Basic Statistics
Author: John M. Cimbala, Penn State University
Latest revision: 16 October 2007
Introduction
•
The purpose of this learning module is to introduce you to some of the fundamental definitions and
techniques related to analyzing measurements with
statistics
.
•
In all the definitions and examples discussed here, we consider a collection (sample) of measurements of a
steady parameter. E.g., repeated measurements of a temperature, distance, voltage, etc.
Basic Data Analysis using Statistics
•
First some definitions are necessary:
o
Population
– the entire collection of measurements, not all of which will be analyzed statistically.
o
Sample
– a subset of the population that is analyzed statistically. A sample consists of
n
measurements.
o
Statistic
– a numerical attribute of the sample (e.g., mean, median, standard deviation).
•
Suppose a
population
– a series of measurements (or readings) of some variable
x
is available. Variable
x
can
be anything that is measurable, such as a length, time, voltage, current, resistance, etc.
•
Consider a
sample
of these measurements – some
portion
of the population that is to be analyzed
statistically. The measurements are
x
1
,
x
2
,
x
3
, .
..,
x
n
, where
n
is the number of measurements in the sample
under consideration. The following represent some of the statistics that can be calculated:
•
Mean
– the
sample mean
is simply
the arithmetic average
, as is commonly calculated, i.e.,
1
1
n
i
i
x
x
n
=
=
∑
,
where
i
is one of the
n
measurements of the sample.
o
We sometimes use the notation
x
avg
instead of
x
to indicate the average of all
x
values in the sample,
especially when using Excel since overbars are difficult to add.