Mode

One of the first steps in the statistical analysis process is to summarize and describe the data set, in the most simple and meaningful way. Specifically, graph models and descriptive statistics enhance the understanding and interpretation of the distribution of values in the data set. Measures of central tendency identify a single numerical value that is most “typical” or representative of the larger data set. The three most common measures of central tendency are mean (the average score), median (the middle score), and mode (most frequent score). Mode is the simplest, and least used, measure of central tendency. It is defined as the value of a measured variable that occurs most frequently, and typically it corresponds with the highest point (or peak) in the distribution. For example, in the data set {3, 6, 6, 6, 7, 9, 9, 12, 14}, the mode is 6. The modal value does not consider how often a value appears (e.g., 6 appeared 3 times), rather just that the score or value occurs most frequently. The least frequent value is called the antimode. This entry defines mode, contrasts mode with mean and medium, and further discusses the related concepts of unimodal, bimodal, trimodal, and multimodal, as well as modal class and modal group.

The measures of central tendency can be used to predict the shape of a distribution. In a normal distribution (e.g., unimodal, symmetrical, and “bell-shaped” curve), all three measures of central tendency are equal in value, and located at the center of the distribution. A symmetrical, bimodal distribution includes a mean and median with equal values, in the center of the distribution, and two distinct modal values on each side of the center score (think of a camel with two humps). A distribution is considered asymmetrical, or skewed, when values cluster to the top or bottom of a distribution, tailing off on the opposite side. Outliers and extreme scores distort the mean score, which is typically dragged to the tail end of an asymmetrical distribution. A distribution is considered negatively skewed, or skewed left, when the mode (the highest peak value) is greater than the median, which is greater than the mean. In this case, the mean is disproportionately impacted by a few low scores. A good example of a negatively skewed distribution is average human life span. Most people live to be 75 to 85 years old; however, deaths that occur at younger ages skew the distribution to the left. When the mode is less than the median, which is less than the mean, a distribution is considered positively skewed or skewed right. A good example of a positively skewed distribution could be the results of a particularly difficult test where a small number of higher scores skews the distribution to the right. All three measures of central tendency (e.g., mode, median, and mean) should be reported when inferences are made based on the shape of the distribution.

The mode is generally used to indicate modality. Unlike mean and median, there can be more than one modal value. A distribution is called unimodal when there is only one mode, bimodal when there are two modes, and trimodal when there are three modes. Any distribution with two or more modes is considered multimodal. A bimodal distribution can be an indication of combining the data from two distinct samples, such as measuring height without considering the sex of the participant (e.g., male or female). Multimodal distributions have been shown to provide useful and necessary information for interpreting data and its distribution accurately, for example, when studying a topic such as bipolar mood swings (e.g., depressive, stable, or manic). Although the mode is technically defined as the value with the absolute highest frequency, often modality considers values with relatively high frequencies. Specifically, multimodal values more often correspond to high peaks, instead of absolute values. Consequently, not all modes will have equal frequencies. When modal values differ, the more prominent value is called the major mode and the less prominent peak is called the minor mode.

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