© 2006 by Thomson Learning, a division of Thomson Asia Pte Ltd.. 1 Slide Slide Slides Prepared by Juei-Chao Chen Fu Jen Catholic University Slides Prepared by Juei-Chao Chen Fu Jen Catholic University

© 2006 by Thomson Learning, a division of Thomson Asia Pte Ltd.. 2 Slide Slide Chapter 2 STATISTICS in PRACTICE The Colgate-Palmolive Company uses statistics in its quality assurance program for home laundry detergent products. One concern is customer satisfaction with the quantity of detergent in a carton. To control the problem of heavy detergent powder, limits are placed on the acceptable range of powder density. Statistical samples are taken and the density of each powder sample is measured. Data summaries are then provided for operating personnel so that corrective action can be taken if necessary to keep the density within the desired quality.

© 2006 by Thomson Learning, a division of Thomson Asia Pte Ltd.. 3 Slide Slide Chapter 2 Descriptive Statistics: Tabular and Graphical Presentations 2.1 Summarizing Qualitative Data 2.2 Summarizing Quantitative Data 2.3 Exploratory Data Analysis: The Stem-and- Leaf Display 2.4 Crosstabulations and Scatter Diagrams

© 2006 by Thomson Learning, a division of Thomson Asia Pte Ltd.. 4 Slide Slide Chapter 2 Descriptive Statistics: Tabular and Graphical Presentations Part A Summarizing Qualitative Data Summarizing Quantitative Data

© 2006 by Thomson Learning, a division of Thomson Asia Pte Ltd.. 5 Slide Slide 2.1 Summarizing Qualitative Data Frequency Distribution Relative Frequency Distributions Percent Frequency Distributions Bar Graphs Pie Charts

© 2006 by Thomson Learning, a division of Thomson Asia Pte Ltd.. 6 Slide Slide A frequency distribution is a tabular summary of A frequency distribution is a tabular summary of data showing the frequency (or number) of items data showing the frequency (or number) of items in each of several nonoverlapping classes. in each of several nonoverlapping classes. A frequency distribution is a tabular summary of A frequency distribution is a tabular summary of data showing the frequency (or number) of items data showing the frequency (or number) of items in each of several nonoverlapping classes. in each of several nonoverlapping classes. The objective is to provide insights about the data The objective is to provide insights about the data that cannot be quickly obtained by looking only at that cannot be quickly obtained by looking only at the original data. the original data. The objective is to provide insights about the data The objective is to provide insights about the data that cannot be quickly obtained by looking only at that cannot be quickly obtained by looking only at the original data. the original data. Frequency Distribution

© 2006 by Thomson Learning, a division of Thomson Asia Pte Ltd.. 7 Slide Slide Frequency Distribution Example: Data from a sample of 50 Soft Drink Purchases Frequency Distribution Soft Drink Frequency Coke Classic 19 Diet Coke 8 Dr. Pepper 5 Pepsi-Cola 13 Sprite 5 Total 50

© 2006 by Thomson Learning, a division of Thomson Asia Pte Ltd.. 8 Slide Slide Example: Marada Inn Guests staying at Marada Inn were asked to rate the quality of their accommodations as being excellent, above average, average, below average, or poor. The ratings provided by a sample of 20 guests are: Below Average Below Average Above Average Above Average Average Average Above Average Above Average Average Average Above Average Above Average Average Average Above Average Above Average Below Average Below Average Poor Poor Excellent Excellent Above Average Above Average Average Average Above Average Above Average Below Average Below Average Poor Poor Above Average Above Average Average Average

© 2006 by Thomson Learning, a division of Thomson Asia Pte Ltd.. 9 Slide Slide Frequency Distribution Poor Below Average Average Above Average Excellent Total 20 RatingFrequency

© 2006 by Thomson Learning, a division of Thomson Asia Pte Ltd.. 10 Slide Slide The relative frequency of a class is the fraction or The relative frequency of a class is the fraction or proportion of the total number of data items proportion of the total number of data items belonging to the class. belonging to the class. The relative frequency of a class is the fraction or The relative frequency of a class is the fraction or proportion of the total number of data items proportion of the total number of data items belonging to the class. belonging to the class. Relative Frequency Frequency of the class Relative frequency of a class= n

