Finite Mathematics for Business, Economics, Life Sciences, and Social Sciences (13th Edition)
13th Edition
ISBN: 9780321945525
Author: Raymond A. Barnett, Michael R. Ziegler, Karl E. Byleen
Publisher: PEARSON
expand_more
expand_more
format_list_bulleted
Concept explainers
Videos
Textbook Question
Chapter 11.1, Problem 15E
Common stocks. The following table shows price-earnings ratios of
(A) Construct a frequency and relative frequency table using a class interval of
(B) Construct a histogram.
(C) Construct a frequency
(D) Construct a cumulative frequency and relative cumulative frequency table. What is the
probability that a price earnings ratio drawn at random from the sample will fall between
(E) Construct a cumulative frequency polygon.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
Based on a sample of 100 participants, the average weight loss the first month under a new (competing) weight-loss plan is 11.4 pounds with a population standard deviation of 5.1 pounds. The average weight loss for the first month for 100 people on the old (standard) weight-loss plan is 12.8 pounds, with population standard deviation of 4.8 pounds.
Find a 90 percent confidence interval for the difference in weight loss for the two plans( old minus new)
Whats the margin of error for your calculated confidence interval?
A 95 percent confidence interval for the average miles per gallon for all cars of a certain type is 32.1, plus or minus 1.8. The interval is based on a sample of 40 randomly selected cars.
What units represent the margin of error?Suppose that you want to decrease the margin of error, but you want to keep 95 percent confidence. What should you do?
Let v₁ = (2,-3,7,8), v2 = (3, 10, -6, 14), v3 = (0, 19, -2, 16), and v₁ = (9, -2, 1, 10).
Is the set {V1, V2, V3, V4} a basis for R4?
Of the two sets
S = {(3x-5y, 4x + 7y, x+9y): x, y = R}
and
T = {2x-3y+z, -7x-3y²+z, 4x + 3z): x, y, z = R}
which is a subspace of R3? (S, T, both, neither) Justify.
Chapter 11 Solutions
Finite Mathematics for Business, Economics, Life Sciences, and Social Sciences (13th Edition)
Ch. 11.1 - Using Figure 3, estimate the median annual income...Ch. 11.1 - Using Figure 6,estimate the revenue and costs in...Ch. 11.1 - Repeat Example 1 for the following intervals: (A)...Ch. 11.1 - The weights (in pounds) were recorded for 20...Ch. 11.1 - (A) Construct a frequency table and histogram for...Ch. 11.1 - (A) Construct a frequency table and histogram for...Ch. 11.1 - The graphing calculator command shown in Figure A...Ch. 11.1 - An experiment consists of rolling a pair of...Ch. 11.1 - Gross domestic product. Graph the data in the...Ch. 11.1 - Corporation revenues. Graph the data in the...
Ch. 11.1 - Gold production. Use the double bar graph on world...Ch. 11.1 - Gasoline prices. Graph the data in the following...Ch. 11.1 - Railroad Freight. Graph the data in the following...Ch. 11.1 - Railroad freight. Refer to Problem 9. If the data...Ch. 11.1 - Federal income. Graph the data in the following...Ch. 11.1 - Gasoline prices. In December 2012, the average...Ch. 11.1 - Starting salaries. The starting salaries (in...Ch. 11.1 - Commute times. Thirty-two people were chosen at...Ch. 11.1 - Common stocks. The following table shows...Ch. 11.1 - Mouse weights. One hundred healthy mice were...Ch. 11.1 - Population growth. Graph the data in the following...Ch. 11.1 - Aims epidemic. One way to gauge the toll of the...Ch. 11.1 - Nutrition. Graph the data in the following table...Ch. 11.1 - Greenhouse gases. The U.S. Department of Energy...Ch. 11.1 - Nutrition. Graph the nutritional information in...Ch. 11.1 - Nutrition. Refer to Problem 21. Suppose that you...Ch. 11.1 - Education. For statistical studies, U.S. states...Ch. 11.1 - Study abroad. Would