Which dataset below shows the greatest variance?

Question

BlackTom AI · Accepted Answer

To determine which dataset has the greatest variance, we examine how spread out each dataset’s values are around its center.
Option: Dataset 3. The red distribution appears quite narrow, with values tightly clustered around its peak near x ≈ 2.0. A narrow spread indicates small variance, so this dataset likely does not have the greatest variance.
Option: They all show the same variance. Visually, the three distributions differ in width: Dataset 3 is narrow, Dataset 1 is quite narrow as well, but Dataset 2 spans a broader range on the x-axis. Therefore, this option is incorrect because the variances are not identical.
Option: Dataset 1. The green distribution is also relatively tight, centered around a negative to near-zero x-value, and spans a smaller interval than Dataset 2. This suggests a smaller variance compared to at least one of the other datasets, so this option is unlikely to be correct.
Option: Dataset 2. The blue distribution covers a noticeably wider range along the x-axis, from roughly -4 to around 0 or so, and the data points are more dispersed from its center. A wider spread corresponds to a larger variance, making this the most plausible choice for the greatest variance among the three datasets.
Overall, by comparing the horizontal spread of the distributions, Dataset 2 shows the largest dispersion, implying the greatest variance among the options.

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Which dataset below shows the greatest variance?

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Which dataset below shows the greatest variance?

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