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QBA 260 Business Statistics

QBA 260 Business Statistics. Chapter 5. Deviating from the Average. Compare two datasets (reported in inches) Dataset 1: 48, 46, 46, 49, 49, 47, 47, 46, 49 Dataset 2: 47, 51, 49, 53, 47, 45, 37, 38, 60 What is the average of each dataset? How are they different?. Comparing Datasets. Mean.

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QBA 260 Business Statistics

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  1. QBA 260Business Statistics Chapter 5

  2. Deviating from the Average • Compare two datasets (reported in inches) • Dataset 1: 48, 46, 46, 49, 49, 47, 47, 46, 49 • Dataset 2: 47, 51, 49, 53, 47, 45, 37, 38, 60 • What is the average of each dataset? • How are they different?

  3. Comparing Datasets Mean Mean Mean (Average) for both datasets is 47.4 inches Variances differ: Dataset 1 = 1.78 sq. inches, Dataset 2 = 51.03 sq. inches

  4. Variance and Deviations • Variance is a measure of how much the data points in a sample deviate from the sample mean • For data: • x1, x2, x3,…, xn • A deviation is the difference between a data value and a central value such as the average

  5. Deviations • Dataset 1: 48, 46, 46, 49, 49, 47, 47, 46, 49 • Average = 47.4 • Deviations • The average deviation is (always) zero

  6. Deviations • Dataset 2: 47, 51, 49, 53, 47, 45, 37, 38, 60 • Average = 47.4 • Deviations • The average deviation is (always) zero

  7. Populations and Samples • Population variance • Sample variance

  8. Sample Variance – Dataset 1 • Sample variance Sq Inches

  9. Sample Variance – Dataset 2 • Sample variance Sq Inches

  10. Variance and Standard Deviation • The calculated variance is in a different unit of measure than the original dataset • Original Dataset measured in inches • Variance measured in inches squared (due to the use of squared deviations before we average them) • To accommodate this, we calculate the standard deviation which is the square root of the Variance

  11. Standard Deviation • Square root of the variance

  12. Excel Functions • VARP(…) Population Variance • VARPA(…) Population Variance (includes cells that contain true/false data) • VAR(…) Sample Variance • VARA(…) Sample Variance (includes cells that contain true/false data)

  13. Excel Functions • STDEVP(…) Population Standard Deviation • STDEVPA(…) Population Standard Deviation (includes cells that contain true/false data) • STDEV(…) Sample Standard Deviation • STDEVA(…) Sample Standard Deviation (includes cells that contain true/false data)

  14. Average Absolute Deviation Absolute Deviation = 10.44/9 = 1.16 EXCEL: AVEDEV

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