When you have completed this chapter, you will be able to: Organize raw data into frequency distribution; produce a histogram, a frequency polygon, and a cumulative frequency polygon from quantitative data; develop and interpret a stem-and-leaf display; present qualitative data using such graphical techniques such as a clustered bar chart, a stacked bar chart, and a pie chart; detect graphic deceptions and use a graph to present data with clarity, precision, and efficiency.
2 1 f requency Distributions Describing Data Describing Data Graphic Presentations Copyright © 2004 by The McGrawHill Companies, Inc. All rights reserved Copyright © 2003 by The McGrawHill Companies, Inc. All rights reserved. 2 2 When you have completed this chapter, you will be able to: Organize raw data into frequency distribution Produce a histogram, a frequency polygon, and a cumulative frequency polygon from quantitative data Develop and interpret a stemandleaf display Copyright © 2004 by The McGrawHill Companies, Inc. All rights reserved. 2 3 Present qualitative data using such graphical techniques such as a clustered bar chart, a stacked bar chart, and a pie chart Detect graphic deceptions and use a graph to present data with clarity, precision, and efficiency Copyright © 2004 by The McGrawHill Companies, Inc. All rights reserved. 2 4 Copyright © 2004 by The McGrawHill Companies, Inc. All rights reserved. 2 5 A Frequency Distribution is a grouping of data into nonoverlapping classes (mutually exclusive)… showing the number of observations in each category or class The range of categories includes all values all values in the in the The range of categories includes data set (collectively exhaustive classes) data set (collectively exhaustive classes) Copyright © 2004 by The McGrawHill Companies, Inc. All rights reserved. 2 6 Class Midpoint or Class Mark: A point that divides a class into two equal parts, i.e. the average of the upper and lower class limits Class frequency: 12.5 17.5 22.5 27.5 32.5 The number of observations in each class. Class interval: The class interval is obtained by subtracting the lower limit of a class from the lower limit of the next class, e.g Copyright © 2004 by The McGrawHill Companies, Inc. All rights reserved. 2 7 Dr. Tillman is Dean of the School of Business. He wishes to prepare a report showing the number of hours per week students spend studying. He selects a random sample of 30 students and determines the number of hours each student studied last week. 15.0, 23.7, 19.7, 15.4, 18.3, 23.0, 14.2, 20.8, 13.5, 20.7, 17.4, 18.6, 12.9, 20.3, 13.7, 21.4, 18.3, 29.8, 17.1, 18.9, 10.3, 26.1, 15.7, 14.0, 17.8, 33.8, 23.2, 12.9, 27.1, 16.6. Organize the data into a frequency distribution Copyright © 2004 by The McGrawHill Companies, Inc. All rights reserved. There are five steps that can be used to 2 8 Construct a Frequency Distribution: Decide how many classes you wish to use Frequency Frequency Distributions Distributions by hand by hand Determine the class width Set up the individual class limits Tally the items into the classes Count the number of items in each class Copyright © 2004 by The McGrawHill Companies, Inc. All rights reserved. Decide how many classes you wish to use 2 9 Rule of Thumb: Rule of Thumb: For most data sets, you would want For most data sets, you would want between 3 and 12 classes! between 3 and 12 classes! Use the 2 to the K rule Choose k so that 2 raised to the power of k is greater than the number of data points (n) or 30 In this In this case… case… 2k = 30 students 25 = 32, so use k = about 5 classes Copyright © 2004 by The McGrawHill Companies, Inc. All rights reserved. Determine the class width 2 10 Generally, the class width should be the same size for all classes Max Min Min Class width >= Max K 15.0, 23.7, 19.7, 15.4, 18.3, 15.0, 23.7, 19.7, 15.4, 18.3, 23.0, 14.2, 20.8, 13.5, 23.0, 14.2, 20.8, 13.5, 20.7, 17.4, 18.6, 12.9, 20.3, 20.7, 17.4, 18.6, 12.9, 20.3, 13.7, 21.4, 18.3, 29.8, 13.7, 21.4, 18.3, 29.8, 17.1, 18.9, 10.3, 26.1, 15.7, 10.3, 17.1, 18.9, 10.3, 26.1, 15.7, 14.0, 17.8, 33.8, 23.2, 33.8, 14.0, 17.8, 33.8, 23.2, 12.9, 27.1, 16.6. 12.9, 27.1, 16.6. Copyright © 2004 by The McGrawHill Companies, Inc. All rights reserved K=5 K=5 (33.8 – 10.3)/ 5 = 4.7 Therefore, use Therefore, use class size of 5 hours class size of 5 hours Stacked Bar 2 54 FullTime University Faculty By Gender, Canada and Jurisdictions, 198788 and 199798 Total Full Professor Associate Professor Other 198788 199798 198788 199798 198788 199798 198788 199798 34,651 33,925 12,829 13,910 12,650 12,095 9,172 7,817 % Female % Male 17 83 25 75 93 13 87 17 83 28 72 32 68 44 56 % of Total Canadian Full Time University Faculty 120 100 80 60 40 20 % males % females 1987-88 Copyright © 2004 by The McGrawHill Companies, Inc. All rights reserved. 