Determine the quartile or interquartile range as specified. -The normal annual precipitation (in inches)is given below for 21 different U.S. cities. Find the first quartile, $\mathrm { Q } _ { 1 } \text {. }$ $\begin{array} { l l l l l l l } 39.1 & 16.4 & 25.4 & 18.4 & 27.1 & 27.8 & 30.6 \end{array}$ $\begin{array} { l l l l l l l l } 15.2 & 42.6 & 18.4 & 13.5 & 19.8 & 32.3 & 10.0 \end{array}$ $\begin{array} { l l l l l l l } 14.8 & 33.6 & 12.9 & 35.0 & 22.3 & 11.2 & 51.7 \end{array}$

A) $15.2 \mathrm { in } .$ B) $14.8 \mathrm { in } .$ C) $14.900 \mathrm { in }$. D) $15.00 \mathrm { in }$. A) $15.2 \mathrm { in } .$ B) $14.8 \mathrm { in } .$ C) $14.900 \mathrm { in }$. D) $15.00 \mathrm { in }$.

Consider the following sample of exam scores, arranged in increasing order: $\begin{array} { l l l l l l } 22 & 35 & 44 & 55 & 67 & 70 \end{array}$ $\begin{array} { l l l l l l } 78 & 81 & 81 & 82 & 84 & 88 \end{array}$ $\begin{array} { l l l l l l } 88 & 89 & 90 & 90 & 91 & 92 \end{array}$ $\begin{array} { l l l l l l } 92 & 93 & 93 & 94 & 94 & 95 \\ 95 & 96 & 96 & 97 & 99 & 100 \end{array}$ $\begin{array} { l l l l l l } 95 & 96 & 96 & 97 & 99 & 100 \end{array}$ Note: $\bar { x } = 82.4$ and $s = 19.5$

A) (i) Use Chebychev's rule to obtain a lower bound on the percentage of observations that lie within 2 standard deviations to either side of the mean. (ii) Use the data to obtain the exact percentage of observations that lie within  standard deviations to either side of the mean. Compare this answer with part (i). (i) Chebychev's rules says that $75 \%$ of the data values will lie between $82.4 - 2 ( 19.5 )$ and $82.4 + 2 ( 19.5 )$, or between $43.4$ and $121.4$; (ii) 26 of the thirty observations (87\%) lie within the interval $43.4$ to $121.4$. "At least $75 \%$ " means $75 \%$ or more, and $87 \%$ is more than $75 \%$, so Chebychev's rule does apply to these data. B) (i) Chebychev's rules says that $75 \%$ of the data values will lie between $82.4 - 2 ( 19.5 )$ and $82.4 + 2 ( 19.5 )$, or between $40.4$ and $123.4$; (ii) 27 of the thirty observations ( $90 \%$ ) lie within the interval $40.4$ to $123.4$. "At least $75 \%$ " means $75 \%$ or more, and $90 \%$ is more than $75 \%$, so Chebychev's rule does apply to these data. C) (i) Chebychev's rules says that $75 \%$ of the data values will lie between $82.4 - 2 ( 19.5 )$ and $82.4 + 2 ( 19.5 )$, or between $43.4$ and $121.4$; (ii) 28 of the thirty observations ( $93 \%$ ) lie within the interval $43.4$ to $121.4$. "At least $75 \% "$ means $75 \%$ or more, and $93 \%$ is more than $75 \%$, so Chebychev's rule does apply to these data. D) (i) Chebychev's rules says that $75 \%$ of the data values will lie between $82.4 - 2 ( 19.5 )$ and $82.4 + 2 ( 19.5 )$, or between $53.4$ and $116.4$; (ii) 28 of the thirty observations ( $93 \%$ ) lie within the interval $53.4$ to $116.4$. "At least $75 \%$ " means $75 \%$ or more, and $93 \%$ is more than $75 \%$, so Chebychev's rule does apply to these data. A) (i) Use Chebychev's rule to obtain a lower bound on the percentage of observations that lie within 2 standard deviations to either side of the mean. (ii) Use the data to obtain the exact percentage of observations that lie within  standard deviations to either side of the mean. Compare this answer with part (i). (i) Chebychev's rules says that $75 \%$ of the data values will lie between $82.4 - 2 ( 19.5 )$ and $82.4 + 2 ( 19.5 )$, or between $43.4$ and $121.4$; (ii) 26 of the thirty observations (87\%) lie within the interval $43.4$ to $121.4$. "At least $75 \%$ " means $75 \%$ or more, and $87 \%$ is more than $75 \%$, so Chebychev's rule does apply to these data. B) (i) Chebychev's rules says that $75 \%$ of the data values will lie between $82.4 - 2 ( 19.5 )$ and $82.4 + 2 ( 19.5 )$, or between $40.4$ and $123.4$; (ii) 27 of the thirty observations ( $90 \%$ ) lie within the interval $40.4$ to $123.4$. "At least $75 \%$ " means $75 \%$ or more, and $90 \%$ is more than $75 \%$, so Chebychev's rule does apply to these data. C) (i) Chebychev's rules says that $75 \%$ of the data values will lie between $82.4 - 2 ( 19.5 )$ and $82.4 + 2 ( 19.5 )$, or between $43.4$ and $121.4$; (ii) 28 of the thirty observations ( $93 \%$ ) lie within the interval $43.4$ to $121.4$. "At least $75 \% "$ means $75 \%$ or more, and $93 \%$ is more than $75 \%$, so Chebychev's rule does apply to these data. D) (i) Chebychev's rules says that $75 \%$ of the data values will lie between $82.4 - 2 ( 19.5 )$ and $82.4 + 2 ( 19.5 )$, or between $53.4$ and $116.4$; (ii) 28 of the thirty observations ( $93 \%$ ) lie within the interval $53.4$ to $116.4$. "At least $75 \%$ " means $75 \%$ or more, and $93 \%$ is more than $75 \%$, so Chebychev's rule does apply to these data.

