What Are We Summarizing? Lecture 13 Sections 4.1 – 4.2 Mon, Feb 4, 2008

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).

What Are We Summarizing? How best to summarize… Political affiliation? Body weight? Steak preference (rare, medium, etc.)? Number of children? Temperature throughout the day? 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 Democrats. 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. Temperature.

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. The average temperature for the day was 82.7 degrees F.

Caution Some qualitative variables may appear to be quantitative. Rate your own level of sexual desire: (1) Way below average (2) Below average (3) Average (4) Above average (5) Way above average

Caution If a person selects #3, does that mean that his sexual desire is average?

Caution If two people select #3, does that mean that they have the same level of sexual desire?

Caution If one person selects #2 and another person selects #4, does that mean that the second person has twice the sexual desire as the first person?

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 are count data A verbal description usually contains the phrase “the number of.”

Discrete vs. Continuous Some data may mistakenly be thought to be discrete. Time Weight Clearly, all measurements must be rounded off. But that does not make the quantity itself discrete.

Discrete vs. Continuous What about heart rate, measured in beats per minute? It is the basic nature of the quantity that matters, not how we choose to record our observations.