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Business Statistics for risk management perspective

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- 1. A groundwork for risk assessment Diane Christina | 2009
- 2. Descriptive Statistics used to describe the main features of a collection of data in quantitative terms Inferential Statistic comprises the use of statistics and random sampling to make conclusion concerning some unknown aspect of a population Sample (mean) Random • Calculate Population sample mean Sample to estimate (mean) population mean
- 3. Measures of central tendency (Mean, Median, Mode) Measures of dispersion (variance, standard deviation) Measures of shape (skewness)
- 4. Mean Arithmetic Mean Geometric Mean Median Mode Quartiles
- 5. Range: the difference between the largest value of data set and the smallest value Interquartile range: the range of values between the first and the third quartile Mean absolute deviation MAD = ∑ | x – x | / n Variance S2 = ∑ X2 – (∑ X)2/n (for sample variance) n-1 Standard Deviation S S2
- 6. Interpretation of Standard Deviation Eg. µ = 100 σ=15 • ± 1σ = 85/115 • ± 2σ = 70/130 • ± 3σ = 55/145 Frequency Value Changes 68% 95% 99.7%
- 7. Skewness is a measure of the asymmetry of the probability distribution of a real-valued random variable Negatively Skew/ Positively Skew/ Skewed to the left Skewed to the right Mean Mean Mode Mode Median Median Sk = 3 (mean − median) / standard deviation
- 8. Relative Cumulative Class Interval Frequency Mid Point Frequency Frequency 20 ≤ x < 30 6 25 .12 6 30 ≤ x < 40 18 35 .36 24 40 ≤ x < 50 11 45 .22 35 50 ≤ x < 60 11 55 .22 46 60 ≤ x < 70 3 65 .06 49 70 ≤ x < 80 1 75 .02 50 Totals 50 1.00
- 9. STEM LEAF 2 3 4 7 86 77 91 60 55 5 5 9 76 92 47 88 67 6 0 7 7 3 5 6 7 8 3 6 8 23 59 73 75 83 9 1 2
- 10. To determine likelihood of an event
- 11. Method of assigning probabilities: Classical (Apriority) probability Relative frequency of occurrence Subjective probability
- 12. General law of addition P X Y P X PY P X Y Special law of addition P X Y P X P Y General law of multiplication P X Y P X P Y | X P Y P X | Y Special law of multiplication P X Y P X PY Law of conditional probability P X | Y P X Y P X PY | X PY P Y
- 13. Construct risk model and measure the degree of relatedness of variables
- 14. Find the equation of regression line ^ Y b0 b1 X _ _ Where as the populationY intercept b0 Y b1 X The population slope X Y XY b1 SSxy n SSxx X 2 X2 n
- 15. Hospitals Number of beds Full Time Employees ^ X Y Y b0 b1 X 1 23 69 ^ 2 29 95 Y 30 .9125 2.232 X 3 29 102 4 35 118 5 42 126 6 46 125 7 50 138 8 54 178 9 64 156 10 66 184 11 76 176 12 78 225
- 16. Measure of how well the regression line approximates the real data points The proportion of variability of the dependent variable (Y) explained by independent variable (X) R2 = 0 ---> no regression prediction of Y by X R2 = 1 ---> perfect regression prediction of Y by X (100% of the variability of Y is accounted for by X )
- 17. r2 = Explained Variation / Total Variation Total Variation = Explained Variation + Unexplained Variation (The dependent variable,Y , measured by sum of squares ofY (SSyy)) Explained Variation = sum of square regression (SSR) SSR Yi Y ) i 2 Unexplained Variation = sum of square of error (SSE) SSE Xi Yi 2 i
- 18. r2 = Explained Variation / Total Variation 2 ^ Y Y r2 = 1 - Y 2 Y 2 n i
- 19. Hospitals Number of beds Full Time Employees ^ X Y Y b0 b1 X 1 23 69 ^ 2 29 95 Y 30 .9125 2.232 X 3 4 29 35 102 118 SSE = 2448.6 5 42 126 6 46 125 r2 = 0,886 7 50 138 8 54 178 9 64 156 10 66 184 11 76 176 12 78 225
- 20. Diane Christina | 2009 diane.christina@apb-group.com | me@dianechristina.com http://dianechristina.wordpress.com

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