Question
Question 3 A)When comparing the means and medians of skewed data, which of the following is correct?(1 point) Responses The mean and median are sometimes the same. The mean and median are sometimes the same. The mean is always greater than the median. The mean is always greater than the median. The mean and median are always the same. The mean and median are always the same. The mean and median are never the same. The mean and median are never the same.
Answers
GPT-4o mini
When comparing the means and medians of skewed data, the correct response is:
**The mean is always greater than the median.**
However, this statement is only true for right-skewed distributions. In left-skewed distributions, the mean is less than the median. Therefore, a more accurate answer that encompasses all cases would be to say:
- The mean and median are sometimes the same, or
- The mean can be greater than or less than the median, depending on the direction of skewness.
Given this context, if you strictly need to choose one response from your options, it's important to note that the mean and median can be the same in some cases, particularly in symmetrical distributions, but they will not be the same in skewed distributions.
To summarize, none of the provided options may completely capture the nuance of the relationship between the mean and median in skewed data, but the most commonly referenced point in very general terms might lean towards stating that they can be different.
**The mean is always greater than the median.**
However, this statement is only true for right-skewed distributions. In left-skewed distributions, the mean is less than the median. Therefore, a more accurate answer that encompasses all cases would be to say:
- The mean and median are sometimes the same, or
- The mean can be greater than or less than the median, depending on the direction of skewness.
Given this context, if you strictly need to choose one response from your options, it's important to note that the mean and median can be the same in some cases, particularly in symmetrical distributions, but they will not be the same in skewed distributions.
To summarize, none of the provided options may completely capture the nuance of the relationship between the mean and median in skewed data, but the most commonly referenced point in very general terms might lean towards stating that they can be different.