STATISTICS - 3.4.
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The _______ represents the number of standard deviations an observation is from the
mean. - Answer: Z-score
Z-score - Answer: The z-sore represents the distance that a data value is from the
mean in terms of the number of standard deviations.
The z-score is unitless. It has mean 0 and standard deviation 1.
The interquartile range - Answer: The interquartile range is the difference between the
third and first quartiles.
It is the range of the middle 50% of the observations in the data set.
Resistance - Answer: The correct answer is resistance. A numerical summary of data is
said to be resistant if extreme values (very large or small) relative to the data do not
affect its value substantially. Notice that for this data set the standard deviation is not
resistant to extreme observations, but the interquartile range is resistant.
Explain the circumstances for which the interquartile range is the preferred measure of
dispersion. What is an advantage that the standard deviation has over the interquartile
range? - Answer: The interquartile range is preferred when the data are skewed or
have outliers. An advantage of the standard deviation is that it uses all the observations
in its computation.
The interquartile range, IQR, is the range of the middle 50% of the observations in a
data set. That is, the IQR is the difference between the first and third quartiles. The
interquartile range is not affected by extreme values. Therefore, when the distribution of
data is highly skewed or contains extreme observations, it is best to use the interquartile
range as the measure of dispersion because it is resistant.
1
APPHIA - Crafted with Care and Precision for Academic Excellence.
Quality content you can rely on!
The _______ represents the number of standard deviations an observation is from the
mean. - Answer: Z-score
Z-score - Answer: The z-sore represents the distance that a data value is from the
mean in terms of the number of standard deviations.
The z-score is unitless. It has mean 0 and standard deviation 1.
The interquartile range - Answer: The interquartile range is the difference between the
third and first quartiles.
It is the range of the middle 50% of the observations in the data set.
Resistance - Answer: The correct answer is resistance. A numerical summary of data is
said to be resistant if extreme values (very large or small) relative to the data do not
affect its value substantially. Notice that for this data set the standard deviation is not
resistant to extreme observations, but the interquartile range is resistant.
Explain the circumstances for which the interquartile range is the preferred measure of
dispersion. What is an advantage that the standard deviation has over the interquartile
range? - Answer: The interquartile range is preferred when the data are skewed or
have outliers. An advantage of the standard deviation is that it uses all the observations
in its computation.
The interquartile range, IQR, is the range of the middle 50% of the observations in a
data set. That is, the IQR is the difference between the first and third quartiles. The
interquartile range is not affected by extreme values. Therefore, when the distribution of
data is highly skewed or contains extreme observations, it is best to use the interquartile
range as the measure of dispersion because it is resistant.
1
APPHIA - Crafted with Care and Precision for Academic Excellence.
