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Business Statistics Review FINA 3320 - Spring 2018 Rachel Li Cox School of Business Southern Methodist University March 18, 2018 1
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1 Numerical Descriptive Measures 1.1 Definitions The central tendency is the extent to which all the data values group around a typical or central value. The variation is the amount of dispersion or scattering of values The shape is the pattern of the distribution of values from the lowest value to the highest value. 1.2 Measures of Central Tendency: The Mean The arithmetic mean (often just called the “mean”) is the most common measure of central tendency For a sample of size n: ¯ X = n i =1 X i n = X 1 + X 2 + ... + X n n Example: House Prices: $2,000,000 $500,000 $300,000 $100,000 $100,000 Sum $3,000,000 Mean: ($3,000,000/5) = $600,000 Geometric mean, used to measure the rate of change of a variable over time ¯ X G = ( X 1 × X 2 × ... × X n ) 1 n 2
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Geometric mean rate of return, measures the status of an investment over time ¯ R G = ((1 + R 1 ) × (1 + R 2 ) × ... × (1 + R n )) 1 n - 1 Example: An investment of $100,000 declined to $50,000 at the end of year one and rebounded to $100,000 at end of year two: Arithmetic mean rate of return (misleading): ¯ X = ( - . 5) + (1) 2 = . 25 Geometric mean rate of return: ¯ R G = ((1 + - . 5) × (1 + 1)) 1 2 - 1 = 0 1.3 Measures of Variation Measures of variation give information on the spread or variability or dispersion of the data values. 1.3.1 Measures of Variation: The Sample Variance Average (approximately) of squared deviations of values from the mean Sample Variance: S 2 = n i =1 ( X i - ¯ X ) 2 n - 1 ¯ X is the arithmetic mean, n is sample size, X i is the i th value of variable X 1.3.2 Measures of Variation: The Sample Standard Deviation Most commonly used measure of variation Shows variation about the mean Is the square root of the variance 3
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Has the same units as the original data Sample Variance: S = s n i =1 ( X i - ¯ X ) 2 n - 1 1.3.3 Example Sample Data (Xi) : 10 12 14 15 17 18 18 24 n = 8 Mean = ¯ X = 16 S = s 8 i =1 ( X i - ¯ X ) 2 8 - 1 S = r (10 - 16) 2 + (12 - 16) 2 + (14 - 16) 2 + ... + (24 - 16) 2 8 - 1 = r 130 7 = 4 . 3095 Sample data-sets with same Mean, different Sample Variance 1.4 Two Measures Of The Relationship Between Two Numerical Variables Scatter plots allow you to visually examine the relationship between two numerical variables and now we will discuss two quantitative measures of such relationships.
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  • Fall '08
  • JACOBS
  • Probability, FINA, σp, Southern Methodist University, Cox School of Business

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