The sets of numbers {1, 1, 1, 1, 50} and {1, 1, 1, 1, 100} have this property. The median of both sets is 1 but the mean is 10.8 for the first set and 20.8 for the second.
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The mean is better than the median when there are outliers.
The median and mode cannot be outliers. For small samples a mode could be an outlier.
MEDIANUse the median to describe the middle of a set of data that does have an outlier.Advantages:• Extreme values (outliers) do not affect the median as strongly as they do the mean.• Useful when comparing sets of data.• It is unique - there is only one answer.Disadvantages:• Not as popular as mean.
Outliers are observations that are unusually large or unusually small. There is no universally agreed definition but values smaller than Q1 - 1.5*IQR or larger than Q3 + 1.5IQR are normally considered outliers. Q1 and Q3 are the lower and upper quartiles and Q3-Q1 is the inter quartile range, IQR. Outliers distort the mean but cannot affect the median. If it distorts the median, then most of the data are rubbish and the data set should be examined thoroughly. Outliers will distort measures of dispersion, and higher moments, such as the variance, standard deviation, skewness, kurtosis etc but again, will not affect the IQR except in very extreme conditions.
I think it means that our data includes outliers.