3.6 Robust Measures

Objectives:By the end of this section, I will beable to…

1) Find quartiles and the interquartile range.2) Calculate the five-number summary of a

data set.3) Construct a boxplot for a given data set.4) Apply robust detection of outliers.

Section 3.6

Robust Measures

What are robust measures?

• Since the mean and the standard deviation are SENSITIVE to outliers, analysts prefer to use more robust measures.

• Three Types of Robust Measures1. Median2. Five Number Summary3. IQR

Quartiles – breaking data into quartersThe five number summary uses the following values:• Minimum, smallest value, Q0, 0th percentile• First Quartile, Q1, 25th Percentile• Second Quartile, Q2, 50th Percentile, MEDIAN• Third Quartile, Q3, 75th Percentile• Maximum, largest value, Q4, 100th Percentile

1. How fast did the bus in the movie Speed need to go in

order not to blow up

50 mph

2. Who did Adam Sandler fight in Happy Gilmore?

Bob Barker

3. The actor who plays Harry Potter.

Daniel Radcliffe

4. The name of Ricky Bobby’s best friend in

Talladega Nights?

Cal Naughton, Jr

5. Mark Walhberg teams up with this actor in The

Fighter.

Christian Bale

6. Jake Gyllenhall starred in this period film that came out

in May 2010?

Prince of Persia

7. Who was the original killer in Friday the 13th?

Jason’s Mom

8. In the movie Tropic Thunder, who is the balding studio exec?

Tom Cruise

9. He is the British actor in Get Him to the Greek?

Russell Brand

10. A new movie just released about Facebook.

The Social Network

11. In Toy Story, what is the evil neighbor’s name?

Sid

12. What does Robert Downey Jr. sell in the movie

Iron Man?

Weapons

13. What are the pet’s names in Homeward Bound?

Shadow, Chance and Sassy

14. What is the first rule that is made in the movie Fight

Club?

Don’t talk about the club.

15. The City where Michael Oher was adopted by the

Touhey family.

Memphis

16. In 300, what is the Persian King’s name?

Xerxes

17. In Fresh Prince of Bel-Air what was the butlers

name

Geoffrey

18. Bradley Cooper starred in this comedy’s first

installment a few years ago.

The Hangover

19. ESPN is based out of which Connecticut city?

Bristol

20. A military movie in 2008 that followed around an

EOD team in Iraq. Jeremy Renner starred in it.

The Hurt Locker

•HOW MANY DID YOU GET RIGHT?

•Find the five number summary.

FIVE NUMBER SUMMARY• Put data into ORDER (either by hand or

on calc)• Find the median = Q2• Cut the data into 2 Halves

• The median of the 1st Half = Q1• The median of the 2nd Half = Q3

• Label the max and min values

Interquartile Range (IQR)

• It is a robust measure of VARIABILITY.

• IQR = Q3 – Q1• Find the IQR.

BOX AND WHISKER PLOT• Graph that displays the Five Number

Summary.• LABEL the five values.

Comparing Box and Whisker Plots

Salaries• Find the following:• The five number summary • The IQR• Create and LABEL a box and whisker plot