Question 1

A teacher records the test scores for the 30 students in her class. Corresponding to each score, she calculates a z-score. If you were the parents of a girl in the class, would you be more interested in knowing your daughter's test score or z-score? Explain your reasoning.

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The answer of A teacher records the test scores for...

Question 2

Do you think it is possible to find two data sets such that the first data set has a smaller range but a larger standard deviation than the second set? If so, give an example of two such data sets. If it is not possible, explain why not.

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The answer of Do you think it is possible to...

Question 3

In the Florida lottery, the numbers (between 1 and 49)are generated randomly with the expectation that each number has an equal chance of winning. Draw a boxplot which should illustrate the data set of all numbers picked for the lottery during the past year.

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Question 4

Explain how two data sets could have equal means and modes but still differ greatly. Give an example with two data sets to illustrate.

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Question 5

A machine fills bottles with juice. The average amount filled in the bottles is 16 ounces; however this amount varies slightly from bottle to bottle. The manufacturer is interested in knowing how much the amount of juice varies from bottle to bottle. How could the manufacturer obtain an estimate of the population standard deviation $\sigma$?

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Question 6

The table below provides a frequency distribution for the winner of the Davis Cup during the period 1977-1994.  $\begin{array}{l} \text { Winner of }\ \begin{array} { l c }  \text { Davis Cup } & \text { Frequency } \ \hline \text { United States } & 6 \ \text { Germany } & 3 \ \text { Czechoslovakia } & 1 \ \text { Australia } & 3 \ \text { France } & 1 \ \text { Sweden } & 4 \end{array} \end{array}$  
Which measure of center, the mean, the median, or the mode is most appropriate here? Why?

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The answer of The table below provides a frequency distribution...

Question 7

Without calculating the standard deviation, compare the standard deviation for the following data sets. (Note: All data sets have a mean of 30.)Which do you expect to have the largest standard deviation and which do you expect to have the smallest standard deviation? Explain your answers in terms of the formula  
$s = \sqrt { \frac { \sum ( x - \bar { x } ) ^ { 2 } } { n - 1 } }$ 
Data set 
1: 30, 30, 30, 30, 30, 30, 30, 30, 30, 30 Data set 2: 20, 25, 25, 30, 30, 30, 30, 35, 35, 40 Date set $3 : 20,20,20,25,25,35,35,40,40,40$

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The answer of Without calculating the standard deviation, compare the...

Question 8

Roughly speaking, the standard deviation indicates how far, on average, the observations are from the mean. Do you think that for the data set below the standard deviation will give a good indication of the typical deviation from the mean? $$2,3,4,4,5,5,6,6,100$$ What drawback of the standard deviation is illustrated by this example?

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Question 9

Can the sample variance ever be a negative number? If so, for what types of data? If not, why not? Can the sample variance ever be zero? If so, for what types of data? If not, why not? Explain your reasoning.

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Question 10

When finding the 5-number summary, it becomes easy to identify the outliers of a data set. Under what conditions should outliers be deleted, and when should they be further investigated?

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The answer of When finding the 5-number summary, it becomes...

Question 11

Construct and interpret a boxplot or a modified boxplot as specified.
-The ages of the 21 members of a track and field team are listed below. Construct a modified boxplot for the data. $\begin{array} { l l l l l l l } 15 & 18 & 18 & 19 & 22 & 23 & 24 \ 24 & 24 & 24 & 25 & 26 & 26 & 27 \ 28 & 28 & 30 & 32 & 33 & 40 & 42 \end{array}$ 
A)

The data is roughly symmetrical with one potential outlier.
B)

The data is roughly symmetrical, possibly bell-shaped, with no outliers. 
C)

The data is roughly symmetrical with two potential outliers.
D)

The data is roughly symmetrical with three potential outliers.

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The answer of Construct and interpret a boxplot or a...

Question 12

Does the mode of a data set always lie near the center? Explain your answer and give an example of a data set to illustrate your answer.

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The answer of Does the mode of a data set...

Question 13

A company advertises an average of 42,000 miles for one of its new tires. In the manufacturing process there is some variation around that average. Would the company want a process that provides a large or a small variance? Justify your answer.

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The answer of A company advertises an average of 42,000...

Question 14

The empirical rule and Chebyshev's rule both relate the percent of data points to the number of standard deviations above or below the mean. What is the significant difference between the two and why do the percents for $\pm 2$ SD and $\pm 3$ SD differ so much?

Accepted Answer

The answer of The empirical rule and Chebyshev's rule both...

Question 15

The median of a data set is always/sometimes/never (select one)one of the data points in a set of data. Explain your answer with brief examples.

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The answer of The median of a data set is...

Question 16

A group of medical researchers is interested in knowing the mean cholesterol level for all men in the U.S. aged between 70 and 80. They pick a sample of 5,000 men and measure their cholesterol levels. They then calculate the mean and standard deviation of these cholesterol levels. Do the mean and standard deviation obtained in this way represent parameters or statistics? Why? What symbols could you use to denote the mean and standard deviation of the 5,000 cholesterol levels?

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The answer of A group of medical researchers is interested...

