Spring 2016
SOA 275: Dr. Leonard
Name___________________
Grade___________________
Practical Exam #2
(Show all work)
Descriptive Statistics: Measures of Central Tendency, Dispersion and z-Scores
The purpose of this assignment is to introduce you to some of the fundamental statistical
techniques used to describe univariate ("uni"=one; "variate"=variable) distributions.
A. Measures of Central Tendency or Central Location
1. Compute the arithmetic mean ( ) and mode (Mo) -- measures of central tendency -- for the
salary variable for the teachers using the grouped frequency distribution constructed in Practical Exam
#1.
a. Compute the
, Md, and Mo for the ungrouped data (raw scores) for the salary variable for
teachers 40 to 50 inclusive. Do not round the raw scores.
2. In 2010, the population of Bloomington, IL was 95,411 and in 2000 it was 71,311. Using
the geometric mean (GM) estimate its population in 2005.
3. Compute the harmonic mean (HM) for the scores of: 1, 3, and 5.
B. Measures of Dispersion or Variation
4. Compute the range, s, variance, Q, and sum of squares for the ungrouped data (raw scores) for
the salary variable for teachers 40 to 50 inclusive (do not round the raw scores).
NOTE: The sum of squares is one of the most conceptually important and widely used computations in statistics. Be sure
you understand its computation and interpretation and its relationship to the three-step method for computing the
standard deviation. It will be used again in Practical Exam #3.
C. Standard Scores (or z-Scores) & the Normal Curve
5. Determine the percentile ranks (from their respective z-scores using the normal curve) for
Teachers 35 and 39. Use the arithmetic mean from question 1a and s from question 4.
6. What is the area (express as a proportion and a percent) under the normal curve (NC) between:
a. +2.13 z and +1.84 z
b. -1.44z and + 1.15 z
7. Assuming a normal distribution of scores and a mean=6 and s= 4.8, what is the z-score equivalent
of a raw score of:
a. 3______
b. 6____
c. 8______
NOTE: The mode, median, arithmetic mean, geometric mean and harmonic mean are measures of central tendency while
the range, interquartile range, standard deviation and variance are measures of dispersion. Be sure to understand,
conceptually, what these measures --central tendency and dispersion – are as well as be able to compute and interpret
each specific statistical index. Also, know what a z-score or standard score is as well as how it is computed and
interpreted. These statistics are among the most commonly used ones for summarizing univariate distributions.
8. Construct a box-and whiskers plot ("boxplot") for the salary data. This graphic technique includes
plotting five descriptive statistics: (1) minimum, (2) maximum, (3) median, (4) first quartile, and (5)
third quartile along the X axis of the Cartesian coordinate system (see p. 108 of Basic Social
Statistics.) Use the data for teachers 40 to 50.
9. Complete Microcomputer Application #2 (See Appendix in website) and submit a "hard copy" (i.e.,
a printed computer copy) of the results.
Staple your work together using this sheet at the cover sheet.
--Keep this assignment after I have graded it because you will need it for
subsequent practical exams.--