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MTH 216 Week 2 MyMathLab® Study Plan for Week 2 Checkpoint

• 6.A Characterizing Data

• Decide if a statement involving data makes sense.
• Find the mean, median and mode of a list of numbers.
• State whether the mean, median, or mode gives the best description of the averages.
• Describe and analyze distributions.
• Solve application problems involving distribution and weighted means.

• 6.B Measures of Variation

• Decide if a statement involving measures of variation makes sense.

Find the mean and median of a data set.

• Solve application problems involving measures of variation.

• 6.C The Normal Distribution

• Decide if a statement involving normal distribution makes sense.
• Work with properties of the Normal distribution.
• Find standard scores and percentiles.
• Solve applications involving Normal distributions.

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.

1. 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.

1. Make a sketch of the distribution. Choose the correct answer below.

1. 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.

1. 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.

1. 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

1. 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.

1. 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.

1. 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.)

1. 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.

1. 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.)

1. 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.

1. 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