Data analysis with R Software
load("Students.RData")
data Transport Score Brotherhood Time
1 Public_Transport F 3 81.2038642
2 Car F 4 3.5746976
3 Public_Transport C 3 51.2451380
4 Public_Transport D 1 1.3638041
5 Bike D 0 5.9409247
6 Public_Transport F 4 45.1287821
7 Public_Transport A 5 4.5104657
8 Public_Transport C 2 30.8991132
9 Car D 4 20.4863186
10 Public_Transport A 4 14.2022303
11 Car D 1 23.9651770
12 Public_Transport D 2 16.3412274
13 Walk F 2 5.5865170
14 Motorbike C 2 17.5496064
15 Public_Transport C 5 14.1716461
16 Car C 2 24.0544996
17 Car B 4 6.1962879
18 Car D 2 3.0405011
19 Public_Transport B 3 13.6939374
20 Car C 3 4.9998038
21 Walk D 2 5.5519060
22 Public_Transport B 1 16.0945605
23 Public_Transport B 1 0.4049663
24 Bike B 2 16.3770644
25 Public_Transport B 3 41.2585527
26 Car C 1 75.5343450
27 Car D 3 9.8758428
28 Bike D 0 10.5529059
29 Car D 2 29.5981719
30 Bike C 1 14.7633491
31 Walk C 3 0.5958972
32 Public_Transport F 3 6.9081739
33 Public_Transport D 2 5.6548999
34 Bike C 3 76.0831409
35 Motorbike A 4 20.9973650
36 Car D 2 0.7479226
37 Public_Transport C 2 5.9238454
38 Car C 2 55.4974577
39 Car D 2 35.0391657
40 Car B 3 1.0689223
41 Car C 3 41.1569394
42 Bike C 4 38.1589737
43 Bike B 2 7.2634336
44 Public_Transport D 4 7.0736842
45 Public_Transport D 0 6.3442236
46 Car B 4 28.2376303
47 Car F 2 14.9208720
48 Public_Transport C 1 19.9026766
49 Car B 2 2.8461171
50 Public_Transport F 5 90.7599587
51 Public_Transport D 2 0.4149180
52 Car D 5 9.2887277
53 Car F 0 42.5346075
54 Public_Transport D 1 4.0768993
55 Public_Transport B 1 14.8170098
56 Public_Transport C 2 40.0210542
57 Car F 3 16.5860951
58 Public_Transport B 4 2.5801303
59 Public_Transport C 2 22.6003957
60 Car B 1 19.6900456
61 Car B 2 42.3684211
62 Car C 3 11.3303147
63 Public_Transport C 1 33.2234480
64 Car A 1 12.6914734
65 Walk C 1 23.7157087
66 Walk A 3 8.8532408
67 Car C 2 37.7323818
68 Car F 1 15.5325145
69 Car C 1 48.0196141
70 Public_Transport C 4 18.7426055
71 Walk D 2 28.8152395
72 Public_Transport B 0 8.0129327
73 Public_Transport A 4 78.1471800
74 Car D 0 1.1424262
75 Public_Transport B 2 8.7399205
76 Public_Transport B 3 19.5185059
77 Public_Transport C 4 0.6533081
78 Car C 1 9.8899481
79 Public_Transport D 4 8.3409416
80 Public_Transport D 4 13.7515735
81 Public_Transport B 1 22.4699005
82 Public_Transport F 3 43.6826990
83 Car C 1 12.2099334
84 Public_Transport C 2 0.2753652
85 Public_Transport D 2 7.8281282
86 Car B 2 5.5432996
87 Bike A 2 3.1448994
88 Bike C 4 42.8764015
89 Public_Transport C 2 3.3911688
90 Public_Transport D 3 38.8366974
91 Car D 5 46.6558061
92 Car C 2 4.4942830
93 Car B 1 10.2924864
94 Car B 0 0.4485110
95 Public_Transport C 3 10.2044983
96 Walk D 0 8.5508167
97 Public_Transport C 2 2.7529707
98 Car F 3 53.8873705
99 Motorbike D 2 7.6115399
100 Bike F 3 33.1478722head(data) Transport Score Brotherhood Time
1 Public_Transport F 3 81.203864
2 Car F 4 3.574698
3 Public_Transport C 3 51.245138
4 Public_Transport D 1 1.363804
5 Bike D 0 5.940925
6 Public_Transport F 4 45.128782attach(data)Qualitative data
