The main difficulty for not using the mean with ordinal data is that its value depends on conventions on coding. Numerical codes such as 1, 2, 3, 4 are usually just chosen for simplicity or convenience, but in principle they could equally well be 1, 23, 456, 7890 as far as corresponding to a defined order as concerned.
Also, assumption of equal distance between categories does not hold for ordinal data.
Hence, Finding a mean for ordinal data is often discouraged.
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