Assuming values are normally distributed, which of the following data points is the most extreme value:

Question

BlackTom AI · Accepted Answer

Question restatement: The problem asks, assuming normal distribution, which data point represents the most extreme value in terms of distance from the mean, expressed in standard deviations (z-score).
Option A: A data point 0.3 standard deviations away from the mean. This is a small deviation from the mean, corresponding to a z-score of ±0.3, which is far from the tails and thus not extreme.
Option B: A data point -0.1 standard deviations away from the mean. This is even closer to the mean with a z-score of -0.1, indicating virtually no extremeness.
Option C: A data point 2.16 standard deviations away from the mean. A z-score of ±2.16 is in the outer region of the normal curve and more extreme than the previous two options, but not as extreme as the next.
Option D: A data point -2.8 standard deviations away from the mean. This has a large negative z-score, with an absolute value of 2.8, placing it far into the tails of the distribution and more extreme than 2.16 or the near-mean values.
Now, comparing the magnitudes of deviation from the mean:
- |0.3| = 0.3, not extreme.
- | -0.1 | = 0.1, even less extreme.
- | 2.16 | = 2.16, substantial extremity but still less than 2.8 in absolute value.
- | -2.8 | = 2.8, the largest absolute deviation among the options, hence the most extreme value.
A potential misconception to avoid: extreme simply means farthest from the mean in terms of standard deviations, not whether the value is positive or negative. The sign does not affect extremity; only the distance from the mean does.
In summary, while 2.16 SD is quite far from the mean, the data point at -2.8 SD sits farther away from the mean in terms of absolute z-score, making it the most extreme value among the options.

Assuming values are normally distributed, which of the following data points is the most extreme value:单项选择题

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