 15.1: Exercises 1 through 4 refer to the data set shown in Table 12. The ...
 15.2: Exercises 1 through 4 refer to the data set shown in Table 12. The ...
 15.3: Exercises 1 through 4 refer to the data set shown in Table 12. The ...
 15.4: Exercises 1 through 4 refer to the data set shown in Table 12. The ...
 15.5: (a) Make a frequency table for the distances in Table 13. (b) Draw ...
 15.6: Draw a bar graph for the data in Table 13.
 15.7: Draw a bar graph for the hometoschool distances for the kindergar...
 15.8: Draw a bar graph for the hometoschool distances for the kindergar...
 15.9: Using the class intervals given in Exercise 7, draw a pie chart for...
 15.10: Using the class intervals given in Exercise 8, draw a pie chart for...
 15.11: Exercises 11 and 12 refer to the bar graph shown in Fig. 15 describ...
 15.12: Exercises 11 and 12 refer to the bar graph shown in Fig. 15 describ...
 15.13: Exercises 13 and 14 refer to the pie chart in Fig. 16.a) Is cause o...
 15.14: Exercises 13 and 14 refer to the pie chart in Fig. 16.Use the data ...
 15.15: Table 14 shows the class interval frequencies for the 2011 Critical...
 15.16: Table 15 shows the class interval frequencies for the 2011 Writing ...
 15.17: Table 16 shows the percentage of U.S. working married couples in wh...
 15.18: Table 17 shows the percentage of U.S. workers who are members of un...
 15.19: Exercises 19 and 20 refer to Table 18, which shows the birth weight...
 15.20: Exercises 19 and 20 refer to Table 18, which shows the birth weight...
 15.21: Exercises 21 and 22 refer to the two histograms shown in Fig. 17 su...
 15.22: Exercises 21 and 22 refer to the two histograms shown in Fig. 17 su...
 15.23: Consider the data set 53, 5, 7, 4, 8, 2, 8, 3, 66. (a) Find the ...
 15.24: Consider the data set 5 4, 6, 8, 5.2, 10.4, 10, 12.6, 136 (a) Fi...
 15.25: Find the average A and the median M of each data set. (a) 50, 1, 2,...
 15.26: Find the average A and the median M of each data set. (a) 51, 2, 1,...
 15.27: Find the average A and the median M of each data set. (a) 55, 10, 1...
 15.28: Find the average A and the median M of each data set. (a) 55, 10, 1...
 15.29: Table 19 shows the results of a 5point musical aptitude test given...
 15.30: Table 20 shows the ages of the firefighters in the Cleansburg Fire ...
 15.31: Table 21 shows the relative frequencies of the scores of a group of...
 15.32: Table 22 shows the relative frequencies of the scores of a group of...
 15.33: Consider the data set 5 5, 7, 4, 8, 2, 8, 3, 66. (a) Find the fi...
 15.34: Consider the data set 5 4, 6, 8, 5.2, 10.4, 10, 12.6, 136. (a) F...
 15.35: For each data set, find the 75th and the 90th percentiles. (a) 51, ...
 15.36: For each data set, find the 10th and the 25th percentiles. (a) 51, ...
 15.37: This exercise refers to the age distribution in the Cleansburg Fire...
 15.38: This exercise refers to the math quiz scores shown in Table 22 (Exe...
 15.39: Exercise 39 and 40 refer to the 2011 SAT scores. In 2011, a total o...
 15.40: Exercise 39 and 40 refer to the 2011 SAT scores. In 2011, a total o...
 15.41: Consider the data set 5 5, 7, 4, 8, 2, 8, 3, 66. (a) Find the fi...
 15.42: Consider the data set 5 4, 6, 8, 5.2, 10.4, 10, 12.6, 136. (a) F...
 15.43: This exercise refers to the distribution of ages in the Cleansburg ...
 15.44: This exercise refers to the distribution of math quiz scores shown ...
 15.45: Exercises 45 and 46 refer to the two box plots in Fig. 18 showing t...
 15.46: Exercises 45 and 46 refer to the two box plots in Fig. 18 showing t...
 15.47: For the data set 5 5, 7, 4, 8, 2, 8, 3, 66, find (a) the range. ...
 15.48: For the data set 5 4, 6, 8, 5.2, 10, 4, 10, 12.6, 136, find (a) ...
 15.49: A realty company has sold N = 341 homes in the last year. The five...
 15.50: This exercise refers to the starting salaries of Tasmania State Uni...
 15.51: For Exercises 51 through 54, you should use the following definitio...
 15.52: For Exercises 51 through 54, you should use the following definitio...
 15.53: For Exercises 51 through 54, you should use the following definitio...
 15.54: For Exercises 51 through 54, you should use the following definitio...
 15.55: The purpose of Exercises 55 through 58 is to practice computing sta...
 15.56: The purpose of Exercises 55 through 58 is to practice computing sta...
 15.57: The purpose of Exercises 55 through 58 is to practice computing sta...
 15.58: The purpose of Exercises 55 through 58 is to practice computing sta...
 15.59: Exercises 59 and 60 refer to the mode of a data set. The mode of a ...
 15.60: Exercises 59 and 60 refer to the mode of a data set. The mode of a ...
 15.61: Mikes average on the first five exams in Econ 1A is 88. What must h...
 15.62: Sarahs overall average in Physics 101 was 93%. Her average was base...
 15.63: In 2011, N = 1,647,123 students took the SAT. Table 15 shows the cl...
 15.64: Explain each of the following statements regarding the median score...
 15.65: In 2006, the median SAT score was the average of d732,872 and d732,...
 15.66: In 2004, the third quartile of the SAT scores was d1,064,256, where...
 15.67: (a) Give an example of 10 numbers with an average less than the med...
 15.68: Suppose that the average of 10 numbers is 7.5 and that the smallest...
 15.69: This exercise refers to the 2008 payrolls of major league baseball ...
 15.70: What happens to the fivenumber summary of the Stat 101 data set (s...
 15.71: Let A denote the average and M the median of the data set 5x1, x2, ...
 15.72: Explain why the data sets 5x1, x2, x3, . . . , xN6 and 5x1 + c, x2 ...
 15.73: Exercises 73 and 74 refer to histograms with unequal class interval...
 15.74: Exercises 73 and 74 refer to histograms with unequal class interval...
 15.75: A data set is called constant if every value in the data set is the...
 15.76: Show that the standard deviation of any set of numbers is always le...
 15.77: (a) Show that if 5x1, x2, x3, . . . , xN 6 is a data set with mean ...
 15.78: Show that if A is the mean and M is the median of the data set 51, ...
 15.79: Suppose that the standard deviation of the data set 5x1, x2, x3, . ...
 15.80: Chebyshevs theorem. The Russian mathematician P. L. Chebyshev (1821...
Solutions for Chapter 15: Graphs, Charts, and Numbers
Full solutions for Excursions in Modern Mathematics  8th Edition
ISBN: 9781292022048
Solutions for Chapter 15: Graphs, Charts, and Numbers
Get Full SolutionsThis expansive textbook survival guide covers the following chapters and their solutions. This textbook survival guide was created for the textbook: Excursions in Modern Mathematics, edition: 8. Chapter 15: Graphs, Charts, and Numbers includes 80 full stepbystep solutions. Since 80 problems in chapter 15: Graphs, Charts, and Numbers have been answered, more than 13545 students have viewed full stepbystep solutions from this chapter. Excursions in Modern Mathematics was written by and is associated to the ISBN: 9781292022048.

