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Which of the following distributions (A, B, C, or D) has the largest standard deviation? Explain your reasoning.
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Step-by-step solution
4 stepsTo determine which distribution has the largest standard deviation, we look for the curve that is the widest and flattest. A wider spread indicates a larger standard deviation, meaning the data points are more dispersed from the mean.
Analyze Distribution A.
Distribution A is relatively narrow and tall, indicating a smaller standard deviation.
Analyze Distribution B.
Distribution B is also relatively narrow and tall, similar to A, suggesting a small standard deviation.
Analyze Distribution C.
Distribution C is wider and flatter than both A and B, indicating a larger standard deviation than A and B.
Analyze Distribution D.
Distribution D is the widest and flattest among all four distributions, meaning its data points are the most spread out from the mean. This indicates the largest standard deviation.
Comparing the visual spread of all four distributions, Distribution D shows the greatest dispersion.
The correct option is D.
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