© 2006 by Thomson Learning, a division of Thomson Asia Pte Ltd.. 11 Slide Slide Relative Frequency Distributions A relative frequency distribution is a tabular summary of a set of data showing the relative frequency for each class. A relative frequency distribution is a tabular summary of a set of data showing the relative frequency for each class. Example: Relative and Percent Frequency Distribution of Soft Drink Purchases Soft Drink Relative Frequency Coke Classic.38 Diet Coke.16 Dr. Pepper.10 Pepsi-Cola.26 Sprite.10 Total 1.00

© 2006 by Thomson Learning, a division of Thomson Asia Pte Ltd.. 12 Slide Slide Percent Frequency Distribution The percent frequency of a class is the relative The percent frequency of a class is the relative frequency multiplied by 100. frequency multiplied by 100. The percent frequency of a class is the relative The percent frequency of a class is the relative frequency multiplied by 100. frequency multiplied by 100. A percent frequency distribution is a tabular A percent frequency distribution is a tabular summary of a set of data showing the percent summary of a set of data showing the percent frequency for each class. frequency for each class. A percent frequency distribution is a tabular A percent frequency distribution is a tabular summary of a set of data showing the percent summary of a set of data showing the percent frequency for each class. frequency for each class. Example: Percent Frequency Distribution of Soft Drink Purchases Soft Drink Percent Frequency Coke Classic 38 Diet Coke 16 Dr. Pepper 10 Pepsi-Cola 26 Sprite 10 Total 100

© 2006 by Thomson Learning, a division of Thomson Asia Pte Ltd.. 13 Slide Slide Relative Frequency and Percent Frequency Distributions Poor Below Average Average Above Average Excellent Total Relative RelativeFrequency Percent PercentFrequency Rating.10(100) = 10 1/20 =.05

© 2006 by Thomson Learning, a division of Thomson Asia Pte Ltd.. 14 Slide Slide Bar Graph A bar graph is a graphical device for depicting qualitative data. On one axis (usually the horizontal axis), we specify the labels that are used for each of the classes. A frequency, relative frequency, or percent frequency scale can be used for the other axis (usually the vertical axis). Using a bar of fixed width drawn above each class label, we extend the height appropriately.

© 2006 by Thomson Learning, a division of Thomson Asia Pte Ltd.. 15 Slide Slide Bar Graph Example: Bar Graph of Soft Drink Purchases

© 2006 by Thomson Learning, a division of Thomson Asia Pte Ltd.. 16 Slide Slide Poor Below Average Below Average Above Average Above Average Excellent Frequency Rating Bar Graph Marada Inn Quality Ratings

© 2006 by Thomson Learning, a division of Thomson Asia Pte Ltd.. 17 Slide Slide Pie Chart The pie chart is a commonly used graphical device for presenting relative frequency distributions for qualitative data. First draw a circle; then use the relative frequencies to subdivide the circle into sectors that correspond to the relative frequency for each class. Since there are 360 degrees in a circle, a class with a relative frequency of.25 would consume.25(360) = 90 degrees of the circle.

© 2006 by Thomson Learning, a division of Thomson Asia Pte Ltd.. 18 Slide Slide Pie Chart Example: Pie Chart of Soft Drink Purchases

© 2006 by Thomson Learning, a division of Thomson Asia Pte Ltd.. 19 Slide Slide Below Average 15% Below Average 15% Average 25% Average 25% Above Average 45% Above Average 45% Poor 10% Poor 10% Excellent 5% Excellent 5% Marada InnQuality Ratings Marada Inn Quality Ratings Pie Chart

© 2006 by Thomson Learning, a division of Thomson Asia Pte Ltd.. 20 Slide Slide Insights Gained from the Preceding Pie Chart Example: Marada Inn One-half of the customers surveyed gave Marada a quality rating of “above average” or “excellent” (looking at the left side of the pie). This might please the manager. For each customer who gave an “excellent” rating, there were two customers who gave a “poor” rating (looking at the top of the pie). This should displease the manager.

