Merits And demerit of mean

Answer 1

Merits:

• The mean uses information from all observations.
• The mean of a large (even infinite) population can be reliably estimated by the mean of random samples (it is an unbiased estimator).
• Statistical properties of the mean are well studied so that there are many tests and techniques that can be applied.

Demerits:

• A mean does not exist for categorical (qualitative) data. If 20 children in a class of 30 like English and 10 like French, then there is no mean language (such as Frenglish) that is the class, as a whole likes.
• A mean may not be a value that is (or even can be) ever realised. In the UK families have a mean of 1.7 dependent children. There is not a single family, though, that has 1.7 children!
• Outliers can distort the value of the mean.
• The mean is probably the hardest measure of central tendency to calculate.