객관식
If the unit of a dataset is , the unit for population variance would be
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3. Describing Data Numerically
Standard Deviation
객관식
If an observation has a z-score of , which of the following is true?
A
The observation is standard deviation above the mean.
B
The observation is at the maximum value of the distribution.
C
The observation is equal to the mean of the distribution.
D
The observation is standard deviation below the mean.
검증된 단계별 안내1
Recall that a z-score represents how many standard deviations an observation is from the mean of the distribution. It is calculated by the formula: \(\displaystyle z = \frac{X - \mu}{\sigma}\), where \(X\) is the observation, \(\mu\) is the mean, and \(\sigma\) is the standard deviation.
Understand that if the z-score is exactly 0, it means the numerator in the formula is zero, i.e., \(X - \mu = 0\).
From the equation \(X - \mu = 0\), deduce that \(X = \mu\), meaning the observation is exactly equal to the mean of the distribution.
Recognize that a z-score of 0 does not indicate the observation is above or below the mean, nor does it indicate it is at the maximum value of the distribution.
Therefore, the correct interpretation of a z-score of 0 is that the observation is equal to the mean of the distribution.
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