Chapter 2: Charts and Graphs. LO1Explain the difference between grouped and un- grouped data and construct a frequency distribution from a set of data.

Chapter 2:Charts and

Graphs

LO1 Explain the difference between grouped and un- grouped data and construct a frequency distribution from a set of data and explain what the distribution represents.

LO2 Describe and construct different types of quantitative data graphs, including histograms, frequency polygons, ogives, and stem and leaf plots. Explain when these graphs should be used.

LO3 Describe and construct different types of qualitative data graphs, including pie charts, bar charts, and Pareto charts. Explain when these graphs should be used.

LO4 Display and analyze two variables simultaneously using cross tabulation and scatter plots.

Learning Objectives

• Ungrouped data– have not been summarized in any way– are also called raw data

• Grouped data– have been organized into a frequency distribution

Ungrouped Versus Grouped Data

Example of Ungrouped Data

Example of Grouped Data

Constructing a Frequency DistributionStart With Data Range

• The number of classes should be between 5 and 15.– Fewer than 5 classes cause excessive summarization.– More than 15 classes leave too much detail.

• Class Width– Divide the range by the number of classes for an approximate class

width– Round up to a convenient number– So if the number of classes is 6, then

Deciding on the Number of Classes and on the Class Width

• The midpoint of each class interval is called the class midpoint or the class mark.

Class Midpoint

The relative frequency is the proportion of the total frequency that is any given class interval in a frequency distribution.

Relative Frequency

• The cumulative frequency is a running total of frequencies through the classes of a frequency distribution.

Cumulative Frequency

Class Midpoints, Relative Frequencies, and Cumulative Frequencies

• The cumulative relative frequency is a running total of the relative frequencies through the classes of a frequency distribution.

Cumulative Relative Frequencies

• Histogram : vertical bar chart of frequencies• Frequency Polygon : line graph of frequencies• Ogive : line graph of cumulative frequencies• Pie Chart : proportional representation for

categories of a whole• Stem and Leaf Plot• Pareto Chart• Scatter Plot

Common Statistical Graphs

Histogram

Class Interval Frequency20-under 30 630-under 40 1840-under 50 1150-under 60 1160-under 70 370-under 80 1

80706050403020

20

15

10

5

0

Years

Frequency

10

20

1

3

1111

18

6

Histogram Construction

Class Interval Frequency20-under 30 630-under 40 1840-under 50 1150-under 60 1160-under 70 370-under 80 1

80706050403020

20

15

10

5

0

Years

Frequency

10

20

1

3

1111

18

6

Frequency Polygon

Class Interval Frequency20-under 30 630-under 40 1840-under 50 1150-under 60 1160-under 70 370-under 80 1

908070605040302010

20

15

10

5

0

Years

Frequency

Ogive

CumulativeClass IntervalFrequency20-under 30 630-under 40 2440-under 50 3550-under 60 4660-under 70 4970-under 80 50

80706050403020

50

40

30

20

10

0

Years

Frequency

Cumulative Relative Frequency (Ogive)

Cumulative

RelativeClass IntervalFrequency20-under 30 .1230-under 40 .4840-under 50 .7050-under 60 .9260-under 70 .9870-under 80 1.00

9080706050403020100

1.0

0.8

0.6

0.4

0.2

0.0

Years

Cum

ula

tive R

ela

tive F

requency

Complaints by Train Passengers

Complaints by Train Passengers

Stations, Etc.40%

Train Performance

21%

Equipment15%

Personnel14%

Schedules, Etc.10%

Second Quarter Truck Production (Hypothetical values)

Pie Chart Calculations for Company A

Second Quarter Truck Production

39%39%

17%4%

1%

A B C D E

Visible Minority Population of Canada Census 2006

Ethnicity Size of population Percentage Equivalent in Degrees

South Asian 1 262 865 24.92 89.71o

Chinese 1 216 595 24.00 86.40o

Black 783 795 15.47 55.69o

Filipino 419 700 8.10 29.16o

Latin American 304 245 6.00 21.60o

Arab 265 550 5.24 18.86o

South East Asia 239 935 4.73 17.03o

West Asians 156 695 3.09 11.12o

Korean 141 890 2.80 10.08o

Japanese 81 300 1.60 5.76o

Other 204 540 4.04 14.54o

Total 5 068 095 100.00 360o

Visible Minorities of Canada 2006

Safety Examination Scores for Plant Trainees

Construction of Stem and Leaf Plot

Pareto Chart

Cross tabulation is a process for producing a two-dimensional table that displays the frequency counts for two variables simultaneously.

Cross Tabulation

Scatter Plot

A scatter plot is a two-dimensional graph plot of pairs of points

from two numerical variables.

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