Suppose you have two histograms, $A$ and $B$, each representing the distribution of exam scores for two different classes. Histogram $A$ shows scores tightly clustered around the mean, while Histogram $B$ shows scores spread out over a wider range. Which histogram depicts a higher standard deviation?

• A. It is impossible to determine from the information given
• B. Histogram $B$
• C. Both histograms have the same standard deviation
• D. Histogram $A$

Answer: (B)

Verified step by step guidance

1. Recall that the standard deviation measures the amount of variation or dispersion of a set of values from the mean.
2. Understand that a histogram with scores tightly clustered around the mean indicates low variability, which corresponds to a smaller standard deviation.
3. Recognize that a histogram with scores spread out over a wider range indicates higher variability, which corresponds to a larger standard deviation.
4. Compare the two histograms: Histogram A has scores tightly clustered, so it has a lower standard deviation; Histogram B has scores more spread out, so it has a higher standard deviation.
5. Conclude that Histogram B depicts a higher standard deviation because the data points are more dispersed from the mean.