Note: Answers are indicated in bold for each question.
ROUND 1
1.
In the northern U.S., schools are sometimes closed during winter due to severe
snowstorms. At the end of the school year, schools have to make up for the days missed.
The following graph shows the frequency distribution of the number of days missed due
to snowstorms per year, using data from the past 75 years. Which of the following should
be used to describe the center of the distribution?
(a)
(b)
(c)
(d)
(e)
Mean, because it is an unbiased estimator.
Median, because the distribution is skewed.
IQR, because it excludes outliers and includes only the middle 50 percent of the
data.
First quartile, because the distribution is left skewed.
Standard deviation, because it is unaffected by outliers.
Histogram
Bad Weather
18
16
14
Count
12
10
8
6
4
2
0
2
4
6
8
Days_Missed
10
12
14
2.
The mean age of 12 of the members attending a mathematics department faculty meeting
is 37. Mr. Myers, who is 50, arrives late. What is the average of all 13 members?
(a)
37
(b)
38
(c)
39
(d)
40
(e)
41
3.
Which of the following are true statements?
I.
The standard deviation is the square root of the variance.
II.
The standard deviation is zero only when all values are the same.
III.
The standard deviation is strongly affected by outliers.
(a)
(b)
(c)
(d)
(e)
I and II
I and III
II and III
I, II, and III
None of the above gives the complete set of true responses.
ROUND 2
1.
In order to rate TV shows, phone surveys are sometimes used. Such a survey might
record several variables, some of which are listed below. Which of these variables are
categorical?
I.
The type of show being watched
II.
The number of persons watching the show
III.
The ages of persons watching the show
IV.
The name of the show being watched
V.
The number of times the show has been watched in the last month
(a)
(b)
(c)
(d)
(e)
II, III, and V
I only
I and V
I and IV
None of the above describes the complete set of correct responses
2.
A study was conducted on the weights of three different species of fish found in a lake in
Finland. These three fish (bream, perch and roach) are commercial fish. Their weights
are displayed in the boxplots below. Which of the following statements comparing these
boxplots is NOT correct?
(a)
The median weights of the three species differ.
(b)
The spread of roach is less than the spread of the other two species.
(c)
The distributions of weights are approximately symmetric for all three
species.
(d)
There are no outliers in weight for the three species.
(e)
The variability in the weights for the three species exceeds the variation in the
three species’ means.
3.
In a frequency distribution of 3000 scores, the mean is 78 and the median as 95. One
would expect this distribution to be:
(a)
skewed to the right
(b)
skewed to the left
(c)
symmetrical and mound-shaped (d)
symmetrical and uniform
(e)
bimodal
ROUND 3
The summary statistics for the number of inches of rainfall in Los Angeles for 117 years,
beginning in 1877, are shown below.
N
Median
trmean
S
x
117
14.941
13.070
14.416
6.747
Semean
min
Max
Q1
q3
.624
4.85
38.18
9.68
19.25
1.
Describe a procedure(without using specific numbers)that uses these summary
statistics to determine whether there are outliers.
An outlier is any value that is more than 1.5*IQR below the lower quartile or
1.5*IQE above the upper quartile in the data set.
2.
Are there outliers in these data? Justify your answer based on the procedure that
you described in part (a).
IQR=19.25-9.68=9.57
Q1-1.5(IQR)
Q1-1.5(IQR)
9.68-1.5(9.57)
19.25+1.5(9.57)
-4.675
33.605
There is at least one outlier on the upper end because the max value is greater than
1.5*IQR about the upper quartile.
3.
The news media reported that in a particular year, there were only 10 inches of
rainfall. Use the information provided to comment on this reported statement.
Since Q1=9.68 inches, more than 25% of the years had less than 10 inches of rain.
Thus, 10 inches of rain is not an unusual value and the new media is being
misleading in their use of the word only in their report.
ROUND 4
Hallux abducto valgus (call it HAV) is a deformation of the big toe that is not common in
youth and often requires surgery. Doctors used X-rays to measure the angle of deformity
in 38 consecutive patients under the age of 21 who came to a medical center for surgery
to correct HAV. The angle is a measure of the seriousness of the deformity. The data is
given in degrees.
A  {28,32,25,34,38,26,25,18,30,26,28,13,20,21,17,16,21,23,14,32,25,21,22,20,18,26,16,
30,30,20,50,25,26,28,31,38,32,21}
1.
Construct a dotplot or stemplot.
Angle of HAV Deformity
Key
1|3,4,6,6,7,8,8
2|3=23degrees
2|0,0,0,1,1,1,1,2,3,5,5,5,5,6,6,6,6,8,8,8
3|0,0,0,1,2,2,2,4,8,8
4|
5|0
2.
Comment on the shape, center, and spread of the distribution.(10 points)
The distribution of the angle of HAV deformity is a skew right. The appropriate
measure of center would be the median which is 25 degrees. The appropriate
measure of spread would be the five number summary which has a min of 13, Q1 of
20, M of 25, Q3 of 30, and max of 38(with 50 as an outlier) degrees.
3.
Would it be appropriate to construct a boxplot based on the given data? Why or
why not?
No, it would not be appropriate to use a boxplot to graph the given data. Boxplots
are used to compare more than one set of distributions and the given is only one set
of data. If we were given male and female HAV angles, then it would be appropriate
to use boxplots to graph the two sets of data.
ROUND 5
1.
Popular magazines rank colleges and universities on their “academic quality” in
serving undergraduate students. List five variables that you would like to see measured
for each college if you were choosing where to study. Identify each as categorical or
quantitative.
Answers vary. Some examples include student to teacher ratio(quantitative),
academic programs available(categorical), number of students who go onto
graduate programs(quantitative).
2. Mary measures the weights of five newly hatched pythons in ounces. John converts
Mary’s measurements to grams. There are 28.35 grams in an ounce. Here are Mary’s
results:
Calculate the mean and standard deviation of Mary’s measurements using the formula for
each.
1
x  1.13  1.02  1.23  1.06  1.16  1.12 grams
5
1
1.13  1.122  1.02  1.122  1.23  1.122  1.06  1.122  1.16  1.122  .0828
s
4
s=.0828grams
3.
Show how you can calculate the mean and standard deviation of John’s weights
without converting the weight of each python to grams.
x grams  28.35 x ounces  28.35(1.12)  31.752 grams
s grams  28.35sounces  28.35(.0828)  2.3474 grams

