The frequency distributions of a trait in two populations, X and Y, are shown in the figure.
Which one of the following statements about the mean and standard deviation (SD) of the two populations is accurate?
The frequency distributions of a trait in two populations, X and Y, are shown in the figure.
Which one of the following statements about the mean and standard deviation (SD) of the two populations is accurate?
Show Hint
- X has higher mean, and Y has higher SD.
- Y has higher mean, and X has higher SD.
- X has higher mean, and X has higher SD.
- Y has higher mean, and Y has higher SD.
The Correct Option is D
Solution and Explanation
Step 1: Analyze the mean.
The mean is determined by the center of the distribution. In the graph, Population X has a sharply peaked distribution, while Population Y has a wider distribution. This suggests that Population Y has a lower peak, indicating that its mean is higher than Population X.
Step 2: Analyze the standard deviation (SD).
The standard deviation measures the spread of the data. A wider distribution indicates a higher SD. Since Population Y has a wider distribution, it also has a higher SD compared to Population X, which has a narrower distribution.
Step 3: Conclusion.
Thus, based on the shape of the frequency distributions, we conclude that Population Y has both a higher mean and a higher SD than Population X.
Final Answer: \boxed{(D)}
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