Describing Data: Displaying and Exploring Data - Seattle Pacific University PDF

Describing Data: Displaying and Exploring Data CHAPTER 4 N A T I O N A L L Y R A N K E D SPU is the only private university in the Pacific Northwest to make U....

Describing Data: Displaying and Exploring Data CHAPTER 4 N A T I O N A L L Y R A N K E D SPU is the only private university in the Pacific Northwest to make U.S. News & World Report’s 2018 “Best National Universities” list. 1-1  Learning Objectives LO4-1 Identify and compute measures of position LO4-2 Construct and analyze a box plot LO4-3 Compute and interpret the coefficient of skewness LO4-4 Create and interpret a scatter diagram LO4-5 Compute and interpret the correlation coefficient 4-2  Measures of Position The standard deviation is the most widely used measure of dispersion. Other methods of describing dispersion include determining the location of values that divide the dataset in equal parts: Measures of position There are three measures of position: Quartiles Deciles Percentiles Measures of position divide the dataset in equal parts. 4-3  Measures of Position Quartiles divide a set of observations into four equal parts Deciles divide a set of observations into 10 equal parts Percentiles divide a set of observations into 100 equal parts 4-4  Measures of Position Example Morgan Stanley is an investment company with offices are located throughout the United States. Listed below are the commissions earned last month by a sample of 15 brokers. Locate the 50th percentile. First, sort the data from smallest to largest 4-5  Measures of Position Example L50 = (15+1)*50/100 = 8 So the 50th percentile (median) is $2,038, the value at position 8 25 75 L25 = (15 +1) =4 L75 = (15 +1) = 12 100 100 Therefore, the first and third quartiles are located at the 4th and 12th positions, respectively: L25 = $1, 721; L75 = $2, 205 $1,460 $1,471 $1,637 $1,721 $1,758 $1,787 $1,940 $2,038 2,047 2,054 2,097 2,205 2,287 2,311 2,406 What if LP is a decimal number? How would you locate the percentile? 4-6  Measures of Position Example What if we wanted to located the 90th percentile ? L90 = (15+1)*90/100 = 14.4 So the 90th percentile is half-way between the 13th and the 14th value. We then use the formula below to compute the 90th percentile: L90 = 14th value + 0.4 (15th value – 14th value) L90 = 2311+ 0.4 (2406 – 2311) = 2349  Practice Problem 1 The Thomas Supply Company Inc. is a distributor of gas-powered generators. As with any business, the length of time customers take to pay their invoices is important. Listed below, arranged from smallest to largest, is the time, in days, for a sample of the Thomas Supply Company Inc. invoices. a. Determine the first and third quartiles. b. Determine the second decile and the eighth decile. 4-8  Problem 1 Answers a. Q1 = 33.25, Q3 = 50.25 b. D2 = 27.8, D8 = 52.6 4-9  Box Plots BOX PLOT A graphic display that shows the general shape of a variable’s distribution. It is based on five descriptive statistics: the maximum and minimum values, the first and third quartiles, and the median. The interquartile range is Q3 – Q1 4-10  Identifying Outliers Outliers A data point that is unusually far from the others. An accepted rule is to classify an observation as an outlier if it is 1.5 times the interquartile range above the third quartile or below the first quartile. On the box plot, outliers are shown as dots or stars above the maximum and below the minimum value. 4-11 4-12 Identifying Outliers Outlier > Q3 + 1.5 (Q3 – Q1) = 52.75 + 1.5 (52.75 - 40) = 71.875 Outlier