If the mean, median and mode are all equal for a continuous random variable, then the random variable is normally distributed.

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Quizplus · Accepted Answer

The mean, median, and mode being equal is a characteristic of a normal distribution, but it is not sufficient to conclude that a continuous random variable is normally distributed solely based on these three measures being equal. Other distributions can also have this property.

If the Mean, Median and Mode Are All Equal for a Continuous