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

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

Answer: (D)

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 smaller standard deviation means data points are closer to the mean, while a larger standard deviation means data points are more spread out.
3. Look at Histogram A, which shows scores tightly clustered around the mean, indicating low variability.
4. Look at Histogram B, which shows scores spread out over a wider range, indicating higher variability.
5. Conclude that the histogram with scores more spread out (Histogram B) depicts a higher standard deviation.