STAT 500 Homework 2 Solution (Penn State University) Latest Verified Review 2023 Practice Questions and Answers for Exam Preparation, 100% Correct with Explanations, Highly Recommended, Download to Score A+

STAT 500 Homework 2 Solution (Penn State University) Latest Verified Review 2023 Practice Questions and Answers for Exam Preparation, 100% Correct with Explanations, Highly Recommended, Download to Score A+ Problem 1 (BY HAND) Consider the following three sets of sample observations: Set 1: 8, 9, 10, 11, 12 Set 2: 8, 9, 10, 11, 100 Set 3: 8, 9, 10, 11, 1000 A) Find the median and IQR for each data set. Median IQR Set 1: 10 3 Set 2: 10 47 Set 3: 10 497 B) Find the mean and standard deviation for each data set. Mean SD Set 1: 10 1.581 Set 2: 27.6 40.5 Set 3: 208 443 C) What do these data sets illustrate about the resistance of the median, IQR, mean, and standard deviation? The median is much less affected than the mean, while the IQR and SD are similarly affected. Problem 2 (BY HAND) A) Find the new mean and standard deviation if four was added to each value in Set 1 of problem 1. Mean = 14 and SD = 1.581 (unchanged) B) Find the new mean and standard deviation if four was multiplied to each value in Set 1 of problem 1. Mean = 40 and SD = 6.324 C) Discuss the differences between the effect of adding and multiplying a constant had on the mean and standard deviation. Adding a constant only affects the mean by increasing the mean by the constant while the SD is unaffected. When multiplying by a constant, both the mean and SD are affected by a factor of that constant.