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What Are We Summarizing?

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Presentation on theme: "What Are We Summarizing?"— Presentation transcript:

1 What Are We Summarizing?
Lecture 13 Sections 4.1 – 4.2 Wed, Feb 7, 2007

2 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).

3 What Are We Summarizing?
How best to summarize… Political affiliation? Body weight? Steak preference (rare, medium, etc.)? Number of children? What is the difference?

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

5 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.

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

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

8 Caution Some qualitative variables may appear to be quantitative.
Rate Katharine McPhee on a scale of 1 to 10. Is this qualitative or quantitative?

9 Quantitative Variables
A quantitative variable may be continuous or discrete.

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

11 Discrete Variables Discrete variable. Typically these are count data
A verbal description usually contains the phrase “the number of.”

12 Discrete vs. Continuous
Some data may be considered to be either discrete or continuous. But what is it really?

13 Discrete vs. Continuous
Example: Time vs. Minutes. How much time do I have for the test? How many minutes do I have for the test? We measure time, but we count minutes.

14 Discrete vs. Continuous
Example: Money vs. Dollars. How much money is in your wallet? How many dollars are in your wallet?

15 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 weights are 0, 1, 2, 3, … lbs. Is that discrete or continuous?


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