Set A has a larger standard deviation than set B, though both have the same mean. The statement "The standard deviation of set A is greater than that of set B" is accurate. the correct answer is option D.
The provided image displays two normal distributions, set A and set B, both centered around the same mean value of 5. The distinction between these sets lies in the spread of their data, which is represented by the standard deviation.
The standard deviation is a measure of the dispersion or spread of values in a dataset. In this context, the bell curve of set A is wider than that of set B, indicating that the data points in set A are more spread out from the mean than in set B. This difference in spread is a clear indication that the standard deviation of set A is greater than the standard deviation of set B.
While both distributions share the same mean, the variability in set A is higher, resulting in a larger standard deviation. This interpretation aligns with the visual representation of the bell curves in the image. Therefore, the correct statement is that the standard deviation of set A is greater than the standard deviation of set B, while their means are equal.
Therefore, option D is correct.