a pie graph be more effective...Ch. 11.1 - Median age. Use the broken-line graph shown to...Ch. 11.1 - State prisoners. In 1980 in the United States, 6...Ch. 11.1 - Grade point Averages. One hundred seniors were...Ch. 11.2 - For many sets of measurements the median lies...Ch. 11.2 - Find the mean for the sample measurements...Ch. 11.2 - Compute the mean for the grouped sample data...Ch. 11.2 - Add the salary $100,000 to those in Example 3 and...Ch. 11.2 - Find the median for the grouped data in the...Ch. 11.2 - Compute the mode(s), median, and mean for each...Ch. 11.2 - In Problems 1-4, find the mean of the data set....Ch. 11.2 - In Problems 1-4, find the mean of the data set....Ch. 11.2 - In Problems 1-4, find the mean of the data set....Ch. 11.2 - In Problems 1-4, find the mean of the data set....Ch. 11.2 - In Problems 5-8, find the indicated sum. (If...Ch. 11.2 - In Problems 5-8, find the indicated sum. (If...Ch. 11.2 - In Problems 5-8, find the indicated sum. (If...Ch. 11.2 - In Problems 5-8, find the indicated sum. (If...Ch. 11.2 - Find the mean, median, and mode for the sets of...Ch. 11.2 - Find the mean, median, and mode for the sets of...Ch. 11.2 - Find the mean, median, and/or mode, whichever are...Ch. 11.2 - Find the mean, median, and/or mode, whichever are...Ch. 11.2 - Find the mean for the sets of grouped data in...Ch. 11.2 - Find the mean for the sets of grouped data in...Ch. 11.2 - Which single measure of central tendency-mean,...Ch. 11.2 - Which single measure of central tendency mean,...Ch. 11.2 - A data set is formed by recording the results of...Ch. 11.2 - A data set is formed by recording the sums on 200...Ch. 11.2 - (A) Construct a set of four numbers that has mean...Ch. 11.2 - (A) Construct a set of five numbers that has mean...Ch. 11.2 - Price earnings ratios. Find the mean, median, and...Ch. 11.2 - Gasoline tax. Find the mean, median, and mode for...Ch. 11.2 - Light bulb lifetime. Find the mean and median for...Ch. 11.2 - Price earnings ratios. Find the mean and median...Ch. 11.2 - Financial aid. Find the mean, median, and mode for...Ch. 11.2 - Tourism. Find the mean, median, and mode for the...Ch. 11.2 - Mouse weights. Find the mean and median for the...Ch. 11.2 - Blood cholesterol levels. Find the mean and median...Ch. 11.2 - Immigration. Find the mean, median, and mode for...Ch. 11.2 - Grade point averages. Find the mean and median for...Ch. 11.2 - Entrance examination scores. Compute the median...Ch. 11.2 - Presidents. Find the mean and median for the...Ch. 11.3 - (A) When is the sample standard deviation of a set...Ch. 11.3 - Find the standard deviation for the sample...Ch. 11.3 - Find the standard deviation for the grouped sample...Ch. 11.3 - Prob. 1ECh. 11.3 - In Problems 1-8, find the indicated sum. (If...Ch. 11.3 - In Problems 1-8, find the indicated sum. (If...Ch. 11.3 - In Problems 1-8, find the indicated sum. (If...Ch. 11.3 - In Problems 1-8, find the indicated sum. (If...Ch. 11.3 - In Problems 1-8, find the indicated sum. (If...Ch. 11.3 - In Problems 1-8, find the indicated sum. (If...Ch. 11.3 - In Problems 1-8, find the indicated sum. (If...Ch. 11.3 - (A) Find set of the ungrouped mean and sample...Ch. 11.3 - (A) Find the mean and standard deviation of the...Ch. 11.3 - In Problems 11 and 12, find the standard deviation...Ch. 11.3 - In Problems 11 and 12, find the standard deviation...Ch. 11.3 - In Problems 13-18, discuss the validity of each...Ch. 11.3 - In Problems 13-18, discuss the validity of each...Ch. 11.3 - In Problems 13-18, discuss the validity of each...Ch. 11.3 - In Problem 1318, discuss the validity of each...Ch. 11.3 - In Problem 1318, discuss the validity of each...Ch. 11.3 - In Problems 13-18, discuss the validity of each...Ch. 11.3 - A