We'll start by calculating the 'average'
or 'mean' of a set of numbers.
||You can use the
terms 'mean' and 'average' interchangeably.
Strictly speaking the 'mean' is the
correct term. The 'average' has a
more general meaning, it can be used
to refer to any value that typifies
a set of numbers.
You may already know how to calculate
the mean, but I want to use the explanation
to make a few points. Suppose you want
to calculate the mean of five values,
You add them up and divide by the number
I’ve introduced a bit of notation, I’ve
represented the mean by the symbol .
The ‘bar’ over the 'x' is a standard way
of representing a mean.
||We say x-bar and
that's the way I'll write it in the
text from now on.
Now let’s introduce some more notation.
We’ll represent the number of values (five
in this case) by the variable ‘n’. Although
we could use other letters, ‘n’ is the
usual first choice when we want to represent
the number of values in a sample.
We’ll also substitute the individual
values by ‘xi’, where the subscript
‘i’ takes a number to represent each individual
value (‘i’ stands for ‘index’):
This formula can be used to find the
mean of any number of values. Just substitute
the symbols x1, x2 and
so on up to xn with the actual
We can introduce yet more mathematical
notation to make it more concise:
Let’s look more closely at the bit on
top (the numerator):
The symbol ‘‘
is the Greek symbol capital Sigma, and
means ‘summation’ in 'mathspeak':
In full the notation means ‘add
all the values of xi
from ‘i’ equals 1 to ‘i’ equals
‘n’ (run your mouse over the image
to see another view of this).
Note that the ‘i = 1’ and ‘i
= n’ are sometimes omitted, if
they are self-evident.
The times taken to repair breakdowns
of critical equipment, in hours,
over the past week were as follows:
What is the mean repair time?