1. Chapter 1 Statistics in Business and Economics

2. I. Data A. Elements, Variables and Observations
1. Elements are entities on which data are collected.
2. Variables are characteristics of interest for the elements.
3. Observations are the set of measurements collected for a particular element.

3. An example

4. Check your understanding
What were the elements in the previous table?
What were the variables?

5. A Sample Data Set
This table contains some statistics for three members of the Indianapolis Colts in We will refer to this table as we discuss the ways in which data are presented and measured.
Player #
Position
Receptions
Yards
Yards per Reception
Pre-season fantasy Ranking at the position 87 WR 92
1493
16.23 12 44 TE 57
611
10.72 5 29 RB 40
356
8.9

6. Scales of Measurement
Nominal: data are labels or names used to identify an attribute of the element. Could be numeric (Player number) or nonnumeric (Position).
Ordinal: data have the properties of nominal data and the order or rank of the data is meaningful (Pre-season ranking). Could be numeric or nonnumeric.

7. More Measurement Scales
Interval: data have properties of ordinal data and the interval between observations is expressed in terms of a fixed unit of measure. Differences make sense, but ratios do not. No natural zero; zero is just another arbitrary point on a scale with numbers above and below it. (temperature, dates, SAT). Numeric.

8. Most common in Econ/Bus
Ratio: data have all properties of interval data and the ratio of two values is meaningful (His salary is twice the salary of his friend.). There is a natural zero if the variable has nothing to be measured (ex. Zero advertising expenditures). Numeric.

9. B. Categorical and Quantitative
Categorical data include labels or names used to identify an attribute of each element.
Categorical data use either nominal or ordinal scales. Note: sometimes categorical data can be numeric!
Quantitative data indicate either how much or how many.
Quantitative data use either the interval or ratio scale of measurement.

10. Categorical Questions
Anything that puts the response in a distinct category (or group).
What is your gender? M ____ F ____
Do you drink alcohol? Y ____ N ____
Are you a Bieber Believer? Y ____ N ____ NFW ____

11. Quantitative Questions
Answers: “How much?” or “How many?”
What is your hourly wage? ____
How many years of education have you completed? ____
How long did you study for the quiz? ____
How many alcoholic drinks do you consume in a typical week? ____

12. Example 2
Ask yourself the following question: Upon which of these numeric values could one reasonably perform statistical analysis? If you cannot, it is just a qualitative label for the element, although it is certainly numeric.

13. C. Cross-Sectional and Time-Series Data
1. Cross-Sectional data are collected at the same point in time.
Example: A comparison of union and non-union wages in a sample of 1990 truck drivers.
2. Time-series data are collected over several time periods.
Example: A study showing how the annual unemployment rate has fluctuated since 1945.

14. Example of Categorical Cross-Sectional Data
Question: Should Marijuana Be Legalized? 104 Hanover Students were surveyed in winter 2014.
Should Marijuana Be Legalized?
Responses No 13
Yes, but only medicinal 34
Yes, medicinal and recreational 57

15. Example of Quantitative Time-Series Data
Monthly Unemployment Rate from January August Source: Bureau of Labor Statistics