data set is formed by recording the sums in 100...Ch. 11.3 - A data set is formed by recording the results of...Ch. 11.3 - Find the mean and standard deviation for each of...Ch. 11.3 - Find the mean and standard deviation for each of...Ch. 11.3 - Find the mean and standard deviation for each of...Ch. 11.3 - Find the mean and standard deviation for each of...Ch. 11.3 - Find the mean and standard deviation for each of...Ch. 11.3 - Find the mean and standard deviation for each of...Ch. 11.3 - Find the mean and standard deviation for each of...Ch. 11.3 - Find the mean and standard deviation for each of...Ch. 11.4 - Find p and q for a single roll of a fair die,...Ch. 11.4 - In Example 2, find the probability of the outcome...Ch. 11.4 - Using the same die experiment as in Example 3,...Ch. 11.4 - Use the binomial formula to expand q+p4.Ch. 11.4 - Repeat Example 5, where the binomial experiment...Ch. 11.4 - Compute the mean and standard deviation for the...Ch. 11.4 - Repeat Example 7 for four patients. The...Ch. 11.4 - Evaluate nCxpxqnx for the values of n,x, and p...Ch. 11.4 - Evaluate nCxpxqnx for the values of n,x, and p...Ch. 11.4 - Evaluate nCxpxqnx for the values of n,x, and p...Ch. 11.4 - Evaluate nCxpxqnx for the values of n,x, and p...Ch. 11.4 - Evaluate nCxpxqnx for the values of n,x, and p...Ch. 11.4 - Evaluate nCxpxqnx for the values of n,x, and p...Ch. 11.4 - In Problems 7-12, a fair coin is tossed four...Ch. 11.4 - In Problems 7-12, a fair coin is tossed four...Ch. 11.4 - In Problems 7-12, a fair coin is tossed four...Ch. 11.4 - In Problems 7-12, a fair coin is tossed four...Ch. 11.4 - In Problems 7-12, a fair coin is tossed four...Ch. 11.4 - In Problems 7-12, a fair coin is tossed four...Ch. 11.4 - In Problems 13-18 construct a histogram for the...Ch. 11.4 - In Problems 13-18 construct a histogram for the...Ch. 11.4 - In Problems 13-18 construct a histogram for the...Ch. 11.4 - In Problems 13-18 construct a histogram for the...Ch. 11.4 - In Problems 13-18 construct a histogram for the...Ch. 11.4 - In Problems 13-18 construct a histogram for the...Ch. 11.4 - In Problems 19-24, round answers to four decimal...Ch. 11.4 - In Problems 19-24, round answers to four decimal...Ch. 11.4 - In Problems 19-24, round answers to four decimal...Ch. 11.4 - In Problems 19-24, round answers to four decimal...Ch. 11.4 - In Problems 19-24, round answers to four decimal...Ch. 11.4 - In Problems 19-24, a fair die is rolled three...Ch. 11.4 - If a baseball player has a batting average of 350...Ch. 11.4 - If a true-false test with 10 questions is given,...Ch. 11.4 - A multiple-choice test consists of 10 questions,...Ch. 11.4 - If 60 of the electorate supports the mayor, what...Ch. 11.4 - Construct a histogram for each of the binomial...Ch. 11.4 - Construct a histogram for each of the binomial...Ch. 11.4 - Construct a histogram for each of the binomial...Ch. 11.4 - Construct a histogram for each of the binomial...Ch. 11.4 - A random variable represents the number of...Ch. 11.4 - A random variable represents the number of...Ch. 11.4 - In Problems 35 and 36 a coin is loaded so that the...Ch. 11.4 - In Problems 35 and 36 a coin is loaded so that the...Ch. 11.4 - Find conditions on p that guarantee the histogram...Ch. 11.4 - Consider two binomial distributions for 1,000...Ch. 11.4 - A random variable represents the number of heads...Ch. 11.4 - A random variable represents the number of times a...Ch. 11.4 - Management training each year a company selects a...Ch. 11.4 - Employee turnover. If the probability of a new...Ch. 11.4 - Quality control A manufacturing process produces,...Ch. 11.4 - Guarantees. A manufacturing process produces, on...Ch. 11.4 - Quality control. A manufacturing process produces,...Ch. 11.4 - Management