Business
U.B.I. STATISTICS AUTUMN 2018 CLASS 2
18th September 2018
Tuesday 18th September 2018
Graphical
Descriptive
Techniques 1
FROM last class
Bring laptops and book
Read Chapter 2
Outline of Course shared - to be further elaborated as the course progresses
Bring example from media/news in which statistics are presented
My found Statistics
Teach Statistics Before Calculus
https://www.ted.com/talks/arthur_benjamin_s_formula_for_changing_math_education?language=en
The graphical & tabular methods presented here apply to both entire populations and samples drawn from populations.
Population
Sample
Subset
POPULATIONS & SAMPLES
QUICK CHECK…
A politician who is running for mayor of a commune with 25,000 registered voters commissions a survey. In the survey, 48% of the 200 registered voters interviewed say they plan to vote for her.
What is the population of interest?
What is the sample?
Is the value 48% a parameter or a statistic?
QUICK CHECK…answers
A politician who is running for mayor of a commune with 25,000 registered voters commissions a survey. In the survey, 48% of the 200 registered voters interviewed say they plan to vote for her.
What is the population of interest? 25,000 registered voters
What is the sample? 200 registered voters
Is the value 48% a parameter or a statistic? Statistic
DEFINITIONS…
A variable is some characteristic of a population or sample.
e.g. student grades.
Typically denoted with a capital letter: X,Y, Z…
The values of the variable are the range of possible values for a variable.
e.g. student marks (0..100)
Data are the observed values of a variable.
e.g. student marks: {67, 74, 71, 83, 93, 55, 48}
TYPES OF DATA & INFORMATION
Data (at least for purposes of Statistics) fall into three main groups:
Interval Data
Nominal Data
Ordinal Data
INTERVAL DATA…
Interval data
Real numbers, i.e. heights, weights, prices, etc.
Also referred to as quantitative or numerical.
NOMINAL DATA…
Nominal Data
The values of nominal data are categories.
e.g. responses to questions about marital status, coded as: Single = 1, Married = 2, Divorced = 3,Widowed = 4
These data are categorical in nature; arithmetic operations don’t make any sense (e.g. does Widowed ÷ 2 = Married?!)
Nominal data are also called qualitative or categorical.
ORDINAL DATA…
Ordinal Data appear to be categorical in nature, but their values have an order ; a ranking to them:
e.g. College course rating system:
poor = 1, fair = 2, good = 3, very good = 4, excellent = 5
While its still not meaningful to do arithmetic on this data (e.g. does 2 x fair = very good?!), we can say things like:
excellent > poor or fair < very good
That is, order is maintained no matter what numeric values are assigned to each category.
CALCULATIONS FOR TYPES OF DATA
As mentioned above,
All calculations are permitted on interval data.
Only calculations involving a ranking process are allowed for ordinal data.
No calculations are allowed for nominal data, save counting the number of observations in each category.
This lends itself to the following “hierarchy of data”…
HIERARCHY OF DATA…
Interval
Values are real numbers. All calculations are valid.
Data may be treated as ordinal or nominal.
Ordinal
Values must represent the ranked order of the data. Calculations based on an ordering process are valid. Data may be treated as nominal but not as interval.
Nominal
Values are the arbitrary numbers that represent categories.
Only calculations based on the frequencies of occurrence are valid. Data may not be treated as ordinal or interval.
You practice…question 2.2
Questions : page 17 Exercises 2.2 and 2.4
2.2
For each of the following examples of data, determine the type.
a. The number of miles joggers run per week
b. The starting salaries of graduates of MBA programs
c. The months in which a firm’s employees choose to take their vacations
d. The final letter grades received by students in a statistics course
You practice…question 2.4
2.4
The placement office at a university regularly surveys the graduates 1 year after graduation and asks for the following information. For each, determine the type of data.
a. What is your occupation?
b. What is your income?
c. What degree did you obtain?
d. What is the amount of your student loan?
e. How would you rate the quality of instruction? (excellent, very good, good, fair, poor)
You practice…question 2.2 (answer)
2.2
For each of the following examples of data, determine the type.
a. The number of miles joggers run per week Interval
b. The starting salaries of graduates of MBA programs Interval
c. The months in which a firm’s employees choose to take their vacations Nominal
d. The final letter grades received by students in a statistics course Ordinal
You practice…question 2.4 (answer)
2.4
The placement office at a university regularly surveys the graduates 1 year after graduation and asks for the following information. For each, determine the type of data.
a. What is your occupation? Nominal
b. What is your income? Interval
c. What degree did you obtain? Nominal
d. What is the amount of your student loan? Interval
e. How would you rate the quality of instruction? (excellent, very good, good, fair, poor) Ordinal
GRAPHICAL & TABULAR TECHNIQUES FOR NOMINAL DATA…
The only allowable calculation on nominal data is to count the frequency of each value of the variable.
We can summarize the data in a table that presents the categories and their counts called a frequency distribution.
A relative frequency distribution lists the categories and the proportion with which each occurs.
Example 2.1 work status in the gss 2008 survey
In a 2008 survey respondents were asked the following.
“Last week were you working full time, part time, going to school, keeping house, or what?” The responses were :
Working full time
Working part time
Temporarily not working
Unemployed, laid off
Retired
School
Keeping house
Other The responses were recorded using the codes 1, 2, 3, 4, 5, 6, 7, and 8, respectively.
Frequency and Relative Frequency Distributions
Bar Charts are often used to display frequencies…
Pie Charts show relative frequencies…
It is all the same information, based on the same data. Just different presentation.
IN-CLASS WORKSHOP
Using any spreadsheet software, open the data file for the class
In the first 2 tabs – this is an example of INTERVAL data. Please do the following for each:
Format the table in a presentable way that you would show in a report.
Add the calculations for Average, Mean, Median, Max, Min, Range & Standard Deviation
Create a bar chart.
Explain how you would interpret the data.
In the third tab – this is an example of NOMINAL data. Please do the following:
Determine how to count and present the results.
Create a pie chart to show the relative frequencies.
Explain how you would interpret the data.
This is a graded assignment.You have to print out your work and hand it in by next week
For NEXT CLASS
Bring laptops and book
Read Chapter 3
Hand-in assignment by the start off class for grading. A paper copy. Colour.
Bring example from media/news in which statistics are presented