 15.1: In 13, determine if the data to be collected is univariate or bivar...
 15.2: In 13, determine if the data to be collected is univariate or bivar...
 15.3: In 13, determine if the data to be collected is univariate or bivar...
 15.4: Name and describe four common ways of obtaining data for a statisti...
 15.5: In order to determine the average grade for all students who took a...
 15.6: Sues grades are 88, 87, 85, 82, 80, 80, 78, and 60. a. What is the ...
 15.7: The hours, xi , that Peg worked for each of the last 15 weeks are s...
 15.8: Each time Kurt swims, he times a few random laps. His times, in sec...
 15.9: In 912, for each of the given scatter plots: a. Describe the correl...
 15.10: In 912, for each of the given scatter plots: a. Describe the correl...
 15.11: In 912, for each of the given scatter plots: a. Describe the correl...
 15.12: In 912, for each of the given scatter plots: a. Describe the correl...
 15.13: A school investment club chose nine stocks at the beginning of the ...
 15.14: The table lists the six states that had the largest percent of incr...
 15.15: The salaries that Aaron earned for four years are shown in the tabl...
 15.16: Mrs. Brudek bakes and sells cookies. The table shows the number of ...
 15.17: In a local park, an attempt is being made to control the deer popul...
 15.18: In 1821, use your answers to Exercises 1417 to estimate the require...
 15.19: In 1821, use your answers to Exercises 1417 to estimate the require...
 15.20: In 1821, use your answers to Exercises 1417 to estimate the require...
 15.21: In 1821, use your answers to Exercises 1417 to estimate the require...
Solutions for Chapter 15: STATISTICS
Full solutions for Amsco's Algebra 2 and Trigonometry  1st Edition
ISBN: 9781567657029
Solutions for Chapter 15: STATISTICS
Get Full SolutionsSince 21 problems in chapter 15: STATISTICS have been answered, more than 30969 students have viewed full stepbystep solutions from this chapter. This expansive textbook survival guide covers the following chapters and their solutions. This textbook survival guide was created for the textbook: Amsco's Algebra 2 and Trigonometry, edition: 1. Amsco's Algebra 2 and Trigonometry was written by and is associated to the ISBN: 9781567657029. Chapter 15: STATISTICS includes 21 full stepbystep solutions.

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

Back substitution.
Upper triangular systems are solved in reverse order Xn to Xl.

Block matrix.
A matrix can be partitioned into matrix blocks, by cuts between rows and/or between columns. Block multiplication ofAB is allowed if the block shapes permit.

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

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.

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

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

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!).

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

Left inverse A+.
If A has full column rank n, then A+ = (AT A)I AT has A+ A = In.

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).

Orthonormal vectors q 1 , ... , q n·
Dot products are q T q j = 0 if i =1= j and q T q i = 1. The matrix Q with these orthonormal columns has Q T Q = I. If m = n then Q T = Q 1 and q 1 ' ... , q n is an orthonormal basis for Rn : every v = L (v T q j )q j •

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.

Rotation matrix
R = [~ CS ] rotates the plane by () and R 1 = RT rotates back by (). Eigenvalues are eiO and eiO , eigenvectors are (1, ±i). c, s = cos (), sin ().

Semidefinite matrix A.
(Positive) semidefinite: all x T Ax > 0, all A > 0; A = any RT R.

Singular matrix A.
A square matrix that has no inverse: det(A) = o.

Special solutions to As = O.
One free variable is Si = 1, other free variables = o.

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

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.

Vandermonde matrix V.
V c = b gives coefficients of p(x) = Co + ... + Cn_IXn 1 with P(Xi) = bi. Vij = (Xi)jI and det V = product of (Xk  Xi) for k > i.