Find the range for the given data set. -The weights, in pounds, of 18 randomly selected adults are given below. $\begin{array} { l l l l l l } 120 & 165 & 187 & 143 & 119 & 132 \\ 127 & 156 & 179 & 159 & 180 & 202 \\ 114 & 146 & 151 & 168 & 173 & 144 \end{array}$

A) $78 \mathrm { lb }$ B) $114 \mathrm { lb }$ C) $202 \mathrm { lb }$ D) $88 \mathrm { lb }$ A) $78 \mathrm { lb }$ B) $114 \mathrm { lb }$ C) $202 \mathrm { lb }$ D) $88 \mathrm { lb }$

Obtain the five-number summary for the given data. -The weekly salaries (in dollars)of sixteen government workers are listed below. $\begin{array} { l l l l } 690 & 609 & 813 & 644 \\ 728 & 571 & 473 & 614 \\ 529 & 678 & 685 & 460 \\ 552 & 787 & 507 & 826 \end{array}$

A) 460, 540.5, 629.0, 709, 826 dollars B) 460,534.75,629.0,718.5,826 dollars C) 460,529,614,690,826 dollars D) 460,534.75,614,718.5,826 dollars A) 460, 540.5, 629.0, 709, 826 dollars B) 460,534.75,629.0,718.5,826 dollars C) 460,529,614,690,826 dollars D) 460,534.75,614,718.5,826 dollars

Exam 3: Descriptive Measures

The range and standard deviation of the data set below are 35 and 12.47 respectively. $5,24,25,26,40$ If the 26 is replaced with 39, how will this affect the range? How will this affect the standard deviation. Use your answers to explain why the standard deviation is preferable to the range as a measure of variation.

(Essay)

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Question 121

Find the mode(s)for the given sample data. -81, 35, 32, 35, 29, 81

(Multiple Choice)

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Question 122

Determine the quartile or interquartile range as specified. -The normal annual precipitation (in inches)is given below for 21 different U.S. cities. Find the first quartile, $\mathrm { Q } _ { 1 } \text {. }$ 39.1 16.4 25.4 18.4 27.1 27.8 30.6 15.2 42.6 18.4 13.5 19.8 32.3 10.0 14.8 33.6 12.9 35.0 22.3 11.2 51.7

(Multiple Choice)

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Question 123

Which score has a higher relative position, a score of 43.5 on a test with a mean of 30 and a standard deviation of 9, or a score of 304 on a test with a mean of 226 and a standard deviation of 52? (Assume that the distributions being compared have approximately the same shape.)

(Multiple Choice)

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Question 124

Consider the following sample of exam scores, arranged in increasing order: 22 35 44 55 67 70 78 81 81 82 84 88 88 89 90 90 91 92 92 93 93 94 94 95 95 96 96 97 99 100 95 96 96 97 99 100 Note: $\bar { x } = 82.4$ and $s = 19.5$

(Multiple Choice)

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Question 125

Find the range for the given data set. -The weights, in pounds, of 18 randomly selected adults are given below. 120 165 187 143 119 132 127 156 179 159 180 202 114 146 151 168 173 144

(Multiple Choice)

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Question 126

Find the range for the given data set. -28, 39, 17, 45, 52

(Multiple Choice)

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Question 127

Which is better, a score of 92 on a test with a mean of 71 and a standard deviation of 15, or a score of 688 on a test with a mean of 493 and a standard deviation of 150? (Assume that the distributions Being compared have approximately the same shape.)

(Multiple Choice)

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Question 128

Solve the problem. -Describe what these boxplots tell you about the relationship between the state you live in and your salary, based on the same occupation.

