Higher Concepts of Mathematics
STATISTICS
The arithmetic mean of a set of N measurements, Xl, X2, X3, ..., XN is equal to the sum of the
measurements divided by the number of data points, N. Mathematically, this is expressed by the
following equation:
x
1
n
n
i 1
xi
where
=
the mean
x
n
=
the number of values (data)
x1
=
the first data point, x2 = the second data point,....xi = the ith data point
xi
=
the ith data point, x1 = the first data point, x2 = the second data point, etc.
The symbol Sigma () 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.
Example:
Determine the mean of the following numbers:
5, 7, 1, 3, 4
Solution:
x
1
n
n
i 1
xi
1
5
5
i 1
xi
where
= the mean
x
n
= the number of values (data) = 5
x1 = 5, x2 = 7, x3 = 1, x4 = 3, x5 = 4
substituting
= (5 + 7 + 1 + 3 + 4)/5 = 20/5 = 4
4 is the mean.
Rev. 0
Page 3
MA-05
