⚡ Quick answer
To calculate sample variance, find the mean, compute squared deviations from the mean, sum them, and divide by n - 1.
Variance Calculator
Compute the sample variance (divide by n − 1) for a comma-separated list.
📖 What it is
Understanding variance is crucial in statistics, particularly when working with sample data. The variance calculator allows you to compute the sample variance, which evaluates how much your data points deviate from the sample mean. This is especially useful in research and data analysis.
To utilize the variance calculator, simply input your data as a comma-separated list. The tool will process these values to provide you with the sample variance. The output will give you a clear numerical representation of the variability within your dataset.
It's important to remember that the sample variance formula divides by n − 1, where n is the number of data points. This adjustment ensures an unbiased estimate of variance, making it essential to have at least two values to obtain a valid result.
How to use
- Input your sample data points into the calculator.
- Calculate the mean of your data points.
- Determine the squared deviations from the mean for each data point.
- Sum all the squared deviations.
- Divide the total by the number of data points minus one.
📐 Formulas
- Mean—mean = Σx / n
- Squared Deviation—d = (x - mean)²
- Sample Variance—variance = Σd / (n - 1)
💡 Example
Consider the data points: 4, 8, 6, 5, 3.
1. Calculate the mean: (4 + 8 + 6 + 5 + 3) / 5 = 5.2.
2. Compute the squared deviations: (4 - 5.2)² = 1.44, (8 - 5.2)² = 7.84, (6 - 5.2)² = 0.64, (5 - 5.2)² = 0.04, (3 - 5.2)² = 4.84.
3. Sum the squared deviations: 1.44 + 7.84 + 0.64 + 0.04 + 4.84 = 14.8.
4. Divide by n - 1: 14.8 / (5 - 1) = 3.7.
Real-life examples
Student Test Scores
In a class with scores 85, 90, 78, 92, and 88, the sample variance is calculated to assess score variability.
Monthly Sales Data
For a store with monthly sales of $2000, $2500, $2200, $2700, and $2400, the variance helps in understanding sales fluctuations.
Scenario comparison
- High Variability vs Low Variability—A set of data points with a high variance (e.g., 1, 10, 20) indicates greater spread compared to a low variance set (e.g., 5, 6, 7), which is more clustered.
- Sample vs Population Variance—Sample variance uses n-1 in the denominator, while population variance uses n, affecting the calculation for small data sets.
Common use cases
- Analyzing test score distributions in education.
- Evaluating financial performance of investments.
- Understanding customer satisfaction survey results.
- Assessing variability in product quality control.
- Conducting research studies requiring statistical analysis.
How it works
The variance calculator computes the average of the squares of the differences between each data point and the overall mean. This involves first determining the mean of the dataset, then calculating how far each point deviates from this mean, squaring those deviations, and finally averaging them while accounting for sample size to ensure accuracy.
What it checks
This tool checks the average squared deviation of a sample around its mean.
Signals & criteria
- Sample values
- Sample mean
- Squared deviations
- Degrees of freedom n − 1
Typical errors to avoid
- Using population variance (÷ n) by mistake.
- Feeding too few values.
- Mixing samples from different populations.
Decision guidance
Trust workflow
Recommended steps after getting a result:
- Gather your sample data points.
- Ensure the data is a single sample from a population.
- Input the values into the variance calculator.
- Review the output for accuracy.
- Interpret the variance in the context of your research.
FAQ
FAQ
Population variance?
This tool uses the sample formula with n − 1; population variance would divide by n.
Units?
Variance is in squared units of your data—take sqrt for original units.