1 1 Slide IS 310 – Business Statistics IS 310 Business Statistics CSU Long Beach

2 2 Slide IS 310 – Business Statistics Chapter 2, Part B Descriptive Statistics: Tabular and Graphical Presentations n Crosstabulations and Scatter Diagrams Scatter Diagrams x y

3 3 Slide IS 310 – Business Statistics Crosstabulations and Scatter Diagrams Crosstabulation and a scatter diagram are two Crosstabulation and a scatter diagram are two methods for summarizing the data for two variables methods for summarizing the data for two variables simultaneously. simultaneously. Often a manager is interested in presentations that Often a manager is interested in presentations that will help understand the relationship between two will help understand the relationship between two variables. variables. Thus far we have focused on presentations that are Thus far we have focused on presentations that are used to summarize the data for one variable at a time. used to summarize the data for one variable at a time.

4 4 Slide IS 310 – Business Statistics Crosstabulation The left and top margin labels define the classes for The left and top margin labels define the classes for the two variables. the two variables. n Crosstabulation can be used when: one variable is qualitative and the other is one variable is qualitative and the other is quantitative, quantitative, both variables are qualitative, or both variables are qualitative, or both variables are quantitative. both variables are quantitative. A crosstabulation is a tabular summary of data for A crosstabulation is a tabular summary of data for two variables. two variables.

5 5 Slide IS 310 – Business Statistics Price Range Colonial Log Split A-Frame Total < $99,000 > $99, Total Home Style Home Style Crosstabulation n Example: Finger Lakes Homes The number of Finger Lakes homes sold for each style and price for the past two years is shown below. quantitative variable variablequantitative qualitative qualitative

6 6 Slide IS 310 – Business Statistics Crosstabulation n Insights Gained from Preceding Crosstabulation Only three homes in the sample are an A-Frame Only three homes in the sample are an A-Frame style and priced at more than $99,000. style and priced at more than $99,000. The greatest number of homes (19) in the sample The greatest number of homes (19) in the sample are a split-level style and priced at less than or are a split-level style and priced at less than or equal to $99,000. equal to $99,000.

7 7 Slide IS 310 – Business Statistics PriceRange Colonial Log Split A-Frame Colonial Log Split A-Frame Total < $99,000 > $99, Total Home Style Home Style Crosstabulation Frequency distribution for the price variable Frequency distribution for the home style variable

8 8 Slide IS 310 – Business Statistics Crosstabulation: Row or Column Percentages n Converting the entries in the table into row percentages or column percentages can provide additional insight about the relationship between the two variables.

9 9 Slide IS 310 – Business Statistics PriceRange Colonial Log Split A-Frame Colonial Log Split A-Frame Total < $99,000 > $99, Note: row totals are actually due to rounding Home Style Home Style (Colonial and > $99K)/(All >$99K) x 100 = (12/45) x 100 Crosstabulation: Row Percentages

10 Slide IS 310 – Business Statistics PriceRange Colonial Log Split A-Frame Colonial Log Split A-Frame < $99,000 > $99, Home Style Home Style Total (Colonial and > $99K)/(All Colonial) x 100 = (12/30) x 100 Crosstabulation: Column Percentages

11 Slide IS 310 – Business Statistics The general pattern of the plotted points suggests the The general pattern of the plotted points suggests the overall relationship between the variables. overall relationship between the variables. One variable is shown on the horizontal axis and the One variable is shown on the horizontal axis and the other variable is shown on the vertical axis. other variable is shown on the vertical axis. A scatter diagram is a graphical presentation of the A scatter diagram is a graphical presentation of the relationship between two quantitative variables. relationship between two quantitative variables. Scatter Diagram and Trendline A trendline is an approximation of the relationship. A trendline is an approximation of the relationship.

12 Slide IS 310 – Business Statistics n A Positive Relationship x y Scatter Diagram and Trendline

13 Slide IS 310 – Business Statistics n A Negative Relationship x y Scatter Diagram and Trendline

14 Slide IS 310 – Business Statistics n No Apparent Relationship x y Scatter Diagram and Trendline

15 Slide IS 310 – Business Statistics Example: Panthers Football Team n Scatter Diagram and Trendline The Panthers football team is interested The Panthers football team is interested in investigating the relationship, if any, between interceptions made and points scored x = Number of Interceptions y = Number of Points Scored Points Scored

16 Slide IS 310 – Business Statistics y x Number of Interceptions Number of Points Scored Scatter Diagram and Trendline

17 Slide IS 310 – Business Statistics n Insights Gained from the Preceding Scatter Diagram The relationship is not perfect; all plotted points in The relationship is not perfect; all plotted points in the scatter diagram are not on a straight line. the scatter diagram are not on a straight line. Higher points scored are associated with a higher Higher points scored are associated with a higher number of interceptions. number of interceptions. The scatter diagram and trendline indicate a The scatter diagram and trendline indicate a positive relationship between the number of positive relationship between the number of interceptions and the number of points scored. interceptions and the number of points scored. Example: Panthers Football Team

18 Slide IS 310 – Business Statistics End of Chapter 2, Part B