Median value on ordinal scales I have been reading about appropriate measures of central tendency for ordinal level data. 
So far I have learned that the median and mode can be used but that the latter can only be used in some cases. Some sources state that the median can only be used with Likert questions when there is an odd number of scores. It is not clear to me what this means and also which cases the median cannot be used. 
Example:
An example may illustrate. 


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*If there was a question: "Climate change is England’s most serious environmental problem" on a response scale: 1=strongly agree 2=agree 3=unsure 4=disagree 5=strongly disagree. Would the median be 3=unsure?

*What if no respondents stated disagree or strongly disagree and all 100 respondents stated either 1, 2, or 3, is the median then 2? 

*what if respondents only stated 2 or 3. In this case is it not possible to identify the median?

 A: Definitional issues:


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*The median is the middle value of the data; it is not by definition the middle value of the scale.

*When the sample size is even, then the median is the mean of the values either side of middle most point after rank ordering all values (see wikipedia description).
When to use median on ordinal data


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*In theory the median can be used on data from any variable where the values can be ordered.

*In practice, the median is  often not the most useful summary of central tendency with ordinal variables. 
This partially depends on what you want to get out of your measure of central tendency.
When you are describing the central tendency of data on an ordinal variable with only a small number of response options (i.e., perhaps less than 20 or 50 or 100), the median can be quite gross (e.g., 1,1,3,3,3 and 1,3,3,5,5 both have a median of 3, but the second example would have a higher mean). 
When it comes to summarising the central tendency of Likert items, I find the mean to be much more useful and sensitive to meaningful differences.
Ordinal variables that are ranks do not suffer from this problem of "grossness".

*Interpolated medians are another way of overcoming the gross nature of the median on ordinal data with few values.

A: No, the median is the value where half the data is less than or equal to that value and half the data is greater than or equal to that value.  
So if your ordinal scale had 100 respondents then find the value that has at least 50 less or equal and 50 greater than or equal.  It would only be 3 if half the responses were to either side.  If 1 person said 1, 2 people said 2, 3 said 3, 4 said 4, and the remaining 90 said 5, then 5 would be the median.
The median works when the data is ordered, but would not make sense for nominal/unordered data, like what is your favorite color?
