Chapter 15

In \(3-8,\) find the mean, the median, and the mode of each set of data. Tips: \(\$ 1.00, \$ 1.50, \$ 2.25, \$ 3.00, \$ 3.30, \$ 3.50, \$ 4.00, \$ 4.75, \$ 5.00, \$ 5.00, \$ 5.00\)

Organize the data in a frequency distribution table. The number of siblings of each of 30 students in a class: \(\begin{array}{lllllllllllllll}{2} & {1} & {1} & {5} & {1} & {0} & {2} & {2} & {1} & {3} & {4} & {0} & {6} & {2} & {0} \\ {3} & {1} & {2} & {2} & {1} & {1} & {1} & {0} & {2} & {1} & {0} & {1} & {1} & {2} & {3}\end{array}\)

In \(9-13 :\) a. Create a scatter plot for the data. b. Determine which regression model is the most appropriate for the data. Justify your answer. c. Find the regression equation. Round the coefficient of the regression equation to three decimal places. $$ \begin{array}{|c|c|c|c|c|c|c|c|c|c|c|}\hline x & {4} & {7} & {3} & {8} & {6} & {5} & {6} & {3} & {9} & {4.5} \\ \hline y & {10} & {7} & {15} & {9} & {5} & {6} & {6} & {14} & {14} & {8} \\ \hline\end{array} $$

In \(7-9,\) find the mean, median, range, and interquartile range for each set of data to the nearest tenth. $$ \begin{array}{|c|c|}\hline x_{i} & {f_{i}} \\ \hline 11 & {5} \\ {16} & {8} \\\ {19} & {9} \\ {31} & {6} \\ {37} & {5} \\ {32} & {5} \\ {35} & {6} \\\ \hline\end{array} $$

In \(7-14,\) for each of the given correlation coefficients, describe the linear correlation as strong positive, moderate positive, none, moderate negative, or strong negative. \(r=-0.1\)

In \(9-14,\) find the median and the first and third quartiles for each set of data values. \(2,3,5,8,9,11,15,16,17,20,22,23,25\)

Graph the histogram of each set of data. \(\begin{array}{|c|c|}\hline x_{i} & {f_{i}} \\ \hline 35-39 & {13} \\ \hline 30-34 & {19} \\ \hline 25-29 & {10} \\ \hline 20-24 & {13} \\ \hline 20-1 & {8} \\ \hline 15-14 & {8} \\ \hline 10-14 & {19} \\ \hline 5-9 & {15} \\\ \hline\end{array}\)

The following data represents the yearly salaries, in thousands of dollars, of 10 basketball players. $$ \begin{array}{rlll}{533} & {427} & {800} & {687} & {264} & {264} & {125} & {602} & {249} & {19,014}\end{array} $$ a. Find the mean and median salaries of the 10 players. b. Which measure of central tendency is more representative of the data? Explain. c. Find the outlier for the set of data. d. Remove the outlier from the set of data and recalculate the mean and median salaries. e. After removing the outlier from the set of data, is the mean more or less representative of the data?

In \(7-14,\) for each of the given correlation coefficients, describe the linear correlation as strong positive, moderate positive, none, moderate negative, or strong negative. \(r=0.3\)

A set of data is normally distributed with a mean of 40 and a standard deviation of \(5 .\) Find a data value that is: a. 1 standard deviation above the mean b. 2.4 standard deviations above the mean c. 1 standard deviation below the mean d. 2.4 standard deviations below the mean

The given values represent data for a sample. Find the variance and the standard deviation based on this sample. 6, 4, 9, 11, 4, 3, 22, 3, 7, 10

In \(9-14,\) find the median and the first and third quartiles for each set of data values. \(34,35,35,36,38,40,42,43,43,43,44,46,48,50\)

Graph the histogram of each set of data. \(\begin{array}{|c|c|}\hline x_{i} & {f_{i}} \\ \hline 101-110 & {3} \\\ \hline 91-100 & {6} \\ \hline 81-90 & {10} \\ \hline 71-80 & {13} \\ \hline 61-70 & {14} \\ \hline 51-60 & {2} \\ \hline 41-50 & {2} \\\ \hline\end{array}\)

In \(9-13 :\) a. Create a scatter plot for the data. b. Determine which regression model is the most appropriate for the data. Justify your answer. c. Find the regression equation. Round the coefficient of the regression equation to three decimal places. $$ \begin{array}{|c|c|c|c|c|c|c|c|}\hline x & {3.3} & {-3.8} & {-2.1} & {0.4} & {3.5} & {-3.8} & {-1.8} & {-0.4} & {2.4} & {1.2} \\ \hline y & {12.5} & {-17.1} & {-3.6} & {0.4} & {15.0} & {-18.9} & {-2.1} & {-0.4} & {4.2} & {3.4} \\\ \hline\end{array} $$

