GG413 Geological Data Analysis, Fall 2014
Homework #3: Statistics and Probability Distributions
Read 1.5 of Wessel
Due Tue. Sept 16
The same requests about explaining your answers and labeling plots applies.
1) A research expedition measured the heat flux, q, out of the seafloor near a mid-ocean ridge. The
expedition returned with 13 independent measurements (in mW/m2):
q = [45.2, 47.4, 55.1, 39.2, 51.2, 46.3, 49.9, 42.9, 75.3, 53.1, 48.8, 58.8, 42.2]
(a) Compute the sample mean, standard deviation, median, and MAD.
(b) Normalizing the deviation of each data point from the median by MAD, produces the robust standard
score for each data point, zi. Use this score to identify any outliers. And if there are any outliers,
remove them from the sample, redo (a), and note how the answers change.
2) “HW3_vesicle1.txt”, “HW3_vesicle2.txt”, “HW3_vesicle3.txt”, and “HW3_vesicle4.txt” are the volume
fractions of vesicles (i.e., vesicularity) found in n = 35 thin sections produced from four different samples
of a lava flow.
(a) Estimate the mean vesicularity of the whole lava flow that was sampled. (see Matlab/Freemat function
“mean”);
(b) Estimate the standard deviation of the vesicularity of the lava flow using two different methods.
(Matlab/FreeMat has a function “std” that you can use);
3) “HW3_corrcoef1.txt” and “HW3_corrcoef2.txt” show two data set of measured quantities, which you
can simply refer to as x and y.
(a) Plot x vs y for both data sets.
(b) Compute the Pearson’s linear correlation coefficients, and explain what the numbers are telling you
about how x and y are related for both data sets.
Matlab/FreeMat hint:
>>dat1=load(‘HW3_corrcoef1.txt’);
>>x=dat1(:,1); y=dat(:,2); n=length(x);
>>sx=sqrt(sum((x-mean(x)).^2.)./(n-1)); %standard deviation of x
(c) Please include your Matlab/FreeMat script.
4) Extensive salinity studies of a water reservoir has revealed that the salinity content is well described as
following a normal distribution with a mean of  = 10 ppm and standard deviation  = 5 ppm. When
randomly testing the tap water in the neighborhood supplied by the reservoir what is the probability that
the salinity will be
(a) less than 4 ppm?
(b) between 8 and 16 ppm?
(c) Do your answers make sense given what you know about normal probability distributions?