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MTH 216
QUANTITATIVE REASONING II
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MTH 216 Week 2 MyMathLab® Week 2 Checkpoint
Prerequisite Assignment: MyMathLab® Study Plan for Weekly Checkpoint
- Click on the Quiz tab.
- Click External Content Launch to access MyMathLab®.
- Click Homework and Tests in MyMathLab® at the top-left of the screen.
- Click Week 2 Checkpoint.
Important Notes: You must earn at least 60% of the Mastery Points in the Weekly MyMathLab® Study Plan, before you may start the Weekly Checkpoint.
It is highly recommended that you earn all Mastery Points in the Weekly MyMathLab® Study Plan Checkpoint. You have 1 attempt to complete the Weekly Checkpoints and do not have access to the Help me Solve This or View an Example features.
MTH 216 Week 2 Checkpoint
Decide whether the following statement makes sense (or is clearly true) or does not make sense (or is clearly false). Explain your reasoning.
The distribution of grades was left-skewed, but the mean, median, and mode were all the same.
Choose the correct answer below.
A.
This does not make sense because the mean and median should lie somewhere to the left of the mode if the distribution is left-skewed.
B.
This makes sense because when outliers have high values, the mean, median, and mode are the same.
C.
This does not make sense because the mean and median should lie somewhere to the right of the mode if the distribution is left-skewed.
D.
This makes sense because when outliers have low values, the mean, median, and mode are the same.
The numbers of words defined on randomly selected pages from a dictionary are shown below. Find the mean, median, and mode of the listed numbers.
70
49
44
77
68
60
38
30
54
35
What is the mean? Select the correct choice below and, if necessary, fill in the answer box within your choice.
A.
The mean is 52.5
.
(Round to one decimal place as needed.)
B.
There is no mean.
What is the median? Select the correct choice below and, if necessary, fill in the answer box within your choice.
A.
The median is 51.5
.
(Round to one decimal place as needed.)
B.
There is no median.
What is(are) the mode(s)? Select the correct choice below and, if necessary, fill in the answer box within your choice.
A.
The mode(s) is(are) nothing
.
(Round to one decimal place as needed. Use a comma to separate answers as needed.)
B.
There is no mode.
Blood alcohol concentrations of drivers involved in fatal crashes and then given jail sentences are shown below. Find the mean, median, and mode of the listed numbers.
0.26
0.17
0.17
0.16
0.13
0.24
0.30
0.24
0.14
0.16
0.10
0.16
The mean is 0.186
.
(Round to the nearest thousandth as needed.)
The median is 0.165
.
(Round to the nearest thousandth as needed.)
What is(are) the mode(s)? Select the correct choice below and, if necessary, fill in the answer box within your choice.
A.
The mode(s) is(are) 0.16
sec. (Use a comma to separate answers as needed.)
B.
There is no mode.
State, with an explanation, whether the mean, median, or mode gives the best description of the following average.
The average household income in this country
Which measurement gives the best description of the given average?
State, with an explanation, whether the mean, median, or mode gives the best description of the following average.
The average number of houses owned by people during their lifetime
Which measurement gives the best description of the given average?
Consider the distribution of exam scores (graded from 0 to 100) for 76
students when 38
students got an A, 22
students got a B, and 16
students got a C. Complete parts (a) through (d) below.
- How many peaks would you expect for the distribution?
A.
There would probably be three peaks, because even though each exam score could be anywhere between 0 and 100, the only grades received were A, B, and C.
B.
There would probably be one peak because there are no obvious reasons why the exam scores would form different groups.
C.
There would probably be no peaks. The distribution of grades always tends to be uniform.
D.
There would probably be many peaks corresponding to the different exam scores that each student had.
- Make a sketch of the distribution. Choose the correct answer below.
- What shape would you expect for the distribution?
A.
The distribution would probably be symmetric because there are no obvious factors to indicate that there would be a higher or lower exam score for any student.
B.
The distribution would probably be symmetric because the only grades received were A, B, and C.
C.
The distribution would probably be left-skewed because many of the students got an A, and very few got a C.
D.
The distribution would probably be right-skewed because a lot of students got either a B or a C.
- What variation would you expect in the distribution?
A.
The variation would probably be large because many students got an A, some got a B, and a small number got a C.
B.
The variation would probably be moderate because the only grades received were A, B, and C.
C.
The variation would probably be moderate because there are no obvious reasons to expect an especially large or small amount of variation.
D.
The variation would probably be small because all the students would tend to have nearly the same exam score.
Suppose you study family income in a random sample of 200
families. Your results can be summarized as the mean family income was $46 comma 000
,
the median family income was $ 30 comma 000
,
the highest and lowest incomes were $254 comma 000
and $2 comma 200
,
respectively.
- Draw a rough sketch of the income distribution, with clearly labeled axes. Choose the correct answer below.
Describe the distribution as symmetric, left-skewed, or right-skewed. Choose the correct answer below.
right-skewed
symmetric
left-skewed
- How many families in the sample earned less than $30 comma 000
?
Explain how you know. Choose the correct answer below.
A.
150
families, because the mode is the most common value in a data set.
B.
50
families, because the mean is the average value of income.
C.
100
families, because the median is the middle value in the sorted data set.
