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CENTRAL TENDENCY
Describes a
distribution
through
numerical
account of
the centre of
a distribution.
> res<c(21,18,12,31,23,
31,44,7)
> mean(res)
[1] 23.375
SPSS: Analyze Menu,
Descriptive Statisitcs
Mean: what most call “average”
CENTRAL TENDENCY
Describes a
distribution
through
numerical
account of
the centre of
a distribution.
> res<c(21,18,12,31,23,
31,44,7)
> median(res)
[1] 22
SPSS: Analyze Menu,
Descriptive Statisitcs
Median: the variate with the same
number of variates both greater and
less than it; the centre variate in an
ordered array
CENTRAL TENDENCY
Describes a
distribution
through
numerical
account of
the centre of
a distribution.
> res<c(21,18,12,31,23,3
1,44,7)
> library(modeest)
> mfv(res)
[1] 31
Mode: the variable class with the
greatest abundance or highest
frequency
WHICH MEASURE?
What best
characterises the centre
of the distribution?
What measures are
most affected by
outliers?
Y=23.4, median=22, mode=31
DISPERSION
Measures of
dispersion tell
us about a
distribution’s
shape or the
spread of
variates
around the
central
tendency.
DISPERSION
Measures of
dispersion tell
us about a
distribution’s
shape or the
spread of
variates
around the
central
tendency.
Range: difference between largest and
smallest variates
> res<-c(21,18,12,31,23,31,44,7)
> max(res)-min(res)
[1] 37
DISPERSION
Measures of
dispersion tell
us about a
distribution’s
shape or the
spread of
variates
around the
central
tendency.
> res<c(21,18,12,31,23,3
1,44,7)
> IQR(res)
Interquartile range: characterizes the
middle 50% of a distribution by
subtracting the 25th percentile from the
75th percentile.
2nd quartile
1st quartile
Yi
Sorted
7
18
12
21
23
3rd quartile
31
31
44
DISPERSION
Measures of
dispersion tell
us about a
distribution’s
shape or the
spread of
variates
around the
central
tendency.
Variance & Standard Deviation: provide
a combined measure of every variates’
deviation from the mean (compare to
spread between only two variates using
range or IQR)
DISPERSION
Measures of
dispersion tell
us about a
distribution’s
shape or the
spread of
variates
around the
central
tendency.
> res<c(21,18,12,31,23,3
1,44,7)
> var(res)
Variance: think of “average” squared
deviation from the mean
Variance is good for some kinds
of distribution comparisons, but s2
not in original units
DISPERSION
Measures of
dispersion tell
us about a
distribution’s
shape or the
spread of
variates
around the
central
tendency.
> res<c(21,18,12,31,23,3
1,44,7)
> sd(res)
[1] 11.79513
Standard Deviation: average deviation
from the mean
COMPARING DISPERSIONS
Comparing s of
distributions of different
“sized” things not useful
Primate
humeri & rat
femurs
The size of s is
determined by value of
variates.
Larger Ys (e.g., length of
primate humeri) create
larger s than smaller Xs
(e.g., length of rat
femurs)
COMPARING DISPERSIONS
Coefficient of variation
“standardizes”
standard deviation by
the mean
 Comparisons must use same
units
From: Pattern and Process in Cultural Evolution (2009), edited by S.
Shennan, pp. 113-132. University of California Press.