1. Chapter 2B
7/12/2019
Chapter 2 continued...
Fall 2000

2. II. Quantitative Data
Techniques for summarizing quantitative data are necessarily different. One difference lies in how classes of data are defined. With qualitative data, a class like “Kentucky” in our previous example is self-explanatory. An observation falls into this class or it does not. With quantitative data, the statistician is responsible for defining the class as a range of values.

3. A. Frequency Distribution
This is the same as with qualitative data but you take more care in selecting classes.
3 important steps:
Determine the number of non-overlapping classes.
Determine the width of each class.
Determine the class limits.
See the next page for an example of a frequency distribution with quantitative data.

4. Step 1: Determine the number of classes.
Suppose the above values represent a sample of 20 supermarkets and the price (in ¢) of beef sold in those markets. With a sample size as small as n=20, it’s recommended to construct no more than 5 classes.

5. Step 2: Determine the width of the classes.
It is very wise to make classes of uniform width.
Approximate class width = (maximum value - minimum value)/Number of classes
In our example, ( )/5 = You should always round up, using classes 7 cents wide.
Some might argue that a good idea would be to use either 5 or 10 cents as a width because people think in terms of 5-cent increments. This is a judgement call. I’ll use 7 cents.

6. Step 3: Determine the class limits.
These are just the smallest and largest values of each class.
Begin by looking at the smallest observation, 85.1 cents and build from there 5 classes, each of which is 7 cents wide.
First class of values: cents.
Note that this is 7 cents wide, not 6. Check for yourself!

7. Building the frequency distribution.

8. B. Relative and Percent Frequency Distributions.
The relative frequency is again found by dividing the number of observations in each class by the sample size (20).