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Lecture Slides

Elementary StatisticsEleventh Edition

and the Triola Statistics Series

by Mario F. Triola

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Chapter 2Summarizing and Graphing

Data

2-1 Review and Preview

2-2 Frequency Distributions

2-3 Histograms

2-4 Statistical Graphics2-5 Critical Thinking: Bad Graphs

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Section 2-4

Statistical Graphics

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Key Concept

This section discusses other types of

statistical graphs.

Our objective is to identify a suitablegraph for representing the data set. The

graph should be effective in revealing the

important characteristics of the data.

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Frequency Polygon

Uses line segments connected to points directly

above class midpoint values

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Relative Frequency Polygon

Uses relative frequencies (proportions or

percentages) for the vertical scale.

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Ogive

A line graph that depicts cumulativefrequencies

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Dot Plot

Consists of a graph in which each data value isplotted as a point (or dot) along a scale of values.

Dots representing equal values are stacked.

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Stemplot (or Stem-and-Leaf Plot)

Represents quantitative data by separating each

value into two parts: the stem (such as the leftmost

digit) and the leaf (such as the rightmost digit)

Pulse Rates of Females

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Bar Graph

Uses bars of equal width to show

frequencies of categories of qualitative data.

Vertical scale represents frequencies or

relative frequencies. Horizontal scaleidentifies the different categories of

qualitative data.

A mult ip le bar graphhas two or more sets ofbars, and is used to compare two or more

data sets.

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Multiple Bar Graph

Median Income of Males and Females

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Pie Chart

A graph depicting qualitative data as slices of a

circle, size of slice is proportional to frequency count

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Scatter Plot (or Scatter Diagram)

A plot of paired (x ,y) data with a horizontal x-axis

and a vertical y-axis. Used to determine whetherthere is a relationship between the two variables

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Time-Series Graph

Data that have been collected at different points in

time: t ime-series data

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Important PrinciplesSuggested by Edward Tufte

For small data sets of 20 values or fewer, usea table instead of a graph.

A graph of data should make the viewer

focus on the true nature of the data, not onother elements, such as eye-catching butdistracting design features.

Do not distort data, construct a graph to

reveal the true nature of the data.

Almost all of the ink in a graph should beused for the data, not the other design

elements.

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Important PrinciplesSuggested by Edward Tufte

Dont use screening consisting of featuressuch as slanted lines, dots, cross-hatching,because they create the uncomfortableillusion of movement.

Dont use area or volumes for data that areactually one-dimensional in nature. (Dontuse drawings of dollar bills to represent

budget amounts for different years.)Never publish pie charts, because they wasteink on nondata components, and they lackappropriate scale.

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Car Reliability Data

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Recap

In this section we saw that graphs are

excellent tools for describing, exploring andcomparing data.

Desc r ib ing data: Histogram - consider

distribution, center, variation, and outliers.

Explor ing data: features that reveal some

useful and/or interesting characteristic of the

data set.Compar ing data: Construct similar graphs to

compare data sets.