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why is the mean and median the same when a distribution is symmetric?

why is the mean and median the same when a distribution is symmetric?

Math   Statistics-And-Probability   
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Answer #1

When a distribution is symmetric, we know that the data is divided in exactly two equal parts. For this symmetric distribution, the probability below the mean and above the mean is equal. Also, we know that the median is the middle most observation when data is in an increasing or decreasing order. For the symmetric distribution, the middle point is exactly located at the place where mean is situated.

The concept is well explained by the following diagram:

Also, we know that the mode is equal to mean and median for the symmetric distribution.

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