Question

Complete: Chapter 4 Problem Set < Back to Assignment Attempts: | Average: /2 Attention: Due to a bug in Google Chrome, this page may not correctly. Click here to learn more. 11. The effect of transformations of scale on the mean and standard deviation You just completed a small research project for your psychology class concerning the effects of an event that happened two years ago on women's opinions and actions today. The mean age of participants in your study is 42.5 years with a standard deviation of 6.1 years. As you write up your results, you realize that what matters is the ages of the participants two years ago when the event happened, not their ages now. You decide to subtract 2 from each of your participants' ages. After you subtract 2 years, the mean age in your sample is years. The new standard deviation of the ages in your sample isyear One of the variables you collected was the study participants' heights in centimeters. The mean height of participants in your study is 163.3 centimeters with a standard deviation of 8.2 centimeters. Your professor, however, requested that you report this value in inches. To convert from centimeters to inches, you multiply by 0.394. After you multiply the heights of your participants by 0.394, the mean height in your sample is deviation of the heights in your sample is inches. The new standard inches

Answer 1

Correct options:

a) Sample standard deviation: $\sqrt{\frac{\sum (X-M)^2}{n-1}}$ (option 3) and description: A measure of average distance from the mean (option a)

b) Sample variance: ${\frac{\sum (X-M)^2}{n-1}}$ (option 2) and description: Average squared distance from the sample mean (option c)

c) Population standard deviation is: $\sqrt{\sigma^2}$ (option 1) description: Square root of population variance (option d)

d) Population variance is: $\frac{SS}{N}$ (option 4): Average squared distance from population mean (option b)

After we subtract 2 years, the mean shifts by 2 to become 40.5 and the standard deviation is 6.1 (unaffected by addition/subtraction)