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3 common measures of dispersion or variability

3 common measures of dispersion or variability. Range Variance Standard Deviation. Range. (Highest value) – (Lowest Value) Quick & easy, but only reflects the extremes, and may be distorted by one extreme value. Variance and Standard Deviation. Standard Deviation.

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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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