1. CHAPTER 2: Visual Description of Data – Part 2
to accompany
Introduction to Business Statistics
fourth edition, by Ronald M. Weiers
Presentation by Priscilla Chaffe-Stengel
Donald N. Stengel
© 2002 The Wadsworth Group

2. Example: Problem 2.53
The average daily cost to community hospitals for patient stays during 1993 for each of the 50 U.S. states was given in the next table.
a) Arrange these into a data array.
b) Construct a stem-and-leaf display.
*) Approximately how many classes would be appropriate for these data? [*not in textbook]
c & d) Construct a frequency distribution. State interval width and class mark.
e) Construct a histogram, a relative frequency distribution, and a cumulative relative frequency distribution.
© 2002 The Wadsworth Group

3. Problem 2.53 - The Data AL $775 HI 823 MA 1,036 NM 1,046 SD 506
AK 1,136 ID MI NY TN
AZ 1,091 IL MN NC TX 1,010
AR IN MS ND UT 1,081
CA 1,221 IA MO OH VT
CO KS MT OK VA
CT 1,058 KY NE OR 1,052 WA 1,143
DE 1,024 LA NV PA WV
FL ME NH RI WI
GA MD NJ SC WY
© 2002 The Wadsworth Group

4. Problem 2.53 - (a) Data Array
CA 1,221 TX 1,010 RI NY KS
WA 1,143 NH LA AL ID
AK 1,136 CO MO GA MN 652
AZ 1,091 FL PA NC NE
UT 1,081 CH TN WI IA
CT 1,058 IL SC ME MS
OR 1,052 MI VA KY WY 537
NM 1,046 NV NJ WV ND
MA 1,036 IN HI AR SD
DE 1,024 MD OK VT MT
© 2002 The Wadsworth Group

5. Problem 2.53 - (b) The Stem-and-Leaf Display
Stem-and-Leaf Display N = 50
Leaf Unit: 100
, 36
, 81, 58, 52, 46, 36, 24, 10
, 61, 60, 40, 17, 02, 00
(11) , 89, 85, 75, 63, 61, 59, 38, 30, 29, 23
, 84, 75, 75, 63, 44, 38, 03, 01
, 76, 66, 59, 52, 26, 12
, 37, 07, 06
Range: $482 - $1,221
© 2002 The Wadsworth Group

6. Problem Continued
To approximate the number of classes we should use in creating the frequency distribution, use Sturges’ Rule, n = 50:
Sturges’ rule suggests we use approximately 7 classes.
© 2002 The Wadsworth Group

7. Constructing the Frequency Distribution
Step 1. Number of classes
Sturges’ Rule: approximately 7 classes.
The range is: $1,221 – $482 = $739
$739/7 ­ $106 and $739/8 ­ $92
Steps 2 & 3. The Class Interval
So, if we use 8 classes, we can make each class $100 wide.
© 2002 The Wadsworth Group

8. Constructing the Frequency Distribution
Step 4. The Lower Class Limit
If we start at $450, we can cover the range in 8 classes, each class $100 in width.
The first class : $450 up to $550
Steps 5 & 6. Setting Class Limits
$450 up to $550 $850 up to $950
$550 up to $650 $950 up to $1,050
$650 up to $ $1,050 up to $1,150
$750 up to $ $1,150 up to $1,250
© 2002 The Wadsworth Group

9. Problem 2.53 - (c) & (d) Average daily cost Number Mark
$450 – under $ $500
$550 – under $ $600
$650 – under $ $700
$750 – under $ $800
$850 – under $ $900
$950 – under $1, $1,000
$1,050 – under $1, $1,100
$1,150 – under $1, $1,200
Interval width: $100
© 2002 The Wadsworth Group

10. Problem 2.53 - (e) The Histogram
© 2002 The Wadsworth Group

11. Problem 2.53 - The Relative Frequency Distribution
Average daily cost Number Rel. Freq.
$450 – under $ /50 = .08
$550 – under $ /50 = .06
$650 – under $ /50 = .18
$750 – under $ /50 = .18
$850 – under $ /50 = .22
$950 – under $1, /50 = .14
$1,050 – under $1, /50 = .12
$1,150 – under $1, /50 = .02
© 2002 The Wadsworth Group

12. Problem 2.53 - (e) The Percentage Polygon
© 2002 The Wadsworth Group

13. Problem 2.53 - The Cumulative Frequency Distribution
Average daily cost Number Cum. Freq.
$450 – under $
$550 – under $
$650 – under $
$750 – under $
$850 – under $
$950 – under $1,
$1,050 – under $1,
$1,150 – under $1,
© 2002 The Wadsworth Group

14. Problem 2.53 - The Cumulative Relative Frequency Distribution
Average daily cost Cum.Freq Cum.Rel.Freq.
$450 – under $ /50 = .02
$550 – under $ /50 = .14
$650 – under $ /50 = .32
$750 – under $ /50 = .50
$850 – under $ /50 = .72
$950 – under $1, /50 = .86
$1,050 – under $1, /50 = .98
$1,150 – under $1, /50 = 1.00
© 2002 The Wadsworth Group

15. Problem 2.53 - (e) The Percentage Ogive (Less Than)
© 2002 The Wadsworth Group