The Mean:

One of the most general uses of statistics is the determination of the mean value of a set of measurements.  The word "Mean" is the statistical word used to state the "average" value of a set of data.  A mean is mathematically determined in the same way as the "average" of a group of numbers is determined.

The arithmetic mean of a set of N measurements, X_l, X₂, X₃, ..., X_N  is equivalent to the sum of the measurements divided through the number of data points, N. Mathematically, that is expressed by the subsequent equation:

where

x¯          =          the mean

n          =          the number of values (data)

X₁        =          the first data point, x₂  = the second data point,....x_i  = the ith data point

 x_i        =          the i data point, x1  = the first data point, x₂  = the second data point, etc.

 The symbol Sigma ( Σ ) is used to indicate summation, and i = 1 to n indicates that the values of xi  from i = 1 to i = n are added.  The sum is then divided by the number of terms added, n.