1 Business 90: Business Statistics Professor David Mease Sec 03, T R 7:30-8:45AM BBC 204 Lecture 11 = Finish Chapter Numerical Descriptive Measures (NDM) Agenda: 1) Reminder about Homework 4 due Thursday 2) Reminder about Midterm Exam (3/16) 3) Lecture over the rest of Chapter NDM

2 Homework 4 – Due Thursday 3/4 1) Read chapter entitled “Numerical Descriptive Measures”. 2) In that chapter do textbook problems 5, 8 and 9 by hand AND check the answers using Excel. 3) The data at ( gives free throw percentages for NBA basketball players for the season. a) Give the 5 number summary for the free throw percentages. b) Graph the box-and-whisker plot by hand. c) Based on your box-and-whisker plot, describe the shape of the data as left-skewed, symmetric or right-skewed. d) Use Excel to compute the mean, variance and standard deviation. e) Using your values from part d, give the empirical rule for this data. 4) Review In Class Exercise #46. (There will be one like this on the quiz.)

3 Midterm Exam: Midterm Exam on Tuesday, March 16 You will NOT be able to use Excel or any notes for the exam, so make sure you know how to do everything by hand (with the help of a calculator). Be sure to bring your calculator. The exam will cover chapters IADC, PDITAC (plus least squares regression from p ), NDM and BP. Worth 100 points Seats will be assigned when you enter the room.

4 Numerical Descriptive Measures Statistics for Managers Using Microsoft ® Excel 4 th Edition

5 Chapter Topics Measures of central tendency, variation, and shape Mean, median, mode, geometric mean Quartiles Range, interquartile range, variance and standard deviation, coefficient of variation Symmetric and skewed distributions Population summary measures Mean, variance, and standard deviation The empirical rule Five number summary and box-and-whisker plots Coefficient of correlation

6 Summary Measures Arithmetic Mean Median Mode Describing Data Numerically Variance Standard Deviation Coefficient of Variation Range Interquartile Range Geometric Mean Skewness Central TendencyVariationShapeQuartiles

7 Shape of a Distribution Describes how data are distributed Measures of shape Symmetric or skewed Mean = Median Mean < Median Median < Mean Right-Skewed Left-SkewedSymmetric

8 Distribution Shape and Box-and-Whisker Plot Right-SkewedLeft-SkewedSymmetric Q1Q2Q3Q1Q2Q3 Q1Q2Q3

9 In class exercise #43: Below is the histogram for the 1500 California house prices from Homework 2 (houses.xls). How would you describe the shape of the data based on the histogram? Confirm this by A) comparing the mean and median B) making the box-and-whisker plot

10 If the data distribution is close to being bell- shaped, then the interval: contains about 68% of the values in the population or the sample The Empirical Rule 68%

11 contains about 95% of the values in the population or the sample contains about 99.7% of the values in the population or the sample The Empirical Rule 99.7%95%

12 In class exercise #44: Give the empirical rule for a population for which the mean is 100 and the standard deviation is 10.

13 In class exercise #45: Compare the empirical rule to the observed percentages for the 1500 house prices (houses.xls).

14 Y X Y X Y X Y X r = -1 r = -.6 r = +.3 r = +1 Coefficient of Correlation (r)

15 Measures the relative strength and direction of the linear relationship between two variables Is equal to the square root of R-squared but will be negative if the relationship is negative I will NOT make you compute this by hand, but this is the formula if you are curious Coefficient of Correlation (r)

16 Features of Correlation Coefficient, r Unit free Ranges between –1 and 1 The closer to –1, the stronger the negative linear relationship The closer to 1, the stronger the positive linear relationship The closer to 0, the weaker any linear relationship

17 In class exercise #46: Match each plot with its correct coefficient of correlation. Choices: r=-3.20, r=-0.98, r=0.86, r=0.95, r=1.20, r=-0.96, r=-0.40 A) B) C) D)E)