The problem involves comparing the standard deviations of two data sets based on their histograms.

• Quantity A refers to the standard deviation of Data Set I.
• Quantity B refers to the standard deviation of Data Set II.

Observing the two histograms:

• Data Set I (on the left) has data that is more concentrated around 17 and 18, with fewer occurrences on the extremes (15 and 19). This suggests that the data points are clustered closer to the mean, implying a smaller standard deviation.
• Data Set II (on the right) shows a more uniform spread across the values, with the frequencies of 15, 16, 17, and 19 being roughly the same. This indicates the data is more spread out, which typically results in a larger standard deviation.

Conclusion:

• Since standard deviation measures how spread out the data points are from the mean, and Data Set II appears to be more spread out compared to Data Set I, the standard deviation of Quantity B (Data Set II) is likely greater.

The correct answer is B: Quantity B is greater.

Do you want further details on standard deviation or any related concepts?

Here are five related questions to expand your understanding:

1. What is the formula for standard deviation, and how is it calculated?
2. How does the shape of a data set affect its standard deviation?
3. Can two data sets have the same mean but different standard deviations? If so, how?
4. What is the difference between standard deviation and variance?
5. How does removing or adding an outlier affect the standard deviation of a data set?

Tip: The standard deviation is sensitive to data points that are far from the mean—these outliers can significantly increase it!