1 1 Slide STATISTICS FOR BUSINESS AND ECONOMICS Seventh Edition AndersonSweeneyWilliams Slides Prepared by John Loucks © 1999 ITP/South-Western College Publishing

2 2 Slide Chapter 3, Part 3 Descriptive Statistics II: Numerical Methods n Exploratory Data Analysis n Measures of Association Between Two Variables n The Weighted Mean and Working with Grouped Data

3 3 Slide Exploratory Data Analysis n Five-Number Summary n Box Plot

4 4 Slide Five-Number Summary n Smallest Value n First Quartile n Median n Third Quartile n Largest Value

5 5 Slide Example: Apartment Rents n Five-Number Summary Lowest Value = 425 First Quartile = 450 Median = 475 Third Quartile = 525 Largest Value = 615

6 6 Slide Box Plot n A box is drawn with its ends located at the first and third quartiles. n A vertical line is drawn in the box at the location of the median. n Fences are located (not drawn) using the interquartile range (IQR). The inner fences are located 1.5(IQR) below Q1 and 1.5(IQR) above Q3.The inner fences are located 1.5(IQR) below Q1 and 1.5(IQR) above Q3. The outer fences are located 3(IQR) below Q1 and 3(IQR) above Q3.The outer fences are located 3(IQR) below Q1 and 3(IQR) above Q3. Continued Continued

7 7 Slide Box Plot (Continued) n Whiskers (dashed lines) are drawn from the ends of the box to the smallest and largest data values inside the inner fences. n The locations of mild outliers are shown with the symbol *. n The locations of extreme outliers are shown with the symbol o.

8 8 Slide Example: Apartment Rents n Box Plot Inner Fences: Q (IQR) = (75) = Inner Fences: Q (IQR) = (75) = Q (IQR) = (75) = Q (IQR) = (75) = Outer Fences: Q1 - 3(IQR) = (75) = 225 Outer Fences: Q1 - 3(IQR) = (75) = 225 Q3 + 3(IQR) = (75) = 750 Q3 + 3(IQR) = (75) = 750 There are no mild or extreme outliers

9 9 Slide Measures of Association Between Two Variables n Covariance n Correlation Coefficient

10 Slide Covariance n Positive values indicate a positive relationship. n Negative values indicate a negative relationship. n If the data sets are samples, the covariance is denoted by s xy. n If the data sets are populations, the covariance is denoted by.

11 Slide Correlation Coefficient n The coefficient can take on values between -1 and +1. n Values near -1 indicate a strong negative linear relationship. n Values near +1 indicate a strong positive linear relationship. n If the data sets are samples, the coefficient is denoted by r xy. n If the data sets are populations, the coefficient is denoted by.

12 Slide The Weighted Mean and Working with Grouped Data n The Weighted Mean n Grouped Data

13 Slide The Weighted Mean n Weighted Sample Mean x where: x i = data value i w i = weight for data value i w i = weight for data value i Weighted Population Mean  Weighted Population Mean 

14 Slide Example: Average Inventory Value American Iron Cycle Works has 74 motorcycles in its inventory. What is the average per-unit value of its inventory? Cycle ModelValue, each Quantity Electra Glide $17,10028 Springer Softtail 15,85016 Sportster 7,21011 Road King 16,77519

15 Slide Example: Average Inventory Value n Weighted Population Mean  = 28($17,100) + 16($15,850) + 11($7,210) + 19($16,775)  = $1,130,435  = $1,130,  = $15,  = $15,276.15

16 Slide Mean for Grouped Data n Sample Data n Population Data where f i = frequency of class i M i = midpoint of class i M i = midpoint of class i

17 Slide Example: Apartment Rents n Given below is the previous sample of monthly rents for one-bedroom apartments presented as grouped data in the form of a frequency distribution.

18 Slide Example: Apartment Rent n Mean for Grouped Data This approximation differs by $2.41 from This approximation differs by $2.41 from the actual sample mean of $ the actual sample mean of $

19 Slide Variance for Grouped Data n Sample Data n Population Data

20 Slide Example: Apartment Rents n Sample Variance for Grouped Data n Sample Standard Deviation for Grouped Data This approximation differs by only $.20 from the actual standard deviation of $ actual standard deviation of $54.74.

21 Slide The End of Chapter 3, Part 3