When finding the median of a dataset, what is the correct procedure if there is an even number of scores?

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 $$6$$.

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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.

Median

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KPU Research Methods in Psychology - 4th American Edition

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 $$6$$.

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