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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.

Symmetrical Distribution

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 researcher collects anxiety scores from 200 participants and plots them in a histogram. She notices that the left half of the histogram is a mirror image of the right half, with a single central peak. Based on this shape, the mean and the median of the anxiety scores should be approximately equal.

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