Physics 257
Lecture 0:
Basic Statistics &
Introduction to Matlab
Prof. Matt Dobbs
Physics Department, McGill U.
Prof. M. Dobbs,
Physics 257
Lecture 0 Stats
2
Outline
±
Orientation session was yesterday, Sept 6. If you missed it,
download the information from WebCT. We covered:
z
z
Brief intro to the interplay between theory & experiment + the
scientific method
TODAY
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Average behavior of data:
Mean, median, mode
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Measures of spread:
Variance, standard deviation
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Correlations: covariance, corr coefficient
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Significant Figures
±
Matlab Introduction
Basic Statistics
Statistics is the mathematical treatment and analysis
of large quantities of data.
It provides us with a means of characterizing a
distribution of data with a few parameters such as the
average and standard deviation.
Prof. M. Dobbs,
Physics 257
Lecture 0 Stats
4
Why Statistics
±
A couple centuries ago:
“If your
experiment needs statistics, you ought to
have done a better experiment”
(B. Russell)
z
First statistics conference was held in 1853.
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Today: To be a statistician is great ! You
never have to be “absolutely sure” of
something .
.. Being “reasonably certain” is
enough!
(from Frank Lehner lecture)
±
Our goal: learn to use statistics as a
quantitative tool to report scientific
results. Learn to understand what other
people’s statistics mean – and when to
trust them.
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Physics 257
Lecture 0 Stats
5
Basic Definitions
±
A complete body of data to be analyzed is called a
population
.
z
E.g. all the red giant stars in our galaxy.
±
Often, we must be satisfied with analyzing a
sample
of the
population.
z
E.g. those red giant stars that have been observed with the CFHT
telescope.
z
(class example)
±
In this case we would like to know how likely it is that a
statistic (mean, std dev) of the sample is characteristic of the
whole population.
z
In physics we are most interested in knowing how good an estimation of
a statistic (like the mean x) is of the true value (like the true mean
μ
).
z
Convention: use greek letters (
μ
,
σ
) for true values and roman letters (x,
s) for estimates.
Prof. M. Dobbs,
Physics 257
Lecture 0 Stats
6
Average and Expectation Values
±
Arithmetic mean of data x
i
±
Expectation value for a
variable x of a continuous
function
z
<x> is the notation for the
expectation value
or
average
value.
±
Both are linear operators
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 Fall '07
 Dobbs
 Physics, Standard Deviation, Mean, Prof. Matt Dobbs, Prof. M. Dobbs

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