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

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BlackTom AI · Accepted Answer

The question asks which data point is the most extreme value assuming a normal distribution. Unfortunately, the provided data has a problem: there are no answer options listed to compare against, and the only explicit piece of information is the answer text stating: 'A data point -2.8 standard deviations away from the mean.'

To reason through this, we would normally compare all candidate data points by their distance from the mean in standard deviation units (z-scores). The data point with the largest absolute z-score would be considered the most extreme. In a normal distribution, larger |z| values indicate more extreme observations.

Because there are no alternative options shown in the answer_options field, we cannot perform a true comparison among multiple choices. If we take the provided candidate data point at face value, its extremeness is determined by |−2.8| = 2.8 standard deviations from the mean, which is indeed relatively far from the mean but not as extreme as points at, say, |z| = 3.0 or higher.

In a complete question with multiple options, the correct choice would be the data point with the largest absolute z-score. Here, with only the single listed option, we can only describe that this point lies at 2.8 standard deviations and would be more extreme than points near the mean, but we cannot conclude it is the most extreme without seeing all the other options to compare their |z| values.

If you can provide the full list of answer options, I can pinpoint exactly which data point is the most extreme by comparing their |z| values and explaining why that one is extreme relative to the others.

PSYC20007_2025_SM2 Goals of Statistical Testing II

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

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