Question

Question 1. (Minitab or R)

The Environmental Protection Agency (EPA) tracks the management of certain toxic chemicals that may pose a threat to human health and the environment. U.S. facilities in different industry sectors must report annually how much of each chemical is released to the environment and/or managed through recycling, energy recovery and treatment. (A "release" of a chemical means that it is emitted to the air or water, or placed in some type of land disposal.) The information submitted by facilities is compiled in the Toxics Release Inventory (TRI). TRI helps support informed decision-making by companies, government agencies, non-governmental organizations and the public. Your data file contains the net releases of toxic chemicals in pounds per square mile for each state of the United States (from https://www.epa.gov/toxics-release-inventory-tri-program ) and whether the state is classified as red or blue politically based on the 2016 election (from http://www-personal.umich.edu/~mejn/election/2016/).

a) Describe the cases and the variables in this data set. Specify the quantitative and the categorical variables?

b) Construct a stem-and-leaf display (or stem plot) of the distribution of the net releases for all states. Preferably, but not required, use the font Courier New in Word when you paste into your report to make it look nice.

c) Describe the shape, center, and spread of the distribution of net releases.

d) Identify any suspected outliers. Based on what you know about the outlying states, explain why they are outliers.

e) Make back-to-back stem plots of the net releases by political color.

f) Write a brief comparison of the two distributions in the back to back stem plot.

Political Color Net Releases per Sq Mile (lb) PCCode 1 State 1635.340679 2 Alabama 997.0682833 Red 3 Alaska 750.2284421 4 Arizona 617.1711968 5 Arkansas 197.5378355 Blue 6 California 0 261.4782378 Blue 7 Colorado 302.9907329 Blue 8 Connecticut 0 3054.706808 Blue 9 Delaware 10 District of Columbia Blue 11 Florida 324.3805472 1042.630486 Red 954.4911872 12 Georgia 397.3250724 Blue 13 Hawaii 562.1544821 14 Idaho 0 15 Illinois Blue 2050.196451 3760.004713 16 Indiana 627.5951055 Red 17 lowa 225.3834134 18 Kansas Red 19 Kentucky 1542.852023 Red 2969.815421 Red 20 Louisiana 0 288.2457295 Blue 21 Maine 0 Blue 773.4575978 22 Maryland Blue 413.3821526 23 Massachusetts 24 Michigan 1246.570745 Red 309.1243261 Blue 25 Minnesota 1361.570007 Red 26 Mississippi 1082.951657 27 Missouri 261.0555825 28 Montana 270.5890505 29 Nebraska Red 2926.155309 0 30 Nevada Blue 50.77868048 31 New Hampshire Blue 32 New Jersey Blue 9582.900453 Pb1 Pb2 |Pb3 Pb4U 30 Nevada 2926.155309 Blue 50.77868048 31 New Hampshire 0 ue 9582.900453 32 New Jersey 33 New Mexico 0 184.2126478 0 34 New York 35 North Carolina Blue 326.766159 0 Red 1255.703922 36 North Dakota 663.5360953 37 Ohio 2618.116231 1 38 Oklahoma Red 384.7319543 39 Oregon Blue 161.7890486 0 40 Pennsylvania Red 1455.127368 41 Rhode Island Blue 419.064358 42 South Carolina 43 South Dakota Red 1252.068122 Red 83.50635735 44 Tennessee Red 2058.158047 45 Texas Red 876.5177672 46 Utah Red 2699.888726 Blue 36.9015181 0 48 Virginia 49 Washington 954.2464747 Blue 0 Blue 382.9761012 50 West Virginia Red 1298.421973 51 Wisconsin Red 571.2200275 52 Wyoming Red 209.7583389 57

Answer 1

(a) Political color Categorical variable (more specifically nominal data) Net Releases per Sq Mile (lb): quantitative variable PC Code Categorical variable.

(b)

Stem-and-Leaf Display: Net Releases per sq Mile

Stem-and-leaf of Net Releases per sq Mile N = 51
Leaf Unit = 100

(32) 0 00011122222233333334455666778999
19 1 0022223456
9 2 006699
3 3 07
1 4
1 5
1 6
1 7
1 8
1 9 5

Note: we round the value 2 decimal places before construct stem-leaf plot.

(c)

Descriptive Statistics: Net Releases per sq Mile

Variable Mean StDev Variance Median Range IQR  
Net Releases per sq Mile 1152 1507 2271938 664 9546 1059

  
Variable Skewness Kurtosis
Net Releases per sq Mile     3.82 19.36

Center:

Mean=1152, Median=664

Spread:

Variance=2271938, standard deviation=1507, IQR=1059, Range=9546

Shape:

Since Measure of skewness>0 so it is positively skewed.

(d)

First quartile=Q1=303, third quartile=Q3=1362, IQR=1059 then

Lower Whisker=Q1-1.5IQR=303-1.5*1059=-1285.5

Upper Whisker=Q3+1.5IQR=1362+1.5*1059= 2950.5

Maximum value=37, Minimum value=9583.

Any value lies outside the interval (-1285.5, 2950.5) treated as an outlier. Hence suspected outliers are:

3054.706808, 3760.004713, 2969.815421, 9582.900453 and the outlying states are:

Delaware, Indiana, Louisiana, New Jersey.

(e)

Stem-and-Leaf Display: Red, Blue

Stem-and-leaf of Red N = 30
Leaf Unit = 100

6 0 022223
15 0 556667899
15 1 00222234
7 1 56
5 2 0
4 2 669
1 3
1 3 7

Stem-and-leaf of Blue N = 21
Leaf Unit = 100

(17) 0 00111223333334479
4 1
4 2 09
2 3 0
1 4
1 5
1 6
1 7
1 8
1 9 5