Final answer:
In a right-skewed distribution, the mean tends to be greater than the median due to the longer tail on the right-hand side where higher values pull the average up. Therefore, for a distribution skewed to the right with no outliers, the correct expression is that the mean is greater than the median.
Step-by-step explanation:
When analyzing the behavior of data points in a distribution, understanding skewness is fundamental. If a distribution is skewed to the right (also known as positive skew), it suggests that the data points stretch out more on the right-hand side of the distribution, creating a long tail in that direction. In this scenario, there tend to be a larger number of lower values, with fewer high-value outliers driving the average up; therefore, the mean is pulled in the direction of the tail and tends to be higher than the median, which is the middle value when the data are sorted in order. In contrast, the mode, which is the most frequently occurring value in the set, often falls to the left of the median.
To illustrate, consider a set of exam scores where a majority of students scored around 80, but a few scored exceptionally high, in the 90s and 100s. The median might be somewhere around 85 (assuming an even number of scores), but the mean could be higher because of the exceptional high scores that pull the average up. Therefore, if a distribution is skewed to the right with no outliers, the correct expression is that the mean is greater than the median.
In conclusion, when faced with a distribution that is skewed to the right, it is generally accurate to state that the mean is greater than the median. This concept applies widely in various fields of study including business, economics, and the natural sciences where data analysis is crucial.