 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 5073 students have viewed full stepbystep solutions from this chapter. Excursions in Modern Mathematics was written by and is associated to the ISBN: 9781292022048.

Adjacency matrix of a graph.
Square matrix with aij = 1 when there is an edge from node i to node j; otherwise aij = O. A = AT when edges go both ways (undirected). Adjacency matrix of a graph. Square matrix with aij = 1 when there is an edge from node i to node j; otherwise aij = O. A = AT when edges go both ways (undirected).

Basis for V.
Independent vectors VI, ... , v d whose linear combinations give each vector in V as v = CIVI + ... + CdVd. V has many bases, each basis gives unique c's. A vector space has many bases!

Cholesky factorization
A = CTC = (L.J]))(L.J]))T for positive definite A.

Companion matrix.
Put CI, ... ,Cn in row n and put n  1 ones just above the main diagonal. Then det(A  AI) = ±(CI + c2A + C3A 2 + .•. + cnA nl  An).

Complete solution x = x p + Xn to Ax = b.
(Particular x p) + (x n in nullspace).

Elimination matrix = Elementary matrix Eij.
The identity matrix with an extra eij in the i, j entry (i # j). Then Eij A subtracts eij times row j of A from row i.

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.

Four Fundamental Subspaces C (A), N (A), C (AT), N (AT).
Use AT for complex A.

Free variable Xi.
Column i has no pivot in elimination. We can give the n  r free variables any values, then Ax = b determines the r pivot variables (if solvable!).

GramSchmidt orthogonalization A = QR.
Independent columns in A, orthonormal columns in Q. Each column q j of Q is a combination of the first j columns of A (and conversely, so R is upper triangular). Convention: diag(R) > o.

Hankel matrix H.
Constant along each antidiagonal; hij depends on i + j.

Kronecker product (tensor product) A ® B.
Blocks aij B, eigenvalues Ap(A)Aq(B).

Length II x II.
Square root of x T x (Pythagoras in n dimensions).

Linearly dependent VI, ... , Vn.
A combination other than all Ci = 0 gives L Ci Vi = O.

Multiplicities AM and G M.
The algebraic multiplicity A M of A is the number of times A appears as a root of det(A  AI) = O. The geometric multiplicity GM is the number of independent eigenvectors for A (= dimension of the eigenspace).

Normal equation AT Ax = ATb.
Gives the least squares solution to Ax = b if A has full rank n (independent columns). The equation says that (columns of A)·(b  Ax) = o.

Pivot.
The diagonal entry (first nonzero) at the time when a row is used in elimination.

Schur complement S, D  C A } B.
Appears in block elimination on [~ g ].

Simplex method for linear programming.
The minimum cost vector x * is found by moving from comer to lower cost comer along the edges of the feasible set (where the constraints Ax = b and x > 0 are satisfied). Minimum cost at a comer!