2 Variables and Their Distributions

# 2 Variables and Their Distributions - BUAD 310 Applied...

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Outline for Today Descriptive statistics Variables and their distributions Finding the center Measuring the spread Relationship between variables 2
Data Consists of values of some variables measured or observed for some individuals . E.g., the data set from the class survey (13 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), could be discrete or continuous 3

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Scales of Measurement Quantitative Ratio variable, almost all quantitative variables are ratio variables Ratios meaningful, inherently defined zero (e.g., salary, weight, distance) Interval variable, very few quantitative variables are interval variables Ratios not meaningful, no inherently defined zero (e.g., temperature) Categorical Ordinal variable Meaningful ordering or ranking of categories (e.g., class) Nominative variable No meaningful ordering or ranking of categories (e.g., gender, color) 4 R a t i o ( a l m o s t a l l ) I n t e r v a l ( v e r y f e w ) Q u a n t i t a t i v e O r d i n a l N o m i n a t i v e Q u a l i t a t i v e ( C a t e g o r i c a l ) D a t a
Data Analysis Initial examination of the data is called Exploratory Data Analysis (EDA). Strategy for EDA: Begin by examining each variable and then move on to the study of relationships At each stage start with graphs and then add numerical summaries 5

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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 6
Describing Categorical Data Describing Categorical Data 7 Motivating Example: Everyday, more than 100 million shoppers visit amazon.com, either by typing amazon.com or by clicking an ad. Which hosts send the most visitors to Amazon’s Web site? Data set consists of 188,996 visits Host is a categorical variable To answer this question we must describe the variation in Host

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Data Table Frequency and Relative Frequency Tables The distribution of a categorical variable is a list of values with its associated count (frequency) A frequency table summarizes the distribution of a categorical variable A relative frequency table shows the proportion (or percentage) in each category 8
9 Looking At Data

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10 Charts of Categorical Data Bar Charts and Pie Charts Unless you need to know exact counts, charts are better than tables for summarizing more than five categories The two most common displays of a categorical variable are a bar chart and a pie chart
11 Charts of Categorical Data The Bar Chart

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