Question 3.94

statebusinesses

94. Trimmed Mean. Because the mean is sensitive to extreme values, the trimmed mean was developed as another measure of center. To find the 10% trimmed mean for a data set, omit the largest 10% of the data values and the smallest 10% of the data values, and calculate the mean of the remaining values. Because the most extreme values are omitted, the trimmed mean is less sensitive, or more robust (resistant), than the mean as a measure of center. For the data in the table, calculate the following:

  1. The mean
  2. The 10% trimmed mean
  3. The 20% trimmed mean

The data represent the number of business establishments in a sample of states.

State Businesses
(1000s)
State Businesses
(1000s)
Alabama 3.8 Michigan 7.5
Arizona 7.9 Minnesota 6.1
Colorado 8.9 Missouri 5.9
Connecticut 3.1 Ohio 9.5
Georgia 10.3 Oklahoma 3.8
Illinois 11.9 Oregon 5.4
Indiana 5.6 South Carolina 4.6
Iowa 2.7 Tennessee 5.4
Maryland 5.7 Virginia 8.6
Massachusetts 6.3 Washington 9.3
Table 3.34: Source: U.S. Census Bureau.