Calculating Standard Deviation
Standard deviation is a statistical measure of diversity or variability in a data set. A low standard deviation indicates that data points are generally close to the mean or the average value. A high standard deviation indicates greater variability in data points, or higher dispersion from the mean.
Standard Deviation Formula
Standard deviation of a data set is the square root of the calculated variance of a set of data.
The formula for variance (s2) is the sum of the squared differences between each data point and the mean, divided by the number of data points.
When working with data from a complete population the sum of the squared differences between each data point and the mean is divided by the size of the data set, n. When working with a sample, divide by the size of the data set minus 1, n - 1.
Standard Deviation and Variance
Standard deviation is a measure of dispersion of data values from the mean. The formula for standard deviation is the square root of the sum of squared differences from the mean divided by the size of the data set.
For a Population:
The formula for the population standard deviation is:
σ = √(Σi=1n (xi − μ)2 / n)
For a Sample:
The formula for the sample standard deviation is:
s = √(Σi=1n (xi − x̄)2 / (n − 1))
Variance
Variance also measures the dispersion of data from the mean. The formula for variance is the sum of squared differences from the mean divided by the size of the data set.
For a Population:
The formula for the population variance is:
σ2 = Σi=1n (xi − μ)2 / n
For a Sample:
The formula for the sample variance is:
s2 = Σi=1n (xi − x̄)2 / (n − 1)
| Type | Unit | Your Format Input | Options | Actual Input Processed |
|---|---|---|---|---|
| Column (New Lines) | 42 54 65 47 59 40 53 |
42, 54, 65, 47, 59, 40, 53 | 42, 54, 65, 47, 59, 40, 53 | 42, 54, 65, 47, 59, 40, 53 |
| Comma Separated (CSV) | 42, 54, 65, 47, 59, 40, 53, |
42, 54, 65, 47, 59, 40, 53 | 42, 54, 65, 47, 59, 40, 53 | 42, 54, 65, 47, 59, 40, 53 |
| Spaces | 42 54 65 47 59 40 53 |
42 54 65 47 59 40 53 | 42, 54, 65, 47, 59, 40, 53 | 42, 54, 65, 47, 59, 40, 53 |
| Mixed Delimiters | 42 54 65,,, 47,,59, 40 53 |
42, 54, 65, 47, 59, 40, 53 | 42, 54, 65, 47, 59, 40, 53 | 42, 54, 65, 47, 59, 40, 53 |
