Standard Deviation Calculator
Understanding Basic Statistics
Statistics are essential for interpreting data and understanding trends. This calculator computes three of the most fundamental measures of descriptive statistics: the mean, variance, and standard deviation. These metrics provide a summary of your data set, helping you understand its central tendency and spread.
How to Use the Calculator
- Enter your data set into the text area. You can separate the numbers with commas, spaces, or even new lines.
- Click the "Calculate" button.
- The calculator will provide the mean, variance, and standard deviation for the numbers you entered.
Key Statistical Concepts
Here is an explanation of the values calculated by this tool.
| Term | Description | Formula |
|---|---|---|
| Mean (μ or x̄) | The average of all the numbers in the data set. It is calculated by summing all the values and dividing by the count of the values. | μ = (Σx) / n |
| Variance (σ²) | A measure of how spread out the numbers in a data set are from their mean. A high variance indicates that the numbers are widely dispersed, while a low variance indicates that they are clustered closely around the mean. | σ² = Σ(x - μ)² / n |
| Standard Deviation (σ) | The square root of the variance. It is the most common measure of spread and is expressed in the same units as the data itself, making it easier to interpret than variance. A low standard deviation means the data points tend to be very close to the mean, while a high standard deviation means the data is spread out over a wider range. | σ = √σ² |
Note: This calculator computes the population standard deviation and variance. If you are working with a sample of a larger population, a slightly different formula (using n-1 in the denominator) is typically used for an unbiased estimate.