Statistics Chapter 3 Homework

What does it mean if a statistic is​ resistant?

Extreme values​ (very large or​ small) relative to the data do not affect its value substantially.

True or​ False: A data set will always have exactly one mode.

False

An insurance company crashed four cars of the same model at 5 miles per hour. The costs of repair for each of the four crashes were ​$432​, ​$443​, ​$466​, and ​$223. Compute the​ mean, median, and mode cost of repair.

Mean: $391 Median: $437.5 No mode

What measure of central tendency best describes the​ "center" of the​ distribution?

mean

In a​ boxplot, if the median is to the left of the center of the box and the right whisker is substantially longer than the left​ whisker, the distribution is skewed

right

The sum of the deviations about the mean always equals

zero

True or​ False: Chebyshev's inequality applies to all distributions regardless of​ shape, but the empirical rule holds only for distributions that are bell shaped.

​True, Chebyshev's inequality is less precise than the empirical​ rule, but will work for any​ distribution, while the empirical rule only works for​ bell-shaped distributions.

For a large sporting event the broadcasters sold 62 ad slots for a total revenue of ​$132 million. What was the mean price per ad​ slot?

$2.1 million

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.

A histogram of a set of data indicates that the distribution of the data is skewed right. Which measure of central tendency will likely be​ larger, the mean or the​ median? Why?

The mean will likely be larger because the extreme values in the right tail tend to pull the mean in the direction of the tail.

What makes the range less desirable than the standard deviation as a measure of​ dispersion?

The range does not use all the observations.

In a certain​ city, the average​ 20- to​ 29-year old man is 72.5 inches​ tall, with a standard deviation of 3.0 ​inches, while the average​ 20- to​ 29-year old woman is 64.3 inches​ tall, with a standard deviation of 3.9 inches. Who is relatively​ taller, a​ 75-inch man or a​ 70-inch woman? Who is relatively​ taller, a​ 75-inch man or a​ 70-inch woman?

The​ z-score for the woman is​ larger, so she is relatively taller.

The U.S. Department of Housing and Urban Development​ (HUD) uses the median to report the average price of a home in the United States. Why do you think HUD uses the​ median?

HUD uses the median because the data are skewed right