Business Statistics for risk management perspective

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   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. 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