What Are We Summarizing? Lecture 11 Sections 4.1 – 4.2 Wed, Sep 20, 2006

What Are We Summarizing? How can we summarize data taken from a sample? We want to reduce the data down to a single number (a statistic). How best to summarize… Political affiliation? Body weight? Steak preference (medium, etc.)? Number of children? What is the difference?

Qualitative Variables The values of a qualitative variable may or may not have a natural order. Examples: Political affiliation. Steak preference.

Summarizing Qualitative Variables Typically, we use percentages or proportions to summarize qualitative variables. 40% of the subjects are female. 50% of the people prefer their steak medium.

Quantitative Variables The values of a quantitative variable always have a natural order. Examples: A person’s weight. Number of children.

Summarizing Quantitative Variables Typically, we use averages to summarize quantitative variables. The people in the sample weigh an average of 156.2 lbs. The people in the sample have an average of 2.3 children.

Quantitative Variables A quantitative variable may be continuous or discrete.

Continuous Variables Continuous variable. Typically these are measured quantities: length, time, area, weight, etc.

Discrete Variables Discrete variable. Typically these is “count” data; a verbal description usually contains the phrase “the number of.”

Discrete vs. Continuous Some data may be considered to be either discrete or continuous. Example: Time vs. Minutes. How much time do I have for the test? How many minutes do I have for the test? Example: Money vs. Dollars. How much money is in your wallet? How many dollars are in your wallet? In such cases, consider it to be continuous.

Discrete vs. Continuous The distinction is based on the nature of the variable, not the manner in which it is measured or recorded. Example: Measure a person’s weight, to the nearest pound. The possible times are 0, 1, 2, 3, … lbs. Is that discrete or continuous?

Qualitative or Quantitative? Caution: Sometimes numbers are used merely as labels on the categories. That alone will not make the data quantitative.

Qualitative or Quantitative? On an opinion survey: 1 = strongly disagree 2 = disagree 3 = neutral 4 = agree 5 = strongly agree Is it legitimate to average the responses?