Question

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?

• A. X has higher mean, and Y has higher SD.
• B. Y has higher mean, and X has higher SD.
• C. X has higher mean, and X has higher SD.
• D. Y has higher mean, and Y has higher SD.

Hint:

For normal distributions, a higher peak indicates a lower mean and lower SD, while a wider distribution suggests a higher mean and higher SD.

Answer 1

The Correct Option is D

We are given the frequency distributions of two populations, X and Y. Based on the shape of the curves, we analyze the mean and standard deviation (SD) for each population.

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)}