Calculate Standard Deviation in R
Introduction & Importance
Standard deviation is a statistical measure that quantifies the amount of variation or dispersion of a set of values. Calculating standard deviation in R is crucial for understanding the spread of data and making informed decisions.
How to Use This Calculator
- Enter comma-separated data in the input field.
- Click ‘Calculate’.
- View the result and chart below.
Formula & Methodology
The formula for standard deviation is:
σ = √[(Σ(x - μ)²) / N]
Where:
σis the standard deviation.xis each value in the dataset.μis the mean of the dataset.Nis the number of values in the dataset.
Real-World Examples
Example 1: IQ Scores
| IQ Scores |
|---|
| 105, 110, 99, 112, 108, 101, 116, 102, 118, 106 |
Standard deviation: 5.2
Example 2: heights (in cm)
| Heights |
|---|
| 160, 170, 155, 165, 175, 162, 178, 168, 180, 164 |
Standard deviation: 7.2
Data & Statistics
| Data Set | Mean | Standard Deviation |
|---|---|---|
| IQ Scores | 108.4 | 5.2 |
| Heights | 168.2 | 7.2 |
Expert Tips
- Standard deviation is sensitive to outliers.
- It’s a useful measure for normally distributed data.
- R provides functions like
sd()andvar()for calculating standard deviation and variance.
Interactive FAQ
What is standard deviation?
Standard deviation is a statistical measure that quantifies the amount of variation or dispersion of a set of values.
Why is standard deviation important?
Standard deviation helps understand the spread of data and makes informed decisions.
For more information, see Statistics How To and Penn State University.