1. Laboratory in Oceanography: Data and Methods
Computing Basic Statistics
MAR599, Spring 2009
Miles A. Sundermeyer

2. Computing Basic Statistics
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3. Computing Basic Statistics
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4. Computing Basic Statistics
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Basic Statistics
Let
min, max - absolute minimum and maximum values of data
(see also nanmin, nanmax)
mean -
median - the value separating the higher half of a sample population, or
probability distribution, and the lower half;
mode - the value that has the largest number of observations
Note: The mode function is most useful with discrete or coarsely rounded data. The mode for a continuous probability distribution is defined as the peak of its density function. Application to a sample from such a distribution is unlikely to provide a good estimate of the peak; it would be better to compute a histogram or density estimate and calculate the peak of that estimate. Also, the mode function is not suitable for finding peaks in distributions with multiple modes.

5. Computing Basic Statistics
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6. Computing Basic Statistics
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7. Computing Basic Statistics
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Variance and Standard Deviation
var - variance of a =
Note: The above calculation of variance is biased low; for unbiased variance, must normalize by (n-1). By default, Matlab computes the unbiased variance, i.e.,
std - standard deviation of a = sqrt(var(a))

8. Computing Basic Statistics
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9. Computing Basic Statistics
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Percentiles
prctile - Percentile (or centile) is the value of a variable below which a certain percent of observations fall; e.g., the 20th percentile is the value (or score) below which 20 percent of the observations may be found.
cdfplot - Plots the cumulative distribution function (CDF) of the observations in the data sample vector.

10. Computing Basic Statistics
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12. Computing Basic Statistics
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Normality
Gaussian - Gaussian or Normal distribution is the probability distribution function given by:
Noteworthy features of Gaussian distributions
symmetry about its mean
the mode and median both equal the mean
the inflection points of the distribution curve occur one standard deviation away from the mean, i.e. at (x − σ) and (x + σ)
Exist numerous tests for normality, e.g., Lilliefors, Kolmogorov-Smirnov, Jarque-Bera, and others. Also many more general tests for comparing distributions.

13. Computing Basic Statistics
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14. Computing Basic Statistics
Useful Tidbits …
Useful Tidbits
if <expression> statements
elseif <expression>
statements
else
end
e.g.,
n=rand(1)
if (n>0.5)
disp('heads')
elseif (n<0.5)
disp('tails')
else
disp('neither!')
end

15. Computing Basic Statistics
Useful Tidbits …
Useful Tidbits
while <expression> statements
end
e.g.,
n=rand(1)
while n>0.5
if (n>0.5)
disp('heads')
elseif (n<0.5)
disp('tails')
else
disp('neither!')
break
end

16. Computing Basic Statistics
Useful Tidbits …
Gaussian Distribution