Measures of Central Tendency

1. A teacher analyzes his students test scores and finds that they have a mean score of 80 and a median score of 90.  He wonders how the mean score can be a B- while the median score is an A-.  What could explain the discrepancy in mean and median?

  1. Several students got a perfect score on the test.
  2. More students got Bs than As on the exam.
  3. A few students must have gotten very low scores on the exam.
  4. No students actually scored a 90 on the exam.
College Textbook Prices, by Subject
EnglishMathematicsBiologyAnatomyEngineeringAccountingPhilosophySociology
\$7.99\$35.99\$67.99\$99.00\$155.00\$78.99\$54.87\$45.00
\$15.99\$67.88\$70.00\$135.99\$12.99\$67.88\$32.88\$32.99
 
2. The table of values above shows the price of college textbooks by subject. The \$12.99 prices is a typo.  It should be $122.99.  If the error is corrected, which of the following measures of the data will not change?
 
  1. The mean and the range.
  2. The mode and the range.
  3. The median and the mode.
  4. The mean and the median.
College Textbook Prices, by Subject
EnglishMathematicsBiologyAnatomyEngineeringAccountingPhilosophySociology
\$7.99\$35.99\$67.99\$99.00\$155.00\$78.99\$54.87\$45.00
\$15.99\$67.88\$70.00\$135.99\$122.99\$67.88\$32.88\$32.99

3. The table above represents the books that a particular student needed to buy for the semester.  If that student decided to drop her Anatomy classes this semester, how would taking those books out of the student's cart change a measure of the student's textbook cost?

  1. The mean would increase.
  2. The mode would decrease.
  3. The mode would increase.
  4. The median would decrease

 

College Textbook Prices, by Subject
EnglishMathematicsBiologyAnatomyEngineeringAccountingPhilosophySociology
\$7.99\$35.99\$67.99\$99.00\$155.00\$78.99\$54.87\$45.00
\$15.99\$67.88\$70.00\$135.99\$122.99\$67.88\$32.88\$32.99

4. The table above represents the books that a particular student needed to buy for the semester.  If that student decided to drop her Accounting classes this semester, how would taking those books out of the student's cart change a measure of the student's textbook cost?

  1. The median would increase.
  2. There would no longer be a mode.
  3. The mode would increase.
  4. There would no longer be a median.

 

5. A student is trying to do research on careers. He finds that the median income for lawyers in the US is \$144,300 a year.  The mean income for lawyers in the US is $130,490. Which of the following might explain the difference between these two numbers?

  1. A small number of very extremely highly paid lawyers.
  2. A small number of extremely lowly paid lawyers.
  3. A very large number of highly paid laywers.
  4. A very small range in lawyer pay in the United States.

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