Statistics for Central Tendency (Mean || Median || Mode)

In many real-life situations, it is helpful to describe data by a single number that is most representative of the entire collection of numbers. Three ways of characterizing any data distribution are:

• Measures of Central Tendency. Describe the center point of a data set with a single value.
• Measures of Dispersion. Describe how far individual data values have strayed from the mean.

Mean: The mean (or average) of a set of data values is the sum of all of the data values divided by the number of data values.

You need to know that some measures of central tendency and variability are inappropriate for qualitative variables.

Characteristics of the mean:

• Every value in the distribution contributes to the value of the mean.
• The mean is very sensitive to extreme scores. An extreme score can pull the mean in one or the other direction and make it less representative of the set of scores and less useful as a measure of central tendency.
• Arithmetic mean is affected by change of both origin and scale.
• Its value may not actually exist in the data (e.g., for the data set 2,3,4 and 5; the mean is 3.5).

Remember that the word average means only the one measure that best represents a set of scores, and that there are many different types of averages. Which type of average you use depends on the question that you are asking and the type of data you are trying to summarize.

Median: The median is the middle value when the data is arranged in order of size.

In other words, the median divides the whole set of values in two parts such that half of the observations are less than or equal to it and half are more than or equal to it.

Mode: The mode of a set of data is the value or values which occur most often.

Advantages:

• It is applicable to nominal data.
• It is unaffected by extreme values.

Disadvantages:

• It may not be unique in a set of data.
• It can not be manipulated using the rules of algebra.