Chapter 2 Graphs, Charts, and Tables - Describing Your Data ©

Chapter 2Chapter 2

Graphs, Charts, and Graphs, Charts, and Tables - Describing Tables - Describing

Your DataYour Data

©

Chapter 2 - Chapter 2 - Chapter Chapter OutcomesOutcomesAfter studying the material in this chapter, you should:

• Be able to construct frequency distributions both manually and with your computer.• Be able to construct and interpret a histogram.• Know how to construct and interpret various types of bar charts.• Understand the purpose of a Pareto chart and be able to construct one.

Chapter 2 - Chapter 2 - Chapter Chapter OutcomesOutcomes

(continued)(continued)

After studying the material in this chapter, you should:

• Be able to create a line chart and interpret the trend in the data.• Be able to construct a scatter plot and interpret it.• Be able to develop and interpret joint frequency tables.

Frequency DistributionsFrequency Distributions

A frequency distributionfrequency distribution is the summary of a set of data that displays the number of observations in each of the distribution’s distinct categories or classes.

Frequency Distribution of Years in Frequency Distribution of Years in CollegeCollege(Figure 2-1)(Figure 2-1)

City #1Years of College Frequency

0 351 212 243 224 315 136 67 58 3

Total 160

Frequency Distribution of Years in Frequency Distribution of Years in CollegeCollege(Figure 2-2)(Figure 2-2)

City #2Years of College Frequency

0 1871 622 343 194 145 76 37 4

Total 330

Discrete DataDiscrete Data

Discrete dataDiscrete data are data whose possible values are countable.

Relative FrequencyRelative Frequency

The relative frequencyrelative frequency is the proportion of total observations contained in a given category.

n

fRF i

Relative Frequency Distribution of Relative Frequency Distribution of Years in CollegeYears in College

(Figure 2-3)(Figure 2-3)

City #1Years of College

RelativeFrequency

0 35/160=0.2191 21/160=0.1312 24/160=0.1503 22/160=0.1384 31/160=0.1945 13/160=0.0816 6/160=0.0387 5/160=0.0318 3/160=0.019

Total 1.000

Relative Frequency Distribution of Relative Frequency Distribution of Years in CollegeYears in College

(Figure 2-3)(Figure 2-3)

City #2Years of College

RelativeFrequency

0 187/330=0.5671 62/330=0.1882 34/330=0.1033 19/330=0.0584 14/330=0.0425 7/330=0.0216 3/330=0.0097 4/330=0.012

Total 1.000

Grouping Data Into Grouping Data Into ClassesClasses

• Continuous data: Data whose possible values are uncountable and which may assume any value in an interval.

• Data array: Data that have been sorted in ascending or descending order.

• Mutually exclusive classes: Classes that do not overlap.

• All inclusive classes: A set of classes that contains all the possible data values.

• Equal width classes: Distance between lowest possible value and highest possible value in each class is the same for all classes.

Steps for Grouping Data Steps for Grouping Data Into ClassesInto Classes

• Step 1: Determine the number of groups or classes to use. (Generally 5-20 classes.)

• Step 2: Establish the class width.

Class WidthClass Width

Classes ofNumber ValueSmallest - ValueLargest

W

Steps for Grouping Data Steps for Grouping Data Into ClassesInto Classes

• Step 1: Determine the number of groups or classes to use.

• Step 2: Establish the class width.

• Step 3: Determine the class boundaries for each class.

Steps for Grouping Data Steps for Grouping Data Into ClassesInto Classes

• Step 1: Determine the number of groups or classes to use.

• Step 2: Establish the class width.

• Step 3: Determine the class boundaries for each class.

• Step 4: Count the number of values in each class.

Cumulative FrequenciesCumulative Frequencies

• Cumulative frequency distribution: A summary of a set of data that displays the number of observations with values less-than-or-equal-to the upper limit of each of its classes.

• Cumulative relative frequency distribution: A summary of a set of data that displays the proportion of observations with values less-than-or-equal-to the upper limit of each of its class.

Frequency HistogramsFrequency Histograms(Figure 1-2)(Figure 1-2)

BAKER CITY HOSPITAL - LENGTH OF STAY DISTRIBUTION

0

10

20

30

40

50

60

70

0<2 2<4 4<6 6<8 8<10 10<12 12<14 14<16 16<18

Frequency HistogramsFrequency HistogramsA histogram shows three general

types of information:• It provides visual indication of

where the approximate center if the data is.

