Messungen der Zentralen Tendenz

Researchers often summarize their data using a particular measure of central tendency—one score that represents the entire set of data points.

The most straightforward measure is the mode—the most frequently occurring score—which is useful when computing totals for categorical data, such as professional occupation. Here, the mode is noted as writer, since they constitute the majority of what careers were reported.

Another measure is the median—the true middle point in a set of numerical data that are arranged in order of magnitude. Here, the median of salaries is $65,000…with half of employees paid at or above…and the other half at or below…this midpoint. In cases with an even number of values, the average of the two middle numbers determines the median.

Finally, the most common measure for numerical data is the mean—the arithmetic average—which is equal to the total sum of all numerical scores, divided by the number of data points.

For example, the total sum of all incomes would be divided by the number of people employed—in this instance, yielding a mean of $140,000. Because this measure takes into account all values in the data set for calculation, researchers usually prefer to report the mean.

In a normal distribution, the mode, mean, and median have approximately equivalent values and are positioned exactly in the center of the curve. However, in skewed distributions—when either very high or very low scores are more prevalent and weighted more heavily—these measurements are not equal.

If the majority of the participants reported low incomes, the mean would rise due to a few extremely high-income scores. Thus, the mean’s sensitivity to extreme values could result in an artificially high or low representation of the data. In this case, the median or mode would serve as a more accurate measurement.

In the end, the best measure of central tendency is one that considers the pattern of distribution in the data at hand.