Final answer:
The mean and median of a data set differ when the data is skewed or contains outliers; the mean is affected by these, whereas the median is not. They are the same or close when the data is perfectly symmetrical, with equal distribution around the center.
Step-by-step explanation:
For data sets, the mean and median can sometimes be different due to the distribution of the data.
The mean is calculated by adding all data points and dividing by the number of points, which makes it sensitive to outliers and can be skewed if the data is not symmetrical.
The median, on the other hand, is the middle value when data points are ordered from least to greatest, making it more resistant to skew and outliers.
Mean and median are the same or very close when the data is perfectly symmetrical, meaning it is equally distributed around the center.
However, when the data is skewed, or contains outliers, the mean will be pulled in the direction of the skew.
Outliers can cause the mean to move away from the median, which stays at the central position where exactly half the data lies above and half below.
The mode is the most frequently occurring value, which can also indicate the shape of the distribution. In skew distributions, the mode tends to align with the bulk of the data and less with the mean if the latter is pulled by the outliers.