FIRST QUIZ: GRADUATE
BASIC TERMS AND UNIVARIATE DISTRIBUTIONS
To instructors: Students found this test remarkably difficult. They had trouble visualizing
the problems in terms of variables, values of a variable, cases on which a variable is
defined, and frequencies. You could consider using the test as a practice test and then
discussing the results with the class (using the power points that display the answers). I
have included hints for some of the questions, but you could leave out the hints—at least
at first—and see what happens.
Warning: Some questions may ask you to provide an answer that is NOT appropriate for the
level of measurement of the variable. If so, put a BIG X in the blank.
Question 1: Petra opened a new pet shop, and, in the first week, she sold 60 dogs, 10 cats, 5
mice, 10 snakes, 25 monkeys, and 5 parakeets. She creates a data file to keep track of the
kinds of animals she sells and how many of each type she sells. (Hint: What is the variable?
On what cases is it defined? What are the values of the variable?)
1. We define a variable for which the cases are individual animals. For each animal,
the variable is TYPE OF ANIMAL. What is the level of measurement of this
variable? ____________
2. If we can make a frequency table, what is the relative frequency of monkeys?
_____________
3. What is the mode of the distribution of the variable TYPE OF ANIMAL SOLD?
___________
4. What is the modal frequency? ___________________
5. What is the mean of the distribution of TYPE OF ANIMAL SOLD? _________
6. Show the calculation:
7. What is the median of the distribution of TYPE OF ANIMAL SOLD? __________
8. What is the standard deviation of the distribution of TYPE OF ANIMAL SOLD?
________
9. Show the calculation:
10. What was the total number of animals that were sold during the week? ____________
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Question 2: Petra’s animals are priced as follows: $100 for dogs, $50 for cats, $10 for mice,
$20 for snakes, $500 for monkeys, and $20 for parakeets.
1. What was the total revenue for the week from the sale of the animals?
_______________
2. What was the mean price of animals sold during the week? (Hint: This question does
NOT ask you to repeat the information about the pricing of each species. It asks you
to obtain the mean price of the animals sold regardless of species. Every
case/animal’s price must be included in the calculation.) ______________________
3. Show the calculation:
4. What was the median price of animals sold during the week? (Hint: Think of a big
parade.)_____________________
5. Jay-Jay Diamond is a snake. Given the information we have, what can we say about
her Z-score in the price distribution? ___negative
___positive
___0
___can’t tell
6. If you think this question can be answered, what would be in the NUMERATOR
(top) of the calculation for the price Z-score for Jay-Jay Diamond? (Show the
expression with actual numbers in the formula.)__________________
Question 3: Petra asks her friends which name they think would be best for her shop: 10
say Petra’s Pet Shop, 5 say Petra’s Pet Parlour, 10 say Pet-Ec-Centric, 10 say Pet World,
and 6 say The Pet-o-phile. In a data file that is separate from the one about the animals, she
keeps track of how her friends responded to her little survey. What is the variable?
_____________ What are the values of the variable? _____________ What are the cases?
_____________
1. NAME PREFERENCE is a variable measured at the _______________ level of
measurement.
2. The results of Petra’s little survey could be displayed in (check ALL that are
appropriate):
___bar chart
___pie chart
___frequency table
___histogram
___box plot
3. What % of Petra’s respondents preferred the name “The Pet-o-phile”?
________________
4. Petra splits the name choices to make a new variable with two categories “normal
names” (Petra’s Pet Shop and Pet World) and “weird names” (Petra’s Pet Parlour,
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Pet-Ec-Centric, and The Pet-o-phile). The new variable is a ________________
variable.
5. If the “weird name choice” category is assigned the code number 1 and the “normal”
category is 0, what is the mean of the new 2-category variable?
__________________
6. What is its variance? _______________________________
Question 4: The Office of Institutional Research at Very Big U collected data on the family
income of students. Staff members have computed the mean, median, and mode of the
family income distribution, but they have not examined any other summary measures or
characteristics of the distribution.
1. The measures they computed are usually called measures of
____________________________.
2. They have failed to examine ___________________________ in the distribution.
Question 5: How do we calculate the variance (not of a proportion but of a regular intervalratio variable)? Either show the formula or list the steps in words (the algorithm). (Hint:
This is a 4-point question.)
Question 6: Look at the following data and chart, and write a paragraph about what these
data imply about the choice of mean, median, and mode.
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Source: Lucy Horwitz and Lou Ferleger, Statistics for Social Change (Boston: South End Press,
1980).
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