Free Statistics

of Irreproducible Research!

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationSat, 11 Dec 2010 10:56:18 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Dec/11/t1292065174ne0xo3cw72hnpw9.htm/, Retrieved Mon, 06 May 2024 12:00:59 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=108058, Retrieved Mon, 06 May 2024 12:00:59 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact160
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
F     [Central Tendency] [Time needed to su...] [2010-09-25 09:42:08] [b98453cac15ba1066b407e146608df68]
-    D    [Central Tendency] [Paper - Central t...] [2010-12-11 10:56:18] [ee4a783fb13f41eb2e9bc8a0c4f26279] [Current]
-    D      [Central Tendency] [Paper - Central t...] [2010-12-13 20:37:20] [1f5baf2b24e732d76900bb8178fc04e7]
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Dataseries X:
25.94
28.66
33.95
31.01
21.00
26.19
25.41
30.47
12.88
9.78
8.25
7.44
10.81
9.12
11.03
12.74
9.98
11.62
9.40
9.27
7.76
8.78
10.65
10.95
12.36
10.85
11.84
12.14
11.65
8.86
7.63
7.38
7.25
8.03
7.75
7.16
7.18
7.51
7.07
7.11
8.98
9.53
10.54
11.31
10.36
11.44
10.45
10.69
11.28
11.96
13.52
12.89
14.03
16.27
16.17
17.25
19.38
26.20
33.53
32.20
38.45
44.86
41.67
36.06
39.76
36.81
42.65
46.89
53.61
57.59
67.82
71.89
75.51
68.49
62.72
70.39
59.77
57.27
67.96
67.85
76.98
81.08
91.66
84.84
85.73
84.61
92.91
99.80
121.19
122.04
131.76
138.48
153.47
189.95
182.22
198.08
135.36
125.02
143.50
173.95
188.75
167.44
158.95
169.53
113.66
107.59
92.67
85.35
90.13
89.31
105.12
125.83
135.81
142.43
163.39
168.21
185.35
188.50
199.91
210.73
192.06
204.62
235.00
261.09
256.88
251.53
257.25
243.10
283.75
300.98




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=108058&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=108058&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=108058&T=0

