Chapter 12 and 13: Homework - University of Washingtonazimmer/Lect12_Ch12_Ch13_part1_rev.pdf · Chapter 12 HomeworkChapter 13 HomeworkChapter 12 ReviewChapter 13 Review Homework Problems

Chapter 12 Homework Chapter 13 Homework Chapter 12 Review Chapter 13 Review

Reminders

• You can go to either of your TAs quiz sections to take thequiz.

• HW 3 scores are finally up (sorry for the delay). Pleasereview the grading and email me and the TAs today if youhave any concerns or questions

1


Key Concepts from Ch. 12 and 13 (part I)

• Median and Quartiles

• Five-number summary

• Boxplots

• Mean and Standard Deviation

• Median and Quartiles vs Mean and SD

• Density Curves

• Normal Curves

• 68-95-99.7 rule

• Standard scores

2


Chapter 12 and 13: Homework

Aaron ZimmermanSTAT 220 - Summer 2014

Department of StatisticsUniversity of Washington - Seattle

3


Homework Problems

We’ll break into 7 groups. Each group needs to choose aspokesperson to briefly explain one of the following problems.

• 12.11

• 12.13

• 12.19

• 12.33

• 13.2 (And how do you interpret the standard score?)

• 13.13

• 13.16 (Parts a, b, and c if you have time)

4


Problem 12.11

• The distribution of individual incomes in the US isstrongly skewed to the right. In 2004, the mean andmedian of the top 1% of Americans were $315,000 and$1,259,700. Which of these numbers is the mean andwhich is the median? Explain.

5


Problem 12.13

• Are the mean and standard deviation suitable as a briefdescription of the distribution in Figure 11.12? Why?

6


Problem 12.19

• A news article reports that of the 411 players on NBArosters in February 1998, only 139 “made more than theleague average salary” of $2.36 million. Is $2.36 millionthe mean or median salary for NBA players? How do youknow?

7


Problem 12.33

• Colleges announce an “average” SAT score for theirentering freshmen. Usually the college would like this“average” to be as high as possible. A New York Timesarticle noted, “Private colleges that buy lots of topstudents with merit scholarships prefer the mean, whileopen-enrollment public institutions like medians.” Usewhat you know about the behavior of means and mediansto explain these preferences.

8


Problem 13.2

• The distribution of heights of young men is approximatelyNormal with mean 70 inches and standard deviation 2.5inches. What is the standard score of a height of 72inches (6 feet)? How do you interpret the standard score?

9


Problem 13.13• Three landmarks of baseball achievement are Ty Cobbs batting

average of .420 in 1911, Ted Williamss .406 in 1941, and GeorgeBretts .390 in 1980. These batting averages cannot be compareddirectly because the distribution of major league batting averageshas changed over the years. The distributions are quite symmetricand (except for outliers such as Cobb, Williams, and Brett)reasonably Normal. While the mean batting average has been heldroughly constant by rule changes and the balance between hittingand pitching, the standard deviation has dropped over time. Hereare the facts:

Decade Mean SD1910s 0.266 0.03711940s 0.267 0.3261970s 0.261 0.317

Compute the standard scores for the batting averages of Cobb,Williams, and Brett to compare how far each stood above hispeers.

10


Problem 13.16

• The distribution of heights of young men is approximatelyNormal with mean 70 inches and standard deviation 2.5inches.

• (a) What percentage of men are taller than 77.5 inches?

• (b) Between what heights do the middle 68% of men fall?

• (c) What percentage of men are shorter than 65 inches?

11


Key Concepts from Ch. 12

• Median and Quartiles - how to find & when to use

• Five-number summary

• Boxplots - how to read and make

• Mean and Standard Deviation - how to find and interpret

• Median and Quartiles vs Mean and SD - when to usewhich option

• Mean and Median reltaionship

12


Mean vs Median in Pictures

13


Mean vs Median in Pictures

14


Hairloss in Monkeys

• The researchers are interested in studying the associationbetween social and non-social housing and primatehairloss in monkeys.

