Slide strategic financial management l02

STRATEGIC FINANCIAL MANAGEMENT
BASIC STATISTICS
KHURAM RAZA


First Principle and Big Picture


Summarizing Data
The problem that we face today is not that we have too
little information but too much. Making sense of large
and often contradictory information is part of what we
are called upon to do when analyzing companies.
 Data Distributions
 Summary Statistics


Data Distributions
 Frequency distribution.
 Discrete distribution.
 Continuous distribution.
 you can summarize even the largest data sets into
one distribution and get a measure of
 What values occur most frequently and
 The range of high and low values.


Summary Statistics
The information that gives a quick and simple description of the
data.
 Measures of Central Tendency

 Mean
Minimum Height: 6.2
 Quintiles
Average Height : 6.68
 Measures of Dispersion
Maximum Height : 7.3
 Variance
Average Change Per Day : 0.03
 standard deviation
 Relative Measures of Variation
 Coefficient of Variation (CV)
 Standardized Variable (Z-Score)


Mean
 The mean is the average of the numbers: a calculated
"central" value of a set of numbers.
 To calculate: Just add up all the numbers, then divide
by how many numbers there are.
 Example: what is the mean of 2, 7 and 9?
Add the numbers: 2 + 7 + 9 = 18
 Divide by how many numbers (i.e. we added 3
numbers):
18
÷
3
=
6
So the Mean is 6
n

X
i
X1  X 2    X n 
X
 i 1
n
n


Quintiles
For
individual
observations/discrete
frequency
distribution, the i th quartile, j th decile and k th
percentile are located in the array/discrete frequency
distribution by the following relations
Qi 

i(n  1)
th observation in the distribution, i 1, 2, 3
4

j(n  1)
th observation in the distribution, j 1, 2, ,9
10
k(n  1)
Pk 
th observation in the distribution, k 1, 2,,99

100
Dj 


Variance & Standard deviation
 The variance and the closely-related standard
deviation are measures of how spread out a
distribution is
 variance measures the variability (volatility) from an
average or mean.
Variance

Standard Deviation


Variance & Standard deviation
Mr.
•  X has eight eggs. Each egg was weighed and recorded as follows:
60 g, 56 g, 61 g, 68 g, 51 g, 53 g, 69 g, 54 g.
Mean = ∑X/n
472/8
=59
Variance = ∑(x- )2/n
320/8
= 40
S.D = √(x- )2/n
√40
= 6.32 gram

Comparing Standard Deviations
Data A
11

12

13

14

15

16

17

18

19

20 21

Mean = 15.5
S = 3.338

20 21

Mean = 15.5
S = 0.926

20 21

Mean = 15.5
S = 4.567

Data B
11

12

13

14

15

16

17

18

19

Data C
11

12

13

14

15

16

17

18

19

 The smaller the standard deviation, the more tightly clustered the scores around
mean
 The larger the standard deviation, the more spread out the scores from mean

02:57:50 PM

10


Coefficient of Variation (CV)
 S 
 100%
CV 

X



Can be used to compare two or more sets
of data measured in different units or
same units but different average size.
02:57:50 PM

11


Use of Coefficient of Variation
 Stock A:
– Average price last year = $50
– Standard deviation = $5
S
$5
CVA   100% 
100% 10%
$50
X

 Stock B:
– Average price last year = $100
– Standard deviation = $5
S
$5
CVB   100% 
100% 5%
$100
X
02:57:50 PM

Both stocks
have the
same
standard
deviation

but stock B is
less variable
relative to its
price


Standardized Variable

02:57:51 PM

13


Performance evaluation by z-scores
The industry in which sales rep Mr. Atif works has mean annual
sales=$2,500
standard deviation=$500.
The industry in which sales rep Mr. Asad works has mean annual
sales=$4,800
standard deviation=$600.

Last year Mr. Atif’s sales were $4,000 and Mr.
Asad’s sales were $6,000.
Which of the representatives would you hire if

you have one sales position to fill?
02:57:51 PM


Performance evaluation by z-scores
Sales rep. Atif

Sales rep. Asad

XB= $2,500

XP =$4,800

S= $500

SP = $600

XB= $4,000

XP= $6,000

ZB

XB  XB

SB

ZB 

4,000  2,500

500

ZP
3

XP  XP

SP

ZP 

6,000  4,800
600

Mr. Atif is the best choice
02:57:51 PM

2


Relationships in the Data
When there are two series of data, there are a number
of statistical measures that can be used to capture
how the two series move together over time.
10000
9000

 Covariance
 Correlations
 Regressions

8000
7000
6000

Sales
COGS
Selling Exp
Admin Exp

5000
4000
3000
2000
1000
0
100

200

300

400

500

600

700

800

900

1000


Covariance
Covariance indicates how two variables are related. A positive covariance means
the variables are positively related, while a negative covariance means the
variables are inversely related. The formula for calculating covariance of sample
data is shown below.

The covariance between the returns
of the S&P 500 and economic growth is
1.53. Since the covariance is positive,
the variables are positively related—they
move together in the same direction.


Correlation
 Correlation is another way to determine how two variables are related. In
addition to telling you whether variables are positively or inversely related,
correlation also tells you the degree to which the variables tend to move
together.
 The correlation measurement, called a correlation coefficient, will always
take on a value between 1 and – 1:

 If the correlation coefficient is one, the variables have a perfect positive correlation.
 If correlation coefficient is zero, no relationship exists between the variables.

 If correlation coefficient is –1, the variables are perfectly negatively correlated (or
inversely correlated).


Correlation

 A correlation coefficient of .66 tells
you two important things:
 Because the correlation coefficient is a positive number, returns on the
S&P 500 and economic growth are positively related.
 Because .66 is relatively far from indicating no correlation, the strength
of the correlation between returns on the S&P 500 and economic
growth is strong.


Regressions
A regression uses the historical relationship between an
independent and a dependent variable to predict the future values
of the dependent variable. Businesses use regression to predict
such things as future sales, stock prices, currency exchange rates,
and productivity gains resulting from a training program.

Y=a+bX
Slope of the Regression

Intercept of the Regression


Regressions