Final answer:
In a roughly symmetric distribution, the mean and the median are likely equal, as they both are located at the central point of the distribution and there is no skew to pull the mean away from the median.
Step-by-step explanation:
If a distribution is roughly symmetric, the relationship between the mean and the median is likely that Mean = Median. This is because in a symmetrical distribution, all measures of central tendency (mean, median, and mode) are located at the central point. The mean represents the average of all values, while the median is the middle value when all data points are ordered from lowest to highest. Since the distribution is symmetric, there is no long tail on one end to pull the mean away from the center. Hence, the mean and the median coincide.
To further explain, in cases of skewness, such as when the distribution is skewed left or right, the mean is often pulled in the direction of the long tail. For example, in a left-skewed distribution, the mean is usually less than the median, which in turn is typically less than the mode. Conversely, in a right-skewed distribution, the mode is often less than the median, which is less than the mean. In a perfectly symmetrical distribution, not only are the mean and median equal, but they also equal the mode unless there is a bimodal or multimodal situation where there are multiple values with the highest frequency.
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