C) Use Google, find and read the article “Airborne Hexavalent Chromium in Southw

Question

C) Use Google, find and read the article “Airborne Hexavalent Chromium in Southwestern Ontario”, by Ronald W. Bell and Jerold C. Hipfner, Journal of the Air and Waste Management Association, 47: 905 – 910, August 1997.

i. Why, in Figure 3 (a bar graph) are the authors depicting the median concentrations of the various airborne pollutants? Why not the arithmetic mean concentrations? (2)

ii. Why are the authors dealing with Geometric Means rather than Arithmetic Means or Medians in Figures 4 and 5 and the ensuing discussions? (2)

Explanation / Answer

Answer 1. Since figure 3 shows the concentration of different pollutants, we can say that it is going to be an skewed distribution with most of the mass on the left side(smaller values). Meadian is a better measure because it is not affected by value of outliers. For example consider a case when you are trying to represent a distribution with only one parameter and you have to choose between mean or median. Also assume that distribution has outliers present which have very high values. When taking mean outiers will shift the mean to a higher value creating the appereance that a significantly large number represents the distribution. But when taking median these outliers cannot affect the result with their values.

X=[2,4,6,9,23,45,66,88,999] In this example when you see the data you get the feeling that 999 is clearly the outlier.If you use mean then it is going to be a very high value which does not represent the data correctly. but if you take median it will be 23, which is well within range. What I mean when I say that outliers cannot affect median by their value is that of I change 999 to 800 or 2000 median will be same beacuse we are not considering its value but only the fact that it is one of the data points.

Answer 2. Airthmatic and geometric mean are both types of mean but airthmatic mean is a better measure when all the data points are independent. But in this case, given the measurement past measurement, this month will not show a drastic change. In other words todays reading will be past reading+ generated pollution + discipated pollution. So consecutive readings will show dependencies and hence geometric mean is a better measure.

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