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Published byAdam Chambers Modified over 6 years ago

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Measures of Variability Objective: Students should know what a variance and standard deviation are and for what type of data they typically used.

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Single values that summarize the degree of variability in a set of quantitative data Most common are: variance standard deviation (The standard deviation is the square root of the variance) Measures of Variability

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Variance and standard deviation are calculated slightly differently depending on whether the data represent an entire population or a sample from the population. Symbols used for populations and samples: Notation

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Formula for population variance ( 2 ) and standard deviation ( ) Formula for sample variance (s 2 ) and standard deviation (s, sd) Calculating Variance and Standard Deviation

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Example of determining a sample standard deviation: 44 – 6 = -24 4 4 55 – 6 = -11 77 – 6 = 11 1010 – 6 = 416 = 30 = 0 = 26 = 6 2

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The standard deviation has important uses for continuous data, particularly when the frequency distribution follows a normal (also called Gaussian, or bell-shaped) distribution The normal distribution is the most important probability distribution in statistics Standard Deviation

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