Calculating Standard Deviation: A Step-by-Step Guide with Example Data Set

standard deviation

Standard deviation is a measure of the dispersion or variability in a set of values

Standard deviation is a measure of the dispersion or variability in a set of values. It quantifies how much the values in a data set differ from the mean (average) value.

To calculate the standard deviation, you can follow these steps:

1. Calculate the mean of the data set.
2. Subtract the mean from each data value and square the result.
3. Calculate the mean (average) of the squared differences.
4. Take the square root of the mean of the squared differences to get the standard deviation.

Let’s go through an example to illustrate this process:

Consider the following set of data: 4, 6, 8, 10, 12.

Step 1: Calculate the mean
Mean = (4 + 6 + 8 + 10 + 12) / 5 = 8

Step 2: Subtract the mean and square the result for each data value:
(4 – 8)^2 = (-4)^2 = 16
(6 – 8)^2 = (-2)^2 = 4
(8 – 8)^2 = (0)^2 = 0
(10 – 8)^2 = (2)^2 = 4
(12 – 8)^2 = (4)^2 = 16

Step 3: Calculate the mean of the squared differences:
Mean of squared differences = (16 + 4 + 0 + 4 + 16) / 5 = 40 / 5 = 8

Step 4: Take the square root of the mean of the squared differences to find the standard deviation:
Standard deviation = √8 ≈ 2.83

Therefore, the standard deviation of the data set {4, 6, 8, 10, 12} is approximately 2.83.

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