What is standard deviation and can you give me an example?

What is standard deviation and can you give me an example?

Standard deviation is a measure of the amount of variation or dispersion in a set of values. For example, if you have the data set: 2, 4, 4, 4, 5, 5, 7, 9, the standard deviation helps you understand how spread out these numbers are.

How do you calculate the standard deviation?

To calculate the standard deviation, follow these steps: 1) Find the mean of the data set. 2) Subtract the mean from each data point and square the result. 3) Find the average of those squared differences. 4) Take the square root of that average.

Can you show me the calculation for the example you gave?

Sure! For the data set 2, 4, 4, 4, 5, 5, 7, 9: 1) Mean = 5. 2) Squared differences: (2-5)², (4-5)², (4-5)², (4-5)², (5-5)², (5-5)², (7-5)², (9-5)² = 9, 1, 1, 1, 0, 0, 4, 16. 3) Average of squared differences = 3. 4) Standard deviation = √3 ≈ 1.73.

What does a high standard deviation indicate?

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