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Online Variance Calculator
Calculate population and sample variance accurately using our online variance calculator. Ideal for statistics, data analysis, and research applications.
| Sample | Population | |
|---|---|---|
| Variance | σ2 = 28.5 | s2 = 24.9375 |
| Standard Deviation | σ = 5.3385 | s = 4.9937 |
| Count | n = 8 | n = 8 |
| Mean | μ = 18.25 | x̄ = 18.25 |
| Sum of Squares | SS = 199.5 | SS = 199.5 |
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What Is This Tool?
This variance calculator is a statistics tool designed to measure the spread of data points around their mean. It supports calculation of both population variance and sample variance using established formulas.
How to Use This Tool?
- Enter your data values separated by commas or spaces
- Choose whether your data represents a population or a sample
- Click the calculate button to process the data
- Review the variance result and related statistical values displayed
- Use the results for further analysis or reporting
Key Features
- Calculates variance using formulas for population and sample data sets
- Accepts multiple numeric data values as input
- Provides high numerical precision results based on floating-point arithmetic
- User-friendly and browser-based for quick statistical analysis
- Displays key variables including mean, number of data points, and calculated variance
Examples
- For data points 4, 7, and 10: Compute the mean as (4 + 7 + 10) / 3 = 7. Then calculate squared differences (4−7)² = 9, (7−7)² = 0, (10−7)² = 9. Population variance is (9 + 0 + 9) / 3 = 6.
Common Use Cases
- Measuring data variability in data science projects
- Assessing financial risk by evaluating data spread
- Conducting quality control analyses in engineering
- Performing statistical research and academic studies
- Supporting machine learning model evaluation through variance analysis
Tips & Best Practices
- Ensure all input values are numeric to avoid calculation errors
- Select the correct variance type: population or sample, based on your dataset
- Input data carefully and double-check for typos to maintain accuracy
- Use consistent units and data formats for reliability
- Interpret variance results in context with other statistics like mean and standard deviation
Limitations
- This tool assumes all input values are numeric and does not perform data type validation
- It does not verify whether the dataset is appropriate for population or sample variance calculation
- The calculator is designed for numerical datasets and may not handle non-numeric or categorical data
- Results depend on the correctness of the input data
Frequently Asked Questions
- What is the difference between population variance and sample variance?
- Population variance divides the sum of squared differences by N, the total number of data points. Sample variance divides by N − 1, known as degrees of freedom, to provide an unbiased estimate.
- Can I use this calculator for non-numeric data?
- No. The calculator requires numeric input values to compute variance correctly.
- How is the mean calculated in variance computation?
- The mean is the arithmetic average of all data points, found by summing all values and dividing by the number of data points.
Key Terminology
- Variance
- A measure of how spread out data points are around the mean.
- Mean
- The arithmetic average of a data set.
- Degrees of Freedom
- In sample variance, the denominator (N − 1) representing independent values that can vary.
- Population Variance
- Variance calculated by dividing the sum of squared differences by N, the total population size.
- Sample Variance
- Variance calculated by dividing the sum of squared differences by (N − 1) to adjust for sample estimation.