chapter 3

Over the past 10​ years, five mutual funds all had the same mean rate of return. The standard deviations for each of the five mutual funds are shown below. Capital​ Investment: 10.5​%; ​Vanity: 7.6​%; Global​ Advisor: 6.1​%; International​ Equities: 9.2​%; ​Nomad: 8.3​% Which mutual fund was least consistent in rate of​ return?

Capital​ Investment

Identify the given statement as either true or false. The standard deviation can be negative.

FALSE

Identify the given statement as either true or false. The standard deviation is a RESISTANT MEASURE of spread.

FALSE

In​ 1994, major league baseball players went on strike. At the​ time, the average salary was​ $1,049,589, and the median salary was​ $337,500. If you were representing the​ owners, which summary would you use to convince the public that a strike was not​ needed? If you were a​ player, which would you​ use? Why was there such a large discrepancy between the mean and median​ salaries? Explain.

If you were representing the​ owners, you would use the average salary to convince the public that a strike was not needed. If you were a​ player, you would use the median salary to convince the public that a strike was needed. The average and median salaries differ so greatly because the distribution of salaries is skewed right.

The peak represents the ...

MODE

True or​ False: When comparing two​ populations, the larger the standard​ deviation, the more dispersion the distribution​ has, provided that the variable of interest from the two populations has the same unit of measure.

True, because the standard deviation describes how​ far, on​ average, each observation is from the typical value. A larger standard deviation means that observations are more distant from the typical​ value, and​ therefore, more dispersed.

The sum of the deviations about the mean always equals ...

ZERO

For a distribution that is​ symmetric, which of the following is​ true?

mean EQUALS median

For a distribution that is skewed​ right, which of the following is​ true?

mean GREATER THAN median

or a distribution that is skewed​ left, which of the following is​ true?

mean LESS THAN median

According to the Empirical​ Rule ...

According to the Empirical​ Rule, if a distribution is​ bell-shaped, then approximately 68% of the data will lie within 1 standard deviation of the​ mean; approximately 95% of the data will lie within 2 standard deviations of the​ mean; approximately 99.7% of the data will lie within 3 standard deviations of the mean.

What can be said about a set of data with a standard deviation of​ 0?

All the observations are the same value.

Why is the median​ resistant, but the mean is​ not?

The mean is not resistant because when data are​ skewed, there are extreme values in the​ tail, which tend to pull the mean in the direction of the tail. The median is resistant because the median of a variable is the value that lies in the middle of the data when arranged in ascending order and does not depend on the extreme values of the data.