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Business Statistics for risk management perspective

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1. 1. A groundwork for risk assessment Diane Christina | 2009
2. 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. 3.  Measures of central tendency (Mean, Median, Mode)  Measures of dispersion (variance, standard deviation)  Measures of shape (skewness)
4. 4.  Mean  Arithmetic Mean  Geometric Mean  Median  Mode  Quartiles
5. 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. 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. 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. 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. 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. 10. To determine likelihood of an event
11. 11. Method of assigning probabilities:  Classical (Apriority) probability  Relative frequency of occurrence  Subjective probability
12. 12.  General law of addition P X  Y   P X   PY   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  PY   Law of conditional probability P  X | Y   P X  Y   P X  PY | X  PY  P Y 
13. 13. Construct risk model and measure the degree of relatedness of variables
14. 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. 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. 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. 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. 18.  r2 = Explained Variation / Total Variation 2  ^   Y  Y     r2 = 1 -  Y 2 Y 2  n i
19. 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. 20. Diane Christina | 2009 diane.christina@apb-group.com | me@dianechristina.com http://dianechristina.wordpress.com