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CDA认证小程序

The average math scores for Class A and Class B are 75 and 75.27, respectively. The standard deviations are 7 and 11.74, and the coefficients of variation are 0.093 and 0.156 for Class A and Class B, respectively. Which statement about the distribution of the data is reasonable?
A. Class A's scores are more dispersed.
B. Class B's scores are more concentrated.
C. Class A's scores are more concentrated.
D. The distribution of scores for both Class A and Class B cannot be determined.
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Class A has a smaller coefficient of variation, indicating that the data has lower dispersion, which means the scores are more concentrated.

正确答案是:C: Class A's scores are more集中。

专业分析如下:

分散程度通常通过标准差和变异系数来衡量。变异系数(Coefficient of Variation, CV)是标准差与平均值的比值,用来衡量数据的相对分散程度。

对于Class A:
- 平均分数:75
- 标准差:7
- 变异系数:0.093

对于Class B:
- 平均分数:75.27
- 标准差:11.74
- 变异系数:0.156

变异系数越小,表示数据越集中。反之,变异系数越大,表示数据越分散。

在这个例子中:
- Class A的变异系数是0.093
- Class B的变异系数是0.156

显然,Class A的变异系数比Class B小,这表明Class A的分数更集中,而Class B的分数更分散。因此,合理的说法是Class A的分数更集中。