Math 225-001, Quiz # 1 Fall 2003             September 15

Name_________________

Student #______________

 

 

 

 

  1. In the above figure would the mean SAT mathematics score be clearly smaller that the median, about the same as the median, or clearly larger than the median? Why?

(5 pts)

 

The distribution of the SAT mathematics scores are roughly symmetrical, therefore we would expect the mean to be close to the median.

 

 

 

 

 

 

  1. Immigrants in the eastern states. Here are the number of immigrants (in thousands ) who settled in each state east of the Mississippi River in 1997:

 

Alabama

1.6

Connecticut

9.5

Delaware

1.4

Florida

82.3

Georgia

12.6

Illinois

38.1

Indiana

3.9

Kentucky

1.9

Maine

1.0

Maryland

19.0

Massachusetts

17.3

Michigan

14.7

Mississippi

1.1

New Hampshire

1.5

New Jersey

41.2

New York

123.7

North Carolina

5.9

Ohio

8.2

Pennsylvania

14.6

Rhode Island

2.5

South Carolina

2.4

Tennessee

4.4

Vermont

0.6

Virginia

19.3

West Virginia

0.6

Wisconsin

3.2

 

 

 

    1. Find the mean and the median of these data with and without New York. Which measure is more changed when we omit the outlier?

(10 points)

 

Type of Data

Sample mean

median

All the data values

16.63461538

13.5th observation = 5.15

Data values without NY

12.352

13th    observation = 4.4

 

The difference between the sample means is about four units whereas the difference between the medians is less than a unit. Thus, the sample mean is more changed compared to sample median when we omit the outlier.

 

 

 

    1. Compute the Range and Standard Deviation of these data.

(5 points)

                             Range = Largest observation minus the smallest observation = 123.7 - 0.6 = 123.1.

 

                             Standard deviation s = 28.22252919.