• Primates don’t regularly exhibit hairloss in the wild, butthey often do in captivity. There are some results thatsuggest social housing helps reduce/prevent hairloss.

15


Hairloss in Monkeys

• Two-years of longitudinal observation with measurementstaken on all animals every quarter.

• Animals enter and leave the center - the dataset doesn’tcontain complete measurements

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1 2 3 4 5 6 7 8

01

23

4

Jittered Traces of all 1007 Primates

Quarter

Alo

peci

a S

core

16


Hairloss in MonkeysI randomly selected 19 observations from monkeys that weresocially housed and another 19 from monkeys that were singlyhoused

• What’s the mean and median relationship for eachgroup of monkeys?

• Which group has a larger difference between themean and the median?

Socially Housed

hairloss score

Fre

quen

cy

0 1 2 3 4 5

02

46

810

14

Singly Housed

hairloss score

Fre

quen

cy

0 1 2 3 4 5

02

46

810

17


Hairloss in Monkeys• What’s the five-number summary for each group?

• Draw a boxplot for each group.

Socially Housed

hairloss score

Fre

quen

cy

0 1 2 3 4 5

02

46

810

14

Singly Housed

hairloss score

Fre

quen

cy

0 1 2 3 4 50

24

68

10

Social: 1 0 1 2 0 1 0 0 0 2 2 1 0 2 2 1 0 1 1Single: 0 2 1 3 0 2 0 0 2 0 2 1 2 3 2 1 1 0 0

18


Hairloss in Monkeys

• What’s the five-number summary for each group?

• Draw a boxplot for each group.

0.0

1.0

2.0

3.0

Socially Housed

hairloss score

0.0

1.0

2.0

3.0

Singly Housed

hairloss score

19


Key Concepts from Ch. 13 (part I)

• Density Curves - Area must be one, non-negative

• Normal Curves - when to use them

• 68-95-99.7 rule - how to use it

• Standard scores - how to calculate and interpret

20


Why do standard scores work?

? When we subtract the mean from every observation, themean of the distribution becomes zero? When we divide every observation by the SD, the SD of thedistribution becomes one

−20 −10 0 10 20 30

Distribution of ACT Scores

x

+/− 1 SD, Area=68%

−20 −10 0 10 20 30


x

+/− 1 SD, Area=68%

−20 −10 0 10 20 30


x

+/− 1 SD, Area=68%

Mean=18, SD=6 Mean=0, SD=6 Mean=0, SD=1

? All of the blue areas are the same size

21


Approximately what percent of adolescent girls have a serumlevel of Vitamin D between 40 pg/ml and 90 pg/ml?

Normally Distributed Variable Mean SDHealthy human body temp 98.6◦F 0.7◦FSerum level of Vit. Din adolescent girls

65.0 pg/ml 12.5 pg/ml

Forced expiratory volumein adult males

4.06 liters 0.66 liters

Heart rate at birth 125.6 bpm 11.6 bpm

22


Approximately 68% of babies are born with a heart ratebetween what two values?


65.0 pg/ml 12.5 pg/ml




23


Approximately what percent of humans have a healthy bodytemperature between 96.5◦F and 100.7◦F?


65.0 pg/ml 12.5 pg/ml




24


A patient has a temperature of 100◦F. What percent ofhumans have a healthy temperature greater than this?


65.0 pg/ml 12.5 pg/ml




25


An adolescent girl has Vitamin D deficiency if she is in thebottom 0.15% of Serum levels of Vitamin D. What is thecutoff value for Vitamin D deficiency?


65.0 pg/ml 12.5 pg/ml




26


An adolescent girl has Vitamin D deficiency if she is in thebottom 0.15% of Serum levels of Vitamin D. What is thestandard score for an adolescent girl who is just at thedeficiency boundary?


65.0 pg/ml 12.5 pg/ml




27

Documents

Chapter 12 and 13: Homework - University of Washingtonazimmer/Lect12_Ch12_Ch13_part1_rev.pdf · Chapter 12 HomeworkChapter 13 HomeworkChapter 12 ReviewChapter 13 Review Homework Problems