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Calculate variance and related statistical measures. Essential for understanding data spread and variability in statistics.
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Variance Calculator
Calculate variance and related statistical measures. Essential for understanding data spread and variability in statistics.
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What is Variance?
Variance measures how far each number in a set is from the mean. It is the square of standard deviation and represents the dispersion of data points around the mean. Variance is used in risk assessment, portfolio theory, quality control, and statistical analysis. Sample variance (using n-1) provides an unbiased estimate when working with a sample of a larger population.
How to use
Enter your dataset values separated by commas, spaces, or new lines. Select whether your data is a sample or population. The calculator displays variance, standard deviation, sum of squares, degrees of freedom, and provides interpretation of the variance level (low, moderate, high, or very high).
Frequently Asked Questions
What is variance?
Variance is a statistical measurement that describes the spread of data points in a data set. It calculates how far each number in the set is from the mean (average). A higher variance indicates that the data points are more spread out from the mean, while a lower variance indicates they are closer to the mean.
What is the difference between Population and Sample variance?
Population variance calculates the variance for an entire dataset (every member of a specific group). Sample variance estimates the variance based on a subset of the population. The main mathematical difference is the denominator: Population variance divides by $N$ (total count), whereas Sample variance divides by $n-1$ (Bessel's correction) to provide a more accurate estimate of the population variance.
How do I format my data input?
You can enter numbers separated by commas, spaces, or new lines. For example, you can enter '10, 20, 30' or '10 20 30' or list them vertically. Ensure that you do not mix text characters with your numbers.
What is the formula used for this calculation?
For Population Variance ($\sigma^2$), the formula is $\frac{\sum(x_i - \mu)^2}{N}$. For Sample Variance ($s^2$), the formula is $\frac{\sum(x_i - \bar{x})^2}{n-1}$, where $x_i$ represents each value, $\mu$ and $\bar{x}$ are the mean, and $N$ and $n$ are the number of data points.
Why does the result show 'NaN' or 'Error'?
This usually happens if the input field is empty, contains non-numeric characters (like letters or symbols), or if you are trying to calculate Sample variance with only one data point (as division by zero is undefined).
Can I calculate variance for grouped data?
This calculator is designed for raw data lists (ungrouped data). To calculate variance for grouped data, you would need to calculate the weighted mean first, then apply the specific grouped variance formula, which is not supported by this standard input format.
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