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 histograms
• B. Histogram A
• C. Histogram B
• D. Both histograms have the same $standard deviation$

Answer: (C)

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. Observe that Histogram A has scores tightly clustered around the mean, indicating less variability in the data.
3. Observe that Histogram B has scores spread out over a wider range, indicating more variability in the data.
4. Understand that a wider spread of data points corresponds to a higher standard deviation because the values deviate more from the mean.
5. Conclude that Histogram B depicts a higher standard deviation since its scores are more spread out compared to Histogram A.