1
Math 165.sobieraj
Answers. Exam 1
Name
Be sure and show all work adjacent to questions
Round all answers to nearest hundredth.
1a.
12.10%
1b.
113.40
1c.
1107.9 and 1196.10
(12 points)
2a. Stream Name – categorical;
Substrate – categorical;
pH – quantitative;
Temperature – quantitative;
BCI – quantitative.
(5 points)
2b. Substrate is a categorical variable, so a pie chart or a bar chart would be a useful display.
(2 points)
3a. Mean
36.31 median
36
IQR
quartiles
Q1 24.5
Q2 50.5
3b & c.
26
range
67
(10 points)
(10 points)
80
60
40
20
0
McGwire
Ruth
(Ruth: Mean 43.93 Median 46
Q1 35
Q3 54
IQR 19 Range 38)
3d. The number of seasons is comparable…16 for McGwire and 15 for Ruth. Ruth has a higher
median and higher low number than McGwire. McGwire, however, has a higher maximum.
Ruth shows more consistency in his record….less spread.
(5 points)
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4a. There were 223 students. Of these, 113, or 50.67%, were oldest or only children.
b. There were 43 Humanities majors. Of these, 15, or 34.88%, were oldest or only
children.
c. There were 113 oldest children. Of these, 15, or 13.27%, were Humanities majors.
d. There were 223 students. Of these, 15, or 6.73%, were oldest children majoring in
Humanities.
e. Overall, 25.56% of the students were Math/Science majors, 41.70% were Agriculture
majors, 19.28% were Humanities majors, and 13.45% had other majors.
f. Of the oldest children, 30.08% of the students were Math/Science majors, 46.02%
were Agriculture majors, 13.27% were Humanities majors, and 10.62% had other
majors.
(18 points)
5a. The count of cars is 38.
(1 point)
5b. The mean displacement is higher than the median displacement, indicating a
distribution of displacements that is skewed to the right. There are likely to be several
very large engines in a group that consists of mainly smaller engines.
(4 points)
5c. 227 cubic inches is smaller than the third quartile of 231, meaning that at least 25% of
cars have a bigger engine.
(4 points)
5d. Using the Outlier Rule (more than 1.5 IQRs beyond the quartiles) to find the fences:
Upper Fence: Q3 + 1.5(IQR) = 231 + 1.5(126) = 420 cubic inches.
Lower Fence: Q1 – 1.5(IQR) = 105 – 1.5(126) = - 84 cubic inches.
Since there are certainly no engines with negative displacements, there are no low
outliers.
Q1 + Range = 105 + 275 = 380 cubic inches. This means that the maximum must be less
than 380 cubic inches. Therefore, there are no high outliers (engines over 420 cubic
inches).
(4 points)
5d. It is not reasonable to expect 68% of the car engines to measure within one standard
deviation of the mean. The distribution engine displacements is skewed to the right, so
the Normal model is not appropriate.
(4 points)
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Math 165
Exam 1a
Fall 2005
Name
9.28.05
Be sure and show all work to get maximum credit.
Include sketches as part of your work where applicable
Round all answers off to the nearest hundredth
1. Based on the model N(1152, 84), for the weights of Angus steers,
a. What percent of the steers weigh over 1250 pounds?
b. What’s the IQR of the weights?
c. What are the cutoff values for the middle 40% of the weights?
2.
3. Listed below are the home run totals for each season that Mark McGwire played through
2001.
3, 49, 32, 33, 39, 22, 42, 9, 9, 39, 52, 58, 70, 65, 32, 27
a. Find the median, mean, IQR, the quartiles, and the range.
b. Draw a boxplot for the homeruns.
Babe Ruth’s homeruns were: 54, 59, 35, 41, 46, 25, 47, 60, 54, 46, 49, 46, 41, 34, 22
c. Draw a boxplot for Ruth’s homeruns next to the one for McGwire’s (above)
d. Write a few sentences comparing the two careers.
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4.
e) What is the marginal distribution of the
majors?
f) What is the conditional distribution of majors
for the oldest children?
5.
a. How many cars were measured?
b. Why might the mean be so much larger than the median?
c. Is a 227-cubic–inch engine unusually large for this data set? Explain.
d. Are there any engines in this data set that you would consider to be outliers? Explain
e. Is it reasonable to expect that about 68% of car engines measure between 88 and 266
cu. in.?