Affine transformation
Tv = Av + Vo = linear transformation plus shift.

Augmented matrix [A b].
Ax = b is solvable when b is in the column space of A; then [A b] has the same rank as A. Elimination on [A b] keeps equations correct.

Characteristic equation det(A  AI) = O.
The n roots are the eigenvalues of A.

Eigenvalue A and eigenvector x.
Ax = AX with x#O so det(A  AI) = o.

Elimination.
A sequence of row operations that reduces A to an upper triangular U or to the reduced form R = rref(A). Then A = LU with multipliers eO in L, or P A = L U with row exchanges in P, or E A = R with an invertible E.

Exponential eAt = I + At + (At)2 12! + ...
has derivative AeAt; eAt u(O) solves u' = Au.

Free columns of A.
Columns without pivots; these are combinations of earlier columns.

GaussJordan method.
Invert A by row operations on [A I] to reach [I AI].

Incidence matrix of a directed graph.
The m by n edgenode incidence matrix has a row for each edge (node i to node j), with entries 1 and 1 in columns i and j .

Lucas numbers
Ln = 2,J, 3, 4, ... satisfy Ln = L n l +Ln 2 = A1 +A~, with AI, A2 = (1 ± /5)/2 from the Fibonacci matrix U~]' Compare Lo = 2 with Fo = O.

Network.
A directed graph that has constants Cl, ... , Cm associated with the edges.

Normal matrix.
If N NT = NT N, then N has orthonormal (complex) eigenvectors.

Outer product uv T
= column times row = rank one matrix.

Projection matrix P onto subspace S.
Projection p = P b is the closest point to b in S, error e = b  Pb is perpendicularto S. p 2 = P = pT, eigenvalues are 1 or 0, eigenvectors are in S or S...L. If columns of A = basis for S then P = A (AT A) 1 AT.

Projection p = a(aTblaTa) onto the line through a.
P = aaT laTa has rank l.

Similar matrices A and B.
Every B = MI AM has the same eigenvalues as A.

Trace of A
= sum of diagonal entries = sum of eigenvalues of A. Tr AB = Tr BA.

Triangle inequality II u + v II < II u II + II v II.
For matrix norms II A + B II < II A II + II B II·

Unitary matrix UH = U T = UI.
Orthonormal columns (complex analog of Q).

Vector addition.
v + w = (VI + WI, ... , Vn + Wn ) = diagonal of parallelogram.