training. Each year a company selects 5...Ch. 11.4 - Medical diagnosis A tuberculosis patient is given...Ch. 11.4 - Harmful drug side effect. A pharmaceutical...Ch. 11.4 - Genetics. The probability that brown-eyed parents,...Ch. 11.4 - Gene mutation the probability of gene mutation...Ch. 11.4 - Epidemics. If the probability of a person...Ch. 11.4 - Drug side effect the probability that a given drug...Ch. 11.4 - Testing A multiple-choice test is given with 5...Ch. 11.4 - Opinion polls. An opinion poll based on a small...Ch. 11.4 - Testing. A multiple-choice test is given with 5...Ch. 11.4 - Sociology. The probability that a marriage will...Ch. 11.4 - Sociology. If the probability is .55 that a...Ch. 11.5 - What percentage of the light bulbs in Example 1...Ch. 11.5 - Refer to Example 1. What is the probability that a...Ch. 11.5 - In Example 3, Use the normal curve to approximate...Ch. 11.5 - Suppose in Example 4 that the manufacturing...Ch. 11.5 - In Problems 1-6, use Appendix C to find the area...Ch. 11.5 - In Problems 1-6, use Appendix C to find the area...Ch. 11.5 - In Problems 1-6, use Appendix C to find the area...Ch. 11.5 - In Problems 1-6, use Appendix C to find the area...Ch. 11.5 - In Problems 1-6, use Appendix C to find the area...Ch. 11.5 - In Problems 1-6, use Appendix C to find the area...Ch. 11.5 - Give a normal distribution with mean 100 and...Ch. 11.5 - Give a normal distribution with mean 100 and...Ch. 11.5 - Give a normal distribution with mean 100 and...Ch. 11.5 - Give a normal distribution with mean 100 and...Ch. 11.5 - Give a normal distribution with mean 100 and...Ch. 11.5 - Give a normal distribution with mean 100 and...Ch. 11.5 - Using the normal distribution described for...Ch. 11.5 - Using the normal distribution described for...Ch. 11.5 - Using the normal distribution described for...Ch. 11.5 - Using the normal distribution described for...Ch. 11.5 - Using the normal distribution described for...Ch. 11.5 - Using the normal distribution described for...Ch. 11.5 - In Problems 27-34, consider the normal...Ch. 11.5 - In Problems 27-34, consider the normal...Ch. 11.5 - Consider the normal distribution with mean 60 and...Ch. 11.5 - In Problems 27-34, consider the normal...Ch. 11.5 - In Problems 27-34, consider the normal...Ch. 11.5 - In Problems 27-34, consider the normal...Ch. 11.5 - In Problems 27-34, consider the normal...Ch. 11.5 - In Problems 27-34, consider the normal...Ch. 11.5 - In Problems 35-40, discuss the validity of each...Ch. 11.5 - In Problems 35-40, discuss the validity of each...Ch. 11.5 - In Problems 35-40, discuss the validity of each...Ch. 11.5 - In Problems 35-40, discuss the validity of each...Ch. 11.5 - In Problems 35-40, discuss the validity of each...Ch. 11.5 - In Problems 35-40, discuss the validity of each...Ch. 11.5 - In Problems 41-48, use the rule-of-thumb test to...Ch. 11.5 - In Problems 41-48, use the rule-of-thumb test to...Ch. 11.5 - In Problems 41-48, use the rule-of-thumb test to...Ch. 11.5 - In Problems 41-48, use the rule-of-thumb test to...Ch. 11.5 - In Problems 41-48, use the rule-of-thumb test to...Ch. 11.5 - In Problems 41-48, use the rule-of-thumb test to...Ch. 11.5 - In Problems 41-48, use the rule-of-thumb test to...Ch. 11.5 - In Problems 41-48, use the rule-of-thumb test to...Ch. 11.5 - The probability of success in a Bernoulli trial is...Ch. 11.5 - For a binomial distribution with n=100, explain...Ch. 11.5 - A binomial experiment consists of 500 trials. The...Ch. 11.5 - A binomial experiment consists of 500 trials. The...Ch. 11.5 - A binomial experiment consists of 500 trials. The...Ch. 11.5 - A binomial experiment consists of 500 trials. The...Ch. 11.5 - A binomial experiment consists of 500 trials. The...Ch. 11.5 - A