(Multiple Choice)

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Question 129

Find the population standard deviation. Round to one decimal place as needed. $0,3,5,7,7$

(Multiple Choice)

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Question 130

Identify potential outliers, if any, for the given data. -The weekly salaries (in dollars)of sixteen government workers are listed below. 690 584 813 643 728 558 458 597 498 651 685 360 526 787 475 986

(Multiple Choice)

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Question 131

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.

(Essay)

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Question 132

Obtain the population standard deviation, Ϭ, for the given data. Assume that the data represent population data. Round your final answer to one more decimal place than that used for the Observations. The normal annual precipitation (in inches)is given below for 8 different U.S. cities. 6.7 8.3 5.7 14.2 15.2 13.7 17.0 14.3

(Multiple Choice)

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Question 133

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.

(Essay)

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Question 134

A variable x has the possible observations shown below. $\text { Possible observations of } \mathrm{x}$ : -3 -1 0 1 1 2 4 4 5 Determine the standardized version of $x$ . Round the values of $\mu$ and $\sigma$ to one decimal place.

(Multiple Choice)

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Question 135

Find the mean for the given sample data. Unless otherwise specified, round your answer to one more decimal place thanthat used for the observations. -The students in Hugh Logan's math class took the Scholastic Aptitude Test. Their math scores are shown below. Find the mean score. 589 532 359 349 497 340 353 626 470 482

(Multiple Choice)

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Question 136

The mean of a set of data is 1.26 and its standard deviation is 3.81. Find the z-score for a value of 3.97. Round your final answer to two decimal places.

(Multiple Choice)

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Question 137

Find the range for the given data set. -Jeanne is currently taking college economics. The instructor often gives quizzes. On the past five quizzes, Jeanne got the following scores. 5 20 4 14 10

(Multiple Choice)

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Question 138

Construct and interpret a boxplot or a modified boxplot as specified. -The weights (in ounces)of 27 tomatoes are listed below. Construct a modified boxplot for the data. 1.7 2.0 2.2 2.2 2.4 2.5 2.5 2.5 2.6 2.6 2.6 2.6 2.6 2.7 2.8 2.8 2.8 2.9 2.9 2.9 3.0 3.0 3.1 3.1 3.3 3.6 4.2

(Multiple Choice)

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Question 139

Obtain the five-number summary for the given data. -The weekly salaries (in dollars)of sixteen government workers are listed below. 690 609 813 644 728 571 473 614 529 678 685 460 552 787 507 826

(Multiple Choice)

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Question 140

Find the mode(s)for the given sample data. -81, 35, 32, 35, 29, 81

Which score has a higher relative position, a score of 43.5 on a test with a mean of 30 and a standard deviation of 9, or a score of 304 on a test with a mean of 226 and a standard deviation of 52? (Assume that the distributions being compared have approximately the same shape.)

Consider the following sample of exam scores, arranged in increasing order: 22 35 44 55 67 70 78 81 81 82 84 88 88 89 90 90 91 92 92 93 93 94 94 95 95 96 96 97 99 100 95 96 96 97 99 100 Note: $\bar { x } = 82.4$ and $s = 19.5$

Find the range for the given data set. -The weights, in pounds, of 18 randomly selected adults are given below. 120 165 187 143 119 132 127 156 179 159 180 202 114 146 151 168 173 144

Find the range for the given data set. -28, 39, 17, 45, 52

Which is better, a score of 92 on a test with a mean of 71 and a standard deviation of 15, or a score of 688 on a test with a mean of 493 and a standard deviation of 150? (Assume that the distributions Being compared have approximately the same shape.)

Solve the problem. -Describe what these boxplots tell you about the relationship between the state you live in and your salary, based on the same occupation.

Find the population standard deviation. Round to one decimal place as needed. $0,3,5,7,7$

Identify potential outliers, if any, for the given data. -The weekly salaries (in dollars)of sixteen government workers are listed below. 690 584 813 643 728 558 458 597 498 651 685 360 526 787 475 986

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.

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.

A variable x has the possible observations shown below. $\text { Possible observations of } \mathrm{x}$ : -3 -1 0 1 1 2 4 4 5 Determine the standardized version of $x$ . Round the values of $\mu$ and $\sigma$ to one decimal place.

The mean of a set of data is 1.26 and its standard deviation is 3.81. Find the z-score for a value of 3.97. Round your final answer to two decimal places.

