Download Discrete Math

Discrete Math
Chapter 14 Test Review
Name _________________________________
Period ______________
For questions 1 – 8, refer to the table below that shows the scores on an Economics 101 test
consisting of 10 questions worth 10 points each.
Student ID
Score
Student ID
Score
Student ID
Score
Student ID
Score
1362
1486
1721
1932
2489
2766
100
90
80
80
80
60
2877
2964
3217
3588
3780
3921
80
70
70
90
90
90
4315
4719
4951
5321
5872
6533
10
10
60
70
40
60
6921
8317
8854
8964
9158
9347
60
70
80
80
90
70
1. Complete the frequency table for the Econ 101 test.
Frequency Table for Economics 101 Test
Score
Frequency
2. Identify the score that corresponds to each data point.
X1 = __________
X3 = __________
X4 = __________
X13 = __________ X23 = __________
3. What is the size of the data set?
N = _______________
4. Find the sum of the data.
X
N
i 1
i
= _______________
5. Find the mean score, the median score, and the mode for the Econ 101 test.
µ = ___________
M = ___________
mode = ___________
6. Find the five-number summary for the Econ 101 test.
Min = ________
Q1 = ________
M = ________
Q3 = ________
Max = ________
7. Determine outlier scores for the Econ 101 test. If there are no outliers, write “None.”
____________________
8. Suppose the grading scale for the test is A: 90-100, B: 80-89, C: 70-79, D: 60-69 and F: 0-59.
a. Find the grade distribution for the exam.
Frequency Table for Grade Distribution
Grade
Frequency
b. Complete the table by (1) determining the percent of students (rounded to one decimal place) that
earned each grade on the Econ 101 test and (2) calculating the size of the central angle (rounded to
the nearest whole degree) of each grade’s wedge in a pie chart. Then make a pie chart showing the
grade distribution for the exam.
Grade
Percent of Students
Central Angle
A
B
C
D
F
c. Make a bar graph showing the relative frequencies of the grades on the test. Be sure to label the
axes.
28
24
20
Frequency
16
12
8
4
0
47
49
51
53
55
57
59
61
63
Speed (mph)
9. To determine an appropriate speed limit for a roadway, traffic engineers conduct radar checks of
the speeds of passing cars at a selected location and under ideal driving conditions. They then
conduct a statistical analysis of the data to determine the safest speed limit to post on the roadway.
The histogram above summarizes the data collected on the speed of cars on a roadway.
Endpoint convention: Speeds on the boundary of an interval belong in the interval to the right. For
example, a speed of 49 mph belongs in the second interval (49-51).
a. How many cars were included in this survey? ____________________
b. What is the size of each interval? ____________________
c. How many cars were clocked at 55 mph or more? ____________________
d. Which interval contains the median speed? ____________________
Traffic studies suggest that posting a speed limit at the 85th percentile speed increases compliance
among drivers and minimizes traffic accidents and traffic jams.
e. What interval contains the 85th percentile speed? ____________________
f. What speed limit would you recommend for this roadway? ____________________
g. Estimate the average (mean) speed of cars surveyed in this study?
10. The table below shows the closing stock prices (in $) on the New York Stock Exchange (NYSE)
for the last seven months for General Motors (GM) and Ford.
Month
Ford
GM
OCT
11.16
25.50
Closing Stock Price ($) on the NYSE
NOV
DEC
JAN
FEB
11.45
12.95
12.95
12.61
25.88
28.83
28.09
27.15
MAR
13.15
27.82
APR
13.12
28.37
a. Find the mean stock price x and the standard deviation s for each auto company (Round all
figures to two decimal places).
Ford Stock
Deviation
Deviation Squared
xi
xi  x
( xi  x ) 2
x = ____________
n
s2 
(x
i 1
 x)2
i
n 1
n
n
 (x
i 1
i
 x) 
s
n
 (x
i 1
 (x
i 1
GM Stock
Deviation
Deviation Squared
xi
xi  x
( xi  x ) 2
 x)2
i
n 1
 x)2 
i
s2 
(x
i 1
 x)2
i
n 1
n
s
 (x
i 1
i
 x) 
n
 (x
i 1
i
 x)2 
= ____________
x = ____________
n
n
= ____________
 (x
i 1
i
= ____________
 x)2
n 1
= ____________
b. Which stock (Ford of GM) appears to have the greater risk. Explain your answer.
c. Determine the outlier prices for Ford stock. If there are no outliers, write “None.”
__________________________
d. Determine the outlier prices for GM stock. If there are no outliers, write “None.”
__________________________