Chapter 15

Explain the difference between interpolation and extrapolation.

Explain the difference between univariate and bivariate data and give an example of each.

In any set of data, is it always true that \(x_{i}=i ?\) For example, in a set of data with more than three data values, does \(x_{4}=4 ?\) Justify your answer.

Does a correlation coefficient of \(-1\) indicate a lower degree of correlation than a correlation coefficient of 0\(?\) Explain why or why not.

A student's scores on five tests were \(98,97,95,93,\) and \(67 .\) Explain why this set of scores does not represent a normal distribution.

The sets of data for two different statistical studies are identical. The first set of data represents the data for all of the cases being studied and the second represents the data for a sample of the cases being studied. Which set of data has the larger standard deviation? Explain your answer.

Adelaide said that since, in Example \(2,\) there are 10 employees whose ages are in the \(45-49\) interval, there must be two employees of age \(45 .\) Do you agree with Adelaide? Explain why or why not.

Cameron said that the number of data values of any set of data that are less than the lower quartile or greater than the upper quartile is exactly 50\(\%\) of the number of data values. Do you agree with Cameron? Explain why or why not.

In a controlled experiment, two groups are formed to determine the effectiveness of a new cold remedy. One group takes the medicine and one does not. Explain why the two groups are necessary.

What are the possible sources of error when using extrapolation based on the line of best fit?

Explain when the power function, \(y=a x^{b},\) has only positive or only negative \(y\) -values and when it has both positive and negative \(y\) -values.

What is the relationship between slope and correlation? Can slope be used to measure the strength of a correlation? Explain.

If you keep a record of the temperature in degrees Fahrenheit and in degrees Celsius for a month, what would you expect the correlation coefficient to be? Justify your answer.

Elaine said that the variance is the square of the standard deviation. Do you agree with Elaine? Explain why or why not.

Gail said that since, in Example \(2,\) there are 10 employees whose ages are in the \(45-49\) interval, there must at least two employees who are the same age. Do you agree with Gail? Explain why or why not.

Carlos said that for a set of 2\(n\) data values or of \(2 n+1\) data values, the lower quartile is the median of the smallest \(n\) values and the upper quartile is the median of the largest \(n\) values. Do you agree with Carlos? Explain why or why not.

In \(3-5 :\) a. Determine the appropriate linear regression model to use based on the scatter plot of the given data. b. Find an approximate value for \(y\) for the given value of \(x .\) Find an approximate value for \(x\) for the given value of \(y .\) b. \(x=5.7 \quad\) c. \(y=1.25\) $$ \begin{array}{|c|c|c|c|c|c|c|c|c|}\hline x & {1} & {2} & {3} & {4} & {5} & {6} & {7} & {8} & {9} & {10} \\ \hline y & {1.05} & {1.10} & {1.16} & {1.22} & {1.28} & {1.34} & {1.41} & {1.48} & {1.55} & {1.62} \\ \hline\end{array} $$

In \(3-6,\) is the set of data to be collected univariate or bivariate? The science and math grades of all students in a school

In \(3-6,\) find the range and the interquartile range for each set of data. $$ 3,5,7,9,11,13,15,17,19 $$

In \(3-9,\) for a normal distribution, determine what percent of the data values are in each given range. Between 1 standard deviation below the mean and 1 standard deviation above the mean

the given values represent data for a population. Find the variance and the standard deviation for each set of data.The given values represent data for a population. Find the variance and the standard deviation for each set of data. 9, 9, 10, 11, 5, 10, 12, 9, 10, 12, 6, 11, 11, 11

In \(3-8,\) find the mean, the median, and the mode of each set of data. Grades: \(74,78,78,80,80,80,82,88,90\)

Organize the data in a stem-and-leaf diagram. The grades on a chemistry test: \(\begin{array}{llllllllll}{95} & {90} & {84} & {85} & {74} & {67} & {78} & {86} & {54} & {82} \\ {75} & {67} & {92} & {66} & {90} & {68} & {88} & {85} & {76} & {87}\end{array}\)

In \(3-6,\) is the set of data to be collected univariate or bivariate? The weights of the 56 first-grade students in a school

In \(3-6,\) find the range and the interquartile range for each set of data. $$ 12,12,14,14,16,18,20,22,28,34 $$

In \(3-9,\) for a normal distribution, determine what percent of the data values are in each given range. Between 1 standard deviation below the mean and 2 standard deviations above the mean

The given values represent data for a population. Find the variance and the standard deviation for each set of data. 11, 6, 7, 13, 5, 8, 7, 10, 9, 11, 13, 12, 9, 16, 10

In \(3-8,\) find the mean, the median, and the mode for each set of data. $$ \begin{array}{|c|c|}\hline x_{i} & {f_{i}} \\ \hline 50 & {8} \\ {40} & {12} \\\ {30} & {17} \\ {20} & {10} \\ {10} & {3} \\ \hline\end{array} $$

In \(3-8,\) find the mean, the median, and the mode of each set of data. Heights: \(60,62,63,63,64,65,66,68,68,68,70,75\)

Organize the data in a stem-and-leaf diagram. The weights of people starting a weight-loss program: \(\begin{array}{lllllllllll}{173} & {210} & {182} & {190} & {175} & {169} & {236} & {192} & {203} & {196} & {201} \\ {187} & {205} & {195} & {224} & {177} & {195} & {207} & {188} & {184} & {196} & {155}\end{array}\)

In \(3-6,\) is the set of data to be collected univariate or bivariate? The weights and heights of the 56 first-grade students in a school

