Resistant Statistic vs Mean

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.

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.

Full entry for resistant statistic

Mean

Describing data

The mean is the arithmetic average of a set of numbers, found by adding all the values and dividing by how many there are.

The mean is the balance point of a distribution, the value where the data would balance if placed on a seesaw. For example, the mean of 4, 8, and 9 is (4+8+9)/3=7(4 + 8 + 9) / 3 = 7. The sample mean is written xˉ=1nxi\bar{x} = \frac{1}{n}\sum x_i, where xi\sum x_i (the sum of the values) is divided by nn (the number of values). Because every value contributes, the mean is sensitive to outliers and skew.

Full entry for mean

Where each one fits in the course