In the majority of Empirical cases the mean will not be equal to the median, so the event is hardly unusual. If the mean is greater, then the distribution is poitivelt skewed (skewed to the right).
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Generally, when the median is greater than the mean it is because the distribution is skewed to the left. This results in outliers or values further below the median than above the median which results in a lower mean value than median value. When a distribution is skewed left, it is generally not very symmetrical or normally distributed.
If the distribution is not symmetric, the mean will be different from the median. A negatively skewed distribution will have a mean hat is smaller than the median, provided it is unimodal.
When the distribution has outliers. They will skew the mean but will not affect the median.
The median, by definition, tells you the "half way point" of your data. Exactly half of the observations in the dataset will be less than the median and half will be greater than the median.
Standard deviation can be greater than the mean.