Embed Size (px)
DESCRIPTION
Business Statistics for risk management perspective
Citation preview
A groundwork for risk assessment
Diane Christina | 2009
Descriptive Statistics used to describe the mainfeatures of a collection of data in quantitativequantitative termsterms
Inferential Statistic comprises the use of statistics Inferential Statistic comprises the use of statisticsand random sampling to make conclusionconcerning some unknown aspect of a population
RandomSample
Sample (mean)
• Calculatesample meanto estimatepopulationmean
Population(mean)
Measures of central tendency
(Mean, Median, Mode)(Mean, Median, Mode)
Measures of dispersion
(variance, standard deviation)
Measures of shape
(skewness)
Mean
Arithmetic Mean
Geometric Mean Geometric Mean
Median
Mode
Quartiles
Range: the difference between the largest value of dataset and the smallest value
Interquartile range: the range of values between thefirst and the third quartilefirst and the third quartile
Mean absolute deviation MAD = ∑ | x – x | / n
Variance S2 = ∑ X2 – (∑ X)2/n(for sample variance) n-1
Standard Deviation 2SS
Interpretation of Standard DeviationEg. µ = 100 σ=15
•± 1σ = 85/115•± 2σ = 70/130•± 3σ = 55/145
68%
95%
99.7%
Fre
qu
ency
Value Changes
•± 3σ = 55/145
Skewnessis a measure of the asymmetry of the probability
distribution of a real-valued random variable
Positively Skew/Skewed to the right
Negatively Skew/Skewed to the left
Mo
de
Med
ian
Mea
n
Mo
de
Med
ian
Mea
n
SkSk = 3 (mean −median) / standard deviation= 3 (mean −median) / standard deviation
Class Interval Frequency Mid PointRelative
FrequencyCumulativeFrequency
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
STEM LEAF
2 3
4 74 7
5 5 9
6 0 7
7 3 5 6 7
8 3 6 8
9 1 2
86 77 91 60 55
76 92 47 88 67
23 59 73 75 83
To determine likelihood of an event
Method of assigning probabilities: Classical (Apriority) probability Relative frequency of occurrence Subjective probability Subjective probability
General law of addition
Special law of addition
YXPYPXPYXP
YPXPYXP
General law of multiplication
Special law of multiplication
Law of conditional probability
YPXPYXP
YXPYPXYPXPYXP ||
YPXPYXP
YP
XYPXP
YP
YXPYXP
||
Construct risk model and measure the degree of relatedness of variables
Find the equation of regression line
XbbY 10
^
Where as the populationY intercept
The population slope
_
1
_
0 XbYb
n
XX
n
YXXY
SSxxSSxyb
2
2
1
Hospitals Number of beds Full Time Employees
X Y
1 23 69
2 29 95
3 29 102
XY
XbbY
232.29125.30^
10
^
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
Measure of how well the regression line
approximates the real data points
The proportion of variability of the dependent 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 )
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)
Unexplained Variation = sum of square of error (SSE)
i
YYiSSR2
)
i
YiXiSSE2
r2 = Explained Variation / Total Variation
r2 = 1 - Y
YY
2
2^
r = 1 -
n
YY
i
2
2
Hospitals Number of beds Full Time Employees
X Y
1 23 69
2 29 95
3 29 102 SSE = 2448.6
XY
XbbY
232.29125.30^
10
^
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
SSE = 2448.6
r2 = 0,886
