Question

Question 1: (MINITAB or R)

Let’s look at the variation of the net releases of toxic chemicals in pounds per square mile for each state in a different way. We are using the same data set as in lab 1 problem 1.

a) Obtain the boxplot of the entire data set (ignore political color for now). Excel does not do this easily so use Minitab or R.

b) Find the five-number summary, the mean, and the standard deviation of the incidence rate. You can use either Minitab, R, or Excel). If you prefer to do this in Excel, Excel has functions for count (N), minimum, maximum, median, quartiles, average, and standard deviation.

c) Use the output from a) and b) to describe the overall pattern of the distribution (use the summary stats.

d) Look at the histograms from your last lab. Did the histograms from the last lab show important characteristics of the data that the boxplot does not show? Explain.

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

Question 1 :

a)The Box plot for the Net releases Per sq mile(lb) is: (minitab 17 used)

Boxplot of Net releases Per sq mile(lb) 10000 8000 6000 4000 2000 0 Variable

b)The five-number summary measure Using Minitab is :

Descriptive Statistics: Net releases Per sq mile(lb)  
Variable Total Count Mean StDev Minimum   Q1 Median Q3 Maximum
Net releases (Per sq mile) 51 1158 1504 37    309 664 1362 9583

c) The distribution of the data set can be interpreted by its Spread, shape.

Spread: The spread is range of the data or graphically the area of the data set. It can be interpreted with the help of standard Deviation or quartile deviation.

Here the standard deviation(S.D)=1504

Q3-Q11362 309 Quartiledeviation(Q、D) =

Which is much high so we can conclude from the above two measures that the data spreads over a vast region.

Shape (skewness):

There are many measures of Skewness like ;-

Using moments

Absolute measure =(mean-Median)

S.k(pearson - 2)3mean-median) S.D

(when <0 negatively skewed

=0 then Symmetric

>0 positively skewed)

USing Quartiles (median is Q₂)

Absolute measure =(Q₃- median)-(median- Q1)

3-meahan Bouley smeasure-median)- median-Q Bowley'smeasure - Q3-91

(when<0 then it is Negatively skewed

=0 then it is symmetric

>0 then it is Positively skewed   

According to the data set,

Bowley's Measure = 0.3257 >0

S.k (pearson-2) = 0.9853 >0

From the above two measures we can say that the distribution is sot perfectly symmetric but Slightly positively skewed .i.e. The longer tail of the distribution Extends on it's right side.

d)

Histogram of Net releases Per sq mile(lb) 20 15 o 10 5- 4000 2000 6000 8000 10000 Net releases Per sq mile(lb)

From the above Diagram of a Histogram we can see the Hypothetical distribution of the given data set but in box plot we can not see it.

Also the skewness here is seen to be Positively skewed which is not noted in the Box plot.