Statistics 401B
Fall 2014
Laboratory Assignment 1
The table on the next page gives data for the two variables MPG.city (miles per US gallon for city driving by
EPA rating) and Weight (in pounds) of 75 cars that were selected at random from among 1993 passenger car
models that were listed in the Consumer Reports issue. Pickup trucks, sport/utility vehicles, and passenger
vans were eliminated. Duplicate models (e.g., Dodge Shadow and Plymouth Sundance) were listed at most once.
They are arranged in two tables, in the increasing order of values for each variable and the make of the car was
appended for your information. The column labelled i indicates the ranks of the ordered observations for each
variable and the column labelled (i−.5)/75 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
P 2
Cars93.txt (from the Download folder) and EXCEL or other software to calculate
x and
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(0.32), Q(.666667), Q(.872), and Q(0.9632). 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 MPG.city 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 of 2, with the midpoint
of the first interval fixed at 15.5 (Bin end-points must be in half units).
(b) A Histogram of frequencies using your frequency table.
(c) Start a Stem and Leaf plot with stems 0, 1, and 3 and expand the stem appropriately to better
represent the shape of the distribution as 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 only the quantiles corresponding to the following 13 pi -values:
0.02, 0.10, 0.18, . . . , 0.98
3. Construct the following tables and plots for the Weight 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 200, with the first bin
beginning at 1800.
(b) A Histogram of frequencies using your frequency table.
(c) A Stem and Leaf plot with stems 1, 2, 3, and 4 after dividing the data values by 100 and rounding to
whole numbers. Expand the stem appropriately to better represent the shape of the distribution as
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 13 quantiles as in Problem 2.
4. Use the link to the Cars93.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 Thursday, September 11, 2014 (turn-in by 2:20 p.m.)
Make
Cadillac DeVille
Cadillac Seville
Chevrolet Caprice
Chevrolet Corvette
Infiniti Q45
Mazda RX-7
Acura Legend
Dodge Stealth
Ford Crown Victoria
Lexus ES300
Lexus SC300
Lincoln Town Car
Mitsubishi Diamante
Volkswagen Corrado
Audi 100
Buick LeSabre
Buick Riviera
Chevrolet Camaro
Mercedes-Benz 300E
Mercury Cougar
Oldsmobile Eighty-Eight
Pontiac Firebird
Pontiac Grand Prix
Pontiac Bonneville
Audi 90
Chrylser Concorde
Chrysler Imperial
Eagle Vision
Hyundai Sonata
Mercedes-Benz 190E
Saab 900
Volvo 850
Chevrolet Lumina
Dodge Dynasty
Ford Taurus
Nissan Maxima
Volkswagen Passat
Volvo 240
Buick Century
Dodge Spirit
Ford Tempo
Ford Mustang
Hyundai Elantra
Toyota Camry
Chrysler LeBaron
Dodge Shadow
Ford Escort
Oldsmobile Cutlass Ciera
Plymouth Laser
Pontiac Sunbird
Subaru Legacy
Ford Probe
Honda Prelude
Honda Accord
Nissan Altima
Oldsmobile Achieva
Acura Integra
Chevrolet Cavalier
Chevrolet Corsica
Subaru Loyale
Toyota Celica
Volkswagen Fox
Mazda 626
Mazda Protege
Saturn SL
Dodge Colt
Eagle Summit
Hyundai Excel
