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Tags: averages mode

Averages

Averages

Definition

An average describes most common items, most frequent items or mean values in a dataset.


Full text

A basic statistical question with a given sample would be to know the average.

The simplest average is the mode. This refers to the most common item in your dataset, the item that has the highest frequency in your dataset. You can of course apply the mode also to the quantitative scales, but interval and ratio are usually grouped in class intervals. The problem with the mode is that it is easily influenced by changes in items (i.e. adding two extra items to a group can make that group become the mode in a small sample) and that it is insensitive to the other groups; they are never taken into account so the mode does not necessarily reflect a useful average.

The median is the value that cuts the dataset in half, with half of the items having higher values and one half of the items having lower values. For example, when you have 50 settlements of which you are studying the ordinal variable of size expressed in small, medium, large, huge etc. you’d have as a median the value of the 25th settlement (ordered of course on the principle of this variable). This can be useful when you have some extreme single values for items that you’d not want to have a large influence on your average as they would have when calculating the mean. On the other hand, the median, like the mode, can be easily influenced by small changes so is not very stable and uses the values only by their relative rank instead of the values themselves.

The mean however is more stable; this is the metric average, calculated by the dividing the sum of the variables by the amount of the variables. Because it is a calculation of the values themselves it can of course not be applied to nominal and ordinal variables. The disadvantage of the mean is that it always takes into account all values and is therefore affected by very small groups with extreme values. This is why sometimes the median is a better representative of average.



Research topics: Software & Technology