Concept 4

Identify outliers and describe their impact on center/spread.

How outliers affect the mean, median, range, standard deviation, and IQR.

Core Idea

An outlier is a value far from the rest of the data. Outliers pull the mean toward them and inflate the range and standard deviation, but they barely affect the median or IQR.

Understanding

Think of the mean as a balance point. Drop a heavy weight far from center and the balance tips toward it. That's what an outlier does to the mean — it drags it in its direction.

The median, by contrast, only cares about position. Whether the largest value is 50 or 5000, the middle value stays in the same spot. That's why the median is called a resistant measure.

The same logic applies to spread. Range and standard deviation use every value in their calculations, so one extreme point can blow them up. IQR only looks at the middle 50%, so outliers don't touch it.

SAT questions on this concept usually describe a scenario — "one student scored much higher than the rest" — and ask which statistic changed or which measure best represents the data.

Step by Step

  1. Check whether the value is far from the rest of the data. A common rule: a value is an outlier if it's more than 1.5 ×IQR below Q1 or above Q3.
  2. Determine whether the question asks about center (mean vs. median) or spread (range/SD vs. IQR).
  3. If there's an outlier: the mean shifts toward it, the range and SD increase. The median and IQR stay roughly the same.

Misconceptions

  • Thinking outliers always increase the mean — an unusually low outlier pulls the mean down.
  • Believing the median is completely immune to data changes — removing or adding values can shift the median's position, though usually by less than the mean shifts.
  • Forgetting that range is affected by outliers — students sometimes treat range as resistant because it seems simple.
Question

Worked Example

Nine students scored 72, 75, 78, 80, 81, 83, 85, 88, and 90 on a test. A tenth student scored 25. Which of the following statements about the effect of adding this score is true?

Select an answer to see the explanation