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Can an asymmetric distribution have the same mean and median?
The mean and median of asymmetrical distributions can be equal.
When mean and median are not equal?
To summarize, generally if the distribution of data is skewed to the left, the mean is less than the median, which is often less than the mode. If the distribution of data is skewed to the right, the mode is often less than the median, which is less than the mean.
Are the mean and median the same in a skewed distribution?
In a normal distribution, the mean and the median are the same number while the mean and median in a skewed distribution become different numbers: A left-skewed, negative distribution will have the mean to the left of the median. A right-skewed distribution will have the mean to the right of the median.
Can mean be always equal to median in all the symmetric distributions?
“If the distribution is symmetric then the mean is equal to the median and the distribution will have zero skewness. If, in addition, the distribution is unimodal, then the mean = median = mode.
What does it mean if the mean and median are equal?
Wikipedia says in relationship between mean and median: “If the distribution is symmetric then the mean is equal to the median and the distribution will have zero skewness. If, in addition, the distribution is unimodal, then the mean = median = mode.
What happens when the mean of a distribution is symmetric?
“If the distribution is symmetric then the mean is equal to the median and the distribution will have zero skewness. If, in addition, the distribution is unimodal, then the mean = median = mode.
When does mean = median imply a unimodal distribution?
If, in addition, the distribution is unimodal, then the mean = median = mode. In the same way that “If the baby animal is a chicken, then its origin is an egg” does not imply that “If the origin is an egg, then the baby animal is a chicken.”
Is the relationship between mean and median weak?
This answer shows that the relationship between third moment skewness and the direction of the relationship between mean and median is weak (third moment skewness and second-Pearson skewness needn’t correspond). Item 1. on this answer gives a discrete counterexample, similar to but different from the one given by Silverfish.