{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Lecture4-1

This preview shows pages 1–14. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Data Consists of values of some variables measured or observed for some individuals . E.g., the data set from the class survey (14 variables for the students in our class). Variable is a characteristic of an individual. Qualitative or Categorical : places an individual into one of several groups or categories (finitely many possible) Quantitative : measurements represent quantities, e.g. “how many” (infinitely many possible) 2
Scales of Measurement Ratio variable Quantitative scale (almost all) Ratios meaningful, inherently defined zero ( e.g., salary, weight, distance ) Interval variable Quantitative scale (very few) Ratios not meaningful, no inherently defined zero ( e.g., temperature ) Ordinal variable Qualitative (Categorical) scale Meaningful ordering or ranking of categories ( e.g., class ) Nominative variable Qualitative (Categorical) scale No meaningful ordering or ranking of categories ( e.g., gender, color ) 3

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Distribution of a Variable Describes what possible values the variable takes and how frequently it takes those values. We describe the overall pattern of a distribution by its shape, center, and spread. There are many ways to describe and display distributions. Graphs Word descriptions Numerical measures 4
Qualitative (Categorical) Variables The values of a categorical variable are the labels for the categories. The distribution of a categorical variable is described by either the count or the percent of individuals who fall in each category. E.g., data on young American adults from the 1999 Current Population Survey 5 Education Count (millions) Percent Less than high school 4.7 12.3 High school graduate 11.8 30.7 Some college 10.9 28.3 Bachelor’s degree 8.5 22.1 Advanced degree 2.5 6.6

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Graphs for Categorical Variables Bar chart: the height of each bar is proportional to the count (or percent) in each category. 6
Graphs for Categorical Variables The proportion (as percent) of all cars sold in the United States by different manufacturers, 1970 versus 1997 7

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Graphs for Categorical Variables Pie chart: the area of each piece is proportional to the percent of individuals in each category 8
Graphs for Categorical Variables The proportion (as percent) of all cars sold in the United States by different manufacturers, 1970 versus 1997 9

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Histogram for Quantitative Variables 10 Histogram To make a histogram: Divide the range of the data set into equal intervals For each interval draw a bar with the base covering the interval and the height proportional to the count of observations that fall into the interval.
Words that describe distributions Unimodal: has one major peak Bimodal: has two major peaks Symmetric: there is a symmetry with respect to the middle point Skewed to the right: when the right tail (larger values) is much longer than the left tail (smaller values) Skewed to the left: when the left tail (smaller values) is much longer than the right tail (larger values) 11

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Symmetric, Unimodal, Bimodal 12 Symmetric, unimodal Bimodal
S k ewness 13 Skewed to the left Skewed to the right

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}