Use tables to organize data Case & Variable Categorical variable & Quantitative variable

Transcription

1 Use tables to organize data Case & Variable Categorical variable & Quantitative variable

2 Population: The total group of individuals (no need to be human) about whom you want to make conclusions. Sample: a representativesubset of the population for whom you actually have data. Sample Population 10 names at random from roster this class 30 Prozac patients all Prozac patients 25 rolls of a die all rolls of similar dice fruit flies trapped at a garbage dump all flies in that dump, or all flies in that region 100 fish trout in lake Michigan All fish trout in lake Michigan 2

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4 RANDOM Question: how do we collect samples? Be random! Be representative! Keep RANDOM in mind. It is the one of the key concepts in Statistics.

5 Case subject gender age high school GPA college GPA Case 1 Case 2 Case 3 Case 4 1 m f f f A caseis an individual about whom or which we have the data. Often, the cases are a sample of cases selected from some larger population that we d like to study.

6 Variable Variable 3 Variable 1 Variable 2 Variable 4 Variable 5 subject gender age high school GPA college GPA 1 m f f f The characteristics recorded about each individual are called variables.

7 Variable & case Variable 3 Variable 1 Variable 2 Variable 4 Variable 5 subject gender age high school GPA college GPA Case 1 Case 2 Case 3 Case 4 1 m f f f To summarize, in the data table, The rows correspond to cases; The columns correspond to variables.

8 Variable subject gender age high school GPA college GPA 1 m f f f Generally, we have two types of variables Categorical Variable; Quantitative Variable.

9 Categorical variable When a variable names categories and answers questions about how cases fall into those categories, we call it a categorical variable. For example, the gender variable is a typical categorical variable because it answers questions about how cases fall into gender. Categorical Variable subject gender age high school GPA college GPA 1 m f f f

10 Quantitative variable Units Units tell how each value has been measured. For example, US dollars, cm, gram and so on. Quantitative Variable When a measured variable with units answers questions about the quantity of what is measured, we call it a quantitative variable. Quantitative Variable subject gender age high school GPA college GPA 1 m f f f

11 Quantitative v.s. categorical If the values of a variable are words rather than numbers, it s a good bet that it is categorical. But if the values of a variable are numbers, is it for sure that the variable is a quantitative one? We can always make meaningful comparisons for the values of a quantitative variable. Categorical Variable subject gender age high school GPA college GPA 1 m f f f

12 An example: A start-up company is building a database of customers and sale information. For each customer, it records name, ID number, region of the country (1=East, 2=South, 3=Midwest, 4= West), date of last purchase, amount of purchase, and item purchased. A part of the database is displayed by using the following data table: (i) How many casesare there in this table? (ii) How many variablesare there in this table? Which are categorical variables? Which are quantitative variables? Customer s Region of the Date of Last Amount of Item ID number Name Country Purchase Purchase Purchased Bill, J May 24,2009 $ Home Appliance Anderson, P Jul 13,2009 $78.23 Food and Grocery Stapleton, J Jun 24,2009 $ Electronics Kaplan, J Apr 15,2009 $27.01 Pharmacy Wang, S Sept 01, 2009 $ Automotive Vince, L Jun 20, 2009 $42.49 Office Supplies Julian, S Mar 23, 2010 $ Electronics Kathy, G Dec 01,2009 $54.92 Office Supplies Beverly, F Feb 23,2010 $ Pharmacy Kevin, T Apr 10, 2010 $52.41 Food and Grocery

13 Categorizing a quantitative variable Amount of Purchase CategorizedAmount of Purchase $ $ $ $ $ $ $ $ $ $ < >400 6

14 which of the following variable is quantitative or categorical? smoking (yes or no) number of flowers in a plant name (Adam, Mike, Christina, Dave...) car speed blood pressure

15 2.7; : Sample: 2500 cars Population: All cars passing bicyclists Variable: Distance of car to bicycle 2.15: Population: All bears in the woods Sample: 54 bears caught Variables: Weight (quantitative) Neck size (quantitative) Length (quantitative) Sex (caegorical)