Variance and Standard Deviation Calculator
Before we find Variance and Standard Deviation Calculator, we should know about Variance and Standard deviation. Here is the definition…
Variance Definition: A measure of the spread of a set of data. It is the average of the squared differences between each value in a sample or population and the mean of that sample or population.
Standard Deviation Definition: Standard deviation is a statistical measure of the amount of variation or dispersion of a set of values.
Variance and Standard Deviation Calculator
Variance and Standard Deviation Calculator
Here are the steps to calculate the variance and standard deviation for a set of data:
- Find the mean (average) of the data set.
- For each data point, subtract the mean and square the result.
- Sum all the squared differences.
- Divide the sum by the number of data points in the set. This is the variance.
- Take the square root of the variance to find the standard deviation.
Example:
Suppose we have a data set {1, 2, 3, 4, 5}.
- Mean = (1 + 2 + 3 + 4 + 5) / 5 = 15 / 5 = 3
- (1 – 3)^2 = 4, (2 – 3)^2 = 1, (3 – 3)^2 = 0, (4 – 3)^2 = 1, (5 – 3)^2 = 4
- Sum = 4 + 1 + 0 + 1 + 4 = 10
- Variance = 10 / 5 = 2
- Standard deviation = sqrt(2) = 1.41
Standard Deviation Calculator
A standard deviation table can be useful for identifying outliers, understanding the distribution of the data, and making inferences about a population based on a sample.
The standard deviation can be calculated using the following steps:
- Calculate the mean of the data set.
- Subtract the mean from each data point and square the result.
- Sum the squared differences.
- Divide the sum by either (n - 1) for sample standard deviation or (N) for population standard deviation.
- Take the square root of the result.
Variance and standard deviation formula
Sample Standard Deviation:
s = sqrt(∑(x_i - x̄)^2 / (n - 1))
Population Standard Deviation:
σ = sqrt(∑(x_i - μ)^2 / N)
To calculate the standard deviation of a set of data, you can use the following formula:
Sample Standard Deviation:
s = sqrt(∑(x_i - x̄)^2 / (n - 1))
where x_i represents each data point, x̄ represents the mean of the data, n represents the number of data points, and ∑ represents the sum of all the differences.
| Standard Deviation | Standard Deviation Calculator |
| Sample Standard Deviation | Sample Standard Deviation Calculator |
| Population Standard Deviation | Population Standard Deviation Calculator |
| Variance Definition | Variance and Standard Deviation Calculator |