In \(11-17 :\) a. Draw a scatter plot. b. Does the data set show strong positive linear correlation, moderate positive linear correlation, no linear correlation, moderate negative linear correlation, or strong negative linear correlation? c. If there is strong or moderate correlation, write the equation of the regression line that approximates the data. The following table shows the number of gallons of gasoline needed to fill the tank of a car and the number of miles driven since the previous time the tank was filled. $$ \begin{array}{|c|c|c|c|c|c|c|c|c|}\hline \text { Gallons } & {8.5} & {7.6} & {9.4} & {8.3} & {10.5} & {8.7} & {9.6} & {4.3} & {6.1} & {7.8} \\ \hline \text { Miles } & {255} & {230} & {295} & {250} & {315} & {260} & {290} & {130} & {180} & {235} \\ \hline\end{array} $$

In \(7-14,\) for each of the given correlation coefficients, describe the linear correlation as strong positive, moderate positive, none, moderate negative, or strong negative. \(r=1\)

In \(11-14,\) select the numeral that precedes the choice that best completes the statement or answers the question. The playing life of a Euclid mp3 player is normally distributed with a mean of \(30,000\) hours and a standard deviation of 500 hours. Matt's mp3 player lasted for \(31,500\) hours. His \(\mathrm{mp} 3\) player lasted longer than what percent of other Euclid mp3 players? $$ \begin{array}{llll}{\text { (1) } 68 \%} & {\text { (2) } 95 \%} & {\text { (3) } 99.7 \%} & {\text { (4) more than } 99.8 \%}\end{array} $$

The given values represent data for a sample. Find the variance and the standard deviation based on this sample. 12.1, 33.3, 45.5, 60.1, 94.2, 22.2

In \(9-14,\) find the median and the first and third quartiles for each set of data values. \(23,27,15,38,12,17,22,39,28,20,27,18,25,28,30,29\)

The ages of students in a Spanish class are shown in the table. Find the range and the interquartile range. $$ \begin{array}{|c|c|}\hline \text { Age } & {\text { Frequency }} \\ \hline 19 & {1} \\ {18} & {8} \\ {17} & {8} \\ {16} & {6} \\ {15} & {2} \\\ \hline\end{array} $$

In \(7-14,\) for each of the given correlation coefficients, describe the linear correlation as strong positive, moderate positive, none, moderate negative, or strong negative. \(r=-0.5\)

In \(11-14,\) select the numeral that precedes the choice that best completes the statement or answers the question. The scores of a test are normally distributed. If the mean is 50 and the standard deviation is \(8,\) then a student who scored 38 had a z-score of $$ \begin{array}{llll}{\text { (1) } 1.5} & {\text { (2) }-1.5} & {\text { (3) } 12} & {\text { (4) }-12}\end{array} $$

The given values represent data for a sample. Find the variance and the standard deviation based on this sample. 15, 10, 16, 19, 10, 19, 14, 17

In \(9-14,\) find the median and the first and third quartiles for each set of data values. \(92,86,77,85,88,90,81,83,95,76,65,88,91,81,88,87,95\)

In \(11-17 :\) a. Draw a scatter plot. b. Does the data set show strong positive linear correlation, moderate positive linear correlation, no linear correlation, moderate negative linear correlation, or strong negative linear correlation? c. If there is strong or moderate correlation, write the equation of the regression line that approximates the data. Jack Sheehan looked through some of his favorite recipes to compare the number of calories per serving to the number of grams of fat. The table below shows the results. $$ \begin{array}{|c|c|c|c|c|c|c|c|c|c|}\hline \text { Calories } & {310} & {210} & {260} & {290} & {320} & {245} & {293} & {220} & {260} & {350} \\ \hline F a t & {5} & {11} & {12} & {14} & {16} & {7} & {10} & {8} & {8} & {15} \\\ \hline\end{array} $$

In \(9-13 :\) a. Create a scatter plot for the data. b. Determine which regression model is the most appropriate for the data. Justify your answer. c. Find the regression equation. Round the coefficient of the regression equation to three decimal places. $$ \begin{array}{|c|c|c|c|c|c|c|c|c|c|}\hline x & {1} & {2} & {3} & {4} & {5} & {6} & {7} & {8} & {9} & {10} \\ \hline y & {2.7} & {2.3} & {2.0} & {1.7} & {1.5} & {1.2} & {1.1} & {0.9} & {0.8} & {0.7} \\ \hline\end{array} $$

