Final answer:
If a statistic is resistant, it means that it is not greatly affected by extreme values or outliers in the data. Resistant statistics provide a more robust measure of central tendency or spread compared to non-resistant statistics. An example of a resistant statistic is the median.
Step-by-step explanation:
If a statistic is resistant, it means that it is not greatly affected by extreme values or outliers in the data. In other words, it is not sensitive to unusual or extreme observations. Resistant statistics are useful because they provide a more robust measure of central tendency or spread, compared to non-resistant statistics.
One commonly used resistant statistic is the median. The median is the middle value in a dataset when it is ordered from least to greatest. Unlike the mean, which can be heavily influenced by extreme values, the median remains relatively stable even in the presence of outliers.
For example, let's say we have a dataset of test scores: 85, 90, 92, 95, and 500. If we calculate the mean, the extreme value of 500 will heavily skew the result. However, if we calculate the median, the extreme value has less impact, and we get a more accurate representation of the typical test score.