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An Introduction to Statistics

Homework for Statistics Lesson 7

  1. Graduating Math and Science Center students have a mean ACT score of 29. Calculate the z-score for their mean relative to the national mean of 21.0 and standard deviation of 4.7.

     

     

  2. Graduating Math and Science Center students have a mean SAT score of 1320. Calculate the z-score for their mean relative to the national mean of 1016 and standard deviation of 157. (Note: this standard deviation was derived by quadratically combining the standard deviations of the subtests—multiplying 111 by the square root of two.)

     

     

  3. Given the fact that 50% of a normally distributed data set is within 0.675 standard deviations of the mean, estimate Q1, Q3, and the interquartile range for Center Senior ACT scores, given also a mean of 29 and standard deviation of 3.0. Would an ACT score of 36 be unusual for a Center student?

     

     

  4. Calculate the 5-number summary (using your TI-84+ calculators) 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

     

  5. Calculate the z-score for the largest value in the above data set. Is it an ordinary score? Is it an outlier? Which definition works best?

     

  6. Using the data set: {0, 2, 4, 5, 6, 3, 6, 1, 1, 50}, as given in the lesson, calculate the lower and upper hinge.

     

     

  7. Using the data set: {0, 2, 4, 5, 6, 3, 6, 1, 1, 50}, as given in the lesson, calculate its 5-number summary, using the quartiles.

     

     

  8. Using the data set of the two previous problems, check if 50 is an outlier three different ways as follows.
    1. Using the hinges and D = upper hinge - lower hinge.
    2. Using the interquartile range = Q3-Q1 for D.
    3. Using the older definition of being more than 2 standard deviations from the mean.
    Show all your work.

     

  9. How low would the outlier have to be to be only 2.0 standard deviations above the mean, assuming all other numbers stayed the same?

     

  10. Round up the number e to the appropriate integer.

     

  11. Using the fifty 1999 class of 2003 Algebra Diagnostic Test scores: 140, 122, 119, 99, 92, 90, 90, 88, 85, 82, 82, 81, 80, 80, 77, 74, 74, 73, 72, 71, 70, 70, 69, 69, 69, 68, 68, 68, 67, 66, 64, 64, 62, 60, 59, 59, 58, 58, 56, 56, 56, 56, 55, 54, 53, 53, 50, 47, 35, 32, find P10, P90 and the 10–90 percentile range. Show all your work.

     

     

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