Which term represents the number of standard deviations an observation is from the $\mathrm{mean}$?

• A. $\mathrm{variance}$
• B. $\mathrm{interquartile range}$
• C. $\mathrm{mean absolute deviation}$
• D. $z-\mathrm{score}$

Answer: (D)

Verified step by step guidance

1. Understand that the problem is asking for the term that measures how far an observation is from the mean in terms of standard deviations.
2. Recall that variance measures the average squared deviation from the mean, but it is not expressed in standard deviation units.
3. Recognize that the interquartile range measures the spread of the middle 50% of data and does not relate to standard deviations from the mean.
4. Know that mean absolute deviation measures the average absolute distance from the mean, but again, it is not expressed in standard deviation units.
5. Identify that the z-score is defined as the number of standard deviations an observation is from the mean, calculated by the formula: \(\text{z-score} = \frac{X - \mu}{\sigma}\), where \(X\) is the observation, \(\mu\) is the mean, and \(\sigma\) is the standard deviation.