 13.5.13.1.151: Measures of dispersion are used to indicate the spread or of the data.
 13.5.13.1.152: The difference between the highest and lowest values in a set of da...
 13.5.13.1.153: The measure of dispersion that measures how much the data differ fr...
 13.5.13.1.154: The symbol, s, is used to indicate the standard deviation of a(n) .
 13.5.13.1.155: The symbol, s, is used to indicate the standard deviation of a(n) .
 13.5.13.1.156: The standard deviation of a set of data in which all the data value...
 13.5.13.1.157: In Exercises 714, determine the range and standard deviation of the...
 13.5.13.1.158: In Exercises 714, determine the range and standard deviation of the...
 13.5.13.1.159: In Exercises 714, determine the range and standard deviation of the...
 13.5.13.1.160: In Exercises 714, determine the range and standard deviation of the...
 13.5.13.1.161: In Exercises 714, determine the range and standard deviation of the...
 13.5.13.1.162: In Exercises 714, determine the range and standard deviation of the...
 13.5.13.1.163: In Exercises 714, determine the range and standard deviation of the...
 13.5.13.1.164: In Exercises 714, determine the range and standard deviation of the...
 13.5.13.1.165: Digital Cameras Determine the range and standard deviation of the f...
 13.5.13.1.166: Years Until Retirement Seven employees at a large company were aske...
 13.5.13.1.167: Camping Tents Determine the range and standard deviation of the fol...
 13.5.13.1.168: Prescription Prices The amount of money seven people spent on presc...
 13.5.13.1.169: Can you think of any situations in which a large standard deviation...
 13.5.13.1.170: Can you think of any situations in which a small standard deviation...
 13.5.13.1.171: Without actually doing the calculations, decide which, if either, o...
 13.5.13.1.172: Without actually doing the calculations, decide which, if either, o...
 13.5.13.1.173: By studying the standard deviation formula, explain why the standar...
 13.5.13.1.174: Patricia Wolff teaches two statistics classes, one in the morning a...
 13.5.13.1.175: Count Your Money Six people were asked to determine the amount of m...
 13.5.13.1.176: a) Adding to or Subtracting from Each Number Pick any five numbers....
 13.5.13.1.177: a) Multiplying Each Number Pick any five numbers. Compute the mean ...
 13.5.13.1.178: Waiting in Line Consider the following illustrations of two bankcu...
 13.5.13.1.179: Height and Weight Distribution The chart shown on the right uses th...
 13.5.13.1.180: Athletes Salaries The tables on page 815 list the 10 highestpaid a...
 13.5.13.1.181: Oil Change Jiffy Lube has franchises in two different parts of a ci...
 13.5.13.1.182: Calculate the range and standard deviation of your exam grades in t...
 13.5.13.1.183: Construct a set of five pieces of data with a mean, median, mode, a...
 13.5.13.1.184: Use a calculator with statistical function keys to find the mean an...
Solutions for Chapter 13.5: Statistics
Full solutions for A Survey of Mathematics with Applications  9th Edition
ISBN: 9780321759665
Solutions for Chapter 13.5: Statistics
Get Full SolutionsThis textbook survival guide was created for the textbook: A Survey of Mathematics with Applications, edition: 9. Since 34 problems in chapter 13.5: Statistics have been answered, more than 69695 students have viewed full stepbystep solutions from this chapter. This expansive textbook survival guide covers the following chapters and their solutions. Chapter 13.5: Statistics includes 34 full stepbystep solutions. A Survey of Mathematics with Applications was written by and is associated to the ISBN: 9780321759665.

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

Associative Law (AB)C = A(BC).
Parentheses can be removed to leave ABC.

Column space C (A) =
space of all combinations of the columns of A.

Factorization
A = L U. If elimination takes A to U without row exchanges, then the lower triangular L with multipliers eij (and eii = 1) brings U back to 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!).

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

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.

Krylov subspace Kj(A, b).
The subspace spanned by b, Ab, ... , AjIb. Numerical methods approximate A I b by x j with residual b  Ax j in this subspace. A good basis for K j requires only multiplication by A at each step.

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.

Nullspace matrix N.
The columns of N are the n  r special solutions to As = O.

Particular solution x p.
Any solution to Ax = b; often x p has free variables = o.

Pivot columns of A.
Columns that contain pivots after row reduction. These are not combinations of earlier columns. The pivot columns are a basis for the column space.

Positive definite matrix A.
Symmetric matrix with positive eigenvalues and positive pivots. Definition: x T Ax > 0 unless x = O. Then A = LDLT with diag(D» O.

Reflection matrix (Householder) Q = I 2uuT.
Unit vector u is reflected to Qu = u. All x intheplanemirroruTx = o have Qx = x. Notice QT = Q1 = Q.

Saddle point of I(x}, ... ,xn ).
A point where the first derivatives of I are zero and the second derivative matrix (a2 II aXi ax j = Hessian matrix) is indefinite.

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

Subspace S of V.
Any vector space inside V, including V and Z = {zero vector only}.

Transpose matrix AT.
Entries AL = Ajj. AT is n by In, AT A is square, symmetric, positive semidefinite. The transposes of AB and AI are BT AT and (AT)I.

Vector v in Rn.
Sequence of n real numbers v = (VI, ... , Vn) = point in Rn.

Volume of box.
The rows (or the columns) of A generate a box with volume I det(A) I.