This chapter discusses methods for describing and exploring data, including dot plots, stem-and-leaf displays, quartiles, box plots, and other statistical techniques. It provides examples of how to construct and interpret these graphical representations of data distribution, and how they can be used to analyze sets of observations and identify patterns. Key concepts covered are quartiles, interquartile range, outliers, and using box plots to visualize the spread and central tendency of data.

1. 4-1
Chapter
Four
McGraw-Hill/Irwin © 2005 The McGraw-Hill Companies, Inc., All Rights Reserved.

2. Chapter Four
4-2
Describing Data: Displaying and Exploring Data
GOALS
When you have completed this chapter, you will be able to:
ONE
Develop and interpret a dot plot.
TWO
Develop and interpret a stem-and-leaf display.
THREE
Compute and interpret quartiles, deciles, and percentiles.
FOUR
Construct and interpret box plots.
Goals

3. Chapter Four
4-3
Describing Data: Displaying and Exploring Data
FIVE
Compute and understand the coefficient of variation and the
coefficient of skewness.
SIX
Draw and interpret a scatter diagram.
SEVEN
Set up and interpret a contingency table.
Goals

4. 4-4
Stem-and-leaf Displays
Stem-and-leaf Note: an advantage
display: A of the stem-and-leaf
statistical technique display over a
for displaying a set frequency
of data. Each distribution is we
numerical value is do not lose the
divided into two identity of each
parts: the leading observation.
digits become the
stem and the
trailing digits the
leaf.
Stem-and-leaf Displays

5. 4-5
Stock prices on twelve
consecutive days for a major
publicly traded company 100
90
80
70
60
86, 79, 92, 84, 69, 88, 91 50
1 2 3 4 5 6 7 8 9 10 11 12
83, 96, 78, 82, 85.
Example 2

6. 4-6
Stem and leaf display of stock prices
stem leaf
6 9
7 89
8 234568
9 126
Example 2 (Continued )

7. 4-7
Quartiles
Divide a set of
observations
into four
equal parts.
Quartiles

8. 4-8
Quartiles
Locate the median,
(50th percentile)
first quartile (25th percentile)
and the 3rd quartile
(75th percentile)
Quartiles (continued)

9. 4-9
Quartiles
P
Lp = (n+1)
100
where
P is the desired percentile
Quartiles (continued)

10. 4-10
Using the twelve stock prices, we can find the
median, 25th, and 75th percentiles as follows:
Quartile 3 L75 = (12 + 1) 75 = 9.75th observation
100
50
Median L50 = (12 + 1) = 6.50th observation
100
25 = 3.25th observation
Quartile 1 L25 = (12+1)
100
Example 2 (continued)

11. 4-11
th
12 96 75 percentile
Q4 11 92 Price at 9.75 observation = 88 + .75(91-88)
10 91 = 90.25
9 88
Q3 8 86
50th percentile: Median
7 85
Price at 6.50 observation = 85 + .5(85-84)
6 84
= 84.50
Q2 5 83
4 82
3 79 25th percentile
Q1 2 78 Price at 3.25 observation = 79 + .25(82-79)
1 69 = 79.75
Example 2 (continued)

12. 4-12
The Interquartile This distance will
range is the distance include the middle 50
between the third percent of the
quartile Q3 and the observations.
first quartile Q1.
Interquartile range = Q3 - Q1
Interquartile Range

13. 4-13
For a set of
observations the third
quartile is 24 and the
first quartile is 10.
What is the quartile
deviation?
The interquartile range is
24 - 10 = 14. Fifty
percent of the observations
will occur between 10 and
24.
Example 3

14. 4-14
A box plot is a graphical
display, based on
quartiles, that helps to
picture a set of data.
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.
Box Plots

15. 4-15
Based on a sample of 20
deliveries,
Buddy’s Pizza determined the
following information. The
minimum delivery time was 13
minutes and the maximum 30
minutes. The first quartile was
15 minutes, the median 18
minutes, and the third quartile
22 minutes. Develop a box plot
for the delivery times.
Example 4

16. 4-16
Example 4 continued

17. 4-17
Min Q Median Q3 Max
1
12 14 16 18 20 22 24 26 28 30 32
Example 4 continued