• We can gain an understanding of the degree of spread, or variation, in the data.

• We can observe the shape of the distribution.

Histograms Showing Histograms Showing Different CentersDifferent Centers

0

10

20

30

40

50

60

70

0<2 2<4 4<6 6<8 8<10 10<12 12<14 14<16 16<18

0

10

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70

0<2 2<4 4<6 6<8 8<10 10<12 12<14 14<16 16<18

Histograms - Same Center, Histograms - Same Center, Different SpreadDifferent Spread

0

10

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60

70

0<2

2<4

4<6

6<8

8<10

10<12

12<14

14<16

16<18

0

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50

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70

0<2 2<4 4<6 6<8 8<10 10<12 12<14 14<16 16<18

Joint Frequency Joint Frequency DistributionsDistributions

A joint frequency distributionjoint frequency distribution is a summary of a bivariate set of data that displays the number of observations that exhibit the respective joint characteristics of one value taken from each of the variables that define the data set.

Bar ChartsBar Charts

A bar chartbar chart is a graphical representation of a categorical data set in which a rectangle or bar is drawn over each category or class. The length of each bar represents the frequency or percentage of observations in each category.

Bar ChartsBar Charts(Table 2-6)(Table 2-6)

Brazil $4.55Mexico $3.97Indonesia $1.74Panama $1.30Chile $1.22Malaysia $1.21Venezuela $0.87Argentina $0.85China $0.81Nigeria $0.78

Bar ChartsBar Charts(Figure 2-14)(Figure 2-14)

$0.00

$1.00

$2.00

$3.00

$4.00

$5.00

Emerging Market Countries

U.S.

Inco

me

(Bill

ions

of

Dolla

rs)

Brazil and Mexico provided the most income

Pareto ChartsPareto Charts

A pareto chartpareto chart is a bar chart that is sorted so that the categories or classes are arranged from the highest to lowest with respect to the magnitude of the displayed variable associated with each category or class.

Pie ChartsPie Charts

A pie chartpie chart is a graph in the shape of a circle: •The circle is divided into “slices” corresponding to the categories or classes to be displayed. •The size of each slice is proportional to the magnitude of the displayed variable associated with each category or class.

Pie ChartsPie Charts

Budget Cartegory Dollars Percent of TotalHealth and Welfare $811.70 25.37%Education $1,477.30 46.17Corrections $209.50 6.55Highways $389.40 12.16Other $312.10 9.75Total $3,200.00 100.00%

Pie ChartsPie Charts(Figure 2-21)(Figure 2-21)

Budget Allocation

Health and Welfare25%

Education46%

Corrections7%

Highways12%

Other10%

Line ChartsLine Charts

A line chartline chart is a two-dimensional chart showing time on the horizontal axis and the variable of interest on the vertical axis.

Line ChartsLine Charts(Figure 2-23)(Figure 2-23)

0

20,000

40,000

60,000

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Week

Sa

les

Increasing SalesSales Trend

Line ChartsLine Charts(Figure 2-25)(Figure 2-25)

010,00020,000

30,00040,00050,000

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

010002000

300040005000

Sales Profits

Profit and sales going in opposite directions

Scatter DiagramsScatter Diagrams

A scatter diagramscatter diagram is a two-dimensional graph of plotted points in which the vertical axis represents values of one variable and the horizontal axis represents values of the other.

Scatter DiagramsScatter Diagrams

0

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20

0 5 10 15 200

2

4

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0 5 10 15 20

X

Y

X

Y

Positive Linear Negative Linear

Scatter DiagramsScatter DiagramsDependent and Independent Dependent and Independent

VariablesVariables

• A dependent variabledependent variable is one whose values are thought to be a function of the values of another variable. (y-axis)

• An independent variableindependent variable is one whose values are thought to impact the values of the dependent variable. (x-axis)

Key TermsKey Terms• All-Inclusive Classes• Bar Chart• Class Boundaries• Class Width• Continuous Data• Cumulative

Frequency• Cumulative Relative

Frequency• Data Array

• Dependent Variable• Discrete Data• Equal-Width Classes• Frequency

Distribution• Frequency Histogram• Independent Variable• Joint Frequency

Distribution• Line Chart

Key TermsKey Terms(continued)(continued)

• Mutually-Exclusive Classes

• Pareto Chart

• Pie Chart

• Relative Frequency

• Scatter Diagram