Statistics Test #2
A professor has recorded exam grades for 10 students in his class, but one of the grades is no longer readable. If the mean score on the exam was 82 and the mean of the 9 readable scores is 86, what is the value of the unreadable score?
10 X 82 = 820 - 9 X 86= 774. 820 - 774 = 46 A= 46
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
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
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 $433, $440, $495, and $207 . Compute the mean, median, and mode cost of repair.
Mean: $393.75 Median:$436.5 Mode: None
The following data represent the weights (in grams) of a simple random sample of a candy. 0.90 0.87 0.83 0.92 0.90 0.86 0.86 0.87 0.81 0.84 Determine the shape of the distribution of weights of the candies by drawing a frequency histogram and computing the mean and the median. Which measure of central tendency best describes the weight of the candy?
Mean: 0.866 Median: 0.865 Which tendency described the weight of the candy better? A: Mean
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 standard deviation is used in conjunction with the ______ to numerically describe distributions that are bell shaped. The ______ measures the center of the distribution, while the standard deviation measures the ______ of the distribution.
mean, mean, spread
The Empirical Rule
the empirical rule can be used to determine the percentage of data that lie within k standard deviations of the mean. To help organize the empirical rule and make the analysis easier, draw a bell-shaped curve, as shown to the right. The line in the center of the curve represents the mean. The other lines are each 1, 2, and 3 standard deviations away from the mean.
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
