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3 common measures of dispersion or variability

Learn about common measures of dispersion like range, variance, and standard deviation in statistics. Understand how these metrics reflect variability in data and help analyze distribution patterns. Explore the computational formulas and practical applications of standard deviation and variance.

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3 common measures of dispersion or variability

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  1. 3 common measures of dispersion or variability • Range • Variance • Standard Deviation

  2. Range • (Highest value) – (Lowest Value) • Quick & easy, but only reflects the extremes, and may be distorted by one extreme value.

  3. Variance and Standard Deviation

  4. Standard Deviation • Standard Deviation of the Population is designated with the lower case of the Greek letter, sigma. It looks like our “o” with a tail on top. σ • Standard Deviation of the Sample is designated with the lower case of our usual letter, s.

  5. Variance • Variance of the Population is the square of the standard deviation, so it is designated with the lower case sigma, squared. σ2 • Variance of the Sample is similarly designated with the lower case s, squared. s 2

  6. Standard Deviation: Computational Formula • Standard deviation is the square root of the variance, and • Variance is the square of the standard deviation.

  7. Standard Deviation Represents • a sort of average variability, or deviation, from the mean • is in the same units as the mean.

  8. Standard Deviation • If the mean = 80, and s = 5, that means one standard deviation is 5 units from the mean of 80. • If we are measuring length, the mean might be 80 ft, and s is then 5 ft. • If we are measuring scores, the mean might be 80 points and s is 5 points.

  9. Standard Deviation • This would be reported by saying the mean is 80 plus or minus a standard deviation of 5. • A little more than 2/3 of the values in a normal distribution will be within 1 standard deviation above and below the mean, here between 75 and 85.

  10. For mean of 120, with sd of 25,

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