Question

a friend tells you about a recent study dealing with the number of years of teaching experience among current college professors. he remembers the mean but cannot recall whether the standard deviation was 6 months, 6 years, or 16 years. tell him which one it must have been, and why. choose the correct answer below. a. the standard deviation is 16 years because some college professors teach for over 50 years, and the study will have had to account for these professors. b. the standard deviation is 6 years because 6 months would result in far too small an interval of reasonable years and 16 years would result in far too large an interval of reasonable years. c. the standard deviation is 6 months because both 6 years and 16 years would result in far too large an interval of reasonable years. d. the standard deviation is 16 years because both 6 months and 6 years would result in far too small an interval of reasonable years.

Explanation:

Step1: Analyze 6 months

6 months is a very small value for the standard - deviation of years of teaching experience among college professors. It would imply that the years of experience are very tightly clustered around the mean, which is not likely as there is natural variation in when professors start and end their careers.

Step2: Analyze 16 years

16 years is a very large value for the standard - deviation. It would mean that the spread of years of teaching experience is extremely wide. While some professors may have long careers, such a large standard - deviation would be unusual.

Step3: Analyze 6 years

6 years is a reasonable value for the standard - deviation of teaching experience among college professors. It allows for a good amount of variation in the data, accounting for professors who start their careers at different ages and have different lengths of service.

Answer:

B. The standard deviation is 6 years because 6 months would result in far too small an interval of reasonable years and 16 years would result in far too large an interval of reasonable years.