2. Introduction to the Practice of Statistics
Chapter 1 Section 1
Introduction to the
Practice of Statistics

3. Chapter 1 – Section 1 The science of statistics is
Collecting
Organizing
Summarizing
Analyzing
information to draw conclusions or answer questions

4. Chapter 1 – Section 1 Organize and summarize the information
Descriptive statistics (chapters 2 through 4)
Draw conclusion/generalization from the information
Inferential statistics (chapters 9 through 11)

5. Chapter 1 – Section 1 A population - Is the group to be studied
- Includes all of the individuals in the group
A sample
Is a subset of the population
Is often used in analyses because getting access to the entire population is impractical

6. Chapter 1 – Section 1
Characteristics of the individuals under study are called variables
Some variables have values that are attributes or characteristics … those are called qualitative or categorical variables
Some variables have values that are numeric measurements … those are called quantitative variables
The suggested approaches to analyzing problems vary by the type of variable

7. Chapter 1 – Section 1 Examples of qualitative variables
Gender
Zip code
Blood type
States in the United States
Brands of televisions
Qualitative variables have category values … those values cannot be added, subtracted, etc.

8. Chapter 1 – Section 1 Examples of quantitative variables
Temperature
Height and weight
Sales of a product
Number of children in a family
Points achieved playing a video game
Quantitative variables have numeric values … those values can be added, subtracted, etc.

9. Chapter 1 – Section 1
Quantitative variables can be either discrete or continuous
Discrete variables
Variables that have a finite or a countable number of possibilities
Frequently variables that are counts
Continuous variables
Variables that have an infinite but not countable number of possibilities
Frequently variables that are measurements

10. Chapter 1 – Section 1 Examples of discrete variables
The number of heads obtained in 5 coin flips
The number of cars arriving at a McDonald’s between 12:00 and 1:00
The number of students in class
The number of points scored in a football game
The possible values of qualitative variables can be listed

11. Chapter 1 – Section 1 Examples of continuous variables
The distance that a particular model car can drive on a full tank of gas
Heights of college students

12. Summary: Chapter 1 – Section 1
The process of statistics is designed to collect and analyze data to reach conclusions
Variables can be classified by their type of data
Qualitative or categorical variables
Discrete quantitative variables
Continuous quantitative variables

13. Organizing and Summarizing Data
Chapter 2
Organizing and
Summarizing Data

14. Chapter 2 Sections Sections in Chapter 2 Organizing Qualitative Data
Organizing Quantitative Data
Graphical Misrepresentations of Data

15. Organizing Qualitative Data
Chapter 2 Section 1
Organizing
Qualitative Data

16. Chapter 2 – Section 1
Qualitative data values can be organized by a frequency distribution
A frequency distribution lists
Each of the categories
The frequency for each category

17. blue, blue, green, red, red, blue, red, blue
Chapter 2 – Section 1
A simple data set is
blue, blue, green, red, red, blue, red, blue
A frequency table for this qualitative data is
The most commonly occurring color is blue
Color
Frequency
Blue 4
Green 1
Red 3

18. Chapter 2 – Section 1
The relative frequencies are the proportions (or percents) of the observations out of the total
A relative frequency distribution lists
Each of the categories
The relative frequency for each category

19. Chapter 2 – Section 1
A relative frequency table for this qualitative data is
A relative frequency table can also be constructed with percents (50%, 12.5%, and 37.5% for the above table)
Color
Relative Frequency
Blue
.500
Green
.125
Red
.375

20. Chapter 2 – Section 1 Bar graphs for our simple data (using Excel)
Frequency bar graph
Relative frequency bar graph

21. Chapter 2 – Section 1 A Pareto chart is a particular type of bar graph
A Pareto differs from a bar chart only in that the categories are arranged in order
The category with the highest frequency is placed first (on the extreme left)
The second highest category is placed second
Etc.
Pareto charts are often used when there are many categories but only the top few are of interest

22. Chapter 2 – Section 1
A Pareto chart for our simple data (using Excel)

23. Chapter 2 – Section 1
An example side-by-side bar graph comparing educational attainment in 1990 versus 2003

24. Chapter 2 – Section 1
An example of a pie chart

25. Organizing Quantitative Data:
Chapter 2 Section 2
Organizing Quantitative Data:

26. Chapter 2 – Section 2 Consider the following data
We would like to compute the frequencies and the relative frequencies

