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