In \(3-6,\) find the range and the interquartile range for each set of data. $$ 12,17,23,31,46,54,67,76,81,93 $$

The given values represent data for a population. Find the variance and the standard deviation for each set of data. 20, 19, 20, 17, 18, 19, 42, 41, 41, 39, 39, 40

In \(3-8,\) find the mean, the median, and the mode for each set of data. $$ \begin{array}{|c|c|}\hline x_{i} & {f_{i}} \\ \hline 12 & {7} \\ {11} & {15} \\\ {10} & {13} \\ {9} & {16} \\ {8} & {16} \\ {8} & {14} \\ {7} & {15} \\\ {6} & {9} \\ {5} & {2} \\ \hline\end{array} $$

In \(3-8,\) find the mean, the median, and the mode of each set of data. Weights: \(110,112,113,115,15,116,118,118,125,134,145,148\)

Organize the data in a stem-and-leaf diagram. The heights, in centimeters, of 25 ten-year-old children: \(\begin{array}{llllllllllll}{137} & {134} & {130} & {144} & {131} & {141} & {136} & {140} & {137} & {129} & {139} & {137} & {144} \\ {127} & {147} & {143} & {132} & {132} & {142} & {142} & {131} & {129} & {138} & {151} & {137}\end{array}\)

In \(3-6,\) is the set of data to be collected univariate or bivariate? The number of siblings for each student in the first grade

In \(3-6,\) find the range and the interquartile range for each set of data. $$ 2,14,33,34,34,34,35,36,37,37,38,40,42 $$

In \(3-9,\) for a normal distribution, determine what percent of the data values are in each given range. Above 1 standard deviation below the mean

The given values represent data for a population. Find the variance and the standard deviation for each set of data. 20, 101, 48, 25, 63, 31, 20, 50, 16, 14, 245, 9

In \(3-8,\) find the mean, the median, and the mode for each set of data. $$ \begin{array}{|r|r|}\hline x_{i} & {f_{i}} \\ \hline 10 & {1} \\ {9} & {1} \\\ {8} & {3} \\ {7} & {7} \\ {6} & {6} \\ {5} & {2} \\ {4} & {2} \\\ \hline\end{array} $$

In \(3-8,\) find the mean, the median, and the mode of each set of data. Number of student absences: \(0,0,0,1,1,2,2,2,3,4,5,9\)

Organize the data in a frequency distribution table. The numbers of books read during the summer months by each of 25 students: \(\begin{array}{lllllllllllll}{2} & {2} & {5} & {1} & {3} & {0} & {7} & {2} & {4} & {3} & {3} & {1} & {8} \\ {5} & {7} & {3} & {4} & {1} & {0} & {6} & {3} & {4} & {1} & {1} & {2}\end{array}\)

In \(7-9,\) find the mean, median, range, and interquartile range for each set of data to the nearest tenth. $$ \begin{array}{|c|c|}\hline x_{i} & {f_{i}} \\ \hline 50 & {3} \\ {45} & {8} \\\ {40} & {12} \\ {35} & {15} \\ {30} & {11} \\ {25} & {7} \\ {20} & {4} \\\ \hline\end{array} $$

The given values represent data for a population. Find the variance and the standard deviation for each set of data. \(\begin{array}{|c|c|}\hline x_{i} & {f_{i}} \\ \hline 30 & {1} \\ {35} & {7} \\\ {40} & {10} \\ {45} & {9} \\ {50} & {9} \\ {55} & {8} \\ {60} & {6} \\\ \hline\end{array}\)

In \(3-8,\) find the mean, the median, and the mode for each set of data. $$ \begin{array}{|c|c|}\hline x_{i} & {f_{i}} \\ \hline \$ 1.10 & {1} \\ {\$ 1.20} & {5} \\ {\$ 1.30} & {8} \\ {\$ 1.40} & {6} \\ {\$ 1.50} & {6} \\\ \hline\end{array} $$

In \(3-8,\) find the mean, the median, and the mode of each set of data. Hourly wages: \(\$ 6.90, \$ 7.10, \$ 7.50, \$ 7.50, \$ 8.25, \$ 9.30, \$ 9.50, \$ 10.00\)

Organize the data in a frequency distribution table. The sizes of 26 pairs of jeans sold during a recent sale: \(\begin{array}{llllllllllllll}{8} & {12} & {14} & {10} & {12} & {16} & {14} & {6} & {10} & {9} & {8} & {13} & {12} \\ {8} & {12} & {10} & {12} & {14} & {10} & {12} & {16} & {10} & {11} & {15} & {8} & {14}\end{array}\)

In \(7-9,\) find the mean, median, range, and interquartile range for each set of data to the nearest tenth. $$ \begin{array}{|c|c|}\hline x_{i} & {f_{i}} \\ \hline 10 & {2} \\ {9} & {4} \\\ {8} & {6} \\ {7} & {9} \\ {6} & {3} \\ {5} & {3} \\ {4} & {2} \\ {3} & {0} \\ {2} & {1} \\ \hline\end{array} $$

In \(3-8,\) find the mean, the median, and the mode for each set of data. $$ \begin{array}{|c|c|}\hline x_{i} & {f_{i}} \\ \hline 95 & {2} \\ {90} & {8} \\\ {85} & {12} \\ {80} & {10} \\ {75} & {9} \\ {70} & {3} \\ {65} & {0} \\\ {60} & {1} \\ \hline\end{array} $$