Lab 1: Descriptive Statistics & Graphical Displays I

OBJECTIVES:    This lab is designed to introduce you to Minitab and show you how to calculate basic descriptive statistics & generate some statistical plots.

DIRECTIONS:    Follow the instructions below, answering all questions. Your answers should be in the form of a brief report (Word), to be handed in to the instructor before you leave.
__________________________________________________________________________________________________________
__________________________________________________________________________________________________________

1.)

Data Description:

In 1798, H. Cavendish set out to determine the density of the earth relative to that of water, using a torsion balance. He conducted 29 very precise experiments assessing this relative density. A working assumption to begin with is that the values of his measurements were taken from a normal distribution centered around the true relative density. The data from all 29 experiments are given below (from Stigler, S., "Do Robust Estimators Work with Real Data?", Annals of Statistics, 5, 1977).

5.50 5.55 5.57 5.42 5.30 5.34

5.61 5.36 5.53 5.79 5.47 5.75

4.88 5.29 5.62 5.10 5.63 5.68

5.07 5.58 5.29 5.27 5.34 5.85

5.26 5.65 5.44 5.39 5.46

a.)    Enter the above data in column one & name it CAVEND.

b.)    Construct a boxplot of the data.

c.)    Construct a histogram with a suitable binwidth.

d.)    Based on the two plots above, does the data seem symmetric  or skewed?  Also , comment on the modality.
Are there outliners in the data?

e.)    Guesstimate the sample mean & standard deviation from the histogram.

f.)    Calculate & record the basic summary statistics, such as the mean, standard deviation, quartiles, minimum, and maximum.

g.)    Find the proportion of the observations within plus or minus one standard deviation of the mean.
Repeat for plus or minus two standard deviations.  Compare with the "standard deviation rule of thumb" from the text.

__________________________________________________________________________________________________________
__________________________________________________________________________________________________________

2.)

b.)    Perform the same analyses (parts b. - g. above) on the second column of actual data ("Fluor2").

c.)    Apply both a logarithmic and fourth-root transformation to the cervical cancer data,
(again, just the second column) and repeat parts b.-d. from number 1.
(The 4th root transformation can be performed using the calculator feature, with the
expression:  "[column name]**0.25").

d.)    How did the transformations affect the histograms?