Question 17

Find the sample standard deviation for the given data. Round your final answer to one more decimal place than that used
for the observations.
-The normal monthly precipitation (in inches)for August is listed for 12 different U.S. cities. 
$\begin{array} { l l l l l l } 3.5 & 1.6 & 2.4 & 3.7 & 4.1 & 3.9 \end{array}$
$\begin{array} { l l l l l l l } 1.0 & 3.6 & 4.2 & 3.4 & 3.7 & 2.2 \end{array}$ 
A)12.03 in.
B)1.05 in.
C)1.00 in.
D)1.09 in.

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The answer of Find the sample standard deviation for the...

Question 18

Describe any similarities or differences in the two distributions represented by the following boxplots. Assume the two boxplots have the same scale. Explain your reasoning.

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The answer of Describe any similarities or differences in the...

Question 19

A population consists of 100 professional gymnasts and 100 professional basketball players. For this group, the average height is 70 inches. However, most of the gymnasts are between 57 and 61 inches tall while most of the basketball players are between 78 and 82 inches tall. For this group, observations far from the mean are more common than observations close to the mean. Describe what a boxplot for the heights of this group would look like. Discuss, in particular, the lengths of the whiskers relative to the width of the box and explain your reasoning.

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The answer of A population consists of 100 professional gymnasts...

Question 20

For a particular population, the _____________ mean is a constant and the ____________ mean is a variable.

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Quiz 3: Descriptive Measures

A teacher records the test scores for the 30 students in her class. Corresponding to each score, she calculates a z-score. If you were the parents of a girl in the class, would you be more interested in knowing your daughter's test score or z-score? Explain your reasoning.

Do you think it is possible to find two data sets such that the first data set has a smaller range but a larger standard deviation than the second set? If so, give an example of two such data sets. If it is not possible, explain why not.

In the Florida lottery, the numbers (between 1 and 49)are generated randomly with the expectation that each number has an equal chance of winning. Draw a boxplot which should illustrate the data set of all numbers picked for the lottery during the past year.

Explain how two data sets could have equal means and modes but still differ greatly. Give an example with two data sets to illustrate.

Can the sample variance ever be a negative number? If so, for what types of data? If not, why not? Can the sample variance ever be zero? If so, for what types of data? If not, why not? Explain your reasoning.

When finding the 5-number summary, it becomes easy to identify the outliers of a data set. Under what conditions should outliers be deleted, and when should they be further investigated?

Does the mode of a data set always lie near the center? Explain your answer and give an example of a data set to illustrate your answer.

A company advertises an average of 42,000 miles for one of its new tires. In the manufacturing process there is some variation around that average. Would the company want a process that provides a large or a small variance? Justify your answer.

The empirical rule and Chebyshev's rule both relate the percent of data points to the number of standard deviations above or below the mean. What is the significant difference between the two and why do the percents for $\pm 2$ SD and $\pm 3$ SD differ so much?

The median of a data set is always/sometimes/never (select one)one of the data points in a set of data. Explain your answer with brief examples.

Describe any similarities or differences in the two distributions represented by the following boxplots. Assume the two boxplots have the same scale. Explain your reasoning.

For a particular population, the _ mean is a constant and the mean is a variable.

Quiz 3: Descriptive Measures

A teacher records the test scores for the 30 students in her class. Corresponding to each score, she calculates a z-score. If you were the parents of a girl in the class, would you be more interested in knowing your daughter's test score or z-score? Explain your reasoning.

Do you think it is possible to find two data sets such that the first data set has a smaller range but a larger standard deviation than the second set? If so, give an example of two such data sets. If it is not possible, explain why not.

In the Florida lottery, the numbers (between 1 and 49)are generated randomly with the expectation that each number has an equal chance of winning. Draw a boxplot which should illustrate the data set of all numbers picked for the lottery during the past year.

Explain how two data sets could have equal means and modes but still differ greatly. Give an example with two data sets to illustrate.

Can the sample variance ever be a negative number? If so, for what types of data? If not, why not? Can the sample variance ever be zero? If so, for what types of data? If not, why not? Explain your reasoning.

When finding the 5-number summary, it becomes easy to identify the outliers of a data set. Under what conditions should outliers be deleted, and when should they be further investigated?

Does the mode of a data set always lie near the center? Explain your answer and give an example of a data set to illustrate your answer.

A company advertises an average of 42,000 miles for one of its new tires. In the manufacturing process there is some variation around that average. Would the company want a process that provides a large or a small variance? Justify your answer.

The empirical rule and Chebyshev's rule both relate the percent of data points to the number of standard deviations above or below the mean. What is the significant difference between the two and why do the percents for ±2\pm 2±2 SD and ±3\pm 3±3 SD differ so much?

The median of a data set is always/sometimes/never (select one)one of the data points in a set of data. Explain your answer with brief examples.

Describe any similarities or differences in the two distributions represented by the following boxplots. Assume the two boxplots have the same scale. Explain your reasoning.

For a particular population, the _____________ mean is a constant and the ____________ mean is a variable.

The empirical rule and Chebyshev's rule both relate the percent of data points to the number of standard deviations above or below the mean. What is the significant difference between the two and why do the percents for $\pm 2$ SD and $\pm 3$ SD differ so much?

For a particular population, the _ mean is a constant and the mean is a variable.