Nominal
x=Transport
(moda=sort(unique(x)))[1] "Bike" "Car" "Motorbike" "Public_Transport"
[5] "Walk" (e=table(x))x
Bike Car Motorbike Public_Transport
10 37 3 43
Walk
7 (n=length(x))[1] 100n=sum(e)
(f=e/n)x
Bike Car Motorbike Public_Transport
0.10 0.37 0.03 0.43
Walk
0.07 pie(f)
barplot(f)
Ordinal
x=Score
(moda=sort(unique(x),dec=T))[1] "F" "D" "C" "B" "A"(e=rev(table(x)))x
F D C B A
13 27 32 21 7 (n=length(x))[1] 100n=sum(e)
(f=e/n)x
F D C B A
0.13 0.27 0.32 0.21 0.07 pie(f)
barplot(f)
(Fc=cumsum(f)) F D C B A
0.13 0.40 0.72 0.93 1.00 barplot(Fc)
x_num=as.numeric(replace(x, x %in% moda, 0:4) )
boxplot(x_num)
Quantative data
Discrete
x=Brotherhood
(moda=sort(unique(x)))[1] 0 1 2 3 4 5(e=table(x))x
0 1 2 3 4 5
8 19 32 20 16 5 (n=length(x))[1] 100n=sum(e)
(f=e/n)x
0 1 2 3 4 5
0.08 0.19 0.32 0.20 0.16 0.05 plot(moda,f,type='h')
(Fc=cumsum(f)) 0 1 2 3 4 5
0.08 0.27 0.59 0.79 0.95 1.00 tau=1
plot(c(min(moda)-tau,moda,max(moda)+tau),c(0,Fc,1),type='s')
mean(x)[1] 2.32var(x)[1] 1.714747sd(x)[1] 1.309484summary(x) Min. 1st Qu. Median Mean 3rd Qu. Max.
0.00 1.00 2.00 2.32 3.00 5.00 quantile(x) 0% 25% 50% 75% 100%
0 1 2 3 5 boxplot(x)
Quantative data
Continuous
x=Time
(moda=sort(unique(x))) [1] 0.2753652 0.4049663 0.4149180 0.4485110 0.5958972 0.6533081
[7] 0.7479226 1.0689223 1.1424262 1.3638041 2.5801303 2.7529707
[13] 2.8461171 3.0405011 3.1448994 3.3911688 3.5746976 4.0768993
[19] 4.4942830 4.5104657 4.9998038 5.5432996 5.5519060 5.5865170
[25] 5.6548999 5.9238454 5.9409247 6.1962879 6.3442236 6.9081739
[31] 7.0736842 7.2634336 7.6115399 7.8281282 8.0129327 8.3409416
[37] 8.5508167 8.7399205 8.8532408 9.2887277 9.8758428 9.8899481
[43] 10.2044983 10.2924864 10.5529059 11.3303147 12.2099334 12.6914734
[49] 13.6939374 13.7515735 14.1716461 14.2022303 14.7633491 14.8170098
[55] 14.9208720 15.5325145 16.0945605 16.3412274 16.3770644 16.5860951
[61] 17.5496064 18.7426055 19.5185059 19.6900456 19.9026766 20.4863186
[67] 20.9973650 22.4699005 22.6003957 23.7157087 23.9651770 24.0544996
[73] 28.2376303 28.8152395 29.5981719 30.8991132 33.1478722 33.2234480
[79] 35.0391657 37.7323818 38.1589737 38.8366974 40.0210542 41.1569394
[85] 41.2585527 42.3684211 42.5346075 42.8764015 43.6826990 45.1287821
[91] 46.6558061 48.0196141 51.2451380 53.8873705 55.4974577 75.5343450
[97] 76.0831409 78.1471800 81.2038642 90.7599587(e=table(x))x
0.275365175679326 0.404966278001666 0.414918037139569 0.448510966753875
1 1 1 1
0.59589723298139 0.653308119159192 0.747922583017498 1.06892227288336
1 1 1 1
1.14242617785931 1.36380407214165 2.58013027580455 2.75297067093056
1 1 1 1
2.84611705863895 3.04050113681577 3.14489944884554 3.39116879263317
1 1 1 1
3.57469761604443 4.07689926726744 4.49428303353488 4.51046571601182
1 1 1 1
4.99980376884604 5.54329959955066 5.55190597940236 5.58651701593772
1 1 1 1
5.654899911955 5.92384540426341 5.94092472602951 6.19628791045398
1 1 1 1
6.34422363684418 6.90817394199961 7.0736842234619 7.26343355700374
1 1 1 1
7.61153993150219 7.82812819648371 8.01293269125745 8.34094155697728
