Based on test score data, which statement about the mean, median, and mode is correct?

The median and the mode being equal can occur in various types of distributions, particularly in symmetric distributions or in certain distributions where the most frequently occurring value aligns with the center of the data set.

The median, being the middle value when the data is ordered, and the mode, representing the most frequently occurring value, can coincide, especially in distributions that exhibit a peak at the center or when the data has a uniform spread around a central value. For example, in a data set where all values are the same, all three measures (mean, median, and mode) will also be equal.

Understanding the relationships between these measures is crucial in analyzing data sets. For instance, in skewed distributions, the mean can be influenced significantly by extreme values, causing it to diverge from the median and mode. Thus, if the median and mode are equal, it provides insights into the distribution's characteristics and suggests that there may not be extreme outliers affecting the data's central tendency.

In summary, when evaluating data based on the mean, median, and mode, it is essential to recognize contexts where the mode can align with the median, reinforcing their relationship in describing the data's center.