How do I calculate the standard deviation of a dataset?

How do I calculate the standard deviation of a dataset?

To calculate the standard deviation, you first need to find the mean of your dataset. Then, subtract the mean from each data point, square the result, and find the average of those squared differences. Finally, take the square root of that average.

Can you show me an example with numbers?

Sure! Let's say your dataset is [4, 8, 6, 5, 3]. First, find the mean: (4+8+6+5+3)/5 = 5.2. Then, subtract the mean from each number: [-1.2, 2.8, 0.8, -0.2, -2.2]. Square those results: [1.44, 7.84, 0.64, 0.04, 4.84]. The average of these squared differences is (1.44+7.84+0.64+0.04+4.84)/5 = 2.16. Finally, the standard deviation is the square root of 2.16, which is approximately 1.47.

What if I have a larger dataset?

The process is the same regardless of the dataset size. Just ensure you calculate the mean accurately and follow the steps for each data point.

Is there a formula I can use?

Yes! The formula for standard deviation (σ) is: σ = √(Σ(xi - μ)² / N), where μ is the mean, xi represents each data point, and N is the number of data points.