Robustness vs Resistant Statistic
Both terms below come up in the same part of the course, and students mix them up. Here is each one defined on its own, side by side, so you can see where they part company.
Robustness
Hypothesis testing
A procedure is robust when it still gives roughly correct results even though one of its conditions is mildly violated.
Real data never satisfy a condition perfectly, so what matters is whether a small violation ruins the answer. The t procedures are robust against mild non-normality, and the larger n is, the more skewness they tolerate: the AP course accepts as enough for the sampling distribution of (x-bar, the sample mean) to be approximately normal, and asks for data free from strong skewness and outliers when n is smaller. For example, a one-sample t-interval from 40 mildly right-skewed measurements is trustworthy, while the same interval from 8 measurements with a clear outlier is not. Robustness has a hard limit: no procedure is robust against a biased sampling method, because bias moves the center rather than the shape.
Resistant statistic
Describing data
A resistant statistic is a numerical summary that changes little when a few extreme values or outliers are present.
A statistic is resistant when extreme values have little effect on it, so it reflects the bulk of the data rather than a few outliers. The median and interquartile range are resistant, while the mean and standard deviation are not. For example, changing the largest value in 2, 4, 6, 8, 10 from 10 to 100 leaves the median at 6 but pulls the mean from 6 up to 24. This is why you prefer resistant measures to summarize skewed data or data with outliers.