© 2006 by Thomson Learning, a division of Thomson Asia Pte Ltd.. 21 Slide Slide 2.2 Summarizing Quantitative Data Frequency Distribution Relative Frequency and Percent Frequency Distributions Dot Plot Histogram Cumulative Distributions Ogive

© 2006 by Thomson Learning, a division of Thomson Asia Pte Ltd.. 22 Slide Slide Frequency Distribution The three steps necessary to define the classes for a frequency distribution with quantitative data are: 1. Determine the number of nonoverlapping classes. we recommend using between 5 and 20 classes. 2. Determine the width of each class. 3. Determine the class limits. Largest data value –Smallest data value Approximate class width= Number of classes

© 2006 by Thomson Learning, a division of Thomson Asia Pte Ltd.. 23 Slide Slide Frequency Distribution Guidelines for Selecting Number of Classes Use between 5 and 20 classes. Data sets with a larger number of elements usually require a larger number of classes. Smaller data sets usually require fewer classes

© 2006 by Thomson Learning, a division of Thomson Asia Pte Ltd.. 24 Slide Slide Frequency Distribution Guidelines for Selecting Width of Classes Use classes of equal width. Approximate Class Width = Largest data value –Smallest data value Number of classes

© 2006 by Thomson Learning, a division of Thomson Asia Pte Ltd.. 25 Slide Slide Frequency Distribution Example: These data show the time in days required to complete year-end audits for a sample of 20 clients of Sanderson and Clifford, a small public accounting firm with the data rounded to the nearest day. YEAR-END AUDIT TIMES (IN DAYS)

© 2006 by Thomson Learning, a division of Thomson Asia Pte Ltd.. 26 Slide Slide Frequency Distribution Example: 1. Number of classes = 5 2. provides an approximate class width of (33 — 12)/5= We therefore decided to round up and use a class width of five days in the frequency distribution. 4. FREQUENCY DISTRIBUTION FOR THE AUDIT TIMES DATA Audit Time Frequency (days) Total 20

© 2006 by Thomson Learning, a division of Thomson Asia Pte Ltd.. 27 Slide Slide Example: Hudson Auto Repair The manager of Hudson Auto would like to have a better understanding of the cost of parts used in the engine tune-ups performed in the shop. She examines 50 customer invoices for tune-ups. The costs of parts, rounded to the nearest dollar, are listed on the next slide.

© 2006 by Thomson Learning, a division of Thomson Asia Pte Ltd.. 28 Slide Slide Example: Hudson Auto Repair Sample of Parts Cost for 50 Tune-ups

© 2006 by Thomson Learning, a division of Thomson Asia Pte Ltd.. 29 Slide Slide Frequency Distribution For Hudson Auto Repair, if we choose six classes: Total 50 Parts Cost ($) Frequency Approximate Class Width = ( )/6 = 9.5  10

© 2006 by Thomson Learning, a division of Thomson Asia Pte Ltd.. 30 Slide Slide Relative Frequency and Percent Frequency Distributions Parts Cost ($) Total 1.00 Relative RelativeFrequency Percent Frequency 2/50.04(100)

© 2006 by Thomson Learning, a division of Thomson Asia Pte Ltd.. 31 Slide Slide Only 4% of the parts costs are in the $50-59 class. The greatest percentage (32% or almost one-third) of the parts costs are in the $70-79 class. 30% of the parts costs are under $70. 10% of the parts costs are $100 or more. Insights Gained from the Percent Frequency Distribution Relative Frequency and Percent Frequency Distributions

© 2006 by Thomson Learning, a division of Thomson Asia Pte Ltd.. 32 Slide Slide Dot Plot One of the simplest graphical summaries of data is a dot plot. A horizontal axis shows the range of data values. Then each data value is represented by a dot placed above the axis. Example: Dot Plot for The Audit Time Data

© 2006 by Thomson Learning, a division of Thomson Asia Pte Ltd.. 33 Slide Slide Cost ($) Dot Plot Tune-up Parts Cost

© 2006 by Thomson Learning, a division of Thomson Asia Pte Ltd.. 34 Slide Slide Histogram Another common graphical presentation of quantitative data is a histogram. The variable of interest is placed on the horizontal axis. A rectangle is drawn above each class interval with its height corresponding to the interval’s frequency, relative frequency, or percent frequency. Unlike a bar graph, a histogram has no natural separation between rectangles of adjacent classes.

