The range is generally more affected by an outlier in a dot plot than the median because it directly captures the distance between the extreme values, which can be significantly altered by an outlier, while the median focuses on the central tendency of the data and is less sensitive to individual extremes.
Median: The median is the middle value when the data is ordered from smallest to largest. It represents the value that divides the dataset into two equal halves. Outliers, by definition, are extreme values that fall far from the main cluster of data points. Unless the outlier is exactly in the middle of the data distribution, it won't significantly impact the median. If it falls on one side of the median, it will only shift the median slightly towards that side, maintaining its position as the central value.
Range: The range is the difference between the largest and smallest values in the data set. An outlier, especially one at the extreme end of the distribution, can significantly inflate or deflate the range. If the outlier is the largest value, it will directly increase the range, while if it's the smallest value, it will directly decrease the range. This can distort the overall picture of the data spread, making it appear more or less variable than it actually is.
Visualizing the effects in a dot plot:
Imagine a dot plot with most points clustered together in the center, and then a single dot far away on one side. This represents an outlier. The median will be positioned somewhere near the main cluster, unaffected by the outlier. However, the range will be stretched considerably due to the inclusion of the outlier. The dot plot will visually show the outlier as a distinct point far away from the main group, highlighting its impact on the range.
Therefore, while both the median and the range can be affected by outliers, the range is typically more susceptible to significant changes due to their extreme values.