San Diego State University Algebra Worksheet

Math | Graded Assignment | Unit Test, Part 2 | Univariate DataName:
Date:
Graded Assignment
Unit Test, Part 2: Univariate Data
Answer the questions below. When you are finished, submit this test to your teacher for full credit.
Total score: ____ of 15 points
(Score for Question 1: ___ of 4 points)
1.
Ling wants to determine the average distance she travels each day in her car. She records the odometer
reading, which measures the cumulative distance the car has traveled, each morning for a week.
Day
Odometer (mi)
1
2
3
4
5
6
7
10,150
10,211
10,424
10,769
10,884
11,155
11,477
What is the mean distance Ling travels each day? Show your work.
Answer:
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Math | Graded Assignment | Unit Test, Part 2 | Univariate Data
(Score for Question 2: ___ of 7 points)
2. The data in the table represent the training times (in seconds) for Adam and Miguel.
Adam
103
105
104
106
100
98
92
91
97
101
Miguel
88
86
89
93
105
85
92
96
97
94
(a) All of the training times of which person had the greatest spread? Explain how you know.
(b) The middle 50% of the training times of which person had the least spread? Explain how you know.
(c) What do the answers to Parts 2(a) and 2(b) tell you about Adam’s and Miguel’s training times?
Answer:
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Math | Graded Assignment | Unit Test, Part 2 | Univariate Data
(Score for Question 3: ___ of 4 points)
3.
The data modeled by the box plots represent the battery life of two different brands of batteries that Mary
tested.
(a) What is the median value of each data set?
(b) Compare the median values of the data sets. What does this comparison tell you in terms of the
situation the data represent?
Answer:
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Math | Graded Assignment | Unit Test, Part 2 | Bivariate Data
Name:
Date:
Graded Assignment
Unit Test, Part 2: Bivariate Data
Answer the questions below. When you are finished, submit this test to your teacher for full credit.
Total score: ____ of 15 points
(Score for Question 1: ___ of 5 points)
1.
The table shows the minimum wage rates for the United States during different years.
Year
1978
1979
1980
1990
1991
1996
1997
2007
2008
2009
Minimum hourly wage ($)
2.65
2.90
3.35
3.80
4.25
4.75
5.15
5.85
6.55
7.25
(a) Write the least squares regression equation that models the data. Let x = time in years since
1900 and let y = minimum hourly wage.
(b) Use the equation to estimate the minimum hourly wage of a U.S. worker in 2025. Show your
work.
Answer:
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Math | Graded Assignment | Unit Test, Part 2 | Bivariate Data
(Score for Question 2: ___ of 5 points)
2. The table shows the soil density of several soil samples at different depths.
Depth (m)
Soil density (
mg/cm3 )
1
5
6
8
10
12
14
21
23
24
28
1045
1063
1102
1140
1191
1232
1249
1254
1265
1268
1273
(a) Write the quadratic regression equation that models the data. Let x = depth below the surface
and let y = soil density.
(b) Use the equation to estimate the soil density of a sample at a depth of 20 m. Show your work.
Answer:
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Math | Graded Assignment | Unit Test, Part 2 | Bivariate Data
(Score for Question 3: ___ of 5 points)
3. Jackson relies on his customers to tell their friends about his business. His business grows as each customer
continues to tell others about his or her experience and they in turn tell others as well.
The table shows the number of people who have recommended Jackson’s business for different days after it
first opens.
Time (days), x
3
4
7
10
12
13
17
18
21
27
30
Number of personal recommendations, y
12
14
18
23
28
31
46
50
67
118
157
(a) Write the exponential regression equation that models the data.
(b) Use the equation to estimate the number of personal recommendations 60 days after Jackson
opens his business. Show your work.
Answer:
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Math | Graded Assignment | Semester B Test, Part 2
Name:
Date:
Graded Assignment
Semester B Test, Part 2
Answer the questions below. When you are finished, submit this test to your teacher for full credit.
Total score: ____ of 30 points
(Score for Question 1: ___ of 10 points)
1. An advertising company charges $40 per half-page advertisement and $75 per full-page advertisement.
Michael has a budget of $800 to purchase 13 advertisements.
(a) Define a variable for each unknown.
Write a system of equations to represent the situation.
(b) How many half-page advertisements does Michael purchase?
Show your work.
(c) How many full-page advertisements does Michael purchase?
Show your work.
Answer:
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Math | Graded Assignment | Semester B Test, Part 2
(Score for Question 2: ___ of 10 points)
2
2. Solve x − 6 x = −5 by completing the square.
Show all work for the steps below.
2
(a) For x − 6 x + c = −5 + c , what value of c is used to complete the square?
(b) Substitute the value for c in Part 2(a). Then complete the square to rewrite the equation as the
square of a binomial.
(c) Solve for x.
Answer:
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Math | Graded Assignment | Semester B Test, Part 2
(Score for Question 3: ___ of 10 points)
3. The table shows the test scores and the sleep averages of several students.
Test Score (%)
88
75
76
92
96
94
83
90
99
65
77
88
82
83
94
97
Average Sleep (h)
7
6.5
6
7.5
8
7
6.5
8
8.5
5
7
9
8
8.5
8.5
9
(a) Write the least squares regression equation that models the data.
Let x = the test score and y = average sleep.
(b) Use the equation to determine the approximate test score of a student who sleeps an average of
8 hours a night.
Show your work.
Answer:
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Name:
Math | Extended Problems | Compare Data Sets
Date:
Extended Problems
Compare Data Sets
Solve the problems. When you have finished, submit this assignment to your teacher by the due date for full
credit.
Total score: ____ of 20 points
Sherelle and Venita find two bags of coins in their grandmother’s attic. Each girl selects a bag, takes a random
sample of 20 coins from that bag, and lists the dates of those coins as the number of years since 1900. Here are
the results.
Sherelle: 72, 56, 81, 84, 75, 26, 39, 62, 65, 66, 85, 71, 74, 68, 73, 66, 83, 60, 58, 72
Venita: 45, 65, 73, 57, 79, 66, 69, 75, 51, 44, 53, 69, 58, 77, 51, 55, 53, 78, 70, 62
(Score for Question 1: ___ of 6 points)
1. Find the five-number summary of each data set. Then construct box-and-whisker plots of the data sets. Draw
both plots above the same number line. Label the plots with the girls’ names.
Answer:
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Math | Extended Problems | Compare Data Sets
(Score for Question 2: ___ of 9 points)
2. Solve.
(a) Contrast the shapes of the data sets displayed in the box-and-whisker plots in Question 1. Explain
what the difference in the shapes means in context of the situation.
(b) Compare the spread of the data sets. Discuss both the overall spread and the spread within the
boxes.
(c) Use an appropriate measure of central tendency to compare the center of the data sets. Explain what
the difference in those measures means in context of the situation.
Answer:
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Math | Extended Problems | Compare Data Sets
(Score for Question 3: ___ of 5 points)
3. Sherelle and Venita’s grandmother said that one of the bags has a coin from 1916.
(a) What reasons might Sherelle give for saying that the 1916 coin is most likely in her bag?
(b) What reasons might Venita give for saying that the 1916 coin is most likely in her bag?
(c) Whose bag do you think is more likely to contain the 1916 coin? Explain your reasoning.
Answer:
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