Calculating SD (complex cases)

<a href="https://www.prepswift.com/quizzes/quiz/prepswift-calculating-sd-complex-cases" target="_blank">Calculating SD (complex cases) Exercise</a>Calculating the Standard Deviation in Complex Cases is relatively easy, if you follow the process. But first of all, what do we mean by "in complex cases"? We just mean a dataset that consists of three or more numbers that are not all equal to each other. For example, the dataset below would be a more complex case: $$1, 2, 3, 4, 5$$ Calculating Standard Deviation - The Process What is the standard deviation of the dataset below? $$1, 4, 9, 16, 25$$ Step 1: Find the average of the dataset. $$\frac{1+4+9+16+25}{5} = 11$$ Step 2: Find the difference between each number in the dataset and the average. For example, our average is $11$ right? Notice how the first number in the dataset, $1$, is $10$ less than our average, so we would give it a difference value of $-10$. Here they are for all five numbers in the dataset: $$(1-11), (4-11), (9-11), (16-11), (25-11) = -10, -7, -2, 5, 14$$ Step 3: Calculate the sum of the square of each number found in step 2. $$(-10)^2 + (-7)^2 + (-2)^2 + 5^2 + 14^2 = 374$$ Step 4: Divide the number from step 3 by the number of items in the dataset (in our case $5$). Take the square root of that result. $$\sqrt{\frac{374}{5}} = \sqrt{74.8}$$ $$\sigma \approx 8.65$$ If You Want the Formula It's ugly, but here ya go: $$\sigma = \sqrt{\frac{1}{N} \sum_{i=1}^{N} (x_i - \mu)^2}$$