Atlas Copco ACTA 3000

ToolsTalk ACTA
155
14.2 How to estimate the variation
Let us suppose that a measured variable follows normal distribution. The
parameters, mean and standard deviation, of this population
7
are estimated by
taking a representative sample of the outcome. The mean,
X
, of the sample is
calculated as:
n
X
X
∑
=
1
All occurrences of the variable constitute the population of the distribution.
X is the value of each individual occurrence of the measured variable in the
sample, and n is the total number of occurrences in the sample.
X
is used as an
estimate for the mean of the total population.
In the same way, the sample standard deviation, S, is used as an estimate for the
population standard deviation:
1
)(
2
−
−
=
∑
n
XX
S
Note!
The sample on which the calculations are based should be relatively large. At least 25 different
occurrences of the measured variable are necessary to obtain consistent results. It is also very important
that the sample is representative of the total population. Any multiple of the standard deviation covers a
corresponding percentage of normal distribution. This percentage value is the same for any normal
distribution, regardless of the values of the mean, µ, and the standard deviation.