Mazda 323
Mitsubishi Mirage
Nissan Sentra
Ford Festiva
Pontiac LeMans
Toyota Tercel
Subaru Justy
i
01
02
03
04
05
06
07
08
09
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
(i-.5)/75
0.00667
0.02000
0.03333
0.04667
0.06000
0.07333
0.08667
0.10000
0.11333
0.12667
0.14000
0.15333
0.16667
0.18000
0.19333
0.20667
0.22000
0.23333
0.24667
0.26000
0.27333
0.28667
0.30000
0.31333
0.32667
0.34000
0.35333
0.36667
0.38000
0.39333
0.40667
0.42000
0.43333
0.44667
0.46000
0.47333
0.48667
0.50000
0.51333
0.52667
0.54000
0.55333
0.56667
0.58000
0.59333
0.60667
0.62000
0.63333
0.64667
0.66000
0.67333
0.68667
0.70000
0.71333
0.72667
0.74000
0.75333
0.76667
0.78000
0.79333
0.80667
0.82000
0.83333
0.84667
0.86000
0.87333
0.88667
0.90000
0.91333
0.92667
0.94000
0.95333
0.96667
0.98000
0.99333
MPG.city
16
16
17
17
17
17
18
18
18
18
18
18
18
18
19
19
19
19
19
19
19
19
19
19
20
20
20
20
20
20
20
20
21
21
21
21
21
21
22
22
22
22
22
22
23
23
23
23
23
23
23
24
24
24
24
24
25
25
25
25
25
25
26
28
28
29
29
29
29
29
29
31
31
32
33
Make
Ford Festiva
Subaru Justy
Toyota Tercel
Volkswagen Fox
Dodge Colt
Eagle Summit
Mitsubishi Mirage
Mazda 323
Hyundai Excel
Pontiac LeMans
Mazda Protege
Chevrolet Cavalier
Subaru Loyale
Saturn SL
Ford Escort
Nissan Sentra
Pontiac Sunbird
Hyundai Elantra
Plymouth Laser
Dodge Shadow
Ford Tempo
Acura Integra
Ford Probe
Saab 900
Chevrolet Corsica
Volkswagen Corrado
Ford Mustang
Honda Prelude
Buick Century
Hyundai Sonata
Oldsmobile Cutlass Ciera
Mazda RX-7
Oldsmobile Achieva
Mercedes-Benz 190E
Toyota Celica
Dodge Spirit
Mazda 626
Volkswagen Passat
Volvo 240
Toyota Camry
Honda Accord
Nissan Altima
Dodge Dynasty
Chrysler LeBaron
Subaru Legacy
Chevrolet Lumina
Nissan Maxima
Chevrolet Camaro
Pontiac Firebird
Volvo 850
Ford Taurus
Audi 90
Chevrolet Corvette
Audi 100
Pontiac Grand Prix
Buick LeSabre
Oldsmobile Eighty-Eight
Eagle Vision
Buick Riviera
Pontiac Bonneville
Lexus ES300
Lexus SC300
Chrylser Concorde
Mercedes-Benz 300E
Acura Legend
Chrysler Imperial
Mercury Cougar
Cadillac DeVille
Mitsubishi Diamante
Dodge Stealth
Chevrolet Caprice
Cadillac Seville
Ford Crown Victoria
Infiniti Q45
Lincoln Town Car
i
01
02
03
04
05
06
07
08
09
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
(i-.5)/75
0.00667
0.02000
0.03333
0.04667
0.06000
0.07333
0.08667
0.10000
0.11333
0.12667
0.14000
0.15333
0.16667
0.18000
0.19333
0.20667
0.22000
0.23333
0.24667
0.26000
0.27333
0.28667
0.30000
0.31333
0.32667
0.34000
0.35333
0.36667
0.38000
0.39333
0.40667
0.42000
0.43333
0.44667
0.46000
0.47333
0.48667
0.50000
0.51333
0.52667
0.54000
0.55333
0.56667
0.58000
0.59333
0.60667
0.62000
0.63333
0.64667
0.66000
0.67333
0.68667
0.70000
0.71333
0.72667
0.74000
0.75333
0.76667
0.78000
0.79333
0.80667
0.82000
0.83333
0.84667
0.86000
0.87333
0.88667
0.90000
0.91333
0.92667
0.94000
0.95333
0.96667
0.98000
0.99333
Weight
1845
2045
2055
2240
2270
2295
2295
2325
2345
2350
2440
2490
2490
2495
2530
2545
2575
2620
2640
2670
2690
2705
2710
2775
2785
2810
2850
2865
2880
2885
2890
2895
2910
2920
2950
2970
2970
2985
2985
3030
3040
3050
3080
3085
3085
3195
3200
3240
3240
3245
3325
3375
3380
3405
3450
3470
3470
3490
3495
3495
3510
3515
3515
3525
3560
3570
3610
3620
3730
3805
3910
3935
3950
4000
4055