Download L643: Evaluation of Information Systems

Social Statistics: Difference
Review
Social statistics
 Descriptive statistics
 Inferential statistics
 Mean, median and mode

Z519--Spring 2015
Outline
Range
 Variance
 Standard deviation
 Using Excel and SPSS to calculate them

The whole story

Descriptive statistics
Centrality tendency (average)
 Measurement of variability (variability)


Average+Variability = describe the
characteristics of a set of data
Measures of variability

Variability


How scores differ from one another
Three sets of data
7, 6, 3, 3, 1
 3, 4, 4, 5, 4
 4, 4, 4, 4, 4


Variability = the difference from the mean
Measures of variability

Three ways
Range
 Variance
 Standard deviation

Range
The most general measure of variability
 How far apart scores are from one another

Range = highest score – lowest score
What is the range for the follow numbers?
98, 86, 77, 56, 48
Variance

Variance

The average of the squared deviations from the
mean
s
2
( x  x)


n 1
2
Standard deviation

Standard deviation (SD)
Average deviation from the mean (average
distance from the mean)
 Represents the average amount of variability

s
 ( x  x)
n 1
2
Variance and SD
𝑥 − 𝑥 : the deviation from the mean
2
 (𝑥 − 𝑥) : the sum of the squared deviations
from the mean
 𝑛 : the number of scores



(𝑥−𝑥)2
𝑛−1
: the variance
(𝑥−𝑥)2
𝑛−1
: the standard deviation
Exercise


The right figure shows 2013 GDP
per Capita for select countries-current US$
Please calculate the variance and
standard deviation by hand or by
using excel (VAR.S() & STDEV.S())
Country
Afghanistan
Brazil
Canada
Chile
Greece
Japan
Lebanon
Norway
Panama
Saudi Arabia
Singapore
Tunisia
United States
Vietnam
Zimbabwe
GDP per Capita
678
11208
51958
15732
21910
38492
9928
100819
11037
25852
55182
4329
53143
1911
905
Data collected from http://data.worldbank.org/
STDEV.S and STDEV.P
s
s
2
(
x

x
)

n 1
2
(
x

x
)

n
STDEV.S
𝑠 2 VAR.S
STDEV.P
𝑠 2 VAR.P
STDEV.S and STDEV.P




STDEV.S is standard deviation for sample (biased SD)
STDEV.P is standard deviation for population
(unbiased SD)
If your dataset is the whole population, use STDEV.P
to calculate standard deviation
If you dataset is the sample of something, use
STDEV.S to calculate standard deviation
Why n or n-1?
To be conservative
 STDEV

This is the standard deviation for sample
 Take n-1 in order to make STDEV a bit larger than
it would be.
 If we have error, we compensate by overestimating
the STDEV

Why n or n-1?
Sample size
Numerator
in standard
deviation
formula
Denominator
Population
standard
deviation
STDEV.P
(dividing by
n)
Denominator
Sample
standard
deviation
STDEV.S
(dividing by
n-1)
Difference
between
STDEVP and
STDEV
10
500
7.07
7.45
0.38
100
500
2.24
2.25
0.01
1000
500
0.7071
0.7075
0.0004
SD vs.Variance

Often appears in the “Results” sections of
journals

They are quite different

Variance is squared SD
SD vs.Variance
9
8
7
mean
6
5
4
3
2
1
0
1
2
3
4
5
6
7
8
9
10
Average distance to mean=(2+2+2+1+1+1+2+3)/10=1.4
SD = 1.76
Variance = 3.1
What to remember
Standard Deviation (SD) = the average
distance from the mean
 The larger SD, the more different data are
from one another
 Since mean is sensitive to extreme scores, so
do SD
 If SD=0, this means that there is no variability
in the set of scores (they are all identical in
value) – this happens very rarely.

Exercise 1

Average life expectancy
for females in 2010-2011
is reported for 10
countries. Please
calculate the range,
variance and SD for
European counties, NonEuropean countries, and
all countries.
Exercise 2

You and your friends have just measured the heights of your dogs
(in millimeters):

The heights (in mm) (at the shoulders) are: 600, 470, 170, 430 and
300.
Find out the Mean, the Variance, and the Standard Deviation.

Exercise 3
Western Airlines Flight Report
Morning Flights
Number of
passengers
Evening Flights
Number of
passengers
Thursday
Friday
To Kansas
To Kansas
258
251
Thursday
Friday
To Kansas
To Kansas
312
Thursday
To
Philadelphia
303
Thursday
To
Philadelphia
331
321
Friday
Thursday Friday
To
To
To
Philadelphia Providence Providence
312
166
176
Friday
Thursday Friday
To
To
To
Philadelphia Providence Providence
331
210
274
Exercise 3
Write a half page summary report to your boss
 Form a group to discuss it
