Statistics 401D
Spring 2016
Laboratory Assignment 1
The table on the next page gives data for the two variables SO2 (Sulfur dioxide content of air in mcg/meter2 )
and Windspeed (average annual wind speed in mph), extracted from a database that gives air pollution and
related values for 40 U.S. cities and were collected from U.S. government publications over the years 1969-1971.
They are arranged in two tables, in the increasing order of values for each variable and the city name has been
appended for your information. The column labelled i indicates the ranks of the ordered observations for each
variable and the column labelled (i − .5)/40 contains the pi values. Use hand calculation to do Problems 1, 2,
and 3.
1. Compute the following statistics for each variable. Show work:
(a) Mean x̄, Variance s2 , Standard Deviation s, and coefficient of variation(CV). You may use the file
P
air pollution.txt (from the Download folder) and EXCEL or other software to calculate x and
P 2
x needed.
(b) Range R, Median Q(0.5), the lower quartile Q(0.25), the upper quartile Q(0.75), and IQR.
(c) The quantiles Q(0.05), Q(0.333333), Q(.45), Q(.8), and Q(0.8925). Must use the pi values shown in
the table (see backpage), and linear interpolation when needed.
2. Construct the following tables and plots for the SO2 variable and use these plots to comment on the shape
of the distribution.
(a) A table of frequencies and relative frequencies. Try bin intervals of equal width 13, with the midpoint
of the first interval fixed at 14.0 (Bin end-points must be in half units).
(b) A Histogram of frequencies using your frequency table.
(c) A Stem and Leaf plot with stems 0, 1, . . . , 11.
(d) The Box Plot. Make sure that it exhibits the value of each key element in the plot and label them.
(e) A Normal Probability Plot using the quantiles only for the following 10 pi -values:0.0125, 0.1125, . . . , 0.9125
3. Construct the following tables and plots for the Windspeed variable and use these plots to comment on the
shape of the distribution.
(a) A table of frequencies and relative frequencies. Use intervals, each of width 1, with the first bin
beginning at 5.95.
(b) A Histogram of frequencies using your frequency table.
(c) A Stem and Leaf plot with stems 6, 7, . . . , 12 after multplying the data values by 10. Expand the
stem appropriately to better represent the shape of the distribution if needed.
(d) The Box Plot. Make sure that it exhibits the value of each key element in the plot and label them.
(e) A Normal Probability Plot using the 10 quantiles as in Problem 2.
4. Use the link to the air pollution.jmp data table provided in the Current Laboratory Assignment
webpage to perform a JMP distribution analysis of these two variables. This analysis must contain the
percentiles and the moments, a histogram, the box plot, a stem-and-leaf diagram, and a normal probability
(quantile) plot of each of the two variables. Turn in only a single Word-edited page for each analysis.
Due Tuesday, January 26, 2016 (turn-in by 10:20 a.m.
during lab)
City
Wichita
i
01
(i–.5)/40
0.0125
New Orleans
02
0.0375
Dallas
03
Phoenix
SO2
8
City
Phoenix
i
01
(i–.5)/40
0.0125
Windspeed
6
9
Charleston
02
0.0375
6.5
0.0625
9
Cincinnati
03
0.0625
7.1
04
0.0875
10
Richmond
04
0.0875
7.6
Miami
05
0.1125
10
Nashville
05
0.1125
7.9
Memphis
06
0.1375
10
Little Rock
06
0.1375
8.2
Houston
07
0.1625
10
Louisville
07
0.1625
8.3
Albuquerque
08
0.1875
11
New Orleans
08
0.1875
8.4
Buffalo
09
0.2125
11
Columbus
09
0.2125
8.6
San Francisco
10
0.2375
12
San Francisco
10
0.2375
8.7
Little Rock
11
0.2625
13
Salt Lake City
11
0.2625
8.7
Kansas City
12
0.2875
14
Albany
12
0.2875
8.8
Omaha
13
0.3125
14
Albuquerque
13
0.3125
8.9
Milwaukee
14
0.3375
16
Denver
14
0.3375
9
Denver
15
0.3625
17
Hartford
15
0.3625
9
Des Moines
16
0.3875
17
Wilmington
16
0.3875
9
Nashville
17
0.4125
18
Miami
17
0.4125
9
Cincinnati
18
0.4375
23
Atlanta
18
0.4375
9.1
Atlanta
19
0.4625
24
Memphis
19
0.4625
9.2
Columbus
20
0.4875
26
Washington
20
0.4875
9.3
Richmond
21
0.5125
26
Pittsburgh
21
0.5125
9.4
Indianapolis
22
0.5375
28
Seattle
22
0.5375
9.4
Salt Lake City
23
0.5625
28
St. Louis
23
0.5625
9.5
Washington
24
0.5875
29
Baltimore
24
0.5875
9.6
Minn-St. Paul
25
0.6125
29
Philadelphia
25
0.6125
9.6
Seattle
26
0.6375
29
Indianapolis
26
0.6375
9.7
Louisville
27
0.6625
30
Kansas City
27
0.6625
10
Norfolk
28
0.6875
31
Detroit
28
0.6875
10.1
Charleston
29
0.7125
31
Chicago
29
0.7125
10.4
Detroit
30
0.7375
35
Minn-St. Paul
30
0.7375
10.6
Wilmington
31
0.7625
36
Providence
31
0.7625
10.6
Albany
32
0.7875
46
Norfolk
32
0.7875
10.6
Baltimore
33
0.8125
47
Houston
33
0.8125
10.8
Hartford
34
0.8375
56
Omaha
34
0.8375
10.9
St. Louis
35
0.8625
56
Cleveland
35
0.8625
10.9
Pittsburgh
36
0.8875
61
Dallas
36
0.8875
10.9
Cleveland
37
0.9125
65
Des Moines
37
0.9125
11.2
Philadelphia
38
0.9375
69
Milwaukee
38
0.9375
11.8
Providence
39
0.9625
94
Buffalo
39
0.9625
12.4
Chicago
40
0.9875
110
Wichita
40
0.9875
12.7