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Standard Deviation

In statistics, the standard deviation is a measure of the dispersion or spread of a dataset. It quantifies how much the individual values in a dataset deviate from the mean. A lower standard deviation indicates that the values are closer to the mean, while a higher standard deviation suggests a greater dispersion or variability.

The standard deviation is represented by the symbol "σ" for a population standard deviation or "s" for a sample standard deviation.

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

Find the mean of the dataset. For each value in the dataset, subtract the mean and square the result. Calculate the mean of the squared differences obtained in step 2. Take the square root of the mean obtained in step 3.

Calculation of the standard deviation:

Consider the following dataset of exam scores: 78, 85, 92, 85, 90, 78, 88, 82, 92, 85.

Find the mean

Mean = (78 + 85 + 92 + 85 + 90 + 78 + 88 + 82 + 92 + 85) / 10 = 860 / 10 = 86

Calculate the squared differences from the mean

(78 - 86)^2 = 64 (85 - 86)^2 = 1 (92 - 86)^2 = 36 (85 - 86)^2 = 1 (90 - 86)^2 = 16 (78 - 86)^2 = 64 (88 - 86)^2 = 4 (82 - 86)^2 = 16 (92 - 86)^2 = 36 (85 - 86)^2 = 1

Calculate the mean of the squared differences

Mean = (64 + 1 + 36 + 1 + 16 + 64 + 4 + 16 + 36 + 1) / 10 = 239 / 10 = 23.9 Take the square root of the mean: Standard Deviation = √23.9 ≈ 4.89

So, in this example, the standard deviation of the dataset is approximately 4.89. This indicates that the scores are relatively spread out from the mean value of 86.

Standard Deviation


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