Based these dotplots do you anticipate that the standard deviation of symptom length will be similar for men and women?

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BlackTom AI · Accepted Answer

Restating the question to ensure clarity: Based on these dotplots, do you anticipate that the standard deviation of symptom length will be similar for men and women?

First, since the answer options aren’t provided in the prompt, I’ll focus on the core idea the question is probing: the standard deviation reflects the spread of data around the mean. If the two dotplots for men and women show similar clustering and similar overall spread around their centers, that suggests comparable variability, hence a similar standard deviation.

Consider the reasoning path you’d use with dotplots:
- Look at the vertical dispersion of points in each group. If both groups show roughly the same range and similar density across that range, the SDs are likely close.
- Pay attention to any outliers or skew that would disproportionately affect SD; a single extreme value in one group could inflate that group’s SD relative to the other, even if the rest are similar.
- Compare central concentration: if one dotplot is markedly more tightly clustered around its mean while the other is more spread out, this points to differing SDs.

Potential misinterpretations to avoid:
- A taller or denser appearance in one plot does not automatically mean a larger SD; you need the overall spread, not just height, to judge variability.
- Equal means with different spreads imply different SDs; don’t rely solely on apparent central tendency.

Given these considerations, if the dotplots indeed display a similar spread (roughly the same range and density of symptom lengths for men and women), then it would be reasonable to anticipate similar standard deviations. If, however, one plot shows noticeably greater spread, the corresponding SD would be larger for that group.

Why this reasoning aligns with standard ideas about SD from dotplots: the standard deviation is a measure of dispersion around the mean, and visual dispersion is the most direct cue to that dispersion when comparing two groups.

In absence of the actual alternative options to critique, the key takeaway is: you judge similarity of SDs by comparing the spreads of the two dotplots, not by the means or by height alone, and when spreads are alike, the SDs are likely similar.

Su25-STATS-141-01/BIO-141-01 P2 Readiness Quiz

Based these dotplots do you anticipate that the standard deviation of symptom length will be similar for men and women?

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