If the data follows a right-skewed distribution, it means that there are extreme values in the data, which will pull the mean towards the higher values. Therefore, mode < median < mean.
When the distribution is symmetrical, the positive and negative deviations cancel each other out when raised to the power of three, resulting in a skewness coefficient numerator equal to 0, and thus the skewness coefficient is 0. When the distribution is not symmetrical, the positive and negative deviations cannot cancel each other out, resulting in a positive or negative skewness coefficient. A positive skewness coefficient indicates that positive deviations are larger, suggesting a positive or right-skewed distribution. Conversely, a negative skewness coefficient indicates that negative deviations are larger, suggesting a negative or left-skewed distribution.
正确答案是:C: Skewness coefficient is greater than 0。
专业分析:
1. **偏度系数(Skewness Coefficient)**:
- 右偏分布(Right-Skewed Distribution)又称为正偏分布(Positively Skewed Distribution),其偏度系数大于0。即Skewness coefficient > 0。因此选项C是正确的。
2. **均值、中位数和众数的关系**:
- 在右偏分布中,数据的右侧尾部较长,大部分数据集中在左侧。通常情况下,均值(Mean)受极端值的影响较大,会大于中位数(Median),而中位数又会大于众数(Mode)。即Mean > Median > Mode。因此选项D也是正确的。
- 选项B描述的是左偏分布(Left-Skewed Distribution)的特征,不适用于右偏分布。
3. **错误选项**:
- 选项A:偏度系数小于0,这描述的是左偏分布,而不是右偏分布。
综上所述,关于右偏分布,正确的陈述是:C: Skewness coefficient is greater than 0。