Mean

The mean is the most common type of average that is computed. It is the sum of all the values in a group, divided by the number of values in that group [1, 5, 12, 33, 35, 36, 37, 39].


\( \bar{x}=\frac{\sum x}{n} \) (6.1)


\( x \) - each individual score in the group of scores;

\( n \) - the size of the sample from which the mean is computed.


In formula (6.1), \( \bar{x} \) and \( n \) represents the sample size for which the mean is being computed. If in the formula \( \mu \) and \( N \) are used, they would represent the population size.


Procedure

Calculation of the mean, follow these steps:

  1. The entire set of values is listed the in one or more columns.
  2. The sum (total) of all the values is calculated.
  3. The sum (total) is divided by the number of values.


Example:

The following data-set is given: [71, 50, 48, 67, 53]


We have to plug the values from the data set into (6.1):

\( \bar{x}=\frac{\sum x}{n}=\frac{71+50+48+67+53}{5}=\frac{289}{5}=57.8 \)

mean
Fig. 6.1 Graphical representation of the data set and its mean