The table shows the number of hours that 40 third graders reported studying a week. Find the range and the interquartile range. $$ \begin{array}{|c|c|c|c|c|c|c|c|c|c|}\hline \text { Hours } & {3} & {4} & {5} & {6} & {7} & {8} & {9} & {10} & {11} & {12} \\ \hline \text { Frequency } & {2} & {1} & {3} & {3} & {5} & {8} & {8} & {5} & {4} & {1} \\\ \hline\end{array} $$

In \(11-14,\) select the numeral that precedes the choice that best completes the statement or answers the question. The heights of 10 -year-old children are normally distributed with a mean of 138 centimeters with a standard deviation of 5 centimeters. The height of a 10 -year-old child who is as tall as or taller than 95.6\(\%\) of all 10 -year-old children is $$ \begin{array}{ll}{\text { (1) between } 138 \text { and } 140 \mathrm{cm} .} & {\text { (2) between } 140 \text { and } 145 \mathrm{cm} .} \\ {\text { (3) between } 145 \text { and } 148 \mathrm{cm} .} & {\text { (4) taller than } 148 \mathrm{cm} .}\end{array} $$

The given values represent data for a sample. Find the variance and the standard deviation based on this sample. 1, 3, 5, 22, 30, 45, 50, 55, 60, 70

In \(13-18,\) find the mean and the median for each set of data to the nearest tenth. $$ \begin{array}{|c|c|}\hline x_{i} & {f_{i}} \\ \hline 2 |-25 & {2} \\ {16-20} & {3} \\ {11-15} & {12} \\ {6-10} & {6} \\ {1-5} & {1} \\\ \hline\end{array} $$

In \(9-14,\) find the median and the first and third quartiles for each set of data values. \(75,72,69,68,66,65,64,63,63,61,60,59,59,58,56,54,52,50\)

Suggest a method that might be used to collect data for each study. Tell whether your method uses a population or a sample. Customer satisfaction at a restaurant

Mrs. Vroman bought \(\$ 1,000\) worth of shares in the Acme Growth Company. The table below shows the value of the investment over 10 years. $$ \begin{array}{|c|c|c|c|c|c|c|c|c|}\hline \text { Year } & {1} & {2} & {3} & {4} & {5} & {6} & {7} & {8} & {9} & {10} \\ \hline \text { Value }(\$) & {1,045} & {1,092} & {1,141} & {1,192} & {1,302} & {1,361} & {1,422} & {1,486} & {1,553} \\ \hline\end{array} $$ a. Find the exponential regression equation for the data with the coefficient and base rounded to three decimal places. b. Predict, to the nearest dollar, the value of the Vromans' investment after 11 years.

The table shows the number of pounds lost during the first month by people enrolled in a weight-loss program. a. Find the range. b. Find the interquartile range. c. Which of the data values is an outlier? $$ \begin{array}{|l|l|l|l|l|l|l|l|l|l|l|}\hline \text { Pounds Lost } & {1} & {2} & {3} & {4} & {5} & {6} & {7} & {8} & {9} & {11} & {15} \\ \hline \text { Frequency } & {1} & {1} & {2} & {2} & {6} & {10} & {7} & {7} & {2} & {1} & {1} \\\ \hline\end{array} $$

In \(7-14,\) for each of the given correlation coefficients, describe the linear correlation as strong positive, moderate positive, none, moderate negative, or strong negative. \(r=-0.95\)

In \(11-14,\) select the numeral that precedes the choice that best completes the statement or answers the question. The heights of 200 women are normally distributed. The mean height is 170 centimeters with a standard deviation of 10 centimeters. What is the best estimate of the number of women in this group who are between 160 and 170 centimeters tall? $$ \begin{array}{llll}{\text { (1) } 20} & {\text { (2) } 34} & {\text { (3) } 68} & {\text { (4) } 136}\end{array} $$

The given values represent data for a sample. Find the variance and the standard deviation based on this sample. \(\begin{array}{|c|c|}\hline x_{i} & {f_{i}} \\ \hline 55 & {11} \\ {50} & {15} \\ {45} & {4} \\ {40} & {1} \\ {35} & {1} \\ {35} & {12} \\ {30} & {4} \\ \hline\end{array}\)

In \(13-18,\) find the mean and the median for each set of data to the nearest tenth. $$ \begin{array}{|c|c|}\hline x_{i} & {f_{i}} \\ \hline 91-100 & {5} \\ {81-90} & {8} \\ {71-80} & {10} \\ {61-70} & {6} \\ {51-60} & {0} \\ {41-50} & {1} \\\ \hline\end{array} $$

In \(9-14,\) find the median and the first and third quartiles for each set of data values. \(32,32,30,30,29,27,26,22,20,20,19,18,17\)

Suggest a method that might be used to collect data for each study. Tell whether your method uses a population or a sample. Temperature of a patient in a hospital over a period of time

The 14 students on the track team recorded the following number of seconds as their best time for the 100 -yard dash: $$ \begin{array}{lllllll}{13.5} & {13.7} & {13.1} & {13.0} & {13.3} & {13.2} & {13.0} \\ {12.8} & {13.4} & {13.3} & {13.1} & {12.7} & {13.2} & {13.5}\end{array} $$ Find the range and the interquartile range.

