Statistics Test #2

8 September 2022
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9 test answers

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question
What does it mean if a statistic is‚Äč resistant?
answer
Extreme values‚Äč (very large or‚Äč small) relative to the data do not affect its value substantially
question
The U.S. Department of Housing and Urban Development‚Äč (HUD) uses the median to report the average price of a home in the United States. Why do you think HUD uses the‚Äč median?
answer
HUD uses the median because the data are skewed right
question
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 ‚Äč$433‚Äč, ‚Äč$440, ‚Äč$495‚Äč, and ‚Äč$207 . Compute the‚Äč mean, median, and mode cost of repair.
answer
Mean: $393.75 Median:$436.5 Mode: None
question
The following data represent the weights‚Äč (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‚Äč candy?
answer
Mean: 0.866 Median: 0.865 Which tendency described the weight of the candy better? A: Mean
question
A professor has recorded exam grades for 10 students in his‚Äč 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‚Äč, what is the value of the unreadable‚Äč score?
answer
10 X 82 = 820 - 9 X 86= 774. 820 - 774 = 46 A= 46
question
The standard deviation is used in conjunction with the‚Äč ______ to numerically describe distributions that are bell shaped. The‚Äč ______ measures the center of the‚Äč distribution, while the standard deviation measures the‚Äč ______ of the distribution.
answer
mean, mean, spread
question
True or‚Äč False: When comparing two‚Äč populations, the larger the standard‚Äč deviation, the more dispersion the distribution‚Äč has, provided that the variable of interest from the two populations has the same unit of measure.
answer
True, because the standard deviation describes how‚Äč far, on‚Äč average, each observation is from the typical value. A larger standard deviation means that observations are more distant from the typical‚Äč value, and‚Äč therefore, more dispersed.
question
True or‚Äč False: Chebyshev's inequality applies to all distributions regardless of‚Äč shape, but the empirical rule holds only for distributions that are bell shaped
answer
True, Chebyshev's inequality is less precise than the empirical‚Äč rule, but will work for any‚Äč distribution, while the empirical rule only works for‚Äč bell-shaped distributions
question
The Empirical Rule
answer
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‚Äč easier, draw a‚Äč bell-shaped curve, as shown to the right. The line in the center of the curve represents the mean. The other lines are each‚Äč 1, 2, and 3 standard deviations away from the mean.