Download first quiz: undergraduate

FIRST QUIZ: UNDERGRADUATE
BASIC TERMS AND UNIVARIATE DISTRIBUTIONS
To the instructor: This test proved very difficult for many students. They became
confused about variables and frequencies. Doing well on this test requires thinking about
variables, cases on which a variable is defined, values of the variable, and frequencies for
the values. You may want to use this test as a practice test, discuss the answers (using the
power points with answers), and then make up a similar test for the students’ “real” test.
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 50 dogs, 40 cats,
10 mice, 10 snakes, 5 gerbils, and 5 parakeets. She decides to keep track of the type of
animals she sold, and, for each type of animal, she records the quantities sold. Helpful hint:
What is the variable? What are the values of this variable? On what cases is this variable
defined?
1. What is the level of measurement of the variable TYPE OF ANIMAL SOLD?
____________
2. If we can make a frequency table, what is the relative frequency of snakes?
_____________
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,
$12 for snakes, $8 for gerbils, 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: Every case/animal’s
price must be included in the calculation. This question asks you about the mean price of
an animal REGARDLESS of which type of animal it is.) ______________________
3. Show the calculation:
4. What was the median price of animals sold during the week? (Hint: Think about a big
parade of animals.) _____________________
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, 6 say Pet-o-rama, and 4 say The Pet-ophile. She creates a new data file for her little survey that is separate from the data file
about types of animals. In this new file, she records how many of her friends picked each
name that was proposed. For this survey, answer these questions: What is the variable?
__________________________________ What are the values? ______________________
What are 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-o-rama) and “weird names” (Petra’s Pet Parlour and
The Pet-o-phile). The new variable is a ________________ variable.
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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 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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