Sensitivity to extreme values is how much a statistic changes when outliers enter a dataset; in AP Stats, the mean, standard deviation, and range are sensitive (nonresistant), while the median and IQR are resistant (robust) because outliers barely affect them.
Sensitivity to extreme values describes how much a summary statistic gets pulled around by outliers. Some statistics use every data value in their formula, so one wild number drags them along. The mean adds up everything, so a single huge value inflates it. The standard deviation squares each distance from the mean, so an outlier counts double-strength. The range literally depends on the most extreme values by definition. The CED calls these statistics nonresistant (or non-robust).
Other statistics only care about position in the ordered list, not the actual size of extreme values. The median is just the middle value, and the IQR is Q3 minus Q1, so an outlier sitting way out in the tail can get bigger and bigger without moving them at all. These are resistant (or robust) statistics. Think of it this way: the mean is a balance point that tips toward outliers, while the median is a count-to-the-middle position that doesn't care how far away the extremes sit.
This concept lives in Topic 1.7 (Summary Statistics for a Quantitative Variable) in Unit 1, and it's the entire point of learning objective AP Stats 1.7.C, which asks you to explain why you'd choose one measure of center or spread over another. The rule the exam wants you to know cold: for skewed distributions or data with outliers, report the median and IQR; for roughly symmetric data with no outliers, mean and standard deviation are fine. It also connects to the two outlier rules in 1.7.C (the 1.5 × IQR fences and the 2-standard-deviations-from-the-mean rule). You can't justify a choice of summary statistics without naming which ones are resistant and which aren't, so this idea shows up in almost every 'describe the distribution' answer you'll write all year.
Keep studying AP® Statistics Unit 1
Mean vs. Median (Unit 1)
These two are the classic sensitivity matchup. The mean chases outliers because every value goes into its formula, while the median ignores them because it only counts to the middle. In a right-skewed distribution, the mean gets pulled above the median, which is also how you can guess skew direction from summary stats alone.
Interquartile Range (IQR) (Unit 1)
The IQR is the resistant measure of spread that pairs with the median. Since it only uses Q1 and Q3, the middle 50% of the data, the most extreme values never touch it. That's also why the 1.5 × IQR outlier rule works: you're using a fence that the outliers themselves can't move.
Range and Standard Deviation (Unit 1)
Both are nonresistant measures of spread, but for different reasons. The range is built entirely from the max and min, so one outlier can blow it up. The standard deviation squares each deviation from the mean, so a far-out point contributes a massively inflated term to the sum.
Influential Points in Regression (Unit 2)
Sensitivity doesn't stop at one-variable data. In Unit 2, the least-squares regression line is built from means and squared distances, so a single high-leverage point can swing the slope and correlation. It's the same nonresistance idea wearing a two-variable costume.
Multiple-choice questions love to hand you a small dataset, add or change one extreme value, and ask which statistic changes more. For example, with study hours of 2, 3, 15, 4, 6, adding a student who studied 20 hours pushes the mean from 6 up to about 8.3, while the median only creeps from 4 to 5. The mean changes dramatically; the median barely flinches. Another common stem gives data like {12, 15, 16, 17, 18, 19, 20, 85} and asks how the 85 affects mean versus median (the mean jumps to 25.25 while the median sits at 17.5). On the free-response side, this idea fuels justification questions tied to 1.7.C. When a distribution is skewed or has outliers, you're expected to choose the median and IQR and explicitly say why, using the words 'resistant' or 'not affected by outliers.' Saying 'median is better' with no reason earns nothing.
These are two sides of the same coin, and mixing them up flips your answer. A statistic that is highly sensitive to extreme values is nonresistant (mean, standard deviation, range). A statistic that is not sensitive is resistant or robust (median, IQR). If a question asks which measure is 'most resistant to outliers,' it wants the one that changes the least, which is the opposite of the most sensitive one.
The mean, standard deviation, and range are nonresistant statistics, meaning outliers can change their values dramatically.
The median and IQR are resistant statistics because they depend on position in the ordered data, not on how extreme the outliers are.
An outlier pulls the mean toward itself, so in a right-skewed distribution the mean ends up larger than the median.
When data are skewed or contain outliers, report the median and IQR; when data are roughly symmetric with no outliers, the mean and standard deviation work well.
On FRQs, you must justify your choice of summary statistics by explicitly stating that the median and IQR are resistant to outliers, not just by naming them.
The same sensitivity idea returns in Unit 2, where a single influential point can drag the least-squares regression line and the correlation.
It's how much a statistic changes when outliers appear in the data. The mean, standard deviation, and range are sensitive (the CED calls them nonresistant), while the median and IQR are resistant because outliers barely affect them.
Barely, and sometimes not at all. Adding an outlier can shift the median by at most one position in the ordered list, so it might move slightly (like from 4 to 5 in a small dataset), but it never gets dragged toward the outlier the way the mean does.
The mean's formula adds every single value, so one extreme number directly inflates the sum. The median only depends on the middle position. In the dataset {12, 15, 16, 17, 18, 19, 20, 85}, the 85 pushes the mean to 25.25 while the median stays at 17.5.
Resistant (robust) statistics like the median and IQR are not greatly affected by outliers. Nonresistant statistics like the mean, standard deviation, and range are influenced by outliers. Sensitivity to extreme values is just the property that makes a statistic nonresistant.
No. Standard deviation squares each value's distance from the mean, so a faraway outlier contributes an enormous squared term and inflates the result. If your data have outliers, the IQR is the resistant measure of spread to report instead.
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