3. Describing Data Numerically

[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.

 Mensa is an organization designed for people of high intelligence. One qualifies for Mensa if one’s intelligence is measured at or above the 98th percentile. Explain what this means.

Explain what each quartile represents.

You Explain It! Percentiles According to the National Center for Health Statistics, a 19-year-old female whose height is 67.1 inches has a height that is at the 85th percentile. Explain what this means.

According to the National Center for Health Statistics, a 10-year-old male whose height is 53.5 inches has a height that is at the 15th percentile. Explain what this means.

The standard deviation is used in conjunction with the_____to numerically describe distributions that are bell shaped. The______measures the center of the distribution, while the standard deviation measures the_____of the distribution.

True or False: Chebyshev’s Inequality applies to all distributions regardless of shape, but the Empirical Rule holds only for distributions that are bell shaped.