What are the characteristics of a population for which it wo

What are the characteristics of a population for which it would be appropriate to use mean/median/mode? When would the characteristics of a population make them inappropriate to use?

Solution

Mean

Mean is the most widely used measure of Central Tendency that is used in Statistical analyses. It is most appropriate with a population that does not have wide fluctuations in data value, i.e. Outliers. Presence of Outliers (extremities) distort Mean.

Mean is valid only if the Population has Interval data or Ratio Data that can be subjected to further algebraic treatment. However, the population must contain only symmetrical Interval data or Ratio data, for mean to be used as appropriate measure.

Mean is accordingly inappropriate to use when there are Outliers present in the populaiton data set, or the distribution is Skewed, or there is a probability that the population distribution may be skewed.

Mean is also not appropriate to use in a population where there can be changes in the data set.

A population having only Cardinal data cannot use mean as an appropriate measure. For a population having asymmetrical Interval or Ratio data, mean cannot be used.

Median

Median is the appropriate measure when we either know for sure that the population has extreme values (outliers) or the distribution is Skewed, or there is a probability that the population distribution may be skewed.

Median is also appropriate when there are only a small number of data points in the population (i.e. population size is small).

Median is appropriate also because it is not much sensitive to changes in data value, since it points out the \"center of the data set\".

When population data is qualitative (e.g. Rankings) and not quantitative, Median is appropriate to use.

Median can be used for population with Ordinal, Interval and Ratio data. Even when population Interval or Ratio data are skewed, Median can be appropriately used.

However, median is inappropriate to use if, the analysis requires all the population data to be used.

Mode

Mode is most appropriate for a Population having Categorical (Nominal) data (e.g. identifying the most popular product in a set having 100 types of product).

For a population having Interval or Ratio data, if the data is spread too thinly with no two data values being the same, Mode will not be appropriate to use or we can have a non-existent Mode as well.