 12.3.1: In 16, find the range for each group of data items.1, 2, 3, 4, 5
 12.3.2: In 16, find the range for each group of data items.16, 17, 18, 19, 20
 12.3.3: In 16, find the range for each group of data items.7, 9, 9, 15
 12.3.4: In 16, find the range for each group of data items.. 11, 13, 14, 15...
 12.3.5: In 16, find the range for each group of data items.. 3, 3, 4, 4, 5, 5
 12.3.6: In 16, find the range for each group of data items.3, 3, 3, 4, 5, 5, 5
 12.3.7: In 710, a group of data items and their mean are given. a. Find the...
 12.3.8: In 710, a group of data items and their mean are given. a. Find the...
 12.3.9: In 710, a group of data items and their mean are given. a. Find the...
 12.3.10: In 710, a group of data items and their mean are given. a. Find the...
 12.3.11: In 1116, find a. the mean; b. the deviation from the mean for each ...
 12.3.12: In 1116, find a. the mean; b. the deviation from the mean for each ...
 12.3.13: In 1116, find a. the mean; b. the deviation from the mean for each ...
 12.3.14: In 1116, find a. the mean; b. the deviation from the mean for each ...
 12.3.15: In 1116, find a. the mean; b. the deviation from the mean for each ...
 12.3.16: In 1116, find a. the mean; b. the deviation from the mean for each ...
 12.3.17: In 1726, find the standard deviation for each group of data items. ...
 12.3.18: In 1726, find the standard deviation for each group of data items. ...
 12.3.19: In 1726, find the standard deviation for each group of data items. ...
 12.3.20: In 1726, find the standard deviation for each group of data items. ...
 12.3.21: In 1726, find the standard deviation for each group of data items. ...
 12.3.22: In 1726, find the standard deviation for each group of data items. ...
 12.3.23: In 1726, find the standard deviation for each group of data items. ...
 12.3.24: In 1726, find the standard deviation for each group of data items. ...
 12.3.25: In 1726, find the standard deviation for each group of data items. ...
 12.3.26: In 1726, find the standard deviation for each group of data items. ...
 12.3.27: In 2728, compute the mean, range, and standard deviation for the da...
 12.3.28: In 2728, compute the mean, range, and standard deviation for the da...
 12.3.29: In 2936, use each display of data items to find the standard deviat...
 12.3.30: In 2936, use each display of data items to find the standard deviat...
 12.3.31: In 2936, use each display of data items to find the standard deviat...
 12.3.32: In 2936, use each display of data items to find the standard deviat...
 12.3.33: In 2936, use each display of data items to find the standard deviat...
 12.3.34: In 2936, use each display of data items to find the standard deviat...
 12.3.35: In 2936, use each display of data items to find the standard deviat...
 12.3.36: In 2936, use each display of data items to find the standard deviat...
 12.3.37: The data sets give the number of platinum albums for the five male ...
 12.3.38: The data sets give the ages of the first six U.S. presidents and th...
 12.3.39: Describe how to find the range of a data set.
 12.3.40: Describe why the range might not be the best measure of dispersion.
 12.3.41: Describe how the standard deviation is computed
 12.3.42: Describe what the standard deviation reveals about a data set
 12.3.43: If a set of scores has a standard deviation of zero, what does this...
 12.3.44: Two classes took a statistics . Both classes had a mean score of 73...
 12.3.45: A sample of cereals indicates a mean potassium content per serving ...
 12.3.46: Over a onemonth period, stock A had a mean daily closing price of ...
 12.3.47: Make Sense? In 4750, determine whether each statement makes sense o...
 12.3.48: Make Sense? In 4750, determine whether each statement makes sense o...
 12.3.49: Make Sense? In 4750, determine whether each statement makes sense o...
 12.3.50: Make Sense? In 4750, determine whether each statement makes sense o...
 12.3.51: Describe a situation in which a relatively large standard deviation...
 12.3.52: If a set of scores has a large range but a small standard deviation...
 12.3.53: Use the data 1, 2, 3, 5, 6, 7. Without actually computing the stand...
 12.3.54: Use the data 0, 1, 3, 4, 4, 6. Add 2 to each of the numbers. How do...
 12.3.55: As a followup to Group Exercise 79 on page 794, the group should r...
 12.3.56: Group members should consult a current almanac or the Internet and ...
Solutions for Chapter 12.3: Measures of Dispersion
Full solutions for Thinking Mathematically  6th Edition
ISBN: 9780321867322
Solutions for Chapter 12.3: Measures of Dispersion
Get Full SolutionsChapter 12.3: Measures of Dispersion includes 56 full stepbystep solutions. This textbook survival guide was created for the textbook: Thinking Mathematically, edition: 6. Thinking Mathematically was written by and is associated to the ISBN: 9780321867322. This expansive textbook survival guide covers the following chapters and their solutions. Since 56 problems in chapter 12.3: Measures of Dispersion have been answered, more than 61864 students have viewed full stepbystep solutions from this chapter.

Commuting matrices AB = BA.
If diagonalizable, they share n eigenvectors.

Dimension of vector space
dim(V) = number of vectors in any basis for V.

Ellipse (or ellipsoid) x T Ax = 1.
A must be positive definite; the axes of the ellipse are eigenvectors of A, with lengths 1/.JI. (For IIx II = 1 the vectors y = Ax lie on the ellipse IIA1 yll2 = Y T(AAT)1 Y = 1 displayed by eigshow; axis lengths ad

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!).

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

Hermitian matrix A H = AT = A.
Complex analog a j i = aU of a symmetric matrix.

Identity matrix I (or In).
Diagonal entries = 1, offdiagonal entries = 0.

Kirchhoff's Laws.
Current Law: net current (in minus out) is zero at each node. Voltage Law: Potential differences (voltage drops) add to zero around any closed loop.

Least squares solution X.
The vector x that minimizes the error lie 112 solves AT Ax = ATb. Then e = b  Ax is orthogonal to all columns of A.

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

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

Permutation matrix P.
There are n! orders of 1, ... , n. The n! P 's have the rows of I in those orders. P A puts the rows of A in the same order. P is even or odd (det P = 1 or 1) based on the number of row exchanges to reach I.

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.

Rank r (A)
= number of pivots = dimension of column space = dimension of row space.

Row space C (AT) = all combinations of rows of A.
Column vectors by convention.

Schwarz inequality
Iv·wl < IIvll IIwll.Then IvTAwl2 < (vT Av)(wT Aw) for pos def A.

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

Toeplitz matrix.
Constant down each diagonal = timeinvariant (shiftinvariant) filter.

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