binomial experiment consists of 500 trials. The...Ch. 11.5 - A binomial experiment consists of 500 trials. The...Ch. 11.5 - A binomial experiment consists of 500 trials. The...Ch. 11.5 - To graph Problems 59-62, use a graphing calculator...Ch. 11.5 - To graph Problems 59-62, use a graphing calculator...Ch. 11.5 - To graph Problems 59-62, use a graphing calculator...Ch. 11.5 - To graph Problems 59-62, use a graphing calculator...Ch. 11.5 - (A) If 120 scores are chosen from a normal...Ch. 11.5 - (A) If 250 scores are chosen from a normal...Ch. 11.5 - Sales Salespeople for a solar technology company...Ch. 11.5 - Guarantees. The average lifetime for a car battery...Ch. 11.5 - Quality control. A manufacturing process produces...Ch. 11.5 - Quality control. An automated manufacturing...Ch. 11.5 - Marketing claims. A company claims that 60 of the...Ch. 11.5 - Labor relation A union representative 60 claims of...Ch. 11.5 - Medicine. The average healing time of a certain...Ch. 11.5 - Agriculture. The average height of a hay crop is...Ch. 11.5 - Genetics. In a family with 2 children, the...Ch. 11.5 - Genetics. In Problem 73, what is the approximate...Ch. 11.5 - Testing. Scholastic Aptitude Tests (SATs) are...Ch. 11.5 - Politics. Candidate Harkins claims that she will...Ch. 11.5 - Grading on a curve. An instructor grades on a...Ch. 11.5 - Psychology. A test devised to measure...Ch. 11 - Graph the following data using a bar graph and a...Ch. 11 - Graph the data in the following table using two...Ch. 11 - (A) Draw a histogram for the binomial distribution...Ch. 11 - For the set of sample measurements...Ch. 11 - If a normal distribution has a mean of 100 and a...Ch. 11 - Given the sample of 25 quiz scores listed in the...Ch. 11 - For the set of grouped sample data given in the...Ch. 11 - (A) Construct a histogram for the binomial...Ch. 11 - What are the mean and standard deviation for a...Ch. 11 - In Problems 10 and 11, discuss the validity of...Ch. 11 - In Problems 10 and 11, discuss the validity of...Ch. 11 - If the probability of success in a single trial of...Ch. 11 - Given a normal distribution with mean 50 and...Ch. 11 - A data set is formed by recording the sums of 100...Ch. 11 - For the sample quiz scores in Problem 6, find the...Ch. 11 - A fair die is rolled five times. What is the...Ch. 11 - Two dice are rolled three times. What is the...Ch. 11 - Ten students take an exam worth 100 points. (A)...Ch. 11 - In the last presidential election, 39 of a city’s...Ch. 11 - A random variable represents the number of wins in...Ch. 11 - Retail sales. The daily number of bad checks...Ch. 11 - Preference survey. Find the mean, median, and/or...Ch. 11 - Plant safety. The weekly record of reported...Ch. 11 - Personnel screening.The scores on a screening test...Ch. 11 - Market research A newspaper publisher claims that...Ch. 11 - Health care. A small town has three doctors on...
Additional Math Textbook Solutions
Find more solutions based on key concepts
ASSESSMENT Find the first five terms in sequences with the following nth terms. a. n2+2 b. 5n+1 c. 10n1 d. 3n2 ...
A Problem Solving Approach To Mathematics For Elementary School Teachers (13th Edition)
Women’s Heights Assume that college women’s heights are approximately Normally distributed with a mean of 65 in...
Introductory Statistics
Version 2 of the Chain Rule Use Version 2 of the Chain Rule to calculate the derivatives of the following funct...
Calculus: Early Transcendentals (2nd Edition)
Three cards are randomly selected, without replacement, from an ordinary deck of 52 playing cards. Compute the ...
A First Course in Probability (10th Edition)
Fill in each blank so that the resulting statement is true. An equation that expresses a relationship between t...
