What is standard deviation and how is it calculated?

What is standard deviation and how is it calculated?

Standard deviation is a measure of the amount of variation or dispersion in a set of values. To calculate it, you first find the mean (average) of the data set, then calculate the variance by finding the average of the squared differences from the mean, and finally take the square root of the variance.

Can you show me an example calculation?

Sure! Let's say we have the data set: 4, 8, 6, 5, 3. First, we find the mean: (4+8+6+5+3)/5 = 5.2. Then, we calculate the variance: ((4-5.2)² + (8-5.2)² + (6-5.2)² + (5-5.2)² + (3-5.2)²) / 5 = 2.56. Finally, the standard deviation is the square root of 2.56, which is approximately 1.6.

What does a higher standard deviation indicate?

A higher standard deviation indicates that the data points are spread out over a wider range of values, meaning there is more variability in the data.

Can you explain the difference between population and sample standard deviation?

Yes! The population standard deviation uses the entire data set, while the sample standard deviation is calculated from a subset of the population. The formula for the sample standard deviation includes a correction factor (n-1) to account for the smaller sample size.