Day 02: Statistics for Business Applications

• statistical self-defense - ask questions about methodology!
• population
• sample
• parameter
• statistic
• error and confidence
• inference

Unresolved issues from last time

As mentioned last time, we want to use complete sentences, and write in complete thoughts when we write up a solution (as demonstrated in the sample solution).

• Would you like to see how to use Minitab for Ex. 8?

• Like peanut butter? - Yes/No
• What's your height? - (some positive real number)
• How was your service? - Poor Okay Excellent
• What's your favorite soda? - cola, root beer, orange, other

We're going to knock it down to two types: those for which you can compute averages, and those for which you can't. The text distinguishes more types than we will.

• Quantitative - can compute averages - averages make sense
• Qualitative - can't or shouldn't compute averages

Question: How do we identify quantitative data?

Answer: Quantitative data are real numbers. They are not numbers arbitrarily assigned to represent qualitative data. An experiment that produces qualitative data always asks for verbal, nonnumerical responses (e.g., yes and no; defective and nondefective; Catholic, Protestant, Jewish, and Other).

Example, 2.5, p. 30.

• How do we look at quantitative data? Example: heights of NKU students.

• We will focus on the histogram for the visual representation of quantitative data, and specifically the following issues:
  • You should be able to use Minitab to construct a histogram

  • You should be able to interpret a histogram:
    • Features that describe the shape of a histogram:
      • symmetric
      • positively skewed
      • negatitively skewed
      • unimodal
      • bimodal (multi-modal)
    • What are typical (central) values?
    • What are the largest and smallest values (range)?
    • Are there unusual or atypical values?
• Let's use Minitab, and see how to create some of these plots with some real data. Again, you can download a fully-functional version of Minitab for 30-day trial from the Minitab Homepage. Example: Minitab data set from chapter 1 about Pepsi.
  • How to load data (again, datasets for the course are available on your CD, which should have come with the book, but they're also on-line.
  • How to make a histogram
  • Interpreting the Histogram
  • How to change class width
  • Sorting data
  An alternative histogram: Telephone bills, from Example 2.1

  Q: How do I choose the number of classes and the width of the classes to be used in constructing a frequency distribution for a histogram?

  A: Although this choice is arbitrary and no hard-and-fast rules can be given, here are a few useful guidelines:

  1. The classes must be nonoverlapping, so that each measurement falls into exactly one class. Therefore, choose the classes so that no measurement falls on a class boundary (or else create a convention for dealing with cases on class boundaries).
  2. Choose the number of classes to be used as a number between 5 and 20, with smaller numbers of classes being chosen for smaller data sets. Some people use the square root of the number of data, but this might not make any sense (in the Pepsi data, for example).
  3. The approximate width of each class is given by the following:

     Approximate class width = (Largest value - Smallest value)/(Number of classes)

  Choose the actual class width to be a value close to the approximate width that is convenient to work with. Avoid awkward fractional values.