Environmental Data Analysis EESC
BC 3017
Homework 5 - due Tu 10/26
Particulate matter in New York City in the
past
1.) (10p) In the article by Eisenbud
(1978),
Fig 3 (see handout) shows the amount of dust that settled in Manhattan
in the 1940s. If that dust would not be resuspended but would stay
where
it settled, how thick would the layer of dust be after one year of
deposition?
Assume that the density of the dust was ~0.1g/cm3.
The deposition of particles in the 1940's according
to Fig. 3 in Eisenbud (1978) was about 125 tons per square mile per
month.
The volume of this amount of dust would be:
V= mass/density = 125 tons / 0.1g/cm3
*
1000 kg/ton * 1000 g/kg = 1.25 * 109 cm3
The thickness of the layer h (per month) can then
be calculated as:
h = V/A = 1.25 * 109 cm3/1
mile2 * (1 mile/1609 m)2 * (1 m/100cm)2
= 0.048 cm
The thickness of the layer deposited over a year
is then:
h = 12*0.048 cm = 0.58 cm = 5.8 mm!
Central limit theorem
2.) (20p)
a) Open a blank workbook and, using the Create Data - Random
Numbers
command from StatPlus, create 20 columns of 100 rows of uniformly
distributed random numbers between 0 and 1.
b) Create a histogram (10 bins) for the first column and overlay the
Normal distribution bell curve (see StatPlus histogram function)
c) Make another column with the averages of the 20 columns (samples)
and create a second histogram of the averages (average
the
rows) and and include the Normal distribution similar to b). How
would you describe the difference between the two histograms?
d) Calculate averages and standard deviation of the first sample and
the averages in the last column. What differences in averages and
standard
deviation would you expect and does your result meet those
expectations?
Hand in the histograms and answers to the questions (not the random
data).