27. Chapter 2 – Section 2
The resulting frequencies and the relative frequencies

28. Chapter 2 – Section 2 Example of histograms for discrete data
Frequencies
Relative frequencies

29. Chapter 2 – Section 2
Continuous data cannot be put directly into frequency tables since they do not have any obvious categories
Categories are created using classes, or intervals of numbers
The continuous data is then put into the classes

30. Chapter 2 – Section 2 For ages of adults, a possible set of classes is
20 – 29
30 – 39
40 – 49
50 – 59
60 and older
For the class 30 – 39
30 is the lower class limit
39 is the upper class limit
The class width is the difference between the upper class limit and the lower class limit
For the class 30 – 39, the class width is
40 – 30 = 10

31. Chapter 2 – Section 2
All the classes have the same widths, except for the last class
The class “60 and above” is an open-ended class because it has no upper limit
Classes with no lower limits are also called open-ended classes

32. Chapter 2 – Section 2
The classes and the number of values in each can be put into a frequency table
In this table, there are 1147 subjects between 30 and 39 years old
Age
Number
(frequency)
20 – 29
533
30 – 39
1147
40 – 49
1090
50 – 59
493
60 and older
110

33. Chapter 2 – Section 2
Good practices for constructing tables for continuous variables
The classes should not overlap
The classes should not have any gaps between them
The classes should have the same width (except for possible open-ended classes at the extreme low or extreme high ends)
The class boundaries should be “reasonable” numbers
The class width should be a “reasonable” number

34. Chapter 2 – Section 2
Just as for discrete data, a histogram can be created from the frequency table
Instead of individual data values, the categories are the classes – the intervals of data

35. Chapter 2 – Section 2
A stem-and-leaf plot is a different way to represent data that is similar to a histogram
To draw a stem-and-leaf plot, each data value must be broken up into two components
The stem consists of all the digits except for the right most one
The leaf consists of the right most digit
For the number 173, for example, the stem would be “17” and the leaf would be “3”

36. Chapter 2 – Section 2 In the stem-and-leaf plot below
The smallest value is 56
The largest value is 180
The second largest value is 178

37. Chapter 2 – Section 2 To draw a stem-and-leaf plot
Write all the values in ascending order
Find the stems and write them vertically in ascending order
For each data value, write its leaf in the row next to its stem
The resulting leaves will also be in ascending order
The list of stems with their corresponding leaves is the stem-and-leaf plot

38. Chapter 2 – Section 2 Modifications to stem-and-leaf plots
Sometimes there are too many values with the same stem … we would need to split the stems (such as having in one stem and in another)
If we wanted to compare two sets of data, we could draw two stem-and-leaf plots using the same stem, with leaves going left (for one set of data) and right (for the other set)

39. Chapter 2 – Section 2
A dot plot is a graph where a dot is placed over the observation each time it is observed
The following is an example of a dot plot

40. Chapter 2 – Section 2
A useful way to describe a variable is by the shape of its distribution
Some common distribution shapes are
Uniform
Bell-shaped (or normal)
Skewed right
Skewed left

41. Chapter 2 – Section 2 A variable has a uniform distribution when
Each of the values tends to occur with the same frequency
The histogram looks flat

42. Chapter 2 – Section 2 A variable has a bell-shaped distribution when
Most of the values fall in the middle
The frequencies tail off to the left and to the right
It is symmetric

43. Chapter 2 – Section 2 A variable has a skewed right distribution when
The distribution is not symmetric
The tail to the right is longer than the tail to the left
The arrow from the middle to the long tail points right
Right

44. Chapter 2 – Section 2 A variable has a skewed left distribution when
The distribution is not symmetric
The tail to the left is longer than the tail to the right
The arrow from the middle to the long tail points left
Left

45. Summary: Chapter 2 – Section 2
Quantitative data can be organized in several ways
Histograms based on data values are good for discrete data
Histograms based on classes (intervals) are good for continuous data
The shape of a distribution describes a variable … histograms are useful for identifying the shapes

46. Graphical Misrepresentations of Data
Chapter 2 Section 3
Graphical Misrepresentations
of Data

47. Chapter 2 – Section 4
The two graphs show the same data … the difference seems larger for the graph on the left
The vertical scale is truncated on the left

48. Chapter 2 – Section 4
The gazebo on the right is twice as large in each dimension as the one on the left
However, it is much more than twice as large as the one on the left
Original
“Twice” as large

49. Summary: Chapter 2 – Section 1
Qualitative data can be organized in several ways
Tables are useful for listing the data, its frequencies, and its relative frequencies
Charts such as bar graphs, Pareto charts, and pie charts are useful visual methods for organizing data
Side-by-side bar graphs are useful for comparing two sets of qualitative data