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Chapter 5 – Measurements of Variability

Chapter 5 – Measurements of Variability. Math 22 Introductory Statistics. Measures of Variability. Range - The difference between the highest and lowest measurement. Range = Highest – Lowest Deviation = Observation – Mean . Standard Deviation and Variance.

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Chapter 5 – Measurements of Variability

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  1. Chapter 5 – Measurements of Variability Math 22 Introductory Statistics

  2. Measures of Variability • Range - The difference between the highest and lowest measurement. • Range = Highest – Lowest • Deviation = Observation – Mean

  3. Standard Deviation and Variance • Population Variance - The average squared distance of all measurements from the population mean. • Sample Variance - The average squared distance of the sample values from the sample mean. • Standard Deviation – A more common measurement of variation.

  4. Empirical Rule If a stem and leaf plot, histogram, or similar descriptive tool has a bell-shaped curve then: • Approximately 68% of the measurements fall within 1 standard deviation of the mean. • Approximately 95% of the measurements fall within 2 standard deviations of the mean.

  5. Empirical Rule • Approximately 99.7% of the measurements fall within 3 standard deviations of the mean.

  6. Chebyshev’s Rule Regardless of the shape of the distribution we have: • At least 75% of the measurements will fall within 2 standard deviations of the mean. • At least 89% of the measurements will fall within 3 standard deviations of the mean. • At least 93.75% of the measurements will fall within 4 standard deviations of the mean.

  7. Five Number Summary as a Measurement of Variability • When the distribution is skewed left or skewed right, we can use the five number summary as a measurement of variability.

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