Chapter 1: Exploring DataChapter 1: Exploring Data

1.1 1.1 Displaying Distributions Displaying Distributions

with Graphswith Graphs

(bar graphs, pie charts)(bar graphs, pie charts)

hw: pg 7: 1, 3, 4, 5, 8; pg 22: 11, 14, 15, 17hw: pg 7: 1, 3, 4, 5, 8; pg 22: 11, 14, 15, 17

Target Goal: Target Goal: I can graph categorical I can graph categorical data. data.

IntroductionIntroductionIndividuals, Variables, EDAIndividuals, Variables, EDA

StatisticsStatistics - science of data - science of data

• Any set of data contains information about Any set of data contains information about some group of some group of individualsindividuals

• The information is organized in The information is organized in variablesvariables..

IndividualsIndividuals - Objects described by a set of - Objects described by a set of data; may be data; may be people, animals, or things.people, animals, or things.

VariablesVariables - - Characteristics of an individualCharacteristics of an individual; ; can take different values for different can take different values for different individuals. individuals.

When exploring data, ask the When exploring data, ask the W’sW’s

WhoWho - What - What individualsindividuals do the data do the data describe; describe; how manyhow many individuals appear individuals appear in the data. in the data.

WhatWhat - How many - How many variablesvariables are there; are there; what are the exact definitions of these what are the exact definitions of these variables; in what variables; in what unitsunits is each variable is each variable recorded. recorded.

WhyWhy - What is the reason the data were - What is the reason the data were gathered. gathered.

Types of VariablesTypes of Variables

Categorical variableCategorical variable – – (counts)(counts) places places an individual into one of several groups an individual into one of several groups or categories.or categories.

Ex. Ex. College major, gender College major, gender Quantitative variableQuantitative variable – – (measurements)(measurements)

Takes numerical value for which Takes numerical value for which arithmetic operations such as adding arithmetic operations such as adding and averaging make sense.and averaging make sense.

Ex. Ex. Grade point average, test scoresGrade point average, test scores

Ex. 1 Census Bureau Web siteEx. 1 Census Bureau Web site(see data on page 7, for exercise 7 & (see data on page 7, for exercise 7 & 8)8)

Who?Who?

RowsRows describes one individual describes one individual subjects.subjects.

What?What?

ColumnsColumns contain value of contain value of one variable.one variable.

Why?Why?

EvaluateEvaluate both categorical and both categorical and quantitative data of people surveyed. quantitative data of people surveyed.

DistributionDistribution of a Variable of a Variable

The The pattern of variationpattern of variation tells us tells us what what values values the variables takes and the variables takes and how how often often it takes these values. it takes these values.

““Think – Show- Tell’Think – Show- Tell’How do we organize data?How do we organize data?

Exploratory data analysisExploratory data analysis (EDA): (EDA): using statistical tools and ideas to:using statistical tools and ideas to:

• Examine dataExamine data in order to describe in order to describe their main features.their main features.Begin with Begin with graph's.graph's.

• DescribeDescribe:: add numerical add numerical summaries.summaries.

Entering data on calculator:Entering data on calculator:Inspire: Use Appendix B:A6Inspire: Use Appendix B:A6

Use data from page 46, example 56Use data from page 46, example 56

• STAT:Clrlist L1:ENTERSTAT:Clrlist L1:ENTER

• STAT;Edit (enter data)STAT;Edit (enter data)

• Quit to main screenQuit to main screen

Store list:Store list:

• L1 DRVTML1 DRVTM(Don’t delete. We will use this (Don’t delete. We will use this later!)later!)

Displaying categorical Displaying categorical variables:variables:

(bar graphs and pie charts)(bar graphs and pie charts)

• The distribution of a categorical The distribution of a categorical variable lists the categories and variable lists the categories and gives either the gives either the countcount or the or the percentpercent of individuals who fall in of individuals who fall in each category.each category.

Ex. 2 The Most Popular SoftdrinkEx. 2 The Most Popular Softdrink

Bar graphBar graph:: • quickly comparesquickly compares

• the heights of bars show the counts.the heights of bars show the counts.

• remember: label axis, remember: label axis, title graphtitle graph, scale axis, , scale axis, leave space between bars.leave space between bars.

Graphs: Good and Bad

This ad for DIRECTV has multiple problems. How many can you point out?

Pie chartPie chart - - Helps to see what part of Helps to see what part of

the whole each group forms.the whole each group forms.

• Remember: must include all categories that make up Remember: must include all categories that make up whole =100%whole =100%.. Pie charts mostly done on computer! Pie charts mostly done on computer!

Pie chart:Pie chart: Advantages -Advantages - helps an audience grasp the helps an audience grasp the distribution quickly. distribution quickly.

Disadvantages -Disadvantages - takes time and space, takes time and space, cannot cannot see count of each category. see count of each category.

Ex. 2 Accidental Deaths Ex. 2 Accidental Deaths

In 1997 there were In 1997 there were 92,35392,353 deaths deaths from accidents in the United States. from accidents in the United States. Among these were 42,340 deaths Among these were 42,340 deaths from motor vehicle accidents, 11,858 from motor vehicle accidents, 11,858 from falls, 10,163 from poisoning, from falls, 10,163 from poisoning, 4,051 from drowning, and 3,601 from 4,051 from drowning, and 3,601 from fires. fires.

a. Find the percent of accidental deaths from each a. Find the percent of accidental deaths from each of these causes, rounded to the nearest percent. of these causes, rounded to the nearest percent. What percent of accidental deaths were due to What percent of accidental deaths were due to other causes? (1 min)other causes? (1 min)

92,353 total deaths92,353 total deaths

42,34042,340

11,85811,858

10,16310,163

4,0514,051

3,6013,601

CauseCause Percent Percent

motor vehicle 46motor vehicle 46

from falls from falls 1313

from poisoning from poisoning 1111

from drowningfrom drowning 44

from fires from fires 44

OtherOther 22 22

Ex. 2 Accidental Deaths cont.Ex. 2 Accidental Deaths cont.

b.b. Make a well-labeled bar graph Make a well-labeled bar graph

of the distribution of causes of of the distribution of causes of accidental deaths. Be sure to include accidental deaths. Be sure to include an “other causes” bar.an “other causes” bar.

Hint:Hint: x axis – causes, 6 types x axis – causes, 6 types

y axis – percent of accidental y axis – percent of accidental deaths deaths

(5 min)(5 min)

Accidental DeathsAccidental DeathsPerc

ent

of

acc

identa

l death

s

Cause of accidental deathsMot. veh Falls Drowning Fires Poison other

0

10

20

30

40

50

Ex. 2 Accidental Deaths cont.Ex. 2 Accidental Deaths cont.

c.c. Would it also be correct to use a pie Would it also be correct to use a pie chart to display these data? If not, chart to display these data? If not, explain why not. explain why not.

You could because the categories You could because the categories use part of a whole (all accidental use part of a whole (all accidental deaths).deaths).