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

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

Problem 2.53 - The Data AL $775 HI 823 MA 1,036 NM 1,046 SD 506 AK 1,136 ID 659 MI 902 NY 784 TN 859 AZ 1,091 IL 917 MN 652 NC 763 TX 1,010 AR 678 IN 898 MS 555 ND 507 UT 1,081 CA 1,221 IA 612 MO 863 OH 940 VT 676 CO 961 KS 666 MT 482 OK 797 VA 830 CT 1,058 KY 703 NE 626 OR 1,052 WA 1,143 DE 1,024 LA 875 NV 900 PA 861 WV 701 FL 960 ME 738 NH 976 RI 885 WI 744 GA 775 MD 889 NJ 829 SC 838 WY 537 © 2002 The Wadsworth Group

Problem 2.53 - (a) Data Array CA 1,221 TX 1,010 RI 885 NY 784 KS 666 WA 1,143 NH 976 LA 875 AL 775 ID 659 AK 1,136 CO 961 MO 863 GA 775 MN 652 AZ 1,091 FL 960 PA 861 NC 763 NE 626 UT 1,081 CH 940 TN 859 WI 744 IA 612 CT 1,058 IL 917 SC 838 ME 738 MS 555 OR 1,052 MI 902 VA 830 KY 703 WY 537 NM 1,046 NV 900 NJ 829 WV 701 ND 507 MA 1,036 IN 898 HI 823 AR 678 SD 506 DE 1,024 MD 889 OK 797 VT 676 MT 482 © 2002 The Wadsworth Group

Problem 2.53 - (b) The Stem-and-Leaf Display Stem-and-Leaf Display N = 50 Leaf Unit: 100 1 12 21 2 11 43, 36 8 10 91, 81, 58, 52, 46, 36, 24, 10 7 9 76, 61, 60, 40, 17, 02, 00 (11) 8 98, 89, 85, 75, 63, 61, 59, 38, 30, 29, 23 9 7 97, 84, 75, 75, 63, 44, 38, 03, 01 7 6 78, 76, 66, 59, 52, 26, 12 4 5 55, 37, 07, 06 1 4 82 Range: $482 - $1,221 © 2002 The Wadsworth Group

Problem 2.53 - 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

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

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 $750 $1,050 up to $1,150 $750 up to $850 $1,150 up to $1,250 © 2002 The Wadsworth Group

Problem 2.53 - (c) & (d) Average daily cost Number Mark $450 – under $550 4 $500 $550 – under $650 3 $600 $650 – under $750 9 $700 $750 – under $850 9 $800 $850 – under $950 11 $900 $950 – under $1,050 7 $1,000 $1,050 – under $1,150 6 $1,100 $1,150 – under $1,250 1 $1,200 Interval width: $100 © 2002 The Wadsworth Group

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

Problem 2.53 - The Relative Frequency Distribution Average daily cost Number Rel. Freq. $450 – under $550 4 4/50 = .08 $550 – under $650 3 3/50 = .06 $650 – under $750 9 9/50 = .18 $750 – under $850 9 9/50 = .18 $850 – under $950 11 11/50 = .22 $950 – under $1,050 7 7/50 = .14 $1,050 – under $1,150 6 6/50 = .12 $1,150 – under $1,250 1 1/50 = .02 © 2002 The Wadsworth Group

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

Problem 2.53 - The Cumulative Frequency Distribution Average daily cost Number Cum. Freq. $450 – under $550 4 4 $550 – under $650 3 7 $650 – under $750 9 16 $750 – under $850 9 25 $850 – under $950 11 36 $950 – under $1,050 7 43 $1,050 – under $1,150 6 49 $1,150 – under $1,250 1 50 © 2002 The Wadsworth Group

Problem 2.53 - The Cumulative Relative Frequency Distribution Average daily cost Cum.Freq. Cum.Rel.Freq. $450 – under $550 4 4/50 = .02 $550 – under $650 7 7/50 = .14 $650 – under $750 16 16/50 = .32 $750 – under $850 25 25/50 = .50 $850 – under $950 36 36/50 = .72 $950 – under $1,050 43 43/50 = .86 $1,050 – under $1,150 49 49/50 = .98 $1,150 – under $1,250 50 50/50 = 1.00 © 2002 The Wadsworth Group

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