Question

In the accompanying display, which has the smaller mean and which has the larger standard deviation?

1) The display with the smaller mean has the larger standard deviation
2) The display with the smaller mean has the smaller standard deviation
3) The display with the larger mean has the larger standard deviation
4) The display with the larger mean has the smaller standard deviation

Answer 1

In the accompanying display, the graph with the larger mean will have the smaller standard deviation.

Step-by-step explanation:

In the accompanying display, the graph with the larger mean will have the larger standard deviation.

The mean represents the average value in a distribution, while the standard deviation measures the spread or dispersion of the data.

If the mean is larger, it means that the data values are spread out from the average, resulting in a larger standard deviation. Conversely, if the mean is smaller, it indicates that the data values are closer to the average, leading to a smaller standard deviation.

Therefore, the correct answer is: 4) The display with the larger mean has the smaller standard deviation.