In a symmetric distribution, the mean is closest to the center and the variation is approximately the same on each side of the center. In a skewed distribution, the median is closest to the center and the variation on either side of the center is different.
A symmetric distribution has a peak that divides the data evenly. The data on the right is approximately a mirror image of the data on the left. Outliers are not common in this type of distribution. The mean is closest to the center.
The variation is approximately the same on both sides of the center. Both the mean and the standard deviation are calculated by using all of the data values. Because of this, these measures are used to describe the center and variation of a symmetric distribution.
Skewed Distribution
In a skewed distribution, the peak is on the right or the left, and most of the data is around it. This distribution is likely to have outliers in the tail of the graph. The outliers will affect the mean and the standard deviation.
In this case, the median is closest to the center and the variation is different on both sides. This is why the median and the five-number summary are used to describe the center and variation of a skewed distribution.
