σ = sqrt [ σ2 ] = sqrt [ Σ ( Xi - μ )2 / N ]
The expression you provided represents the standard deviation (σ) of a set of numbers. Let's break down the formula step by step to understand how to calculate it.
The formula for the standard deviation can be written as:
σ = √[ σ^2 ] = √[ Σ( Xi - μ )^2 / N ]
Here is how to calculate it:
1. Calculate the mean (average) of the set of numbers.
μ = Σ Xi / N
This step involves adding up all the values (Σ Xi) in the set and dividing it by the total number of values (N) to find the mean (average) (μ).
2. Subtract the mean from each value in the set.
(Xi - μ)
For each value (Xi) in the set, subtract the mean (μ) from it.
3. Square the result from step 2 for each value.
(Xi - μ)^2
Take each result from step 2, and square it (multiply it by itself).
4. Sum up all the squared values from step 3.
Σ( Xi - μ )^2
Add up all the squared values obtained in step 3.
5. Divide the sum from step 4 by the total number of values (N).
Σ( Xi - μ )^2 / N
Take the sum obtained in step 4 and divide it by the total number of values (N) to find the variance (σ^2).
6. Take the square root of the result from step 5 to find the standard deviation.
√[ Σ( Xi - μ )^2 / N ]
Finally, take the square root of the variance (σ^2) obtained in step 5 to find the standard deviation (σ).
So, by following these steps, you can calculate the standard deviation for a given set of numbers.