Adding a single extreme outlier to a small dataset can pull the mean so far that it no longer accurately represents the typical behavior in the distribution.

In a study on reaction times, a researcher calculates a mean of 245 ms for a set of four participants (200, 250, 280, and 250 ms). If a fifth participant provides an outlier score of 5,000 ms, the mean drastically increases to 1,445 ms. Which statement best explains why this new mean is a poor representation of the 'typical' behavior in this dataset?

A researcher records the following scores on a memory task: 10, 15, 20, and 15, resulting in an initial mean of 15. Match each possible fifth participant score with the resulting mean and its effect on the dataset's representativeness.

To analyze how a single outlier can invalidate a mean, arrange the following steps in the order they describe the mathematical distortion of a reaction-time dataset (initial scores: 200, 250, 280, and 250 ms; outlier: 5,000 ms).

Imagine you are constructing a numerical demonstration for a psychology textbook to show how a single extreme outlier can pull the mean of a small dataset. You start with four typical reaction times: $200$, $250$, $280$, and $250$ ms (which currently sum to $980$ ms). To create a final dataset of five scores where the mean is pulled to a target value of exactly 1,000 ms, what specific value must you generate for the fifth outlier?

In a dataset where a single outlier (5,000 ms) raises the mean to 1,445 ms—a value higher than $80\%$ of the scores—a researcher must evaluate the mean as _____ of the typical behavior in that distribution.

In the example provided, adding an outlier of 5,000 ms to the dataset results in a new mean that is larger than _____ percent of the scores in the distribution.

A cognitive psychologist records typing speeds (in words per minute) for five children: 20, 22, 18, 24, and 21 wpm. A sixth score of 300 wpm is later discovered to be a data-entry error. If the erroneous score is included in the analysis, the new mean will exceed 75% of the original five scores.

Using the reaction-time example from your textbook (original dataset: 200, 250, 280, and 250 ms; outlier added: 5,000 ms), match each description on the left to the statement on the right that best explains its statistical role or outcome.

A researcher analyzing reaction-time data suspects that one participant's extremely high score may be an outlier. Arrange the following steps in the order the researcher should complete them when evaluating whether the mean is still an appropriate measure of central tendency for this dataset.

Based on the textbook example of reaction times ($200$, $250$, $280$, and $250$ ms), recall and state the initial mean of the dataset, the value of the added outlier, and the new mean. Explain the behavioral cause of the outlier as described in the text, and describe how this change illustrates the limitation of using the mean to represent typical behavior in a skewed distribution.

Based on this scenario, explain why the mean reaction time of 1,445 ms is not an accurate representation of the group's performance. Support your explanation by referencing how the new mean compares to the individual scores in the dataset.

Assume you have a dataset of four reaction times: $200$ ms, $250$ ms, $280$ ms, and $250$ ms. Apply the formulas for central tendency to calculate the new mean after adding an outlier of 5,000 ms, and explain how this calculation demonstrates the sensitivity of the mean to extreme values.