variance
Description: Calculate standard deviation, mean, and variance from a dataset. Use our Standard Deviation Calculator for statistics and research.

Standard Deviation Calculator

Quickly find the standard deviation, variance, and mean of your data using our powerful Standard Deviation Calculator. Essential for data analysts and researchers.

• Handles grouped and ungrouped data.
• Shows calculation steps.
• Great for statistics students and professionals.
  
  A standard deviation calculator measures data variability and dispersion from the mean value. This essential standard deviation calculator helps analyze data sets, understand statistical distributions, and measure data consistency for research and analysis.
• The standard deviation calculator handles both population and sample standard deviation calculations. This comprehensive standard deviation calculator uses appropriate formulas for different data types and provides accurate statistical measurements for various applications.
• Our advanced standard deviation calculator includes variance calculations and statistical interpretations. This detailed standard deviation calculator explains what your results mean and provides context for understanding data spread and distribution patterns.
• The standard deviation calculator is crucial for statistics students and researchers. This educational standard deviation calculator supports coursework in statistics, psychology, business analytics, and scientific research with reliable calculations and clear explanations.
• Professional data analysts trust our standard deviation calculator for quality control and research applications. This reliable standard deviation calculator provides accurate measurements that support statistical analysis, hypothesis testing, and data-driven decision making.
• The standard deviation calculator also includes coefficient of variation and percentile calculations. This comprehensive standard deviation calculator provides additional statistical measures that enhance understanding of data characteristics and distribution properties.
• Quality control professionals use our standard deviation calculator for process monitoring and improvement. This industrial standard deviation calculator helps identify process variations, maintain quality standards, and implement continuous improvement initiatives effectively.
• The standard deviation calculator handles large data sets and provides instant results. This efficient standard deviation calculator processes hundreds of data points quickly while maintaining accuracy and providing detailed statistical summaries for analysis.
• Financial analysts rely on our standard deviation calculator for risk assessment and portfolio analysis. This financial standard deviation calculator measures investment volatility, market risk, and helps make informed investment decisions based on statistical evidence.
• Research scientists use the standard deviation calculator for experimental data analysis. This scientific standard deviation calculator supports hypothesis testing, experimental validation, and ensures statistical significance in research findings and publications.
• Analyze data variability with our accurate standard deviation calculator. This standard deviation calculator provides the statistical tools you need for comprehensive data analysis, research validation, and informed decision-making processes.
  
  Standard Deviation Calculator:
• Calculate population & sample standard deviation, variance, and other statistical measures with detailed step-by-step solutions
• Enter Your Data
• Data Set (comma or space separated):Data Type:PopulationSampleDecimal Places:                                 2                                 3                                 4                                 5                             Calculate StatisticsReset
• Statistical Summary
• Data Points
• 10
• Mean (Average)
• 20.50
• Standard Deviation
• 3.03
• (Population)
• Variance
• 9.20
• Median
• 20.50
• Mode
• –
• Range
• 9.00
• Sum
• 205.00
• Data Distribution
• Step-by-Step Calculation
• 1
• Input Data
• Your dataset contains 10 values:
• 24
• 17
• 19
• 22
• 18
• 21
• 20
• 23
• 16
• 25
• 2
• Calculate the Mean (Average)
• The mean is the sum of all values divided by the number of values.
• Mean = (Σx) / N = (24 + 17 + 19 + 22 + 18 + 21 + 20 + 23 + 16 + 25) / 10 = 205 / 10 = 20.5
• 3
• Calculate Deviations from Mean
• For each value, subtract the mean and square the result:
• (24-20.5)² = 12.25
• (17-20.5)² = 12.25
• (19-20.5)² = 2.25
• (22-20.5)² = 2.25
• (18-20.5)² = 6.25
• (21-20.5)² = 0.25
• (20-20.5)² = 0.25
• (23-20.5)² = 6.25
• (16-20.5)² = 20.25
• (25-20.5)² = 20.25
• 4
• Calculate Variance
• For population variance, divide the sum of squared differences by the number of values (N). For sample variance, divide by N-1.
• Sum of squared differences = 12.25 + 12.25 + 2.25 + 2.25 + 6.25 + 0.25 + 0.25 + 6.25 + 20.25 + 20.25 = 82.5
• Population Variance = Σ(x – μ)² / N = 82.5 / 10 = 8.25
• 5
• Calculate Standard Deviation
• Standard deviation is the square root of the variance.
• Population Standard Deviation = √(Variance) = √8.25 ≈ 2.87
• Sample Standard Deviation:
   It is worth noting that there exist many different equations for calculating sample standard deviation since, unlike sample mean, sample standard deviation does not have any single estimator that is unbiased, efficient, and has a maximum likelihood. The equation provided below is the “corrected sample standard deviation.”
   As such, the “corrected sample standard deviation” is the most commonly used estimator for population standard deviation, and is generally referred to as simply the “sample standard deviation.” It is a much better estimate than its uncorrected version, but still has a significant bias for small sample sizes (N<10).
  
• 2025 Standard Deviation Calculator | Statistical Analysis Tool