© 2006 by Thomson Learning, a division of Thomson Asia Pte Ltd.. 35 Slide Slide Histogram Example: Histogram for The Audit Time Data

© 2006 by Thomson Learning, a division of Thomson Asia Pte Ltd.. 36 Slide Slide Histogram Parts Cost ($) Parts Cost ($) Frequency Tune-up Parts Cost

© 2006 by Thomson Learning, a division of Thomson Asia Pte Ltd.. 37 Slide Slide Histogram provides information about the shape. Symmetric Left tail is the mirror image of the right tail Examples: heights and weights of people Histogram Relative Frequency

© 2006 by Thomson Learning, a division of Thomson Asia Pte Ltd.. 38 Slide Slide Histogram Moderately Skewed Left A longer tail to the left Example: exam scores Relative Frequency

© 2006 by Thomson Learning, a division of Thomson Asia Pte Ltd.. 39 Slide Slide Moderately Right Skewed A Longer tail to the right Example: housing values Histogram Relative Frequency

© 2006 by Thomson Learning, a division of Thomson Asia Pte Ltd.. 40 Slide Slide Histogram Highly Skewed Right A very long tail to the right Example: executive salaries Relative Frequency

© 2006 by Thomson Learning, a division of Thomson Asia Pte Ltd.. 41 Slide Slide Cumulative frequency distribution  shows the Cumulative frequency distribution  shows the number of items with values less than or equal to number of items with values less than or equal to the upper limit of each class.. the upper limit of each class.. Cumulative frequency distribution  shows the Cumulative frequency distribution  shows the number of items with values less than or equal to number of items with values less than or equal to the upper limit of each class.. the upper limit of each class.. Cumulative relative frequency distribution – shows Cumulative relative frequency distribution – shows the proportion of items with values less than or the proportion of items with values less than or equal to the upper limit of each class. equal to the upper limit of each class. Cumulative relative frequency distribution – shows Cumulative relative frequency distribution – shows the proportion of items with values less than or the proportion of items with values less than or equal to the upper limit of each class. equal to the upper limit of each class. Cumulative Distributions Cumulative percent frequency distribution – shows Cumulative percent frequency distribution – shows the percentage of items with values less than or the percentage of items with values less than or equal to the upper limit of each class. equal to the upper limit of each class. Cumulative percent frequency distribution – shows Cumulative percent frequency distribution – shows the percentage of items with values less than or the percentage of items with values less than or equal to the upper limit of each class. equal to the upper limit of each class.

© 2006 by Thomson Learning, a division of Thomson Asia Pte Ltd.. 42 Slide Slide Cumulative Distributions Example: Cumulative Frequency, Cumulative Relative Frequency and Cumulative Percent Frequency Distributions for the Audit Data.

© 2006 by Thomson Learning, a division of Thomson Asia Pte Ltd.. 43 Slide Slide Cumulative Distributions Hudson Auto Repair <59 <69 <79 <89 <99 <109 Cost ($) Cumulative CumulativeFrequency RelativeFrequency CumulativePercent Frequency Frequency /50.30(100)

© 2006 by Thomson Learning, a division of Thomson Asia Pte Ltd.. 44 Slide Slide Ogive An ogive is a graph of a cumulative distribution. The data values are shown on the horizontal axis. Shown on the vertical axis are the: cumulative frequencies, or cumulative relative frequencies, or cumulative percent frequencies The frequency (one of the above) of each class is plotted as a point. The plotted points are connected by straight lines.

© 2006 by Thomson Learning, a division of Thomson Asia Pte Ltd.. 45 Slide Slide Because the class limits for the parts-cost data are 50-59, 60-69, and so on, there appear to be one-unit gaps from 59 to 60, 69 to 70, and so on. Ogive These gaps are eliminated by plotting points halfway between the class limits. Thus, 59.5 is used for the class, 69.5 is used for the class, and so on. Hudson Auto Repair

© 2006 by Thomson Learning, a division of Thomson Asia Pte Ltd.. 46 Slide Slide Ogive Example: Ogive for the Audit Time Data.

© 2006 by Thomson Learning, a division of Thomson Asia Pte Ltd.. 47 Slide Slide Parts Parts Cost ($) Parts Parts Cost ($) Cumulative Percent Frequency (89.5, 76) Ogive with Cumulative Percent Frequencies Cumulative Percent Frequencies Tune-up Parts Cost

© 2006 by Thomson Learning, a division of Thomson Asia Pte Ltd.. 48 Slide Slide End of Chapter 2, Part A