Copyright © 2009 Pearson Education, Inc.

Welcome MM207 SeminarUnit 3

Mr. Anthony Feduccia

enjoy….

Copyright © 2009 Pearson Education, Inc.

3.1 Frequency Tables

LEARNING GOALBe able to create and interpret: frequency tables,

basic bar graphs, dotplots, pie charts, histograms,

stem-and-leaf plots, line charts, and time-series diagrams.

Slide 3.1- 3Copyright © 2009 Pearson Education, Inc.

DefinitionA basic frequency table has two columns:

• One column lists all the categories of data.

• The other column lists the frequency of each category, which is the number of data values in the category.

Slide 3.1- 4Copyright © 2009 Pearson Education, Inc.

EXAMPLE 1 Taste TestThe Rocky Mountain Beverage Company wants feedback on its new product, Coral Cola, and sets up a taste test with 20 people. Each individual is asked to rate the taste of the cola on a 5-point scale:

(bad taste) 1 2 3 4 5 (excellent taste)

The 20 ratings are as follows:

1 3 3 2 3 3 4 3 2 4 2 3 5 3 4 5 3 4 3 1

Construct a frequency table for these data.

Slide 3.1- 5Copyright © 2009 Pearson Education, Inc.

Solution:The variable of interest is taste, and this variable can take on five values: the taste categories 1 through 5. (Note that the data are qualitative and at the ordinal level of measurement.) We construct a table with these five categories in the left column and their frequencies in the right column, as shown in Table 3.2.

EXAMPLE 1 Taste Test

Slide 3.1- 6Copyright © 2009 Pearson Education, Inc.

Slide 3.1- 7Copyright © 2009 Pearson Education, Inc.

Binning Data

Definition

When it is impossible or impractical to have a category for every value in a data set, we bin (or group) the data into categories (bins), each covering a range of possible data values.

Slide 3.1- 8Copyright © 2009 Pearson Education, Inc.

Slide 3.1- 9Copyright © 2009 Pearson Education, Inc.

Slide 1.1- 10Copyright © 2009 Pearson Education, Inc.

Slide 1.1- 11Copyright © 2009 Pearson Education, Inc.

Slide 1.1- 12Copyright © 2009 Pearson Education, Inc.

Slide 1.1- 13Copyright © 2009 Pearson Education, Inc.

Bar Graphs

A bar graph is one of the simplest ways to picture a distribution. Bar graphs are commonly used for qualitative data.

Each bar represents the frequency (or relative frequency) of one category: the higher the frequency, the longer the bar. The bars can be either vertical or horizontal.

Vertical Bar Graph

Histograms A graph in which the bars have a natural order and the

bar widths have specific meaning, is called a histogram.

The bars in a histogram touch each other because there are no gaps between the categories, the data are continuous

Pie ChartsPie charts are usually used to show relative frequency distributions. A circular pie represents the total relative frequency of 100%, and the sizes of the individual slices, or wedges, represent the relative frequencies of different categories. Pie charts are used almost exclusively for qualitative data.

Slide 1.1- 18Copyright © 2009 Pearson Education, Inc.

Pareto Chart A bar graph in which the bars are arranged in

frequency order is often called a Pareto chart.

Graphing Quantitative Data Sets

Stem-and-leaf plot Each number is separated into a stem and a leaf. Similar to a histogram. Still contains original data values.

Larson/Farber 4th ed.20

Data: 21, 25, 25, 26, 27, 28, 30, 36, 36, 45

26

2 1 5 5 6 7 8

3 0 6 6

4 5

Find the original data from the stem-and-leaf plot.

a. 11, 18, 23, 23, 27, 33, 34, 38, 39, 43, 44

b. 2, 9, 2, 2, 4, 8, 4, 4, 6, 11, 12, 7, 8, 12

c. 13, 13, 14, 21, 21, 23, 27, 31, 31, 43, 44

d. 11, 18, 21, 21, 23, 27, 31, 33, 33, 38, 39, 43, 44

Stem1234

Leaves1 81 1 3 71 3 3 8 93 4

The time series line chart shows the prices of a volatile stock from January 1999 to December 1999.

Time Series Chart

Slide 1.1- 23Copyright © 2009 Pearson Education, Inc.

DistortionsThe lengths of the bars represent the data, but our eyes tend to focus on the areas of the bars. For example, the right bar is supposed to show that a dollar in 2006 was worth 41% as much as a dollar in 1980. Its length is indeed 41% of that of the left bar, but its area is much smaller in comparison (about 17% of the area of the left bar).

Figure 3.38 The lengths of the dollars are proportional to their spending power, but our eyes are drawn to the areas, which decline more than the lengths.

Distortions

The Kappa Iota Sigma Fraternity polled its members on the weekend party theme. The vote was as follows: six for toga, four for hayride, eight for beer bash, and two for masquerade. Display the vote count in a Pareto chart.

a. b.

c. d.

0

1

2

3

4

5

6

7

8

9

Toga Hayride Beer Bash Masquerade

0

1

2

3

4

5

6

7

8

9

Toga Hayride Beer Bash Masquerade0

1

2

3

4

5

6

7

8

9

Beer Bash Toga Hayride Masquerade

0

1

2

3

4

5

6

7

8

9

Masquerade Hayride Toga Beer Bash

A nurse measured the blood pressure of each person who visited her clinic. Following is a relative frequency histogram for the systolic blood pressure readings for those people aged between 25 and 40.

a. 8 b. 6 c. 64 d. 640

Given that 800 people were aged between 25 and 40, approximately how many had a systolic blood pressure reading greater than 140 and less than or equal to 150? 100 110 120 130 140 150 160

0.000.050.100.150.200.250.300.35

Systolic Blood Pressure (mm Hg)

Slide 1.1- 28Copyright © 2009 Pearson Education, Inc.

Slide 1.1- 29Copyright © 2009 Pearson Education, Inc.