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Dr. David Pillow
Name:
Practice Problem Set #1
1. A characteristic that describes a sample is called a
a. parameter
b. statistic
c. discrete variable
d. nominal variable
2. Describe the differences between descriptive statistics and inferential statistics.
3. The formula
a.
b.
c.
d.
e.
SS
--n-1
is refered to as
the sample variance
the sample standard deviation
the popluation variance
the population standard deviation
the degrees of freedom
4. When all the people from the population have an equal likelihood of being included
in the study's sample, the experimenter has fulfilled the requirements for
a. internal validity
b. external validity
c. random assignment
d. random sampling
5. How would the following mathematical operation be expressed in summation
notation? "Square each score, sum those scores, and then subtract the population
mean from this resultant value."
a. ΣX - μ2
b. (ΣX - μ)2
c. Σ(X - μ)2
d. (ΣX2) - μ
6. In a negatively skewed distribution of exam scores, Tom scored at he mean, Mary
scored at the median, ad Jane scored at the mode. Who most likely had the highest
score?
a. Tom
b. Mary
c. Jane
d. cannot be determined from the information given
7. Which measure would provide the best desciption of central tendency for the
followng set of scores: 0, 30, 31, 33, 33, 34, 35, 37, 38.
a. the mean
c. the mode
b. the median
d. all three are equally good
8. A positively skewed distribution has a mean of 80. If 10 points are added to each
individual score, the new mean woulod be
a. 80
b. 90
c. 80 + 10/N
d. cannot be determined from the information given
9. A population has μ = 50 and σ = 10. If each score is multiplied by 2, the new
standard deviation will be:
a. 5
b. 10
c. 20
d. insufficient information, cannot be determined.
Match the following:
10.
11.
12.
13.
Characteristic
Best to worst football teams
Temperature
Felony record? Yes or NO
Age
Scale of Measurement
a. nominal
b. ordinal
c. interval
d. ratio
14. List and describe the four primary ways of describing a distribution of numbers.
15. What are the valid rules of summation? List them.
A recent report concludes that subjects given a diet including oat bran had lower
cholesterol levels than subjects on a similar diet without oat bran.
16. For this study the independent variable is?
a. the subjects
b. cholesterol levels
c. the type of diet
d. the group given a diet including oat bran
17. The dependent variable for the the study described above would be treated by
statisticians as a
a. dichotomous variable
b. categorical variable
c. continuous variable
18.
is the formula for
a.
b.
c.
d.
e.
sample standard deviation
population standard deviation
sample variance
population variance
none of the above, the formula is incorrect
19. The correct symbol for the sample variance is
a.
b.
c.
d.
s
s2
σ
σ2
20. When is it appropriate to use the semi-quartile range rather than the standard
deviation?
21. Frequency distribution polygons are intended for use with
a. either interval or ratio scales of measurement
b. only ratio scales
c. either nominal or ordinal scales
d. only nominal scales
PART TWO OF EXAM 1: Answer in space provided and show work.
1. Complete the following table (5 pts):
Cumulative
Cumulative
Interval
Frequency Frequency Proportion Percent Percentage
17-20
5
13-16
8
9-12
9
5-8
12
1-4
16
(a) Compute N. What does N equal? (1 pt):
(b) What is the score at the 32nd percentile? (2 pt)
(c) What is the score at the 50th percentile? (show work)
(4 pts)
(d) What is the percentile rank for a score of 8.5? (2 pt)
(e) What is the percentile rank for a score of 18? (3 pts)
(show work)
2. What is the formula for the mean of a sample of scores? (3)
3. (a) What is the definitional formula for a sample variance? (3 pts)
(b) Compute the sample variance for the following set of scores using the definitional
formula: 0, 8, 3, 9. (show work) (3 pts)
(c) What is the sum of squares (SS) from 3b? (2 pt)
(d) What are the degrees of freedom from 3b? (2 pt)
4. Calculate the mean, median, and mode for the following sets of scores. Show your
work for the mean and median. (5 pts)
Xi: 7, 5, 10, 8, 10, 16, 20, 21, 40
5. Calculate the median and modes of the following data sets. Show your work.
(a) Xi: 1, 4, 6, 17
(b) Xi: 15, 15, 15, 17, 17
6. Assume you have measured the percentage of individuals in three suburbs of a
major city who endorse a particular bond issue. Make a graph of the results. Be sure
to properly label your axes. (5 pts)
Western suburbs
Southern suburbs
Eastern suburbs
25%
20%
10%
7. Make a stem-and-leaf display for the following data. Use an interval width of 10.
Xi: 30, 23, 58, 28, 35, 67, 27, 42, 46, 35, 51, 33, 18, 33, 25,
38, 48, 36, 31, 39,
8. For added practice, construct a grouped frequency histogram for the above
distribution of data.
9. For the set of scores above, find the following.
(a) (2 pt) Find the range using the raw scores:
(b) (2 pt) Using your calculator, find ΣX: _________
(c) (2 pt) Using your calculator, find ΣX2: _________
(d) (2 pt) Find the mean:
(e) (2 pt) Find the sample std deviation using the computational formula:
Formulae to memorize
Mean
Median
Mode
Range
Semi-interquartile range
Variance (definitional!, but also computational)
Standard deviation (definitional!, but also computational).