SOLUTION: � Does all statistical data have a mean, median, or mode?

Question 499197: � Does all statistical data have a mean, median, or mode?
Answer by oberobic(2304) (Show Source): You can put this solution on YOUR website!
Any set of data can be described by statistics.
That does not make it "statistical data". it's still just data being described with statistics.
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So, the answer is: It depends on the data.
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If you have an empty set, then it will have neither a mean, nor a median, nor a mode.
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If you have a set with one element, you cannot reasonably claim to have a mean or median. You could argue it has a mode (most frequent data value), but this is a weak argument.
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If you have a set with two elements, then the mean can be calculated as sum of observations divided by the number of observations. If you sort the data, the median will be the midpoint. With only two points, if they are not the same, then the median will have to be interpolated (but logically, it will equal the mean). If the two points are the same value, then you will have a mode; otherwise, you will not.
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If you have three or more elements, you always can find the mean (sum/count) and median (value in the middle of the sorted list), but not always a mode. If all of the values are unique, there is no mode. But if at least two points are the same, then that defines the mode.
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Consider the set: { 2, 2, 2, 5, 5, 5 }.
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The mean = 2+2+2+5+5+5 / 6 = 21/6 = 3.5
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The median is the midpoint, which is the midpoint between the third 2 and the first 5 in the sorted list.
We interpolate the value using a formula that looks surprisingly like the mean: (2+5)/2 = 3.5.
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The mode is the most frequent occurrence, which is hard to define. You have 3 2's and 3 5's. You have two modes. It is "bimodal." You would not interpolate or average these. You would report the distribution is bimodal with most frequent values of 2 and 5.
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Hope this helps.
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