Variability
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Measures of central tendency are the mean, median, range, mode ect.
Median
If the wide range is evenly spread between the very small and the very large (the distribution is symmetric) then there is not much to choose between the median and the mean. If not, the median will have some advantages as a measure of central tendency.
Yes, but the two are measures of very different things. The median is a measure of central tendency whereas the range is a measure of spread. Nevertheless, the set 1, 2, 3, 4, 4 has a range of 3 and a median of 3.
Central tendency is important because it is used to calculate an average on a collection of data. Central Tendency includes the mean, median, and mode.