For Hanze Year 1 students

1. IBS Statistics Year 1
Dr. Ning DING
n.ding@pl.hanze.nl
I007, Friday & Monday

2. Table of content
• Chapter 1: What is statistics?
– Why study statistics?
– What is meant by statistics?
– Types of statistics
– Types of variables
– Levels of measurement
• Norminal-Level Data
• Ordinal-Level Data
• Interval-Level Data
– Ethics and Statistics
• Chapter 2: Describing data
– Frequency tables
– Frequency distributions
– Graphic presentation

3. Learning Goals
• Chapter 1: What is statistics?
– Understand why we study statistics
– Explain what is meant by descriptive and inferential statistics
– Distinguish between a qualitative and quantitative variable
– Describe how a discrete variable is different from a continous
variable
– Distinguish among the nominal, ordinal, interval and ratio
levels of measurement
• Chapter 2: Describing data
– Organize qualitative data into a frequency table
– Present a frequency table as a bar chart or a pie chart
– Organize quantitative data into a freqency distribution
– Present a frequency distribution for quantitative data using
histograms, frequency polygons, and cumulative frequency
polygons.

4. Chapter 1: What is Statistics?
1. Introduction
Statistics are
everywhere.

5. Chapter 1: What is Statistics?
1. Introduction

6. Chapter 1: What is Statistics?
1. Introduction
Statistics
help you
make
decisions.

7. Chapter 1: What is Statistics?
1. Introduction
Statistics give
you a better
understanding.

8. Chapter 1: What is Statistics?
1. Introduction
1. Adequate information? Additional information?
2. No misleading information?
3. Summarize the information.
4. Analyze available information.
5. Conclusions!

9. Chapter 1: What is Statistics?
1. Introduction
Statistics:
The science of collecting, organizing,
presenting, analyzing and interpreting data
to assist in making more effective decisions.

10. Chapter 1: What is Statistics?
1. Introduction
Making decisions
Interpret data
Present data
Analyze data
Organize data
Collect data

11. Chapter 1: What is Statistics?
2. Types of Statistics
Descriptive Statistics:
Methods of organizing, summarizing and
presenting data in an informative way.
Inferential Statistics:
Methods used to estimate a property of a
population on the basis of a sample.

12. Chapter 1: What is Statistics?
2. Types of Statistics
Descriptive Inferential
Statistics: Statistics:

13. Chapter 1: What is Statistics?
2. Types of Statistics
Population:
The entire set of individual or objects of
interest or the measurements obtained from all
individuals or objects of interest.
Sample:
A portion, or part, of the population of interest.

14. Chapter 1: What is Statistics?
2. Types of Statistics
Population:
Sample:
Play

15. Chapter 1: What is Statistics?
3. Types of Variables
Qualitative:
nonnumeric, attribute
Quantitative:
numerical

16. Chapter 1: What is Statistics?
3. Types of Variables
Quantitative:
Qualitative:

17. Chapter 1: What is Statistics?
3. Types of Variables
Discrete counting or Continuous measuring

18. Chapter 1: What is Statistics?
4. Levels of Measurement
Nominal:
•Data categories are represented by labels or names.
•Even when the labels are numerically coded, the data categories
have no logical order.
•Example:
•Eye colour, gender, religious affiliation
Ordinal:
•Data classifications are represented by sets of labels or names
(high, medium, low) that have relative values.
•Because of the relative values, the data classified can be ranked or
ordered.
•Example:
•During a taste test of 4 soft drinks, Mellow Yellow was
ranked number 1, Sprite number 2, Seven-up number 3, and
Orange Crush number 4.

19. Chapter 1: What is Statistics?
4. Levels of Measurement
Nominal: Ordinal:
No logical order Ranked or ordered

20. Chapter 1: What is Statistics?
4. Levels of Measurement
Interval:
•Similar to the ordinal level, with the additional property that
meaningful amounts of differences between data values can be
determined.
•There is no natural zero point.
•Example:
•Temperature on the Fahrenheit scale.
Ratio:
•The interval level with an inherent zero starting point.
•Differences and ratios are meaningful for this level of measurement.
•Examples:
•Monthly income; distance travelled by manufacturer’s
representatives per month.

