Comparing Samples

Two optometrists (eye doctors) each compiled data from 10 different random samples. The table contains their respective data sets.

The Corrective lenses are in the 700s Column. The Glasses are in the 600s Column. The Contacts Are the 100s and 90s Column.

Doctor A Doctor B

A Corrective Lenses, Glasses, Contacts. B Corrective Lenses, Glasses, Contacts.

745 643 102763 651 112

726 634 92736 625 111

769 670 99735 622 113

765 658 107759 624 135

756 636 120748 631 117

742 624 118 756 621 135

757 641 116 765 653 112

748 655 93 761 647 114

770 649 121 768 646 122

738 629 109761 646 115

Part A

Are there any noticeable outliers in either of the data sets? What does this mean about the best measures to use for center and variability?

Part B

What is the mean for Doctor A's data set on corrective lenses? What is the mean for Doctor B's data set on corrective lenses? Write a sentence comparing the number of people who wear corrective lenses in the two data sets.

Part C

What is the mean for Doctor A's data set on glasses? What is the mean for Doctor B's data set on glasses? Write a sentence comparing the number of people who wear glasses in the two data sets.

Part D

What is the mean for Doctor A's data set on contacts? What is the mean for Doctor B's data set on contacts? Write a sentence comparing the number of people who wear contacts in the two data sets.

Part E

What is the mean absolute deviation for Doctor A's data set on corrective lenses? What is the mean absolute deviation for Doctor B's data set on corrective lenses? Write a sentence comparing the variation of the two data sets using their mean absolute deviations.

Part F

What is the mean absolute deviation for Doctor A's data set on glasses? What is the mean absolute deviation for Doctor B's data set on glasses? Write a sentence comparing the variation of the two data sets using their mean absolute deviations.

Part G

What is the mean absolute deviation for Doctor A's data set on contacts? What is the mean absolute deviation for Doctor B's data set on contacts? Write a sentence comparing these two data sets using their mean absolute deviations.

Part H

In parts E, F, and G, which data sets (corrective lenses, glasses, or contacts) show the most similar variation between Doctors?

Part I

Compare the difference of the means of the two data sets found in part H as a multiple m of their variability.