Graphs for Data

Mrs. WatkinsAP Statistics Chapter 3/4

Frequency Table

Variable Tally Frequency 9th III ? 10th IIIIIII ? 11th IIIIIIIII ? 12th IIIII ?Purpose: To organize raw data

Relative Frequency Table

Variable Tally Freq. Relative. Freq

9th III 3 ? 10th IIIIIII 6 ? 11th IIIIIIIII 9 ? 12th IIIII 5 ?Purpose: to show proportions/percents

Cumulative Relative Frequency

Variable Freq. Rel. Freq Cum. Rel.Freq

9th 3 ? ? 10th 6 ? ? 11th 9 ? ? 12th 5 ? ?

Should add up to 100% or 1.00 (or close)

Bar Chart

Purpose: To display counts or percentages for categorical data

**should have space between bars

Contingency Table (two way table)

Displays two categorical variablesMale Female

Yes

No

Vocabulary: cells (entries), variables, experimental units

Marginal Distribution—calculates relative frequency across one variable

Male FemaleYes

No

Marginal Distribution by Gender

Marginal Distribution by Instrument

Conditional Distributions

Breakdown of ONE variable within the CONDITIONED category:

Given MALE, what is distribution of instruments?_____Yes _______ No

Given NO instruments, what is distribution of gender?______Male ______ Female

Segmented Bar Chart

Category 1 Category 2 Category 3 Category 40%

20%

40%

60%

80%

100%

Series 3Series 2Series 1

Issues with Two-Way Tables and Categorical Data Analysis

1.Independence2.Simpson’s Paradox3.Relative Risk

IndependenceWhen the distribution of one variable is the

same across the categories of another variable

It means that one variable does not seem to affect the other

Segmented bar graphs will be identicalExample: text page 28 Eye Color

Simpson’s Paradox

When using an overall percentage instead of breaking the data down into relevant categories

**shows “unreal” preference

Examples: hospital death rates, pilot errors,school admission (page 33 in text)

Relative RiskUsually used for disease:

Incidence/Non-incidence Ratio

Example: Risk of Heart attack between smokers and non-smokers

RR for Female: 2.24:1RR for Male: 1.43:1

More Relative Risk

Injuries at Naval Academy (soccer, rugby and basketball)

RR Female:Male---3.96:1

Injuries during military training at Naval Academy

RR Female:Male—9.74:1

Graphs for Quantitative Data

DotplotStem/Leaf PlotHistogram

Dot Plot

Types: Quantitative; small data sets Best Used: Show distribution of discrete values;

shows gaps

Stem/Leaf Plot

Types: Quantitative; small data setsBest used: when data values should be

preserved

Back to Back Stem/Leaf Plot

Histogram

Types: Quantitative, large range of valuesBest Used: To display large amount of data

Histograms—two choices

FREQUENCYshowing actual counts for each variablevalue

RELATIVE FREQUENCYshowing proportion/percent for eachvariable value

Affects the vertical axis only

BEWARE of CUMULATIVE

Read histograms carefully…the vertical axis might be CUMULATIVE

GRAPH ANALYSIS--SOCS

AP questions will ask you to “comment on the distribution”.

S: SHAPE? Symmetric, skewed, bimodalO: OUTLIERS? Any unusual values, gapsC: CENTER ? Middle of the dataS: SPREAD? range of data -- is range big or

small?