- Based on the given data, can you determine how many families earned more than $ 46 comma 000
?
Why or why not? Choose the correct answer below.
A.
No, because the number of families that earned more than $ 46 comma 000
depends on the distribution.
B.
Yes, because the mean is the middle value in the sorted data set.
The table to the right gives the cost of living index (COLI) for six East Coast counties and six Midwest counties (using an index where 100 represents the average cost of living for all participating cities with a population of more than 1.5 million). Answer parts (a) through (e) below.
- Find the mean, median, and range for each of the two data sets.
The mean for the East Coast Counties is 157.68
.
(Type an integer or decimal rounded to two decimal places as needed.)
The median for the East Coast Counties is 131.4
.
(Type an integer or decimal rounded to two decimal places as needed.)
The range for the East Coast Counties is 210.8
.
(Type an integer or decimal rounded to two decimal places as needed.)
The mean for the Midwest Counties is 115.83
.
(Type an integer or decimal rounded to two decimal places as needed.)
The median for the Midwest Counties is 95.4
.
(Type an integer or decimal rounded to two decimal places as needed.)
The range for the Midwest Counties is 141.3
.
(Type an integer or decimal rounded to two decimal places as needed.)
- Give the five-number summary and draw a boxplot for each of the two data sets.
Give the five number summary for the East Coast Counties.
Low Value
equals
104.1
Lower Quartile
equals
123.10
Median
equals
131.4
Upper Quartile
equals
141.2
High Value
equals
314.9
(Type integers or decimals rounded to two decimal places as needed.)
Give the five-number summary for the Midwest Counties.
Low Value
equals
87.2
Lower Quartile
equals
92.2
Median
equals
95.4
Upper Quartile
equals
96.3
High Value
equals
228.5
(Type integers or decimals rounded to two decimal places as needed.)
Choose the correct boxplot for the Midwest Counties below.
A.
80120160200240x
A boxplot is above a number line that is labeled from 80 to 240 in increments of 20. A box extends from 123 to 141. A horizontal line segment extends from the left side of the box and intersects a short vertical line segment at 104. A horizontal line segment extends from the right side of the box to 240. All values are approximate.
B.
80120160200240x
A boxplot is above a number line that is labeled from 80 to 240 in increments of 20. A box extends from 111 to 113. A horizontal line segment extends from the left side of the box and intersects short vertical line segments at 105 and 87. A horizontal line segment extends from the right side of the box and intersects a short vertical line segment at 229. All values are approximate.
C.
80120160200240x
A boxplot is above a number line that is labeled from 80 to 240 in increments of 20. A box extends from 92 to 96, with a vertical line segment through the box at 95. A horizontal line segment extends from the left side of the box and intersects a short vertical line segment at 87. A horizontal line segment extends from the right side of the box and intersects a short vertical line segment at 229. All values are approximate.
- Find the standard deviation for each of the two data sets.
The standard deviation for the East Coast Counties is 78.05
.
(Type an integer or decimal rounded to two decimal places as needed.)
The standard deviation for the Midwest Counties is 55.30
.
(Type an integer or decimal rounded to two decimal places as needed.)
- Apply the range rule of thumb to estimate the standard deviation of each of the two data sets. How well does the rule work in each case? Briefly discuss why it does or does not work well.
The standard deviation for the East Coast Counties is approximately 52.7
,
using the range rule of thumb.
(Type an integer or decimal rounded to two decimal places as needed.)
The standard deviation for the Midwest Counties is approximately 35.33
,
using the range rule of thumb.
(Type an integer or decimal rounded to two decimal places as needed.)
How well does the rule work in each case? Briefly discuss why it does or does not work well. Choose the correct answer below.
A.
They work well in both of the two data sets because there are no outliers in anyone of the two data sets.
B.
It works well in the Midwest data set, but it does not work well in the East Coast data set, because there is a outlier in the East Coast data set.
C.
They do not work well in both of the two data sets because there are outliers in both of the two data sets.
D.
It works well in the East Coast data set, but it does not work well in the Midwest data set, because there is a outlier in the Midwest data set.
- Based on all the results, compare and discuss the two data sets in terms of their center and variation. Choose the correct answer below. Select all that apply.
A.
The variation of COLI for the six East Coast counties is higher than that for the six Midwest Counties, which means the level of COLI in most Midwest Counties varies in a larger range.
B.
The mean of COLI for the six East Coast counties is higher than that for the six Midwest Counties, which means the average level of COLI for the East Coast counties is higher.
C.
The variation of COLI for the six East Coast counties is higher than that for the six Midwest Counties, which means the level of COLI in most Midwest Counties varies in a smaller range.
D.
The mean of COLI for the six East Coast counties is higher than that for the six Midwest Counties, which means the average level of COLI for the East Coast counties is lower.
Decide whether the following statement makes sense or does not make sense.
The heights of male basketball players at a local college are normally distributed with a mean of 6 feet 3 inches and a standard deviation of 3 inches.
Choose the correct answer below.
Does not make sense
Makes sense
Decide whether the following statement makes sense or does not make sense.
The weights of babies born at Belmont Hospital are normally distributed with a mean of 6.8 pounds and a standard deviation of 7 pounds.
Choose the correct answer below.
Does not make sense
Makes sense