Statistics Homework

 

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Memorandum

To: Make up a name for your boss From: Group XX: Include All Member Names Date: Self explanatory Re: Short Title for the Memo    

 

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EDA  For  Heavy  Metal  Data     Introduction   Data on heavy metal levels (ppm) were collected at 324 to 326 surface sites and at depth for 168 sites. The main purpose of this EDA is to summarizing heavy metal concentrations for surface soil (≤ 2 ft.) and soil greater than two feet deep. While the metals were measured at multiple depths, all data were assigned to one of the two depth groups.   Data  Summaries   Summary statistics for the five measured metals are shown in Table 1. The summaries show that the distributions of the metals are strongly right skewed. After a natural log transformation, the data are approximately symmetric. For all metals, the concentrations are lower for the deeper samples. Also, in most cases the variability is lower for the deeper samples.

Table 1. Summary statistics, in ppm, for subsets of soil data.

Metal Data Sample Subset n Min. 1st Qu. Median Mean 3rd Qu. Max. SD

Arsenic

Original

≤ 2 ft. 326 2.77 36.10 72.45 110.50 134.50 1420.00 134.126 > 2 ft. 168 0.994 3.38 6.445 12.98 15.15 199.00 19.883 Natural log

transformed ≤ 2 ft. 326 1.019 3.59 4.283 4.20 4.90 7.26 1.061

> 2 ft. 168 –0.006 1.22 1.86 1.99 2.72 5.29 1.019

Cadmium

Original

≤ 2 ft. 324 0.054 0.638 2.055 3.091 4.380 19.30 3.282 > 2 ft. 168 0.001 0.0571 0.111 0.232 0.269 3.460 0.461 Natural log

transformed ≤ 2 ft. 324 –2.917 –0.450 0.720 0.456 1.477 2.960 1.341

> 2 ft. 168 –6.954 –2.863 –2.203 –2.273 –1.315 1.241 1.390

Copper

Original

≤ 2 ft. 324 8.94 57.42 201.00 301.50 403.00 3110.00 383.576 > 2 ft. 168 2.56 6.958 11.750 17.940 20.420 252.00 25.936 Natural log

transformed ≤ 2 ft. 324 2.191 4.050 5.303 5.040 5.999 8.042 1.266

> 2 ft. 168 0.940 1.940 2.464 2.502 3.017 5.529 0.795

Lead

Original

≤ 2 ft. 324 4.29 16.78 44.30 92.64 102.00 3620.00 224.989 > 2 ft. 168 2.580 4.962 7.315 9.577 11.420 79.500 9.646 Natural log

transformed ≤ 2 ft. 324 1.456 2.820 3.791 3.799 4.625 8.194 1.143

> 2 ft. 168 0.9478 1.602 1.990 2.035 2.436 4.376 0.606

Zinc

Original

≤ 2 ft. 324 17.50 73.60 186.50 293.80 330.20 7400.00 569.129 > 2 ft. 168 9.79 25.20 32.70 38.76 48.22 163.00 22.628 Natural log

transformed ≤ 2 ft. 324 2.862 4.299 5.228 5.130 5.800 8.909 0.991

> 2 ft. 168 2.281 3.227 3.487 3.528 3.876 5.094 0.499 The distributions of arsenic, both in original units and in log transformed units, are shown in Figure 1. The effect of the log transformation is clearly shown in the histograms. The transformation gives unimodal, approximately symmetric distributions. There boxplots show a

 

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few potential outliers for surface soil and one potential high outlier for the deeper soil on the log transformed scale.

Figure 1. Histograms (left) and boxplots (right) for arsenic in soil samples less than 2 ft. and greater than 2 ft. The y-axes for each set of histograms have identical scales to make it easier to compare the two distributions.

< 2 ft (n = 326)

Arsenic (ppm)

F re qu en cy

0 500 1500

0 50

10 0

15 0

20 0

25 0

30 0

> 2 ft (n = 168)

Arsenic (ppm)

F re qu en cy

0 50 150

0 50

10 0

15 0

20 0

25 0

30 0

0 20 0

40 0

60 0

80 0

12 00

< 2 ft (n = 326)

A rs

en ic

( pp

m )

0 50

10 0

15 0

20 0

> 2 ft (n = 168)

A rs

en ic

( pp

m )

< 2 ft (n = 326)

ln(Arsenic (ppm))

F re qu en cy

1 3 5 7

0 10

20 30

40 50

60 70

> 2 ft (n = 168)

ln(Arsenic (ppm))

F re qu en cy

0 2 4

0 10

20 30

40 50

60 70

1 2

3 4

5 6

7 < 2 ft (n = 326)

ln (A

rs en

ic (

pp m

))

0 1

2 3

4 5

> 2 ft (n = 168)

ln (A

rs en

ic (

pp m

))