21. Chapter 1: What is Statistics?
4. Levels of Measurement
Online Animation
Nominal:
Ordinal:
Interval:
Ordered, Equal differences
Ratio:
Zero

22. vels of Measurement Chapter 1: What is Statistics?
4. Levels of Measurement

23. Chapter 1: What is Statistics?
Exercises 1-a
For each of the following, determine whether the group is a
sample or a population.
•The participants in a study of a new cholesterol drug. Sample
•The drivers who received a speeding ticket Kansas City last month.
Population
•Those on welfare in Cook County (Chicago), Illinois.
Population
•The 30 stocks reported as a part of the Dow Jones Industrial
Average. Sample
P14. N.4 Ch.1

24. Chapter 1: What is Statistics?
Exercises 1-b
Refer to the Real Estate data at the back of the text, which
report information on homes sold in the Denver, Colorado,
area last year. Consider the following variables: selling
price, number of bedrooms, township, and distance
from the center of the city.
•Which of the variables are qualitative and which are
quantitative?
township all the rest…
•Determin the level of measurement for each of the
variables.
Township = nominal level All the rest…=ratio
P18. N.16 Ch.1

25. Chapter 2: Describing data
2.1 Frequency Table
Frequency Table:
•A grouping of qualitative data into mutually exclusive classes
showing the number of observations in each class.
Example: Ice cream 20 vendors
Choco 6 7 5 7 7 8 7 6 9 7
Vanilla 4 10 6 8 8 9 5 6 4 8

26. Chapter 2: Describing data
2.1 Frequency Table
Relative Class Frequencies:
•Show the fraction of the total number of observations in each class
Example: Ice cream 20 vendors
Choco 6 7 5 7 7 8 7 6 9 7
Vanilla 4 10 6 8 8 9 5 6 4 8

27. Chapter 1: What is Statistics?
Exercises 2-a
A total of 1,000 residents in Minnesota were asked which season they preferred. The
results were 100 liked winter best, 300 liked spring, 400 liked summer, and 200 liked
fall.
If the data were summarized in a frequency table, how many classes would be
used? What would be the relative frequencies for each class?
P27. N.3 .Ch.2

28. Chapter 2: Describing data
2.2 Graphic Presentation
of Qualitative Data
Bar Chart:
•The classes are reported on the horizontal axis
•The class frequencies on the vertical axis
•The class frequencies are proportional to the heights of the bars.
Example: Ice cream 20 vendors
Ice Cream Sales
70 Choco, 69
Vanilla, 68
65
Choco
Axis
60
Vanilla
55
50
Choco Vanilla
Types

29. Chapter 2: Describing data
2.2 Graphic Presentation
of Qualitative Data
Pie Chart:
•Shows the proportion or percent that each class represents of the
total number of frequencies
Example: Ice cream 20 vendors
49.64%
50.36%
1
2

30. Chapter 2: Describing data
2. Frequency Distribution
Frequency Distribution:
•A grouping of data into
mutually exclusive
classes showing the
number of observations in
each class.

31. Chapter 2: Describing data
2. Frequency Distribution
Frequency Distribution:
•A grouping of data into mutually exclusive classes showing the
number of observations in each class.

32. Chapter 2: Describing data
2. Frequency Distribution
Step 1: Just enough recipe 2 to the k rule
N=27 number of class=5
Step 2: Class Interval
10 -< 20 4
20 -< 30 1
(55-14)/5 ≈ 8 30 -< 40 10
Step 3: Choose nice “round” boundaries 40 -< 50 9
Step 4: Try to avoid empty and open classes
50 -< 60 3
N=27
Practice

33. Chapter 2: Describing data
Exercises 2-b
A set of data consists of 45 observations between $0 and $29. What size would you
recommend for the class interval?
25 = 32, 26 = 64, suggests 6 classes
i> $30 - $0 =5
6
Use interval of 5
P33. N.8 .Ch.2

34. Chapter 2: Describing data
Exercises 2-b
The Quick Change Oil Company has a number of outlets in the metropolitan Seattle
area. The daily number of oil changes at the Oak Street outlet in the past 20 days
are:
65 98 55 62 79 59 51 90 72 56
70 62 66 80 94 79 63 73 71 85
a. How many classes would you recommend?
a. 24 = 16, 25 = 32, suggests 5 classes
b. What class interval would you suggest?
99 - 51
i> ≈ 9 b. Use interval of 10
5 P34. N.12.Ch.2

35. Chapter 2: Describing data
Exercises 2-b
The Quick Change Oil Company has a number of outlets in the metropolitan Seattle
area. The daily number of oil changes at the Oak Street outlet in the past 20 days
are:
65 98 55 62 79 59 51 90 72 56
70 62 66 80 94 79 63 73 71 85
c. What lower limit would you recommend for the first class?
c. 50
P34. N.12.Ch.2

36. Chapter 2: Describing data
3. Graphic Presentation
Histogram
•The classes are marked on the horizontal axis
•The class frequencies on the vertical axis
•The class frequencies are represented by the heights of the bars
and the bars are adjacent to each other.
Polygon:
•The shape of a distribution
•Similar to a histogram

37. Chapter 2: Describing data
3. Graphic Presentation
Histogram
Example:
16 Amount of € spent on books by 50 students
14
12
No. of students
10
8
6
4
2
0
25 75 125 175 225 275 325 375 425
Amount in €

38. Chapter 2: Describing data
3. Graphic Presentation
Polygon
Example:
Amount of € spent on books by 50 students
16
14
12
No. of students
10
8
6
4
2
0
125 175 225 275 325 375 425
Amount in €

39. Chapter 2: Describing data
3. Graphic Presentation
Cumulative frequency distribution:
used to determine how many or what proportion of
the data values are below or above a certain value.
Amount of € spent on books by 50
students
60
50
Cumulative frequency
40
30
20
10
0
100 150 200 250 300 350 400 450
Amount in €

40. Chapter 2: Describing data
3. Graphic Presentation

41. Chapter 1: What is Statistics?
Summary
• Chapter 1: What is statistics?
– Understand why we study statistics
– Explain what is meant by descriptive and inferential statistics
– Distinguish between a qualitative and quantitative variable
– Describe how a discrete variable is different from a continous
variable
– Distinguish among the nominal, ordinal, interval and ratio
levels of measurement
• Chapter 2: Describing data
– Organize qualitative data into a frequency table
– Present a frequency table as a bar chart or a pie chart
– Organize quantitative data into a freqency distribution
– Present a frequency distribution for quantitative data using
histograms, frequency polygons, and cumulative frequency
polygons.

42. Chapter 1: What is Statistics?
Exercises 1-a
What is the level of measurement for each of the following
variables?
• A. student IQ ratings Interval
• B. distance students travel to class Ratio
• C. student scores on the first statistics test Interval
• D. a classification of students by state of birth Nominal
• E. a ranking of students as freshmen, sophomore, junior, and
senior Ordinal
• F. Number of hours students study per week Ratio

43. Chapter 1: What is Statistics?
Exercises 1-b
Place these variables in the following classification tables.
a. Salary
b. Gender Discrete Continuous
c. Sales
volumen of
b. Gender d. Soft drink preference
MP3 players Qualitative
d. Soft drink
preference
e. Temperature f. SAT scores
f. SAT scores a. Salary
g. Student rank
g. Student rank in class c. Sales volume of MP3 players
in class Quantitative
h. Rating of a
h. Rating of a finance professor e. Temperature
finance
professor
i. Number of home computers
i. Number of
home
computers P16. N.9 Ch.1

44. Chapter 1: What is Statistics?
Exercises 1-c
Place these variables in the following classification tables.
a. Salary
b. Gender Discrete Continuous
c. Sales
volumen of
b. Gender
MP3 players Nominal
d. Soft drink
preference d. Soft drink preference
e. Temperature
Ordinal
f. SAT scores g. Student rank in class h. Rating of a finance professor
g. Student rank
in class f. SAT scores e. Temperature
h. Rating of a
Interval
finance a. Salary
professor
i. Number of Ratio c. Sales volume of MP3 players
home
computers i. Number of home computers

45. Chapter 1: What is Statistics?
Exercises 1-d
The table below reports the number of
cars and light trucks sold by the Big
Three automobile manufacturers for
June 2004 and June 2005.
1. Compare the total sales in the two months. What do you conclude? Has
there been an increase in sales?
P17. N.13 Ch.1

46. Chapter 1: What is Statistics?
Exercises 1-d
The table below reports the number of
cars and light trucks sold by the Big
Three automobile manufacturers for
June 2004 and June 2005.
1. Compare the total sales in the two months. What do you conclude? Has
there been an increase in sales?
(1,056,144-866,243)
Total sales increased 189,901 units or 21.9%. 866,243

47. Chapter 1: What is Statistics?
Exercises 1-d
The table below reports the number of
cars and light trucks sold by the Big
Three automobile manufacturers for
June 2004 and June 2005.
2. Compare the percent of the Big Three market for each company. Did the
market increase or did GM steal sales from the other companies? Cite
evidence.

48. Chapter 1: What is Statistics?
Exercises 1-d
The table below reports the number of
cars and light trucks sold by the Big
Three automobile manufacturers for
June 2004 and June 2005.
2. Compare the percent of the Big Three market for each company. Did the
market increase or did GM steal sales from the other companies? Cite
evidence.
GM increased the market share by 9 percentage points from 43% to 52%.
Crysler lost 3% and Ford lost 6%.
All three companies increased the nubmer of units sold.