3. Describing Data Numerically

Using and Interpreting Concepts

Using and Interpreting Concepts Finding Quartiles, Interquartile Range, and Outliers In Exercises 11 and 12,

(c) identify any outliers.

56 63 51 60 57 60 60 54 63 59 80 63 60 62 65

Finding a Percentile In Exercises 33–36, use the data set, which represents the ages of 30 executives.

43 57 65 47 57 41 56 53 61 54

56 50 66 56 50 61 47 40 50 43

54 41 48 45 28 35 38 43 42 44

Which ages are above the 75th percentile?

Finding and Interpreting Percentiles In Exercises 37– 40, use the data set, which represents wait times (in minutes) for various services at a state’s Department of Motor Vehicles locations.

6 10 1 22 23 10 6 7 2 1 6 6 2 4 14 15 16 4

19 3 19 26 5 3 4 7 6 10 9 10 20 18 3 20 10 13

14 11 14 17 4 27 4 8 4 3 26 18 21 1 3 3 5 5

Which wait time represents the 50th percentile? How would you interpret this?

Extending Concepts

Midquartile Another measure of position is called the midquartile. You can find the midquartile of a data set by using the formula below.

Midquartile = (Q₁ + Q₃) / 2

In Exercises 55 and 56, find the midquartile of the data set.

5 7 1 2 3 10 8 7 5 3

Interpreting Percentiles In Exercises 29–32, use the ogive, which represents the cumulative frequency distribution for quantitative reasoning scores on the Graduate Record Examination in a recent range of years. (Adapted from Educational Testing Service)

What score represents the 65th percentile? How should you interpret this?

You Explain It! Percentiles Explain the meaning of the following percentiles. Source: National Center for Health Statistics. a. The 5th percentile of the weight of males 36 months of age is 12.0 kg. b. The 95th percentile of the length of newborn females is 53.8 cm.

Roller Coaster Speed Outlier Identify any outliers among the data listed for Exercise 1.

[DATA] Wait Time The following data represent the wait time (in minutes) for a random sample of 40 visitors to Disney’s Dinosaur Ride in Animal Kingdom.

a. Determine and interpret the quartiles. b. Check the data set for outliers.

In Problems 3 and 4, (a) identify the shape of the distribution and (b) determine the five-number summary. Assume that each number in the five-number summary is an integer.

[NW] You Explain It! Percentiles Explain the meaning of the following percentiles. Source: Advance Data from Vital and Health Statistics. a. The 15th percentile of the head circumference of males 3 to 5 months of age is 41.0 cm. b. The 90th percentile of the waist circumference of females 2 years of age is 52.7 cm. c, Anthropometry involves the measurement of the human body. One goal of these measurements is to assess how body measurements may be changing over time. The following table represents the standing height of males aged 20 years or older for various age groups. Based on the percentile measurements of the different age groups, what might you conclude?

 Morningstar is a mutual fund rating agency. It ranks a fund’s performance by using one to five stars. A one-star mutual fund is in the bottom 10% of its investment class; a five-star mutual fund is at the 90th percentile of its investment class. Interpret the meaning of a five-star mutual fund.

The ________ ________ is the range of the middle 50% of the observations in a data set.

[DATA] Fraud Detection As part of its “Customers First” program, a cellular phone company monitors monthly phone usage. The program identifies unusual use and alerts the customer that their phone may have been used by another person. The data below represent the monthly phone use in minutes of a customer enrolled in this program for the past 20 months. The phone company decides to use the upper fence as the cutoff point for the number of minutes at which the customer should be contacted. What is the cutoff point?

Threaded Problem: Tornado The data set “Tornadoes_2017” located at www.pearsonhighered.com/sullivanstats contains a variety of variables that were measured for all tornadoes in the United States in 2017. a. Determine and interpret the quartiles of the length for all tornadoes. Hint: If you are using StatCrunch, enter “State=IA” in the Where: box of the Summary Stats dialogue window. Determine the interquartile range of the length of tornadoes in Kansas (KS). Which state has lengths of tornadoes that are more dispersed? Explain.

Threaded Problem: Tornado The data set “Tornadoes_2017” located at www.pearsonhighered.com/sullivanstats contains a variety of variables that were measured for all tornadoes in the United States in 2017. b. Determine the interquartile range of the length of tornadoes in Iowa (IA). Hint: If you are using StatCrunch, enter “State=IA” in the Where: box of the Summary Stats dialogue window. Determine the interquartile range of the length of tornadoes in Kansas (KS). Which state has lengths of tornadoes that are more dispersed? Explain.