Math 6 Homework #1

Due on Friday, September 10

1.  Caution is necessary when constructing histograms from frequency distributions given in magazines, newspapers, journal articles, etc.  The authors of "Self-Reports of Academic Performance," an article which appeared in Soc. Methods and Research (1981), studied the difference in GPA, reported - actual, for each of the students in a sample.  Specify the height of each bar in a correct histogram for the frequency distribution below and sketch the histogram.

  Frequency distribution for errors in reported GPA
Class Interval Relative Frequency Height
[-2.0, -0.4)   .023
[-0.4, -0.2)   .055
[-0.2, -0.1)   .097
[-0.1,  0.0)  .210
[ 0.0,  0.1)   .189
[ 0.1,  0.2)   .139
[ 0.2,  0.4)   .116
[ 0.4,  2.0)   .171

2.  String Activity

a.  Display the guesses for the lengths of the strings graphically and describe the plots.
b.

2. The 1997 salaries for all players in Major League Baseball have been entered into a Minitab worksheet. (p:\data\math\stats\MLB97sal.MTW) Open this worksheet and perform the following tasks for the salary data:

a. Construct appropriate graphical displays of the data;

b. Describe the shape of the distribution with regard to symmetry, skewness, clusters and gaps, and outliers;

c. Calculate appropriate numerical measures of center and compare them;

d. Calculate appropriate numerical measures of variability and compare them.
 

2. Have one member of your lab group pick 12 numbers from the whole numbers 0 to 12, with repeats allowed. (i.e., you may pick each number more than once.) Enter these 12 numbers into column C1 in a MINITAB worksheet. Now have the other member of the lab group pick 12 numbers and enter them into C2.

a. Compute the following descriptive statistics for the first set of numbers by hand and then check your answers using MINITAB commands.

Measures of Center (Mean and Median)

Measures of Spread (Standard Deviation and Interquartile Range)

b. Use MINITAB to compute the same descriptive statistics for the second set of numbers. (You do not need to do the calculations by hand if you understand how MINITAB computes each of the statistics.) Compare the descriptive statistics for the two sets of numbers.

c. Subtract 6 from each of the numbers in C1. The easiest way to do this is to use CALC > Calculator to create the new variable C3 = C1 - 6. Describe what happens to each of the descriptive statistics. Do the results make sense to you? If so, explain why. If not, explain why not.

d. Multiply each of the numbers in C2 by 4. The easiest way to do this is to use CALC > Calculator to create the new variable C4 = C2*4. Describe what happens to each of the descriptive statistics. Do the results make sense to you? If so, explain why. If not, explain why not.

e. Construct boxplots using the data in C3 and C4. Explain how each member of the five-number summary is represented on the boxplot. Are the distributions similar?

f. Change the smallest value in C1 to -50. What happens to the two measures of center? What does this tell you about the two measures of center?

For the remaining two parts you will again be asked to consider picking 12 numbers from the whole numbers 1 to 12, with repeats allowed.

g. Pick 12 numbers that have the smallest possible standard deviation. Can you find another set of 12 numbers with this same value of s?

h. Pick 12 numbers that have the largest possible standard deviation. Can you find another set of 12 numbers with this same value of s?
 

3. Section 1.2 Exercises

42, 44, 53, 54, 62, 65, 66