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In statistics, a measure is called resistant if it is not heavily affected by extreme values or outliers. Think of it as a sturdy object that doesn't budge easily no matter how much pressure is applied at the ends. When you look at a dataset, some values might be vastly different from the majority; these are called outliers. They can distort many statistical calculations, but resistant measures maintain their values relatively stable despite these outliers.

Take, for example, the median. It stands strong even when there are a few data points way off from the rest. This stability is what makes resistant statistics valuable for getting a true sense of the data's central tendencies without being misled by extreme values.

The median and mean are both measures of central tendency, but they behave quite differently when it comes to resistance.

The median is the middle number in a data set when all numbers are ordered. It's a line in the sand, not swayed by how high or low other numbers might be. For instance, if you have the dataset \(1, 2, 3, 50\), the median will be 2.5, perfectly in the middle and completely unfazed by the outlier 50.

The mean, or average, is a different story. It is calculated by adding all numbers together and dividing by the number of data points. Because this calculation includes every value, the mean gets pulled towards any outlier. In the same dataset \(1, 2, 3, 50\), the mean is 14, a number significantly bumped up by the 50.

This difference explains why statisticians often prefer the median over the mean when dealing with skewed data or data with outliers.

The mode is another measure of central tendency, defined as the most frequently occurring value in a dataset. While the mode can sometimes be resistant, it is not always. This is because the mode is based on frequency alone, not the value of the data.

Consider a simple example: \(1, 1, 2, 3, 50\). The mode here is 1, which seems unaffected by the outlier 50. In this case, the mode might appear resistant.

However, imagine a shift in frequency like \(1, 2, 2, 3, 50\). Now the mode changes to 2, showing that the mode can indeed be influenced by changes in the dataset. While it isn't typically affected by the magnitude of outliers, varying frequencies can sway the mode, making it less reliable as a resistant measure compared to the median.

This susceptibility is worth noting, as relying solely on the mode can sometimes give a misleading picture of a dataset's central tendency.