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 $\mathrm{standard} \mathrm{deviation}$?

• A. Histogram $B$
• B. It is impossible to determine from the histograms
• C. Both histograms have the same $\mathrm{standard} \mathrm{deviation}$
• D. Histogram $A$

Answer: (A)

Verified step by step guidance

1. Understand that the standard deviation measures the amount of variation or dispersion in a set of data values.
2. Recall that a tightly clustered distribution around the mean indicates low variability, which corresponds to a smaller standard deviation.
3. Recognize that a distribution 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 around the mean, suggesting a smaller standard deviation, while Histogram B has scores spread out over a wider range, suggesting a larger standard deviation.
5. Conclude that the histogram with the wider spread (Histogram B) depicts a higher standard deviation.