1 1 1 1
8.55081665236503 8.73992045596242 8.8532408173196 9.28872770676389
1 1 1 1
9.87584280781448 9.8899481180124 10.2044982714579 10.2924863896333
1 1 1 1
10.5529058668762 11.330314733088 12.2099333798822 12.6914733713939
1 1 1 1
13.6939374154743 13.7515735320302 14.1716461034801 14.2022303298425
1 1 1 1
14.7633491179284 14.8170097612059 14.9208719928127 15.5325145481463
1 1 1 1
16.0945604591491 16.3412274479499 16.3770644340973 16.5860950650956
1 1 1 1
17.5496063687204 18.7426054600935 19.5185058651872 19.6900456391584
1 1 1 1
19.9026765769657 20.4863185614657 20.9973649980989 22.4699005049031
1 1 1 1
22.6003957150813 23.7157087162032 23.9651770475004 24.0544995513007
1 1 1 1
28.2376303107915 28.8152395174525 29.5981718580646 30.8991131526105
1 1 1 1
33.1478721634172 33.2234479932428 35.0391657356791 37.732381836415
1 1 1 1
38.158973651602 38.8366974142376 40.0210542382241 41.1569394103352
1 1 1 1
41.2585526851002 42.3684210699979 42.5346074958328 42.8764014762253
1 1 1 1
43.6826990041977 45.1287821267727 46.6558060606006 48.019614090149
1 1 1 1
51.2451380164667 53.887370515934 55.4974576653286 75.5343449557191
1 1 1 1
76.083140894211 78.1471800053484 81.2038641715414 90.7599586962091
1 1 1 1 (n=length(x))[1] 100n=sum(e)
(f=e/n)x
0.275365175679326 0.404966278001666 0.414918037139569 0.448510966753875
0.01 0.01 0.01 0.01
0.59589723298139 0.653308119159192 0.747922583017498 1.06892227288336
0.01 0.01 0.01 0.01
1.14242617785931 1.36380407214165 2.58013027580455 2.75297067093056
0.01 0.01 0.01 0.01
2.84611705863895 3.04050113681577 3.14489944884554 3.39116879263317
0.01 0.01 0.01 0.01
3.57469761604443 4.07689926726744 4.49428303353488 4.51046571601182
0.01 0.01 0.01 0.01
4.99980376884604 5.54329959955066 5.55190597940236 5.58651701593772
0.01 0.01 0.01 0.01
5.654899911955 5.92384540426341 5.94092472602951 6.19628791045398
0.01 0.01 0.01 0.01
6.34422363684418 6.90817394199961 7.0736842234619 7.26343355700374
0.01 0.01 0.01 0.01
7.61153993150219 7.82812819648371 8.01293269125745 8.34094155697728
0.01 0.01 0.01 0.01
8.55081665236503 8.73992045596242 8.8532408173196 9.28872770676389
0.01 0.01 0.01 0.01
9.87584280781448 9.8899481180124 10.2044982714579 10.2924863896333
0.01 0.01 0.01 0.01
10.5529058668762 11.330314733088 12.2099333798822 12.6914733713939
0.01 0.01 0.01 0.01
13.6939374154743 13.7515735320302 14.1716461034801 14.2022303298425
0.01 0.01 0.01 0.01
14.7633491179284 14.8170097612059 14.9208719928127 15.5325145481463
0.01 0.01 0.01 0.01
16.0945604591491 16.3412274479499 16.3770644340973 16.5860950650956
0.01 0.01 0.01 0.01
17.5496063687204 18.7426054600935 19.5185058651872 19.6900456391584
0.01 0.01 0.01 0.01
19.9026765769657 20.4863185614657 20.9973649980989 22.4699005049031
0.01 0.01 0.01 0.01
22.6003957150813 23.7157087162032 23.9651770475004 24.0544995513007
0.01 0.01 0.01 0.01
28.2376303107915 28.8152395174525 29.5981718580646 30.8991131526105
0.01 0.01 0.01 0.01
33.1478721634172 33.2234479932428 35.0391657356791 37.732381836415
0.01 0.01 0.01 0.01
