An example of a symmetrical distribution can be visualized as a bell-like shape where the left and right halves are mirror images of each other, indicating that scores are spread evenly on either side of the center.

Example of a Symmetrical Distribution

When a distribution shape is both unimodal (having one peak) and perfectly symmetrical, all three measures of central tendency—the mean, the median, and the mode—will be located very close to each other exactly at the peak of the distribution.

Central Tendency in a Symmetrical Distribution

What is the primary characteristic of a symmetrical distribution in descriptive statistics?

A symmetrical distribution is a specific shape of data distribution where the left and right halves are mirror images of each other. In such a distribution, the scores spread out evenly on both sides of a central peak.

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The shape of a quantitative variable's distribution describes the visual pattern formed when its scores are plotted, such as in a histogram. A distribution's shape is characterized by the number of distinct peaks it contains—such as being unimodal or bimodal—and whether its tails fall symmetrically or are skewed to one side.

Distribution Shape

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KPU Research Methods in Psychology - 4th American Edition

Symmetrical Distribution

A unimodal distribution is a specific shape of a distribution that features exactly one distinct peak. In a histogram, this appears as a single prominent high point from which the tails taper off.

Unimodal Distribution

A bimodal distribution is a specific shape of data distribution characterized by two distinct peaks, representing two scores or categories that occur most frequently. While less common than unimodal distributions in psychological research, they can emerge when different subsets of a sample respond divergently.

Bimodal Distribution

A skewed distribution is an asymmetrical shape of a data distribution where scores cluster heavily toward one end of the scale, creating a prominent peak, while a relatively long tail trails off toward the opposite end.

Skewed Distribution

The shape of a distribution affects the relationship between the mean, median, and mode. In a unimodal and symmetrical distribution, all three measures are very close to each other at the peak. In a bimodal distribution, the mode aligns with the tallest peak, while the mean and median fall between the peaks. In a skewed distribution, the mean is pulled in the direction of the longer tail (the skew), causing it to differ from the median. For highly skewed data, the median is generally preferred because the mean becomes an inaccurate representation of the distribution's center.

Impact of Distribution Shape on Central Tendency

When describing the visual pattern of a quantitative variable's distribution on a histogram, which of the following characteristics are primarily used to define its shape?

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