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# Measures of Central Tendency

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(1.) Using a random sample from 2002 general Social Survey, you find the following grouped distribution

Age Category Frequency
18-29 54
30-39 54
40-49 60
50-59 36
60-69 31
70-89 27

a- Calculate the median age category.

b- Also, report which age contains the 20th and 80th percentile.

(2.) Aids is a serious health problem for this country. Data from the Centers Disease Control and Prevention for 2002 and 2003 show the number of AIDS cases in various metropolitan statistical areas (MSAs) the top 10 MSA are listed

Statistical area 02 03

New York 5,649 5,580
Miami 1,139 1,072
Newark 569 534
Washington 1,832 1,743
Baltimore 1,257 1,028
Chicago 1,849 1,527
Los Angeles 1,549 2,558
Boston 721 664
Fort Lauderdale 750 690

Source: Data adapted from centers for Disease Control and Prevention, HIV/AIDS Surveillance Report

a. Calculate the mean number of AIDS cases in the Urban areas for both 2002 and 2003. How would you characterize the difference in the number of AIDS cases between 2002 & 2003?

Does the mean adequately represent the central tendency of the distribution of AIDS cases in each year? why or why not?

b. Recalculate the mean for each year after removing the New York MSA. Is the mean now a better representation of central tendency for the remaining MSAs? explain?

(3.) Exercise 3 used ISSP date on the number of hours worked per week for a sample of 75 Japanese adults

a. Calculate the mean for worked hours worked per week.

b.Compare the value of the mean with those you have already calculated for the median. Without constructing a histogram, describe whether and how the distribution of hours worked per week skewed.

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#### Solution Preview

1. Using a random sample from 2002 general Social Survey, you find the following grouped distribution

Age Category Frequency
18-29 54
30-39 54
40-49 60
50-59 36
60-69 31
70-89 27

a- Calculate the median age category.

There are 262 total people in the sample. The median age will be the age of the 131st person (when they are listed in order of age). This person will be in the 40-49 age group.

b- Also, report which age contains the 20th and 80th percentile. Metropolitan Statistical Area.

The age at the 20th percentile (20% of the way up the list) will be the age of the 52nd person. That person will be in the 18-29 age group.

The age at the 80th percentile will be the age of the age of the 209th person. That person will be in the 60-69 age group.