Variance calculator
Simplify the calculation of variance with this handy online tool. Variance is a statistical measure that quantifies the spread or dispersion of a set of data points around their mean (average) value.
Population variance and sample variance calculator
Easily calculate the variances of your data set with this convenient online tool. Whether you have the entire population data or just a sample, this calculator can compute both the population variance and sample variance. Simply input your data points separated by commas or spaces, and let the calculator do the rest. Obtain accurate measures of variability and gain insights into the spread of your data.
Discrete random variable variance calculator
Simplify the calculation of variance for a discrete random variable with this efficient online tool. A discrete random variable is one that takes on distinct values with specific probabilities.
What is Variance
Variance is a statistical measure that quantifies the spread or dispersion of a set of data points around their mean (average) value. It provides information about how far the individual data points deviate from the average.
In simple terms, variance tells us how much the data points in a dataset differ from each other and from the mean. A higher variance indicates a wider spread or greater variability, while a lower variance suggests a more tightly clustered dataset.
The formula for calculating variance depends on whether you are dealing with a population or a sample:
Population Variance: The population variance measures the spread of the entire population. The formula is:
Variance = Σ((xᵢ - μ)²) / N
where:
- xᵢ represents each data point in the population
- μ denotes the population mean
- Σ signifies summation (summing up all the values)
- N represents the total number of data points in the population
Sample Variance: The sample variance estimates the spread of a sample of data taken from a larger population. The formula is slightly different to account for the degree of freedom in a sample:
Variance = Σ((xᵢ - x̄)²) / (n - 1)
where:
- x̄ denotes the sample mean
- n represents the number of data points in the sample
Variance is an important measure in statistical analysis as it helps to compare and interpret data sets. It plays a key role in various statistical techniques and models, such as hypothesis testing, regression analysis, and analysis of variance (ANOVA).
Whole population variance calculation
Population mean:
Population variance:
Sampled data variance calculation
Sample mean:
Sample variance:
Discrete random variable variance calculation
Random variable mean:
Random variable variance:
variance calculation Example
Let's say we have a dataset of exam scores for a class of students:
| Student | Exam Score |
|---|---|
| 1 | 80 |
| 2 | 85 |
| 3 | 90 |
| 4 | 95 |
| 5 | 100 |
To calculate the variance, you can follow these steps:
-
Find the mean (average) of the dataset by summing up all the scores and dividing by the total number of data points. In this case, the mean would be (80 + 85 + 90 + 95 + 100) / 5 = 90.
-
Calculate the deviation of each score from the mean by subtracting the mean from each score. The deviations would be:
- For student 1: 80 - 90 = -10
- For student 2: 85 - 90 = -5
- For student 3: 90 - 90 = 0
- For student 4: 95 - 90 = 5
- For student 5: 100 - 90 = 10
-
Square each deviation to get the squared differences. The squared differences would be:
- For student 1: (-10)^2 = 100
- For student 2: (-5)^2 = 25
- For student 3: (0)^2 = 0
- For student 4: (5)^2 = 25
- For student 5: (10)^2 = 100
-
Calculate the sum of the squared differences. The sum would be 100 + 25 + 0 + 25 + 100 = 250.
-
Divide the sum of squared differences by the total number of data points to get the variance. In this case, the variance would be 250 / 5 = 50.
Therefore, the variance of this dataset would be 50.
Please note that this is just a simple example, and there are different formulas and methods for calculating variance depending on the context and purpose.
