Page 49 - MATLAB Recipes for Earth Sciences

40 3 Univariate Statistics

NaN·s result in NaN·s, whereas the function nanmean simply skips the miss-
ing value and computes the mean of the remaining data. As a second ex-
ample, we now explore a data set characterized by a signifi cant skew. The
data represent 120 microprobe analyses on glass shards hand-picked from a
volcanic ash. The volcanic glass has been affected by chemical weathering
in an initial stage. Therefore, the glass shards show glass hydration and sodi-
um depletion in some sectors. We study the distribution of sodium contents
(in wt%) in the 120 measurements using the same principle as above.
sodium = load('sodiumcontent.txt');

As a first step, it is always recommended to visualize the data as a histo-
gram. The square root of 120 suggests 11 classes, therefore we display the
data by typing

hist(sodium,11)
[n,v] = hist(sodium,11);

Since the distribution has a negative skew, the mean, median and mode are
signifi cantly different.

mean(sodium)

ans =
5.6628
median(sodium)
ans =
5.9741
v(find(n == max(n)))

ans =
6.5407
The mean of the data is lower than the median, which is in turn lower than
the mode. We observe a strong negative skew as expected from our data.

skewness(sodium)
ans =
-1.1086

Now we introduce a significant outlier to the data and explore its impact on

the statistics of the sodium contents. We used a different data set contained
in the fi le sodiumcontent_two.txt, which is better suited for this example
than the previous data set. The new data set contains higher sodium values