Statistical techniques in business ecohomics chap004

Describing Data: Displaying and Exploring Data Goals... Dot plots: Report the details of each observation  Are useful for comparing two or more data sets Dot Plot Dot Plot... women pa

Describing Data: Displaying and

Set up and interpret a contingency table

Describing Data: Displaying and

Exploring Data

Goals

Dot plots:

 Report the details of each observation

 Are useful for comparing two or more data sets

Dot Plot

Dot Plot

women participating in the workforce in a recent

year for the fifty states of the United States

Compare the dispersions of labor force

participation by gender.

Example 1

women participating in the workforce in a recent

year for the fifty states of the United States

Compare the dispersions of labor force

participation by gender.

Example 1

(continued)

Percentage of men participating

In the labor force for the

Stem-and-leaf Displays

Note: an advantage

of the stem-and-leaf display over a

frequency distribution is we

do not lose the identity of each observation.

divided into two

parts: the leading

digits become the

stem and the

trailing digits the

leaf.

50 60 70 80 90 100

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

Stock prices on twelve

consecutive days for a major

publicly traded company

86, 79, 92, 84, 69, 88, 91

83, 96, 78, 82, 85.

Example 2

L ocate th e m ed ian , (50th p ercen tile)

Quartiles (continued)

L ocate th e m ed ian , (50th p ercen tile)

th e first q u artile (25th p ercen tile)

Quartiles (continued)

L ocate th e m ed ian , (50th p ercen tile)

first q u artile (25th p ercen tile)

an d th e 3rd q u artile (75th p ercen tile)

Quartiles (continued)

P 100

w here

P is the desired percentile

L p = (n+1)

Quartiles (continued)

Using the twelve stock prices, we can find the

median, 25 th , and 75 th percentiles as follows:

50th percentile: MedianPrice at 6.50 observation = 85 + 5(85-84) = 84.50

75th percentilePrice at 9.75 observation = 88 + 75(91-88) = 90.25

Interquartile Range

The Interquartile

range is the distance

between the third

quartile Q3 and the

first quartile Q1

This distance will include the middle 50

percent of the observations

Example 3

For a set of

observations the third

quartile is 24 and the

24

Box Plots

Five pieces of data are needed to

construct a box

plot: the Minimum

Value, the First Quartile, the Median, the Third Quartile, and the Maximum Value.

A box plot is a graphical display, based on quartiles, that helps to picture a set of

data

15 minutes, the median 18 minutes, and the third quartile

22 minutes Develop a box plot

for the delivery times.

Example 4 continued

Example 4 continued

Coefficient of Variation

%) 100

percentage:

M ean

Relative dispersion

Some software packages use a different formula which results

in a wider range for the coefficient.

s

Median X

sk  3 

Using the twelve stock prices, we find the mean to be

84.42, standard deviation, 7.18, median, 84.5

Coefficient of variation

= 8.5%

%) 100

The twelve days of stock prices and the overall market

index on each day are given as follows:

Variables must be at least interval scaled

Relationship can be positive (direct) or negative (inverse)

Scatter diagram

96 92 91 88 86 85 84 83 82 79 78 69

Relationship between Market Index

and Stock Price

50 60 70 80 90 100

Weight Loss

45 adults, all 60 pounds overweight, are randomly assigned to three weight loss programs Twenty weeks

into the program, a researcher gathers data on weight loss and divides the loss into three categories:

less than 20 pounds, 20 up

to 40 pounds, 40 or more pounds Here are the

results

Example 5

Weight

Loss

Plan

Less than 20 pounds

20 up to

40 pounds

40 pounds