Find the range for the given data set. -Jeanne is currently taking college economics. The instructor often gives quizzes. On the past five quizzes, Jeanne got the following scores. 5 20 4 14 10

Construct and interpret a boxplot or a modified boxplot as specified. -The weights (in ounces)of 27 tomatoes are listed below. Construct a modified boxplot for the data. 1.7 2.0 2.2 2.2 2.4 2.5 2.5 2.5 2.6 2.6 2.6 2.6 2.6 2.7 2.8 2.8 2.8 2.9 2.9 2.9 3.0 3.0 3.1 3.1 3.3 3.6 4.2

Obtain the five-number summary for the given data. -The weekly salaries (in dollars)of sixteen government workers are listed below. 690 609 813 644 728 571 473 614 529 678 685 460 552 787 507 826

The Nature of Statistics

Organizing Data

Probability Concepts

Discrete Random Variables

The Normal Distribution

The Sampling Distribution of the Sample Mean

Confidence Intervals for One Population Mean

Hypothesis Tests for One Population Mean

Inferences for Two Population Means

Inferences for Population Standard Deviations

Inferences for Population Proportions

Chi-Square Procedures

Descriptive Methods in Regression and Correlation

Inferential Methods in Regression and Correlation

Analysis of Variance Anova

Filters

Exam 3: Descriptive Measures

Find the mode(s)for the given sample data. -81, 35, 32, 35, 29, 81

Which score has a higher relative position, a score of 43.5 on a test with a mean of 30 and a standard deviation of 9, or a score of 304 on a test with a mean of 226 and a standard deviation of 52? (Assume that the distributions being compared have approximately the same shape.)

Consider the following sample of exam scores, arranged in increasing order: 22 35 44 55 67 70 78 81 81 82 84 88 88 89 90 90 91 92 92 93 93 94 94 95 95 96 96 97 99 100 95 96 96 97 99 100 Note: xˉ=82.4\bar { x } = 82.4xˉ=82.4 and s=19.5s = 19.5s=19.5

Find the range for the given data set. -The weights, in pounds, of 18 randomly selected adults are given below. 120 165 187 143 119 132 127 156 179 159 180 202 114 146 151 168 173 144

Find the range for the given data set. -28, 39, 17, 45, 52

Which is better, a score of 92 on a test with a mean of 71 and a standard deviation of 15, or a score of 688 on a test with a mean of 493 and a standard deviation of 150? (Assume that the distributions Being compared have approximately the same shape.)

Solve the problem. -Describe what these boxplots tell you about the relationship between the state you live in and your salary, based on the same occupation.

Find the population standard deviation. Round to one decimal place as needed. 0,3,5,7,70,3,5,7,70,3,5,7,7

Identify potential outliers, if any, for the given data. -The weekly salaries (in dollars)of sixteen government workers are listed below. 690 584 813 643 728 558 458 597 498 651 685 360 526 787 475 986

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.

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.

A variable x has the possible observations shown below. Possible observations of x\text { Possible observations of } \mathrm{x} Possible observations of x : -3 -1 0 1 1 2 4 4 5 Determine the standardized version of xxx . Round the values of μ\muμ and σ\sigmaσ to one decimal place.

The mean of a set of data is 1.26 and its standard deviation is 3.81. Find the z-score for a value of 3.97. Round your final answer to two decimal places.

Find the range for the given data set. -Jeanne is currently taking college economics. The instructor often gives quizzes. On the past five quizzes, Jeanne got the following scores. 5 20 4 14 10

Construct and interpret a boxplot or a modified boxplot as specified. -The weights (in ounces)of 27 tomatoes are listed below. Construct a modified boxplot for the data. 1.7 2.0 2.2 2.2 2.4 2.5 2.5 2.5 2.6 2.6 2.6 2.6 2.6 2.7 2.8 2.8 2.8 2.9 2.9 2.9 3.0 3.0 3.1 3.1 3.3 3.6 4.2

Obtain the five-number summary for the given data. -The weekly salaries (in dollars)of sixteen government workers are listed below. 690 609 813 644 728 571 473 614 529 678 685 460 552 787 507 826

The Nature of Statistics

Organizing Data

Probability Concepts

Discrete Random Variables

The Normal Distribution

The Sampling Distribution of the Sample Mean

Confidence Intervals for One Population Mean

Hypothesis Tests for One Population Mean

Inferences for Two Population Means

Inferences for Population Standard Deviations

Inferences for Population Proportions

Chi-Square Procedures

Descriptive Methods in Regression and Correlation

Inferential Methods in Regression and Correlation

Analysis of Variance Anova

Filters

Consider the following sample of exam scores, arranged in increasing order: 22 35 44 55 67 70 78 81 81 82 84 88 88 89 90 90 91 92 92 93 93 94 94 95 95 96 96 97 99 100 95 96 96 97 99 100 Note: $\bar { x } = 82.4$ and $s = 19.5$

Find the population standard deviation. Round to one decimal place as needed. $0,3,5,7,7$

A variable x has the possible observations shown below. $\text { Possible observations of } \mathrm{x}$ : -3 -1 0 1 1 2 4 4 5 Determine the standardized version of $x$ . Round the values of $\mu$ and $\sigma$ to one decimal place.