Question 4

A has the greatest standard deviation.

Distribution A has the widest spread, indicating that it has the greatest standard deviation among the options provided.

A) A

Option A is correct because it represents the distribution with the largest spread, which is a key indicator of a higher standard deviation. A wider spread suggests that the data points are more dispersed from the mean, reflecting greater variability.

B) B

Option B is incorrect as it shows a narrower spread compared to Option A. This indicates a smaller standard deviation, as the data points are closer to the mean than in distribution A.

C) C

Option C is also incorrect because, like Option B, it exhibits a tighter distribution. The lesser spread of data points signifies a lower standard deviation than that of distribution A.

D) D

Option D is incorrect as well since it has a similar or even narrower spread compared to options B and C. This suggests a standard deviation that is not greater than that of distribution A.

Conclusion

In summary, Option A is definitively correct as it exhibits the greatest spread, which directly correlates with a higher standard deviation. All other options (B, C, and D) demonstrate narrower distributions, indicating lower variability and thus smaller standard deviations.