STATISTICS - 3.2 MEASURES OF DISPERSION.
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The sum of the deviations about the mean always equals - Answer: Zero
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. - Answer: mean,
mean, spread
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. - Answer: 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.
Chebyshev's Inequality - Answer: For any data set or distribution, at least (1 -
1/k^2)=100% of the obserationslie within k standard deviations of the mean, where k is
any number greater than 1.
Empirical Rule - Answer: If data have a distribution that is bell shaped, the Emperical
Rule can be used to determine the percentage of data that will lie within k standard
deviations of the mean. (pg 139)
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. - Answer: 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.
In a statistics class, the standard deviation of the heights of all students was 3.9 inches.
The standard deviation of the heights of males was 3.4 inches and the standard
1
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Quality content you can rely on!
The sum of the deviations about the mean always equals - Answer: Zero
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. - Answer: mean,
mean, spread
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. - Answer: 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.
Chebyshev's Inequality - Answer: For any data set or distribution, at least (1 -
1/k^2)=100% of the obserationslie within k standard deviations of the mean, where k is
any number greater than 1.
Empirical Rule - Answer: If data have a distribution that is bell shaped, the Emperical
Rule can be used to determine the percentage of data that will lie within k standard
deviations of the mean. (pg 139)
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. - Answer: 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.
In a statistics class, the standard deviation of the heights of all students was 3.9 inches.
The standard deviation of the heights of males was 3.4 inches and the standard
1
APPHIA - Crafted with Care and Precision for Academic Excellence.
