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Analyze and answer the following problems. Show your complete solutions. 1. A testing lab wishes to test two experimental of outdoor paint to see how long each paint will last before fading. The testing lab makes use of 6 gallons of paint for each brand name to test. The result (in months) are as follows: Brand A: 10 60 50 30 40 20 Brand B: 35 45 30 35 40 25 Find:a. Find the variance, mean deviation and standard deviation of Brand A. b. Find the variance, mean deviation and standard deviation of Brand B. c. Which brand performed more consistent? d. Which brand shows more variability?

Analyze and answer the following problems. Show your complete solutions. 1. A testing lab wishes to test two experimental of outdoor paint to see how long each paint will last before fading. The testing lab makes use of 6 gallons of paint for each brand name to test. The result (in months) are as follows: Brand A: 10 60 50 30 40 20 Brand B: 35 45 30 35 40 25 Find:a. Find the variance, mean deviation and standard deviation of Brand A. b. Find the variance, mean deviation and standard deviation of Brand B. c. Which brand performed more consistent? d. Which brand shows more variability?

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter4: Eigenvalues And Eigenvectors
Section4.6: Applications And The Perron-frobenius Theorem
Problem 22EQ
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# Educational Website Content ## Statistical Analysis Problems ### Problem 1: A testing lab wishes to test two experimental types of outdoor paint to see how long each paint will last before fading. The testing lab makes use of 6 gallons of paint for each brand name to test. The results (in months) are as follows: #### Paint Duration (in months): - **Brand A**: 10, 60, 50, 30, 40, 20 - **Brand B**: 35, 45, 30, 35, 40, 25 Analyze and answer the following problems. Show your complete solutions: #### Requirements: a. Find the variance, mean deviation, and standard deviation of Brand A. b. Find the variance, mean deviation, and standard deviation of Brand B. c. Which brand performed more consistently? d. Which brand shows more variability? ### Problem 2: There were 12 boys and 13 girls in a class of 25 students, who were given a test. The mean mark for the 12 boys was 31, and the standard deviation of the boys was 6.2. The mean mark for the girls was 36, and the standard deviation of the girls' mark was 4.3. Find the mean mark and the standard deviation of the marks of the whole class of 25 students. --- ### Instructions for Solving the Problems: 1. **Calculate the Mean**: Sum all the values, then divide by the number of values. 2. **Calculate the Variance**: Subtract the mean from each value to find the deviation for each value. Square each deviation. Sum all the squared deviations and divide by the number of values minus one. 3. **Calculate the Standard Deviation**: Take the square root of the variance. 4. **Compare Consistency and Variability**: - Consistency: Lower standard deviation indicates higher consistency. - Variability: Higher standard deviation or variance indicates higher variability.
Transcribed Image Text:# Educational Website Content ## Statistical Analysis Problems ### Problem 1: A testing lab wishes to test two experimental types of outdoor paint to see how long each paint will last before fading. The testing lab makes use of 6 gallons of paint for each brand name to test. The results (in months) are as follows: #### Paint Duration (in months): - **Brand A**: 10, 60, 50, 30, 40, 20 - **Brand B**: 35, 45, 30, 35, 40, 25 Analyze and answer the following problems. Show your complete solutions: #### Requirements: a. Find the variance, mean deviation, and standard deviation of Brand A. b. Find the variance, mean deviation, and standard deviation of Brand B. c. Which brand performed more consistently? d. Which brand shows more variability? ### Problem 2: There were 12 boys and 13 girls in a class of 25 students, who were given a test. The mean mark for the 12 boys was 31, and the standard deviation of the boys was 6.2. The mean mark for the girls was 36, and the standard deviation of the girls' mark was 4.3. Find the mean mark and the standard deviation of the marks of the whole class of 25 students. --- ### Instructions for Solving the Problems: 1. **Calculate the Mean**: Sum all the values, then divide by the number of values. 2. **Calculate the Variance**: Subtract the mean from each value to find the deviation for each value. Square each deviation. Sum all the squared deviations and divide by the number of values minus one. 3. **Calculate the Standard Deviation**: Take the square root of the variance. 4. **Compare Consistency and Variability**: - Consistency: Lower standard deviation indicates higher consistency. - Variability: Higher standard deviation or variance indicates higher variability.
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