Understanding Right Skewed Distributions

D

large positive deviations dominate large negative deviations.

In a right-skewed distribution, also known as a positively skewed distribution, the tail of the distribution extends towards the right side. This means that there are more values on the left side of the distribution with smaller values, and fewer values on the right side with larger values.

Now let's evaluate each answer choice to determine the correct statement for a right-skewed distribution:

A. The median is larger than the mean. In a right-skewed distribution, the median will typically be smaller than the mean. This is because the mean is influenced by the presence of the larger values on the right side, which "pull" the mean in that direction. The median, on the other hand, is the value that separates the distribution into two equal halves, and in a right-skewed distribution, this value tends to be smaller than the mean. Therefore, option A is incorrect.

B. Large negative deviations dominate large positive deviations. In a right-skewed distribution, the tail extends towards the right side, which means that there are relatively fewer larger values compared to smaller values. Consequently, large negative deviations (values smaller than the mean) are less common than large positive deviations (values larger than the mean). This is because there are fewer values on the right side that can contribute to large negative deviations. Therefore, option B is incorrect.

C. The mean is positive. The mean of a distribution can be positive, negative, or zero, regardless of whether the distribution is right-skewed or not. The skewness of the distribution does not determine the sign of the mean. Therefore, option C is incorrect.

D. Large positive deviations dominate large negative deviations. This statement correctly describes a right-skewed distribution. As mentioned earlier, in a right-skewed distribution, there are more values on the left side with smaller values and fewer values on the right side with larger values. Consequently, large positive deviations (values larger than the mean) are more prevalent than large negative deviations (values smaller than the mean). Therefore, option D is correct.

In summary, the correct answer is D. In a right-skewed distribution, large positive deviations dominate large negative deviations.