1997-98 Data Source: Statistics Canada 2 55 Make sure that your Make sure that your charts charts are are not not overly cluttered overly cluttered Copyright © 2004 by The McGrawHill Companies, Inc. All rights reserved. 2 56 Shapes of Moda Histograms ls Clas There are four typical shape characteristics Copyright © 2004 by The McGrawHill Companies, Inc. All rights reserved. 2 57 …a balanced effect! Both ‘balanced’ or Both ‘balanced’ or ‘have symmetry’ ‘have symmetry’ Copyright © 2004 by The McGrawHill Companies, Inc. All rights reserved. 2 58 … occurs when the observations are graphed as … occurs when the observations are graphed as being skewed or tilted more to one side of the centre being skewed or tilted more to one side of the centre of the observations than the other of the observations than the other The skewness, if on the The skewness, if on the right side is said to be left side is said to be ‘positive’ Copyright © 2004 by The McGrawHill Companies, Inc. All rights reserved. ‘negative’ Modal 2 59 Class A modal class is the one with the A modal class is the one with the largest number of observations largest number of observations This is a uniModal Histogram Copyright © 2004 by The McGrawHill Companies, Inc. All rights reserved. biModal Modal Class biModal biModal This is a biModal Histogram Copyright © 2004 by The McGrawHill Companies, Inc. All rights reserved. 2 60 2 61 Population distributions are often bell shaped. Drawing a histogram helps verify the shape of the population in question. Copyright © 2004 by The McGrawHill Companies, Inc. All rights reserved. Line 2 62 Line charts are particularly useful when the trend over time is to be emphasized Examples … 3D Copyright © 2004 by The McGrawHill Companies, Inc. All rights reserved. In combination Line 2 63 Time Plot Time Plot n th c tio M oMn ot h l yly SSt te e ee ll PPro r oddu u c t ino n Millions of Tons 8.5 7.5 6.5 5.5 Mo n th J F MAM J J A S O N D J F MAM J J A S ON D J F MAMJ J A S O 2000 Copyright © 2004 by The McGrawHill Companies, Inc. All rights reserved. 2001 2002 Line 2 64 Employment Rate in Canadian Cities % employment 70 68 66 64 62 60 58 56 54 52 r n e n g ia uve to ipe oon ina Bay on ner ilto nto bec ok eal ifax r n d o o e o t e o r n g o n tr a l a e c e n h am or Qu rbr ct T on H Vi Van Edm Wi ask R nd Lo Kitc H e M u S Sh Th Preparing a Line Chart for this type of data is not overly useful! Preparing a Line Chart for this type of data is not overly useful! Copyright © 2004 by The McGrawHill Companies, Inc. All rights reserved. Line 2 65 Employment Rate in Canadian Cities % employment 70 68 66 64 62 60 58 56 54 52 r n er lton to bec ria uve to ipeg oon ina Bay on ke eal ifax n o i n o n t l d e t e o n g r n o c a h am oro Qu ro ntr Ha c b Vi anc dm Win sk Re nde Lo t o r H T e M V E Ki u Sa Sh Th Is this combination any better for displaying the data? Is this combination any better for displaying the data? Copyright © 2004 by The McGrawHill Companies, Inc. All rights reserved. Line 2 66 Relative Frequency frequency Polygon 0.3 0.2 0.1 0.0 10 20 30 40 50 Sales Copyright © 2004 by The McGrawHill Companies, Inc. All rights reserved. Cumulative Relative Frequency requency Polygon Polygon and and Ogive Ogive ffrequency Ogive 1.0 0.5 0.0 10 20 30 Sales 40 50 Test your learning… … Test your learning … … n o n o k ilcick CCl www.mcgrawhill.ca/college/lind Online Learning Centre for quizzes extra content data sets searchable glossary access to Statistics Canada’s EStat data …and much more! Copyright © 2004 by The McGrawHill Companies, Inc. All rights reserved. 2 67 2 68 This completes Chapter 2 Copyright © 2004 by The McGrawHill Companies, Inc. All rights reserved. ... Copyright © 2004 by The McGrawHill Companies, Inc. All rights reserved. Frequency Graphic Presentation of a Graphic Presentation of a Frequency Distribution Frequency Distribution Class 2 29 Graphic Presentation of a Graphic Presentation of a ... 2 27 Graphic Graphic Presentation of a Presentation of a Frequency Frequency Distribution Distribution Copyright © 2004 by The McGrawHill Companies, Inc. All rights reserved. Graphic Presentation of a ... Construct a Frequency Distribution: Decide how many classes you wish to use Frequency Frequency Distributions Distributions by hand by hand Determine the class width Set up the individual class limits