Applied Statistics
Chapter 2: Analysis of univariate data
1. Representations and graphs.


Frequency tables.
Bar charts, pictograms, histograms, frequency polygons and box
plots
2. Numerical summary.



Measures of location.
Measures of spread.
Measures of form.
Recommended reading:
• Bad charts
• Capítulos 3 a 7 del libro de Portilla (2004)
Applied Statistics
2.1: Representations and graphs
DESCRIPTION OF QUALITATIVE VARIABLES
Absolute frequency
Relative frequency
Bar chart
Pie chart
DESCRIPTION OF QUANTITATIVE VARIABLES
Absolute frequency / cumulative absolute frequency
Relative frequency / cumulative relative frequency
Histogram
Frequency polygon
Recommended reading:
 Capítulos 3 y 4 del libro de Portilla (2004)
Applied Statistics
Description of qualitative variables
SAMPLE: 70 madrileño university students
VARIABLE: Preferred political party
OBJECTIVE: Classification and representation of the information
PP
IU
PP
IU
PP
PP
IU
IU
PSOE
PSOE
IU
PP
PSOE
IU
PSOE
PSOE
PSOE
IU
IU
PSOE
Otros
IU
IU
PSOE
PP
UPD
IU
PSOE
PSOE
UPD
PP
PSOE
PP
IU
PP
PSOE
PP
UPD
IU
UPD
PSOE
PSOE
PSOE
IU
PSOE
PP
PSOE
UPD
PP
PP
Otros
UPD
Otros
PSOE
IU
Otros
IU
IU
PSOE
PP
Otros
IU
PSOE
PSOE
UPD
IU
PSOE
PP
IU
PSOE
Applied Statistics
The frequency table
Absolute frequency
Relative frequency
Class (i)
ni
fi
PSOE
23
0,33
PP
15
0,21
IU
20
0,29
UPD
7
0,10
Otros
5
0,07
Total
70
1
= 23+15+20+7+5
= 15/70
= 0,33+0,21+ …+0,07
Applied Statistics
The general outline of a frequency table
Class (i)
ni
fi
1
n1
f1
2
n2
f2
3
n3
f3
k
nk
fk
Total
N
1
= n1 + n2 +… + nk
= f1 + f2 +… + fk
= n1/N
Applied Statistics
The bar chart
Applied Statistics
How to lie with bar charts
Data on the previous computer of iMac owners
Previous Ownership
Frequency
Relative Frequency
None
85
0.17
Windows
60
0.12
Macintosh
355
0.71
Total
500
1.00
Applied Statistics
It appears that nearly everyone buys Macs …
Applied Statistics
… but now not so much!
Applied Statistics
Comparative bar charts
http://cnx.org/content/m10927/latest/
Applied Statistics
The pie chart
7%
10%
33%
29%
21%
Applied Statistics
The pictogram
PSOE
PP
IU
UPD
OTROS
The area of the graph is proportional to the frequency.
Applied Statistics
A real example of a pictogram
Applied Statistics
How to lie with pictograms
Letting height be proportional to frequency gives a false impression.
Applied Statistics
Exercise
TYPE OF CRIME
No.
Theft
5996
Battery
5059
Criminal damage
3866
Narcotics
3134
Burglary
2289
Assault
1641
Others
1802
Crimes commited in Chicago
between 5/11/2009 and
5/12/2009
Summarize these data in graphical
form
Chicago crime database
Applied Statistics
Exercise
Final grades in a statistics course:
GRADE
No. Students
Didn’t sit exam
17
D/E
16
C
29
B
24
A
2
Is this a nominal or an ordinal
variable?
What percentage of the students
didn’t pass?
Are there any other graphs that
could be useful here?
Applied Statistics
Exercise (Test question)
The 40 students in a statistics class rate their lecturer from 1 (extremely
boring) to 5 (fantastic). The table partially shows the survey results.
Evaluation
Absolute frequency
Relative frequency
1
0,05
2
3
5
4
9
5
19
TOTAL
Complete the table.
Applied Statistics
Exercise (Test question)
The following table comes from the CIS survey of January 2011. The values
are given as (approximate) percentages of a total number of 2478
respondents.:
Which of the following affirmations is correct?
a) The number of respondents who have a lot
of confidence (mucha confianza) in the
Mariano Rajoy is approximately 619.
b) Approximately 1953 of the respondents have
little or no confidence (poca o ninguna
confianza) in the leader of the PP.
c) The relative frequency of respondents who
don’t know (NS) or don’t reply (NC) is 0.19.
d) None of the above.
Applied Statistics
Exercise (Exam question)
The following pie chart shows the distribution of the autonomous
communities visited by foreign tourists.
Which of the following is the correct
response?
a) The percentage of tourists who visit the
islands is lower than the percentage for
the rest of the destinations.
b) The percentage of tourists who visit the
islands is higher than the percentage for
the rest of the destinations.
c) Cataluña and the Comunidad de Madrid
are the communities with the highest
percentages of foreign tourists.
d) None of the above.
Applied Statistics
Exercise (Exam question)
The following pie chart concerns the voting concerns of students at the
University of Houston University before the 2010 elections.
Which of
correct?
the
following
affirmations
is
a) 160 students said that the main
issues were Jobs or Immigration.
b) 327 students said that the main
issues were Public schools or Health
care.
c) 25 students said that the main issue
was Other.
d) 259 students said that the main
issue was College costs.