Spring 2016
Name___________________
SOA 275: Dr. Leonard
Grade___________________
Practical Exam #1
(Show all Work)
Descriptive Statistics: Frequency Distributions and their Graphic Representation
The purposes of this assignment are to introduce you to some of the fundamental statistical
procedures and techniques used to assemble and describe univariate ("uni"=one; "variate"=variable)
distributions and to compute and interpret various statistical indices.
A. Constructing a Grouped Frequency Distribution
1. Construct a grouped frequency distribution (following the conventions discussed in the text and
outlined in class) for the 50 teachers (data are found in microcomputer assignment #1) for the
variable salary. Make each class interval three units wide, beginning with (see below):
Then, on a separate sheet, fill in the information requested below:
Class Interval
etc.
.
.
.
24-26
21-23
18-20
f
F
%*
Cum%*
Midpoint
*Round to two decimal places, i.e., go out three places beyond the decimal point and round back to
two.
NOTE: Be sure you understand the engineer's rule (see Appendix B in Basic Social Statistics).
B. Graphic Representations of a Frequency Distribution
2. Construct three graphs -- (1) frequency polygon, (2) percentage histogram, and (3) stemplot-- to
pictorially represent this data distribution. Properly label with X (abscissa) and Y (ordinate) axes of
the Cartesian coordinate system. Use graph paper and employ the 3/4 high rule discussed in your
text (Ch. 3). Salary is an interval/ratio level of measurement variable; hence these graphic
representations are appropriate.
NOTE: The purpose of graph construction is to facilitate and simplify your understanding of the data beyond that conveyed
by the frequency and percentage distributions by creating a picture of the data.
a. Identify the four statistical properties – (1) central tendency, (2) dispersion (variation),
(3)skewness, and (4) kurtosis – of the frequency polygon for the salary variable. What do the graphs
enable you to infer about the distribution of the teachers' salaries? Don't write the answer out but
give the question some thought since the exam will contain questions requiring you to draw some
conclusions and interpretations from graphic representations of data.
NOTE: Be sure to use and understand the 3/4 high rule.
C. Computing Various Statistical Indices
3. Compute the percentile ranks for Teachers 28 and 41. Use the raw scores; do not round.
NOTE: Be sure you know how to interpret a percentile.
4. The percentage of all women 16 and over who were working in 1965, 1980, 1985, 1990, 1995,
2005 and 2010 was:
1965
1980
1985
1990
1995
2005
2010
36.7
51.1
54.7
59.8
63.8
69.2
74.2
Compute the percentage change (PC) in women working between 1980 and 1990.
5. In 2014 there were about 2,152,000 marriages in the United States and 1,116,000
divorces. Using a numerical base of 1000, compute the divorce rate (DR) for 2014.
6. In Fall, 2014, there were about 8,345 ISU males and 11,218 females. Compute the sex ratio (SR)
for 2014 using a numerical base of 100.
7. Assuming there are 7.30 billion people in the world in 2015 and a probability sample of
322,000,000 was selected, what would be the sampling fraction (SF)? Express as a proportion (p)
and as a percent (P).
NOTE: Be sure to understand the interpretation of percentile rank, percentage change, and divorce rate, sex ratio,
numerical base and sampling fraction.
8. Over the years more than one student has asked me, "How is statistics relevant to my area(s) of
concentration?" How do data, numbers, graphs, tables, charts and formulae apply to the real
world? These are good questions! THEREFORE, submit two illustrations/examples of the use of
statistics in your area(s) of interest. These may be photocopied tables, charts, figures, and/or graphs
from textbooks or research articles.
9. Complete Microcomputer Application #1 (See Appendix in website) and submit a "hard copy" (i.e.,
a printed computer copy) of the data file created.
Staple your work together using this sheet as the cover sheet.
--Keep this assignment after I have graded it because you will need
it for
subsequent practical exams.--