AP Statistics

Today's Topic: CUSSing

Warm-Up

Consumer Reports did a study of ice cream bars (unfortunately, only vanilla flavored) in their August 1998 issue. Twenty-six bars having a taste-test rating of at least “fair” were listed, and calories per bar was included. Calories vary quite a bit partly because bars are not of uniform size.

Here is the data set:

342, 377, 319, 353, 295, 234, 294, 286, 377, 182, 310, 126, 541

439, 111, 201, 182, 197, 209, 147, 190, 151, 131, 151, 173, 247


Answer this question in your groups: Just how many calories should an ice cream bar contain?

In order to answer this question, create a histogram, a stem-and-leaf plot (maybe split stems?), and a boxplot to justify your answer.

OBJECTIVES

  • Use correct statistical vocabulary to describe the four main components of a quantitative data distribution
  • Use comparative language to compare two back-to-back or side-by-side graphs
  • Evaluate which measure of center is most appropriate for different distribution shapes

Describing Distributions Game

Statistical Vocabulary for Describing Distributions

CUSS it!

CENTER

Where is the center of the distribution located? What is the median? What is the mean? If you have a boxplot or stem-and-leaf you can give the exact median. In a histogram, you'll need to use the frequency of each class to determine in which interval the median is located.

UNUSUAL

Are there any outliers or gaps? Sometimes this is the most interesting part of the distribution or the only one we are concerned with.

SHAPE

What general shape does it have? Describe both the number of modes and the symmetry.

Unimodal, Bimodal, Multi-modal

Symmetric, Skewed to the right, Skewed to the left, Uniform

SPREAD

Measured with the standard deviation. Until we learn about standard deviation, it's a little ambiguous. Think about the context of the data and the story they tell.

Example 1

Here are the number of home runs that Babe Ruth hit in his 15 years with the New York Yankees 1920 to 1934.

54, 59, 35, 41, 46, 25, 47, 60, 54, 46, 49, 46, 41, 34, 22


Roger Maris broke Babe Ruth's record one year when he hit 61 home runs in 1961. Here are Maris's home run totals for his 10 years in the American League.

13, 23, 26, 16, 33, 61, 28, 39, 14, 8


Compare the two distributions by constructing back-to-back stem-and-leaf plots.

Example 2

The scores of 18 first year college women on the Survey of Study Habits and Attitudes (this psychological test measures motivation, study habits and attitudes toward school) are given below:

154, 109, 137, 115, 152, 140, 154, 178, 101

103, 126, 126, 137, 165, 165, 129, 200, 148

The college also administered the test to 20 first-year college men. There scores are also given:

108, 140, 114, 91, 180, 115, 126, 92, 169, 146

109, 132, 75, 88, 113, 151, 70, 115, 187, 104

Compare the two distributions by constructing boxplots. Are there any outliers in either group? Are there any noticeable differences or similarities between the two groups?