Example of Finding the Median

Sensitivity of the Mean to Outliers

What does the median represent in a distribution of scores?

A psychologist is analyzing the number of words recalled by a group of participants in a memory study. Arrange the steps below in the correct order to determine the median value of these recall scores.

A psychologist is evaluating how modifications to a dataset of reaction times (measured in milliseconds) affect the median. Match each potential data change to its specific analytical impact on the median value.

A psychologist studying cognitive test scores finds that most participants score near 50, but one participant scores 0 due to a computer error. The psychologist’s decision to report the median as the representative value is methodologically sound because the median’s focus on the middlemost position prevents this extreme score from distorting the perceived typical performance of the group.

A psychology researcher is designing a set of hypothetical results for a textbook to illustrate how the median remains stable despite extreme outliers. They need to construct a dataset of $5$ reaction times (measured in milliseconds) that satisfies two specific design criteria: (1) the median must be exactly $400$, and (2) the mean must be at least $600$ to demonstrate a significant positive skew. Which of the following datasets correctly assembles these parameters?

Example of Calculating the Median

For any distribution of scores, the median must always be one of the actual observed scores present in the original dataset.

A psychological researcher is analyzing different sets of participant scores. Match each dataset scenario with the correct rule or property used to identify or describe its median.

A researcher measures the reaction times (in seconds) of six participants completing a cognitive task. The recorded times are: 14, 8, 21, 10, 18, and 12. The median reaction time for this group of participants is _____.

A psychology researcher analyses a set of reaction times and observes that the median is a value that does not equal any of the actual observed scores in the dataset. By analyzing this outcome, the researcher can deduce that the dataset contains a(n) _____ number of scores.

A researcher is determining the most appropriate measure of central tendency to report for a dataset of cognitive processing times. Arrange the steps in the correct order to evaluate the data properties and select the representative metric.

In the context of analyzing psychological data, define the median as a measure of central tendency. Specifically explain the procedural steps a researcher must take to identify the median when working with a dataset that contains an even number of scores.

Based on the researcher's finding that the median is 4, explain what this value indicates about the distribution of aggressive play behaviors among the children in the classroom.

A clinical psychologist administers a short anxiety inventory to four patients. The recorded scores are 12, 18, 9, and 15. Briefly explain how the psychologist should calculate the median for this specific set of scores and provide the final median value.

How is the median determined if a distribution contains an even number of scores?

Arrange the necessary steps to calculate the median for a distribution that contains an even number of scores.

A cognitive psychologist measures the reaction times (in milliseconds) of six participants in a memory task: $410$, $520$, $440$, $420$, $500$, and $460$. The median reaction time for this distribution is $430$ milliseconds.

A cognitive psychologist records the reaction times (in milliseconds) of five participants: $300$, $400$, $500$, $700$, and $800$. The initial median of this distribution is $500$. Analyze how different modifications to this dataset affect the measure of central tendency. Match each specific dataset adjustment with its newly calculated median.

A research assistant is analyzing the stress level scores of six participants, recorded in the following order: $18$, $12$, $14$, $28$, $30$, and $22$. The assistant calculates the median by taking the two middlemost recorded scores ($14$ and $28$) and finding the value exactly halfway between them, resulting in a reported median of $21$. Evaluate the assistant's methodology based on the principles of calculating the median.

When all values in a distribution are arranged from lowest to highest, the measure of central tendency that identifies the exact middle score is called the ____.

A clinical psychologist reports that the median anxiety score for a group of patients is $45$. Based on the definition of the median, which of the following statements correctly interprets this finding?

A developmental psychologist records the number of aggressive behaviors displayed by six children during a play session: $12$, $5$, $8$, $3$, $14$, and $10$. The median number of aggressive behaviors for this distribution is ____.

A researcher analyzes an ordered distribution of ten anxiety scores where the calculated median is exactly $50$. If a new participant with an anxiety score of exactly $50$ is added to the dataset, the new median will remain $50$, but it will now represent a single exact middle score from the dataset rather than a value calculated halfway between two middlemost scores.

Evaluate each researcher's approach to determining or interpreting the median. Match the specific evaluation with the corresponding researcher's scenario.