Page 47 - MATLAB Recipes for Earth Sciences

38 3 Univariate Statistics

alternative measure of central tendency.

median(corg)
ans =
12.4712

which is not much different in this example. However, we will see later that
this difference can be signifi cant for distributions that are not symmetric in
respect with the arithmetic mean. A more general parameter to defi ne frac-
tions of the data less or equal to a certain value is the quantile. Some of the
quantiles have special names, such as the three quartiles dividing the distri-
bution into four equal parts, 0-25%, 25-50%, 50-75% and 75-100% of the
total number of observations.
prctile(corg,[25 50 75])

ans =
11.4054 12.4712 13.2965

The third parameter in this context is the mode, which is the midpoint of the
interval with the highest frequency. MATLAB does not provide a function
to compute the mode. We use the function find to located the class that has
the largest number of observations.
v(find(n == max(n)))

ans =
11.9500 12.6000 13.2500
This statement simply identifies the largest element in n. The index of this

element is then used to display the midpoint of the corresponding class v. In
case there are several n·s with similar values, this statement returns several
solutions suggesting that the distribution has several modes. The median,
quartiles, maximum and minimum of a data set can be summarized and
displayed in a box and whisker plot.

boxplot(corg)
The boxes have lines at the lower quartile, median, and upper quartile val-
ues. The whiskers are lines extending from each end of the boxes to show
the extent of the rest of the data.
The most popular measures for dispersion are range, standard deviation

and variance. We have already used the range to define the midpoints of the
classes. The variance is the average squared deviation of each number from
the mean of a data set