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Example of the Impact of Skew on the Mean
In a set of four simple reaction times (, , , and milliseconds), the mean is milliseconds. If one extreme outlier score of milliseconds is added, the mean rises to milliseconds. This resulting mean is greater than % of the scores and fails to represent the typical behavior in the distribution, demonstrating why researchers prefer the median for highly skewed distributions.
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Research Methods in Psychology - 4th American Edition @ KPU
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Example of the Impact of Skew on the Mean
In a distribution with highly skewed data, how is the relationship between the mean and median affected, and which measure of central tendency is generally preferred?
Match each distribution shape with the correct description of how the mean and median relate to each other within that distribution.
A psychology researcher measures the time it takes for participants to solve a complex puzzle. Most participants finish in about 5 minutes, but a few participants take over 30 minutes, creating a distribution with a long tail of high scores (positive skew). Arrange the following measures of central tendency in order from the lowest numerical value at the top to the highest numerical value at the bottom.
A researcher studying the number of words recalled in a memory task finds that the mean score is words, while the median score is words. Based on an analysis of the relationship between these two measures, the researcher can conclude that the distribution of memory scores is ________ skewed.
A researcher evaluates a distribution of test scores and finds it to be highly positively skewed; in this scenario, they are justified in choosing the mean as the most representative measure of central tendency because it is the only measure that incorporates the value of every participant's score.
In a bimodal distribution, where are the mean and median typically located in relation to the peaks?
In a skewed distribution, the ________ is the measure of central tendency that is typically pulled furthest away from the peak because its calculation incorporates the numerical value of every score in the dataset.
A clinical psychologist measures the reaction times of participants under a high-stress condition and finds that the distribution has a long right tail with a few extremely slow times. If the researcher chooses to report the mean rather than the median because they believe the mean remains an accurate representation of the distribution's center, their choice is correct.
Analyze the characteristics of the following distribution shapes and match each shape with the correct spatial relationship between its mean, median, and mode.
A developmental psychologist is preparing to report the central tendency of scores from a new memory test. Place the steps of the evaluation process in the correct order to determine and justify the most representative measure of central tendency based on the distribution's shape.
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A researcher records four reaction times (200, 250, 280, and 250 milliseconds) with a mean of 245 milliseconds. After adding one extreme outlier of 5,000 milliseconds, the new mean rises to 1,445 milliseconds. Why is this new mean considered an unrepresentative measure of the group's 'typical' behavior?
A cognitive psychologist collects simple reaction times from five participants: 180, 200, 190, 190, and 6,000 milliseconds. Match each statistical component to the effect produced by adding the 6,000 ms outlier.
A researcher is evaluating how a single extreme outlier affects the representativeness of the mean in a study on reaction times. Arrange the following steps to reflect the logical progression of how skew disrupts the mean's function as a measure of 'typical' behavior.
True or False: If a researcher adds an outlier of milliseconds to a set of four reaction times (, , , and milliseconds), they should evaluate the resulting mean of milliseconds as an unrepresentative measure of typical behavior because it exceeds % of the scores in the distribution.
According to the course's example of four simple reaction times (, , , and milliseconds), adding an extreme outlier score of milliseconds causes the mean to rise to milliseconds. This specific example is used to demonstrate why researchers prefer which measure of central tendency for highly skewed distributions?
True or False: When an extreme outlier of milliseconds is added to a set of four reaction times (, , , and milliseconds), the resulting mean of milliseconds remains a representative measure of typical behavior because it mathematically accounts for every score in the distribution.
A researcher records four simple reaction times of 200, 250, 280, and 250 milliseconds, yielding a mean of 245 milliseconds. After one extreme outlier score of 5,000 milliseconds is added to the data set, the new mean becomes _____ milliseconds.
A researcher studying reaction times encounters four different dataset scenarios. Match each scenario description to the most appropriate conclusion about which measure of central tendency best represents the data.
The addition of a single outlier score of ms to a dataset of four reaction times (, , , ms) causes the mean to shift from ms to ms. This represents an increase of _____ ms in the mean—a change that exceeds the entire range of the four original scores combined—demonstrating how a single extreme value can move the mean far beyond what any typical participant produced.
A researcher conducting a reaction time study discovers that one participant produced an unusually slow response of ms, far above the other four scores (, , , ms). The researcher must decide which measure of central tendency to report. Arrange the following steps in the order that reflects a sound, evidence-based process for choosing and justifying the most appropriate measure of central tendency.