Algebra and Trigonometry (6th Edition)
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, subject and related others by exploring similar questions and additional content below.Similar questions
- Can you help me solve this?arrow_forwardFind a basis and dimension for the null space of the following matrix: 3 -2 0 7 -2 1-1 1 5 3 19-2 8 06 1 -2 -4 -5-6 -9 4-6 11 6 Find a basis and dimension for the column space of the same matrix (above).arrow_forward3. (i) Below is the R code for performing a X2 test on a 2×3 matrix of categorical variables called TestMatrix: chisq.test(Test Matrix) (a) Assuming we have a significant result for this procedure, provide the R code (including any required packages) for an appropriate post hoc test. (b) If we were to apply this technique to a 2 × 2 case, how would we adapt the code in order to perform the correct test? (ii) What procedure can we use if we want to test for association when we have ordinal variables? What code do we use in R to do this? What package does this command belong to? (iii) The following code contains the initial steps for a scenario where we are looking to investigate the relationship between age and whether someone owns a car by using frequencies. There are two issues with the code - please state these. Row3<-c(75,15) Row4<-c(50,-10) MortgageMatrix<-matrix(c(Row1, Row4), byrow=T, nrow=2, MortgageMatrix dimnames=list(c("Yes", "No"), c("40 or older","<40")))…arrow_forward
- Describe the situation in which Fisher’s exact test would be used?(ii) When do we use Yates’ continuity correction (with respect to contingencytables)?[2 Marks] 2. Investigate, checking the relevant assumptions, whether there is an associationbetween age group and home ownership based on the sample dataset for atown below:Home Owner: Yes NoUnder 40 39 12140 and over 181 59Calculate and evaluate the effect size.arrow_forwardsolve these pleasearrow_forwardA factorization A = PDP 1 is not unique. For A= 7 2 -4 1 1 1 5 0 2 1 one factorization is P = D= and P-1 30 = Use this information with D₁ = to find a matrix P₁ such that - -1 -2 0 3 1 - - 1 05 A-P,D,P P1 (Type an integer or simplified fraction for each matrix element.)arrow_forward
- Matrix A is factored in the form PDP 1. Use the Diagonalization Theorem to find the eigenvalues of A and a basis for each eigenspace. 30 -1 - 1 0 -1 400 0 0 1 A= 3 4 3 0 1 3 040 3 1 3 0 0 4 1 0 0 003 -1 0 -1 Select the correct choice below and fill in the answer boxes to complete your choice. (Use a comma to separate vectors as needed.) A basis for the corresponding eigenspace is { A. There is one distinct eigenvalue, λ = B. In ascending order, the two distinct eigenvalues are λ₁ ... = and 2 = Bases for the corresponding eigenspaces are { and ( ), respectively. C. In ascending order, the three distinct eigenvalues are λ₁ = = 12/2 = and 3 = Bases for the corresponding eigenspaces are {}, }, and { respectively.arrow_forwardN Page 0.6. 0.4. 0.2- -0.2- -0.4- -6.6 -5 W 10arrow_forwardDiagonalize the following matrix, if possible. 8 0 6 - 8 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. 8 0 OA. For P= D= 0 3 6 0 B. For P = D= 0 -6 8 0 C. For P = D= 0 - 8 D. The matrix cannot be diagonalized.arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Big Ideas Math A Bridge To Success Algebra 1: Stu...AlgebraISBN:9781680331141Author:HOUGHTON MIFFLIN HARCOURTPublisher:Houghton Mifflin Harcourt
Holt Mcdougal Larson Pre-algebra: Student Edition...AlgebraISBN:9780547587776Author:HOLT MCDOUGALPublisher:HOLT MCDOUGAL
Glencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw Hill
Big Ideas Math A Bridge To Success Algebra 1: Stu...
Algebra
ISBN:9781680331141
Author:HOUGHTON MIFFLIN HARCOURT
Publisher:Houghton Mifflin Harcourt
Holt Mcdougal Larson Pre-algebra: Student Edition...
Algebra
ISBN:9780547587776
Author:HOLT MCDOUGAL
Publisher:HOLT MCDOUGAL
Glencoe Algebra 1, Student Edition, 9780079039897...
Algebra
ISBN:9780079039897
Author:Carter
Publisher:McGraw Hill
The Shape of Data: Distributions: Crash Course Statistics #7; Author: CrashCourse;https://www.youtube.com/watch?v=bPFNxD3Yg6U;License: Standard YouTube License, CC-BY
Shape, Center, and Spread - Module 20.2 (Part 1); Author: Mrmathblog;https://www.youtube.com/watch?v=COaid7O_Gag;License: Standard YouTube License, CC-BY
Shape, Center and Spread; Author: Emily Murdock;https://www.youtube.com/watch?v=_YyW0DSCzpM;License: Standard Youtube License