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An Introduction to Statistics

Homework for Statistics Lesson 6

  1. Find the mean, and standard deviation for the data set below.

    ProfessionSalaryfrequency
    Teacher36,0001,000,000
    notebook assembler360,000100,000
    Netscape® programmer3,600,000100
    Windows® programmer36,000,00010
    Bill Gates360,000,0001

     

     

  2. Trim 10% of the data from both the top and bottom of the above data set and repeat the problem above.

     

  3. Apply the symmetry of IQ distribution and the empirical rule (68–95–99.7) to find the proportion of a population with an IQ between 85 and 130.

     

  4. What does Chebyshev's Theorem say about the number of IQs between 85 and 115?

     

  5. The Unibomber (Theodore Kaczynski) has been often cited with an IQ of 170. Calculute how many standard deviations above the mean this corresponds to. Round your answer to two decimal places.

     

  6. Using the mean of 54.8 and the standard deviation of 6.2, list the inauguration ages for any president beyond two standard deviations from the mean.

     

  7. What percent of the inauguration data is within two standard deviations of the mean?

     

  8. Assume the inauguration data was presented in an earlier homework in chronological order. Which ordinal (first, second, third, etc.) president do these correspond with?

     

    For one bonus point each, please supply the names of the presidents in the previous problem.

     

  9. Add five years (L1+5=>L2) to your presidential inauguration data and recompute the mean and standard deviation. How did they each change?

     

  10. Increase your original presidential inauguration data by 10% (L1×1.1=>L2) and recompute the mean and standard deviation. How did they each change?

     

  11. Add 5 years then increase your original presidential inauguration data by 10% ((L1+5)×1.1=>L2) and recompute the mean and standard deviation. How did they each change?

     

  12. Increase your original presidential inauguration data by 10% then add 5 years (L1×1.1+5=>L2) and recompute the mean and standard deviation. How did they each change?

     

  13. Use your TI-83+ calculator to find more precisely the percentage of data expected between -1.0000 and 1.0000 standard deviations from the mean. Use DISTR (2nd VARS) normalcdf(-1.0000,1.0000).

     

  14. Repeat the question above for -2.0000 and 2.0000 standard deviations.

     

  15. Repeat the question above for -3.0000 and 3.0000 standard deviations.

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