49. What is a basic assumption of a z-score?
Answer: C
The mean is equal to zero with a standard deviation of 1
A basic assumption of a z-score is that it is standardized such that the mean of the distribution is zero and the standard deviation is one. This allows for comparison across different data sets.
A) The mean is equal to zero with a standard deviation of 2
This option is incorrect because a z-score is defined specifically with a mean of zero and a standard deviation of one, not two. A mean of zero with a standard deviation of two would not align with the standardization process inherent in calculating z-scores.
B) Outlier data points are critical to a z-score calculation
This statement is misleading because while outliers can affect the calculation of the mean and standard deviation, they are not critical for the z-score itself. Z-scores can still be calculated regardless of the presence of outliers; however, the interpretation may be skewed if outliers are present.
C) The mean is equal to zero with a standard deviation of 1
This option is correct as it accurately describes the fundamental properties of a z-score. By standardizing data in this manner, z-scores facilitate comparison across different distributions, allowing for a uniform understanding of how far a data point is from the mean.
D) Outlier data points must be eliminated from a z-score calculation
This option is incorrect because eliminating outliers is not a requirement for calculating z-scores. In fact, z-scores can be calculated inclusive of outliers, but doing so may distort the interpretation of the results, as outliers can significantly affect the mean and standard deviation.
Conclusion
The correct answer, C, reflects the foundational principles of z-scores, which standardize data to a mean of zero and a standard deviation of one. Options A and B misrepresent the properties and significance of z-scores, while D incorrectly suggests that outliers must be removed, which is not a prerequisite for their calculation. Thus, C is definitively the only accurate representation of a z-score's basic assumptions.