AP Statistics

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					AIG                                                       Name: __________________________
Describing Distributions Homework                         Date: __________      Period: ____
1) Create a set of five positive numbers (repeats allowed) that have a median of 10 and a mean
   of 7. Explain your thought process in complete sentences.

2) The table below gives the distribution of grades earned by students taking the AP Calculus A
   and AP Statistics exams in 2005.

   A. Make a graphical display to compare the exam grades for Calculus AB and Statistics.

   B. Write a few sentences comparing the two distributions of exam grades. Do you now
      know which exam is easier? Why or why not?

3) Which measure of center, the mean or the median, should you use in each of the following
   A. Middletown is considering imposing an income tax on citizens. The city governor wants
      to know the average income of citizens so that it can estimate the total tax base.

   B. In a study of the standard of living of typical families in Middletown, a sociologist
      estimates the average income in that city.
AIG                                                          Describing Distributions Homework

4) Suppose a Major League Baseball team’s mean yearly salary for a player is $1.2 million, and
   that the team has 25 players on its active roster.
   A. What is the team’s annual payroll for players? (How much does the team pay out all

   B. If you only knew the median salary, would you be able to answer the question? Why or
      why not?

5) Last year a small accounting firm paid each of its five clerks $22,000, two junior accountants
   $50,000 each, and the firm’s owner $270,000.
   A. What is the mean salary paid at this firm?

   B. How many of the employees earn less than the mean?

   C. What is the median salary?

   D. Write a sentence to describe how an unethical recruiter could use statistics to mislead
      prospective employees.

6) The distribution of household incomes in the United States is strongly skewed to the right. In
   2003, the mean and median household incomes in America were $43,318 and $59,067.
   Which of these numbers is the mean and which is the median? Explain your reasoning.

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