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MAT 312
Test #1
Name _______________
50 points
Calculator Used _______________
Impact on Course Grade: approximately 10%
Score _______________
Part I: Multiple Choice: For questions (1) through (25), choose the one best response and circle
the letter of that response on the response sheet.
1. Which visual representation preserves the values in a data set?
A) circle graph
B) dot plot
C) ogive plot
D) relative frequency histogram
E) More than one of the representations (A) through (D) preserve the values in a data set.
F) None of these representations (A) through (D) preserve the values in a data set.
For items 2-5, select one of the following data types to best describe each variable.
A) nominal data
2. weight in kg
A
B
C
B) ordinal data
3. eye color
D
A
B
C) interval data
4. family birth order
C
D
A
B
For questions 6-9, use the following data set: 2, 4, 5, 7, 12, 12
6. Determine the range of the data.
A) 2
B) 8
C) 10
D) 12
7. Determine the median of the data.
A) 6
B) 7
C) 8
D) 9
C
D
D) ratio data
5. air temperature in Fº
A
B
C
D
8. Determine the midspread of the data.
A) 4
B) 6
C) 8
D) 10
9. Determine the mean absolute deviation of the data.
A) 3
B) 3.33
C) 9.38
D) 12
10. Consider the following data set: 13, 18, 28, 28, 31, 26, 35, 19. Which measure of central
tendency will change the most if the "19" should have been a "49"?
A) mean
B) median
C) mode
11. What are the three fundamental characteristics of a 1-variable data set?
A) shape, direction, strength
B) spread, location, direction
C) spread, shape, location
D) strength, shape, spread
Use the diagram below for questions 12 through 15.
12. In the box plot, where is the 25th percentile located?
A) at 5
B) at 10
C) at 14
D) at 20
D) somewhere between -4 and 5
13. Which quartile in the data set exhibits the most spread?
A) the lowest quartile
B) the 25th to 50th percentile
C) the 50th to 75th percentile
D) the highest quartile
14. What value in the data set is the smallest value inside the lower inner fence?
A) -4
B) 5
C) 14
D) 28
E) More than one of the values (A) through (D) satisfies the conditions stated.
F) None of these values (A) through (D) satisfy the conditions stated.
15. Although not shown in the plot, which of the following values would be considered an outlier in
this data set?
A) -5
B) 6
C) 17
D) 25
E) More than one of these values would be an outlier.
F) None of these values would be outliers.
16. In which situation is it appropriate to use the mode as the preferred measure of central
tendency?
A) in determining what size shirts to reorder in a retail establishment
B) in reporting average selling price for homes in a suburban community
C) when the data has a bimodal distribution
D) when the distribution is significantly skewed to the left or to the right
17. The student council at Bradbury HS wants to survey students at the school to determine the
flavors of fruit juices they want in the school’s drink machines. The council randomly samples
30 freshmen, 30 sophomores, 30 juniors, and 30 seniors. What is the type of sampling used by the
council?
A) cluster sampling
B) convenience sampling
C) simple random sampling
D) stratified random sampling
E) systematic random sampling
18. The distribution of the life span of a certain South African fruit fly has a symmetric, moundshaped (normal) distribution with a mean of 400 hours and a standard deviation of 25 hours. Within
what bounds do we expect approximately 95% of the life spans to fall?
A) 350 to 425 hours
B) 350 to 450 hours
C) 375 to 425 hours
D) 375 to 450 hours
For questions 19-21, use this setting:
A light bulb manufacturer wants to show that a new bulb outlasts a major competitor's light bulb.
The manufacturer tests 30 bulbs and records how long each bulb lasts. The data are shown here.
19. Of the 30 light bulbs sampled, what is the relative frequency of light bulbs lasting longer than
400 hours?
A) 6
B) 20%
C) 24
D) 80%
20. What value represents the 25th percentile of the observations?
A) 420 hrs
B) 480 hrs
C) 490 hrs
D) 500 hrs
21. What is the midspread of the light bulb data?
A) 150 hours
B) 480 hours
C) 510 hours
D) 630 hours
E) The midspread is impossible to determine here.
22. The 5-number summary for a 1-variable data set is {5,18,20,40,75}. If you were to construct a
modified box plot for the data set (that is, a plot that would show Tukey’s outliers, if there were
any) what would be the maximum possible length of the right side “whisker?”
A) 5
B) 33
C) 35
D) 53
E) 55
23. Which of the following orders correctly represents the measures of central tendency for the
distribution shown here?