38.158973651602 38.8366974142376 40.0210542382241 41.1569394103352
0.01 0.01 0.01 0.01
41.2585526851002 42.3684210699979 42.5346074958328 42.8764014762253
0.01 0.01 0.01 0.01
43.6826990041977 45.1287821267727 46.6558060606006 48.019614090149
0.01 0.01 0.01 0.01
51.2451380164667 53.887370515934 55.4974576653286 75.5343449557191
0.01 0.01 0.01 0.01
76.083140894211 78.1471800053484 81.2038641715414 90.7599586962091
0.01 0.01 0.01 0.01 plot(moda,f,type='h')
hist(x)
hist(x,freq=F)
hist(x,freq=F,nclass=12)
hist(x,freq=F,breaks=quantile(x,seq(0,1,len=8)))
(Fc=cumsum(f))0.275365175679326 0.404966278001666 0.414918037139569 0.448510966753875
0.01 0.02 0.03 0.04
0.59589723298139 0.653308119159192 0.747922583017498 1.06892227288336
0.05 0.06 0.07 0.08
1.14242617785931 1.36380407214165 2.58013027580455 2.75297067093056
0.09 0.10 0.11 0.12
2.84611705863895 3.04050113681577 3.14489944884554 3.39116879263317
0.13 0.14 0.15 0.16
3.57469761604443 4.07689926726744 4.49428303353488 4.51046571601182
0.17 0.18 0.19 0.20
4.99980376884604 5.54329959955066 5.55190597940236 5.58651701593772
0.21 0.22 0.23 0.24
5.654899911955 5.92384540426341 5.94092472602951 6.19628791045398
0.25 0.26 0.27 0.28
6.34422363684418 6.90817394199961 7.0736842234619 7.26343355700374
0.29 0.30 0.31 0.32
7.61153993150219 7.82812819648371 8.01293269125745 8.34094155697728
0.33 0.34 0.35 0.36
8.55081665236503 8.73992045596242 8.8532408173196 9.28872770676389
0.37 0.38 0.39 0.40
9.87584280781448 9.8899481180124 10.2044982714579 10.2924863896333
0.41 0.42 0.43 0.44
10.5529058668762 11.330314733088 12.2099333798822 12.6914733713939
0.45 0.46 0.47 0.48
13.6939374154743 13.7515735320302 14.1716461034801 14.2022303298425
0.49 0.50 0.51 0.52
14.7633491179284 14.8170097612059 14.9208719928127 15.5325145481463
0.53 0.54 0.55 0.56
16.0945604591491 16.3412274479499 16.3770644340973 16.5860950650956
0.57 0.58 0.59 0.60
17.5496063687204 18.7426054600935 19.5185058651872 19.6900456391584
0.61 0.62 0.63 0.64
19.9026765769657 20.4863185614657 20.9973649980989 22.4699005049031
0.65 0.66 0.67 0.68
22.6003957150813 23.7157087162032 23.9651770475004 24.0544995513007
0.69 0.70 0.71 0.72
28.2376303107915 28.8152395174525 29.5981718580646 30.8991131526105
0.73 0.74 0.75 0.76
33.1478721634172 33.2234479932428 35.0391657356791 37.732381836415
0.77 0.78 0.79 0.80
38.158973651602 38.8366974142376 40.0210542382241 41.1569394103352
0.81 0.82 0.83 0.84
41.2585526851002 42.3684210699979 42.5346074958328 42.8764014762253
0.85 0.86 0.87 0.88
43.6826990041977 45.1287821267727 46.6558060606006 48.019614090149
0.89 0.90 0.91 0.92
51.2451380164667 53.887370515934 55.4974576653286 75.5343449557191
0.93 0.94 0.95 0.96
76.083140894211 78.1471800053484 81.2038641715414 90.7599586962091
0.97 0.98 0.99 1.00 tau=1
plot(c(min(moda)-tau,moda,max(moda)+tau),c(0,Fc,1),type='s')
mean(x)[1] 20.33484var(x)[1] 405.0834sd(x)[1] 20.12668summary(x) Min. 1st Qu. Median Mean 3rd Qu. Max.
0.2754 5.8566 13.9616 20.3348 29.9234 90.7600 quantile(x) 0% 25% 50% 75% 100%
0.2753652 5.8566090 13.9616098 29.9234072 90.7599587 boxplot(x)