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Standard Deviation

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The standard deviation is a popular measure of variability. The standard deviation is the square root of the variance.

Population Standard Deviation

The population deviation is denoted by . It is given by the formula:

The capital Greek letter sigma is commonly used in mathematics to represent a summation of all the numbers in a grouping.

N is the number of terms in the population.

Sample Standard Deviation

The sample standard deviation is denoted by s. It is given by the formula

Like the variance, the standard deviation utilizes the sum of the squared deviations about the mean. It is computed by averaging these squared deviations and taking the square root of that average. One feature of the standard deviation that distinguishes it from a variance is that the standard deviation is expressed in the same unit as the raw data, whereas, the variance is expressed in those units squared.

The following video will give:
A review of Population Mean and Sample Mean, Population Variance and the Sample Variance.
An introduction to Population Standard Deviation and Sample Standard Deviation.

The following video shows how to solve a word problem involving mean and standard deviation.

Rotate to landscape screen format on a mobile phone or small tablet to use the Mathway widget, a free math problem solver that answers your questions with step-by-step explanations.

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

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