Project 2
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School
University of Michigan, Flint *
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Course
105
Subject
Mathematics
Date
Apr 3, 2024
Type
docx
Pages
5
Uploaded by CorporalBookAnt87
MTH 105-W2 Liberal Arts Mathematics
Written Project TWO (Total Points: 40)
Due: November 12, 2023
Name:_______________________
ID: _________________________
Objectives:
You will understand:
Mean and median provide different information about the set of data.
Conclusions derived from statistical summaries are subject to misinterpretation.
The difference between frequency and relative frequency.
Histograms are graphical displays useful for showing the shape of a distribution.
The base value (the whole amount associated with a percent) in a pie graph.
Estimate the size of the portions of a pie chart if given the base value.
Use the data displayed on graphs to compare absolute and relative of change.
The format of a stem-and-leaf plot and how to read data presented in the plot.
Perquisites:
Order numbers and identify place values.
Interpret the labels of a graph.
Compute the amount of a whole from a given percent of the whole.
Instructions:
Answer all parts and show all supporting work.
Complete and type your work on this Word Document.
Save your work as a PDF file.
Include your name as part of the PDF file name.
Upload it to Project 2.
Question 1:
A sample of individuals reported the balance on their credit cards. This histogram summarizes this report.
A.
(2 pts) How many individuals are included in this sample?
B.
(2 pts) Estimate the mean credit balance of this sample of individuals represented in this
histogram.
C.
(1pt) According to the histogram, which bin contains the median credit balance?
D.
(3 pts) Given a data set that matches the histogram shown above: $1000, $1000, $3000, $4000, $6000, $6000, $6000, $6000, $9000, $9000, $9000, $9000,
$9000, $11000, $11000, $11000, $11000, $13000, $13000, $14000.
Compute the mean and median of this data set. How does the answer compare to your
estimate from (B) and (C)?
E.
(2 pts) Mark both the mean and the median of the given data set in (D) on the horizontal
axis of the histogram shown above.
F.
(1 pt) Which of the following phrase best describe the median of the data set in (D)?
1.
Significantly less than the mean.
2.
Roughly the same as the mean.
3.
Significantly greater than the mean.
Question 2:
The U.S. government tracks gas mileage by the size of the car. The table shown gives the highway gas mileage for 2020 cars in the hatchback class.
A.
(2 pts) What information can you gain from a very quick glance at this table? B.
(5 pts) Another type of table, known as a frequency table, helps to organize the data into
a more useful form. To begin creating a frequency table, tally the data from the mpg table
shown above. Fill in all blanks to complete this frequency table. (For relative frequency
in the third column, round to the nearest tenth of a percent.)
Range
Frequency
Relative Frequency
27 to 30
31 to 34
35 to 38
39 to 42
43 or higher
C.
(3 pts) Return to Part (A). Does this frequency and relative frequency columns help you
form a better understanding of the gas mileage of 2020 hatchback cars? Explain.
Question 3:
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Stem-and-leaf plots can also be used to compare two data sets. Here is an example of test grades for two American history classes.
A.
Summarize the scores in the 8 a.m. class.
a.
(1 pt) How many students scored in the 90s?
b.
(1 pt) What is average?
c.
(3 pts) Find the first, second, and third quartiles.
B.
Summarize the scores in the 11 a.m. class.
a.
(1 pt) How many students scored in the 90s?
b.
(1 pt) What is average?
c.
(3 pts) Find the first, second, and third quartiles.
Question 4:
The pie charts below represent the U.S. voting populations in 1960 and 2016. Use the graphs to answer the following questions.
A.
(2 pts) Based on the graph, can we conclude that more people voted in 1960 than in
2016? Why or why not? Explain.
B.
(2 pts) Based on the graph, can we conclude that in 1960, a larger percentage of the US
population voted than in people voted than in 2016? Why or why not? Explain.
C.
The U.S. voting population in 1960 and 2016 were about 110 million and 245 million,
respectively. a.
(4 pts) Estimate the number of people who voted in 1960 and the number of
people who voted in 2016.
b.
(1 pt) Use your answer in the previous part to determine whether the statement in
part (A) is true or false.