What are the best measures of central tendency?

Answer 1

It depends on the particular set of numbers. Which is closest to the majority of the numbers.

If all are random or completely Different numbers maybe the median?

If they are really different, median is the best.

If they are close to the same, the mode is better.

There is no measurement better than the other, unless the data contains outliers.

Mean is the most common, but if the data set contains outliers then consider using median or mode.

In ADDITON:

Which is better between mean, median and mode also depends on which type of data are we considering. There are basically 3 kinds of data:

Nominal Data (qualitative data). For eg, marital status can be married, single, divorced or de facto.

Ordinal data = the data are actually ranked, for eg Google is the number 1 search engine and Yahoo is the no 2 search engine.

Interval (numerical): for example: age, height, length, breadth etc.

If we are looking at an interval(numerical) data, we can use any mean, median or mode. Mean is generally the best measure for statistical interference if there are no extreme values. When there are extreme values it is better to use median. Mode is very rarely used.

If we are looking at nominal data, we cannot calculate mean. Like in the given example, marital status can be married, single, divorced or de facto. Now look at the following table

Status Frequency

Married 40

Single 60

Divorced 20

De facto 10

In this case we have to choose mode. The same is applicable for shoe size, waist size etc.

If we are looking for an ordinal data, where data are ranked, the best measure of central tendency will be median.

Apart from the type of data, nature of investigation in hand also affects which measure should be choose. In such cases, a personal judgment should be applied. An example is, if we are tying to compare how good a class did, in comparison with other classes, the best measure of central tendency would be mean. however, if we are looking inside a class and trying to compare how well we did in our class, median would be the best measure of central tendency. Unless the data is nominal, it is very rare that mode is the best measure of central tendency.