The given values represent data for a sample. Find the variance and the standard deviation based on this sample. \(\begin{array}{|c|c|}\hline x_{i} & {f_{i}} \\ \hline 33 & {3} \\ {34} & {1} \\\ {35} & {4} \\ {36} & {6} \\ {37} & {5} \\ {38} & {11} \\ {39} & {6} \\\ \hline\end{array}\)

In \(13-18,\) find the mean and the median for each set of data to the nearest tenth. $$ \begin{array}{|c|c|}\hline & {x_{i}} & {f_{i}} \\ \hline \$ 1.51-\$ 1.60 & {2} \\ {\$ 1.41-\$ 1.50} & {5} \\ {\$ 1.31-\$ 1.40} & {14} \\ {\$ 1.21-\$ 1.30} & {4} \\ {\$ 1.11-\$ 1.20} & {2} \\ {\$ 1.01-\$ 1.10} & {3} \\\ \hline\end{array} $$

A student received the following grades on six tests: \(90,92,92,95,95, x\) a. For what value(s) of \(x\) will the set of grades have no mode? b. For what value(s) of \(x\) will the set of grades have only one mode? c. For what value (s) of \(x\) will the set of grades be bimodal?

Steve kept a record of the height of a tree that he planted. The heights are shown in the table. $$ \begin{array}{|l|l|l|l|l|l|l|}\hline \text { Age of Tree in Years } & {1} & {3} & {5} & {7} & {9} & {11} & {13} \\ \hline \text { Height in lnches } & {7} & {12} & {15} & {16.5} & {17.8} & {19} & {20} \\ \hline\end{array} $$ a. Write an equation that best fits the data. b. What was the height of the tree after 2 years? c. If the height of the tree continues in this same pattern, how tall will the tree be after 20 years?

The orbital speed in kilometers per second and the distance from the sun in millions of kilo- meters of each of six planets is given in the table. $$ \begin{array}{|c|c|c|c|c|c|c|}\hline \text { Planet } & {\text { Venus }} & {\text { Earth }} & {\text { Mars }} & {\text { Jupiter }} & {\text { Saturn }} & {\text { Uranus }} \\ \hline \text { Orbital Speed } & {34.8} & {29.6} & {23.9} & {12.9} & {9.6} & {6.6} \\ \hline \text { Distance from the Sun } & {108.2} & {149.6} & {227.9} & {778.0} & {1,427} & {2,871} \\\ \hline\end{array} $$ a. Find the regression equation that appears to be the best fit for the data with the coefficient rounded to three decimal places. b. Neptune has an orbital speed of 5.45 \(\mathrm{km} / \mathrm{sec}\) and is \(4,504\) million kilometers from the sun. Does the equation found for the six planets given in the table fit the data for Neptune?

The following data represent the waiting times, in minutes, at Post Office \(\mathrm{A}\) and Post Office \(\mathrm{B}\) at noon for a period of several days. $$ \begin{array}{l}{\mathrm{A} : 1,2,2,2,3,3,3,3,3,3,3,9,10} \\ {\mathrm{B} : 1,2,2,3,3,5,5,6,6,7,7,8,8,9,10}\end{array} $$ a. Find the range of each set of data. Are the ranges the same? b. Graph the box-and-whisker plot of each set of data. c. Find the interquartile range of each set of data. d. If the data values are representative of the waiting times at each post office, which post office should you go to at noon if you are in a hurry? Explain.

The length of time that it takes Ken to drive to work represents a normal distribution with a mean of 25 minutes and a standard deviation of 4.5 minutes. If Ken allows 35 minutes to get to work, what percent of the time can he expect to be late?

The given values represent data for a sample. Find the variance and the standard deviation based on this sample. \(\begin{array}{|c|c|}\hline x_{i} & {f_{i}} \\ \hline 1 & {3} \\ {2} & {3} \\\ {3} & {3} \\ {4} & {3} \\ {5} & {3} \\ {6} & {3} \\ {7} & {3} \\\ \hline\end{array}\)

In \(13-18,\) find the mean and the median for each set of data to the nearest tenth. $$ \begin{array}{|c|c|}\hline x_{1} & {f_{1}} \\ \hline 17-19 & {20} \\ {14-16} & {27} \\ {11-13} & {32} \\ {8-10} & {39} \\ {5-7} & {32} \\\ \hline\end{array} $$