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, meaning the data points are close to the average score.
3. Recognize that a histogram with scores spread out over a wider range indicates higher variability, meaning the data points are more spread out from the mean.
4. Since Histogram B shows scores spread out over a wider range, it suggests a larger spread of data and therefore a higher standard deviation.
5. Conclude that Histogram B depicts a higher standard deviation compared to Histogram A.