Geoscience Reference
In-Depth Information
b
a
Fig. 3.2
Measures of
central tendency
.
a
In an unimodal symmetric distribution, the mean,
the median and the mode are identical.
b
In a skewed distribution, the median lies between
the mean and the mode. h e mean is highly sensitive to outliers, whereas the median and the
mode are little inl uenced by extremely high and low values.
if
N
is even. Although outliers also af ect the median, their absolute values
do not inl uence it.
Quantiles
are a more general way of dividing the data
sample into groups containing equal numbers of observations. For example
the three
quartiles
divide the data into four groups, the four
quintiles
divide
the observations in i ve groups and the 99
percentiles
dei ne one hundred
groups.
h e third important measure for central tendency is the
mode
. h e mode
is the most frequent
x
-value or - if the data are grouped in classes - the
center of the class with the largest number of observations. h e data set has
no mode if there are no values that appear more frequently than any of the
other values. Frequency distributions with a single mode are called
unimodal
,
but there may also be two modes (
bimodal
), three modes (
trimodal
) or four
or more modes (
multimodal
) (Fig. 3.3).
h e mean, median and mode are used when several quantities add
together to produce a total, whereas the
geometric mean
is ot en used if these
quantities are multiplied. Let us assume that the population of an organism
increases by 10% in the i rst year, 25% in the second year, and then 60% in
the last year. h e average rate of increase is not the arithmetic mean, since
the original number of individuals has increased by a factor (not a sum) of
1.1 at er one year, 1.25 at er the second year, and 1.6 at er the third year. h e
average growth of the population is therefore calculated by the geometric
mean:
