Question

which of the following statements would you expect to be true? the mean is greater than the median. the mean is equal to the median. the mean is less than the median.

Explanation:

To determine the relationship between the mean and the median, we need to consider the distribution of the data (though the data set isn't provided here, we can reason about common cases).

Key Concept:

• In a symmetric distribution (e.g., normal distribution), the mean and median are equal.
• In a right - skewed (positively skewed) distribution (where there are a few large outliers), the mean is pulled up by the outliers and is greater than the median.
• In a left - skewed (negatively skewed) distribution (where there are a few small outliers), the mean is pulled down by the outliers and is less than the median.

Since the problem is likely referring to a common scenario (e.g., a right - skewed distribution is common in real - world data like income, where a few high - income earners pull the mean up), or if we assume a left - skewed distribution, but generally, if we consider typical test - like scenarios:

If we assume a right - skewed distribution (the most common case for such questions when data isn't given), the mean is greater than the median. But wait, actually, if we consider a left - skewed distribution, the mean is less than the median. However, in many introductory statistics questions, when they ask this without data, they might be referring to a right - skewed distribution (e.g., income data). But actually, the question as presented is incomplete because we don't have the data set. But if we assume a common case (for example, if the data has a few large values, right - skewed), then:

To determine the relationship between mean and median, we analyze skewness:

• In a right - skewed (positively skewed) distribution, the mean is pulled upward by large outliers, so the mean > median.
• In a left - skewed (negatively skewed) distribution, the mean is pulled downward by small outliers, so the mean < median.
• In a symmetric distribution, mean = median.

Since the problem likely refers to a right - skewed scenario (common in introductory stats questions without data), the mean is greater than the median.

Answer:

The mean is greater than the median.