A real estate agent is marketing a neighborhood of 10 homes. Nine of the homes are valued at approximately $200,000 each, while one newly built mansion is valued at $3,200,000. The agent advertises the 'average home value' in the neighborhood as $500,000. Which statement best evaluates the agent's use of this figure?

Example of the Mean's Sensitivity to Outliers

In a highly skewed distribution, how does the presence of extreme scores typically affect the mean?

In a distribution of reaction times, the mean will typically be more significantly shifted by the presence of a few extreme outliers than the median will.

Match each research scenario with the expected relationship between the mean and the median, based on how the presence of extreme scores (outliers) influences the mean.

A researcher is analyzing a dataset of participants' reaction times that is positively skewed due to a few participants who took an exceptionally long time to respond (outliers). Based on the sensitivity of the mean to these extreme scores, arrange the following values in order from the lowest numerical value to the highest numerical value within this specific distribution.

A researcher is developing a reporting protocol for a psychology study on reaction times. One participant's response is $10$ times slower than everyone else's. Arrange the following steps in the correct order to create a data-summary protocol that ensures the final report accurately represents the 'typical' participant by accounting for the mean's sensitivity to extreme scores.

In a skewed distribution, the mean is typically pulled away from the median in the direction of the shorter tail of the distribution.

A researcher is examining the weekly study hours of a group of psychology students. Most students study between $10$ and $20$ hours per week, but two students report studying $80$ hours per week. Which statement best explains why the mean of this dataset is not a good representation of the typical student's study hours?

A researcher is evaluating the central tendency of a dataset containing several extreme outliers that have significantly shifted the average value. After reviewing the data, the researcher concludes that the mean is a(n) _____ representation of the typical score because its high sensitivity to those outliers causes it to no longer accurately reflect the center of the distribution.

Analyze the impact of different distribution characteristics on central tendency measures by matching each concept with the statement that best describes its behavior or role in a dataset.

A researcher is evaluating a reaction time dataset and finds that a few extremely long response times have created a highly skewed distribution. The researcher must determine which measure of central tendency provides the most accurate representation of the typical score. Because the mean is pulled away from the center by these extreme scores, the researcher decides that the mean is not an accurate representation and evaluates that they should report the _____ instead.

Why do researchers often prefer the median over the mean when describing the typical score of a highly skewed distribution?

Because the mean utilizes every data point in a psychological dataset, it is always the most accurate representation of the typical score, even when the distribution contains extreme outliers.

A psychology researcher is analyzing different datasets from a recent study. Match each dataset scenario with the most appropriate statistical decision regarding its measure of central tendency.

A cognitive psychology researcher is analyzing three datasets of reaction times to understand how measures of central tendency behave under different conditions. Arrange the following datasets in order from the one where the mean is LEAST pulled away from the median to the one where the mean is MOST drastically pulled away from the median.

A peer reviewer is evaluating a research manuscript which claims that participants typically required fifteen trials to learn a maze, based entirely on the mean score. However, the data shows a severe positive skew: most participants learned it in four to six trials, but two participants required over eighty trials. To ensure the statistical summary is logically defensible and not distorted by extreme outliers, the reviewer should demand that the authors report the _____ instead.

In a highly skewed distribution, the mean is pulled away from the median in the direction of the _____.

A psychology researcher calculates both the mean and the median for a dataset of reaction times. If the dataset contains a few unusually slow reaction times (extreme high values), how will these outliers affect the relationship between the two measures?

A developmental psychology researcher observes the number of words spoken by toddlers in a 10-minute play session. Most toddlers speak between 15 and 20 words, but one highly verbal toddler speaks 110 words. If the researcher wants to describe the typical vocabulary output of the group without the summary being distorted by the extreme score, they should use the mean as their primary measure of central tendency.

A psychology researcher is analyzing how different dataset characteristics affect measures of central tendency. Match each dataset scenario with the resulting structural relationship between its mean and median.

A research committee is critiquing a draft report that incorrectly uses the mean to describe a psychological dataset containing extreme outliers. Arrange the logical sequence of arguments the committee should use to justify revising the report to use the median instead.