The Variance Calculator is a valuable tool used in statistics to measure the spread or dispersion of a dataset. It helps in understanding how far individual numbers in the dataset are from the mean (average) and provides insights into the data’s consistency or variability.
Formula of Variance Calculator
The formula used by the Variance Calculator is:
Variance = Σ((x – Mean)²) / (n – 1)
Here,
- Σ represents summation, where you sum up all the squared differences between each data point and the mean.
- n stands for the number of data points in the sample.
- x denotes each data point in the dataset.
Table of General Terms
| Term | Description |
|---|---|
| Mean | The average value of a dataset. |
| Standard Deviation | A measure of the amount of variation or dispersion in a dataset. |
| Population Variance | Variance calculation considering the entire population. |
| Sample Variance | Variance calculation based on a subset or sample of the population. |
Example of Variance Calculator
Suppose we have a dataset of exam scores: 75, 80, 85, 90, and 95. Using the Variance Calculator, we find the mean (average) to be 85. The variance is then calculated by taking each score, finding the difference from the mean, squaring those differences, summing them, and dividing by the number of data points minus one ((75-85)² + (80-85)² + (85-85)² + (90-85)² + (95-85)²) / (5-1).
Most Common FAQs
A: Using n – 1 (instead of n) in the formula is known as Bessel’s correction. It helps to provide an unbiased estimation of the population variance based on a sample.
A: A higher variance signifies that the data points are more spread out from the mean, indicating greater variability in the dataset.
A: Variance and standard deviation both measure the spread of data, but the standard deviation is the square root of the variance. Standard deviation is preferre when we want the measurement in the same units as the original data.