To find the median, scores must first be arranged from lowest to highest. For the set of seven scores $$8, 4, 12, 14, 3, 2, 3$$, the ordered sequence is $$2, 3, 3, 4, 8, 12, 14$$. The middle score is $$4$$, which is the median. If an eighth score of $$15$$ is added, the new ordered set is $$2, 3, 3, 4, 8, 12, 14, 15$$. The two middle scores are $$4$$ and $$8$$, so the median is the value halfway between them, which is $$6$$.

Example of Finding the Median

A key characteristic of the mean is its high sensitivity to extreme scores, or outliers. In highly skewed distributions, the mean is pulled away from the median in the direction of the skew (the longer tail). Because extreme scores heavily influence its value, the mean may cease to be an accurate representation of the typical score in such datasets, leading researchers to often prefer the median for skewed distributions.

Sensitivity of the Mean to Outliers

To find the median of a set of seven scores ($$8$$, $$4$$, $$12$$, $$14$$, $$3$$, $$2$$, $$3$$), the scores are rearranged from lowest to highest ($$2$$, $$3$$, $$3$$, $$4$$, $$8$$, $$12$$, $$14$$), making the middle score $$4$$. If an even number of scores exists, such as by adding a score of $$15$$ to the set, there are two scores in the middle of the distribution ($$4$$ and $$8$$), and the median is the value halfway between them, which is $$6$$.

Example of Calculating the Median

What does the median represent in a distribution of scores?

The median is a measure of central tendency that identifies the exact middle score of a distribution when all values are arranged from lowest to highest. It divides the distribution perfectly in half, meaning that $$50\%$$ of the scores are less than the median and $$50\%$$ are greater. If a distribution contains an even number of scores, the median is calculated as the value exactly halfway between the two middlemost scores.

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Measures of central tendency are descriptive statistics used to describe the typical, average, or center scores within a distribution. Common examples of these measures include the mean, median, and mode.

Measures of Central Tendency

Spielman, R. M., Jenkins, W. J., & Lovett, M. D. (2020, April 22). Psychology (2nd ed.). OpenStax. https://openstax.org/books/psychology-2e/pages/1-introduction

OpenStax Psychology (2nd ed.) Textbook

https://kpu.pressbooks.pub/psychmethods4e/

KPU Research Methods in Psychology - 4th American Edition

A researcher reports that the 'typical' number of hours of video games played per week by a group of 10 participants is 8 hours. Upon examining the raw data, you discover that 5 of the participants played for 1 hour and the other 5 participants played for 15 hours. Critique the researcher's use of the single 8-hour value to describe this group. Why might this summary value be misleading in this specific case?

Interpreting a 'Typical' Value

A developmental psychologist studies the number of words spoken in a day by a group of 20 toddlers. The data shows a wide variation, with some toddlers speaking very few words and others speaking many. The psychologist wants to calculate a single value to best represent the 'typical' number of words spoken by a toddler in this group. What is the primary justification for this statistical approach?

Median

The mode is a measure of central tendency that identifies the most frequent score occurring within a distribution. Unlike the mean and median, the mode is uniquely capable of summarizing categorical variables, as it simply represents the category with the highest count.

Mode

The mean is a measure of central tendency representing the average of a distribution, symbolized as $$M$$. It is calculated by finding the sum of all the scores and dividing by the total number of scores. The mean is widely used because it provides a reliable indication of central tendency, is easy to understand, and has properties that are valuable for inferential statistics.

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