A) A: mean, B: median, C: mode
B) A: mean, B: mode, C: median
C) A: median, B: mean, C: mode
D) A: median, B: mode, C: mean
E) A: mode, B: mean, C: median
F) None of these orders is correct.
Use this information for questions 24 and 25:
The consumption of caffeine has become an increasingly important concern to consumers, because research has suggested that caffeine may be associated with birth defects, cancer, cardiovascular disease, and other health problems. Federal FDA scientists have conducted studies to assess the possible association between caffeine and these various health problems. Although many results have been inconclusive with regard to implicating caffeine as a cause for such health problems, the consumption of caffeine in moderation seems to be important (FDA Consumer, Dec 1987/Jan 1988). One FDA study found that the distribution of the amount of caffeine in a 12-­‐ounce can of a specific brand and variety of cola (Coke Classic) had a mound-­‐shaped (normal) distribution with a mean of 19 milligrams (mg) and a standard deviation of 2 mg. 24. Based on this study, where can you expect about 95% of the caffeine measurements for 12ounce cans of Coke Classic to fall?
A) between 17 and 21 mg
B) between 15 and 23 mg
C) between 13 and 25 mg
D) at least 19 mg
25. Suppose that one 12-ounce can of cola—with its brand identification masked—is randomly
selected from a super-market shelf where there are many varieties of cola. The cola in this can is
determined to have a caffeine content of 26 mg. What would you conclude about the brand of this
randomly selected can of cola, and why?
A) It is impossible for it to be a can of Coke Classic, because 26 mg of caffeine was never found in
the experimental study.
B) It is very unlikely to be a can of Coke Classic, because 26 mg falls outside the expected range of
caffeine measurements for Coke Classic.
C) It could be a can of Coke Classic, because 26 mg is only 7 mg more than the mean of 19 mg.
D) It may or may not be Coke Classic. Although 26 mg seems like a lot, the next can of cola will
probably have less caffeine.
Part II: Open Response
Answer each question and write your response in the space provided. Please include descriptive
comments where requested.
26. At the bottom of the page is a relative frequency histogram that shows points earned by 200
students in physical education classes at an elementary school. Use the histogram to answer
questions (A) through (E) below.
A) What range of points was earned by the top 5% of the students?
_________________
B) Suppose a child was chosen at random from the top 50% of those earning points. What is the
minimum number of points that student could have earned?
_________________
C) How many students earned less than 5 points?
_________________
D) In what measurement class does the 25th percentile lie?
_________________
E) Suppose this histogram was used to create a cumulative frequency histogram. What would be the
height (cumulative frequency) for the measurement class spanning 11 to 13 points?
_________________
27. A data set of flange lengths has a midspread of 12 cm and a median of 50 cm. State a flange
length that will lie between the lower inner fence and the lower outer fence if we know that the
median divides the middle 50% of the data symmetrically. Describe the process you used to
determine a value.
28. We have considered the properties of spread and location to help characterize a 1-variable data
set. Describe how these two properties differ. Be specific!
29. Male and female heights (in cm) are given for two high school basketball teams.
Male
Female
A)
169
163
170
168
170
172
173
173
174
175
175
175
178
178
180
180
183
180
185
183
185
187
191
188
195
Construct parallel box-and-whisker plots of the data. Be sure to clearly label each plot.
160 cm
170 cm
180 cm
190 cm
Male and Female Heights (cm): Two High School Basketball Teams B)
Construct back-to-back stem-and-leaf plots of the data. Be sure to clearly label each part of
your plot.
C)
Compare the distribution of heights of male and female basketball players. Be precise and
specific.
D)
What information is more readily available to you using the box-and-whisker plot that is
not with the stem-and-leaf plot? Be precise and specific.
E)
What information is more readily available to you using the stem-and-leaf plot that is not
with the box-and-whisker plot? Be precise and specific.
Scoring
Part I: 25 Multiple Choice Questions (1 pt each)
Part II: 4 Open-Response Questions (5,5,5,10 pts)
Total: 50 points
Impact on Course Grade: approximately 10% of your Semester Grade
Criteria Used to Evaluate Part II Responses
26: 5 points (1 pt each: correct response)
27: 5 points
• 2 pts for a numerical value
• 3 pts for description of the process
28: 5 points for clear, accurate, and specific description
29: 10 points
A) 2 pts (accuracy)
B) 2 pts (accuracy)
C) 2 pts (clear, accurate, and specific description)
D) 2 pts (accurate and specific information)
E) 2 pts (accurate and specific information)
Name
___________________________________________________________
Response Form: Multiple Choice Questions
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Response Choices: Circle one
best response for each question.
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