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean75.60315384615386.721862575374911.2473519055747
Geometric Mean40.1346925720332
Harmonic Mean21.4236384347145
Quadratic Mean107.445335765180
Winsorized Mean ( 1 / 43 )75.47092307692316.6886141228412511.2834918700414
Winsorized Mean ( 2 / 43 )75.12307692307696.6084277941962111.3677684409374
Winsorized Mean ( 3 / 43 )75.03492307692316.589227016906911.3875152403151
Winsorized Mean ( 4 / 43 )75.02569230769236.5866165799928111.3906269473142
Winsorized Mean ( 5 / 43 )74.8249230769236.5426550489384311.4364768610357
Winsorized Mean ( 6 / 43 )74.43861538461546.4623361995703411.5188397950519
Winsorized Mean ( 7 / 43 )74.00623076923086.3752107519647111.608436747981
Winsorized Mean ( 8 / 43 )72.52007692307696.0968569901199411.8946658976251
Winsorized Mean ( 9 / 43 )72.10538461538466.0229242904418211.9718231772917
Winsorized Mean ( 10 / 43 )71.74384615384625.9617704719505912.0339832758393
Winsorized Mean ( 11 / 43 )71.61184615384625.9341775127098112.0676953125295
Winsorized Mean ( 12 / 43 )71.07646153846155.8419703271293212.1665221763267
Winsorized Mean ( 13 / 43 )70.91846153846155.8038515078456912.2192067530662
Winsorized Mean ( 14 / 43 )70.79784615384625.7826462920838812.2431569523394
Winsorized Mean ( 15 / 43 )70.78284615384625.7769384304761612.2526571826406
Winsorized Mean ( 16 / 43 )70.41238461538465.7146620782945512.3213557775927
Winsorized Mean ( 17 / 43 )70.02269230769235.6496125626798112.3942467790177
Winsorized Mean ( 18 / 43 )68.89561538461545.474750628339412.5842472217795
Winsorized Mean ( 19 / 43 )68.26861538461545.3779458815828312.6941804339100
Winsorized Mean ( 20 / 43 )68.1045.3451285280631612.7413213063892
Winsorized Mean ( 21 / 43 )68.01192307692315.3243650186172212.7737153330232
Winsorized Mean ( 22 / 43 )67.39084615384625.2204584648857312.9089900067467
Winsorized Mean ( 23 / 43 )66.62123076923085.1080721320830913.0423433825047
Winsorized Mean ( 24 / 43 )65.62615384615384.966392389025713.2140492948501
Winsorized Mean ( 25 / 43 )63.734.7070262810246113.5393337948662
Winsorized Mean ( 26 / 43 )63.5244.6782794002379313.5784964012131
Winsorized Mean ( 27 / 43 )62.72853846153854.5697379220634913.7269444181195
Winsorized Mean ( 28 / 43 )62.16207692307694.4955081745139413.8275973505037
Winsorized Mean ( 29 / 43 )62.0844.4807974064594913.8555695266428
Winsorized Mean ( 30 / 43 )61.27169230769234.3746068188785714.0062169800666
Winsorized Mean ( 31 / 43 )59.91723076923084.1947923801881714.2837178431565
Winsorized Mean ( 32 / 43 )59.72523076923084.1698837768179114.3229965068254
Winsorized Mean ( 33 / 43 )59.00176923076924.0756383836805914.4766938762331
Winsorized Mean ( 34 / 43 )58.82653846153854.0447666264877914.5438646759750
Winsorized Mean ( 35 / 43 )56.80730769230773.8053652858454314.9282140938243
Winsorized Mean ( 36 / 43 )55.1793.6084565947815115.2915792529690
Winsorized Mean ( 37 / 43 )54.51015384615383.5265841025184915.4569272308651
Winsorized Mean ( 38 / 43 )53.00769230769233.3509106791598215.8188914546009
Winsorized Mean ( 39 / 43 )51.00669230769233.1251764856801816.3212197907572
Winsorized Mean ( 40 / 43 )51.04976923076923.1063102095977916.4342148034788
Winsorized Mean ( 41 / 43 )50.77538461538463.0690961789169216.5440838785649
Winsorized Mean ( 42 / 43 )50.28430769230773.0179661886415616.6616537592628
Winsorized Mean ( 43 / 43 )50.22146153846152.9702630304443316.9080855882817
Trimmed Mean ( 1 / 43 )74.37781256.5716566545472111.3179699442354
Trimmed Mean ( 2 / 43 )73.256.4415348077430311.3715134958131
Trimmed Mean ( 3 / 43 )72.26814516129036.3435461588932811.3923889495113
Trimmed Mean ( 4 / 43 )71.28540983606566.2420615707794111.4201708886964
Trimmed Mean ( 5 / 43 )70.27241666666676.1294833954110311.4646556868524
Trimmed Mean ( 6 / 43 )69.26932203389836.0154515979605111.5152322158794
Trimmed Mean ( 7 / 43 )68.30379310344835.9067661449969211.5636528392617
Trimmed Mean ( 8 / 43 )67.37482456140355.8033364454395411.6096706084220
Trimmed Mean ( 9 / 43 )66.62830357142865.7404348367803711.6068391099094
Trimmed Mean ( 10 / 43 )65.90909090909095.6820200077582211.5995879667968
Trimmed Mean ( 11 / 43 )65.20675925925935.6255496971185711.5911800215112
Trimmed Mean ( 12 / 43 )64.4926415094345.5653593694464311.5882258859142
Trimmed Mean ( 13 / 43 )63.80682692307695.5102458376098411.5796697286294
Trimmed Mean ( 14 / 43 )63.10960784313735.4523293391637411.5747974704728
Trimmed Mean ( 15 / 43 )62.39575.3887020049433811.5789850585096
Trimmed Mean ( 16 / 43 )61.65397959183675.3162933080220211.5971742000773
Trimmed Mean ( 17 / 43 )60.91270833333335.2414776389349811.6212855475828
Trimmed Mean ( 18 / 43 )60.17159574468095.163983371166111.6521668293237
Trimmed Mean ( 19 / 43 )59.48673913043485.0976380877136211.6694708621646
Trimmed Mean ( 20 / 43 )58.81911111111115.0330835829707511.6864959902759
Trimmed Mean ( 21 / 43 )58.13329545454554.9619262371908211.715872561511
Trimmed Mean ( 22 / 43 )57.42220930232564.881439625290211.7633759116527
Trimmed Mean ( 23 / 43 )56.72095238095244.8009826686415911.8144463947839
Trimmed Mean ( 24 / 43 )56.03853658536594.7215557002019911.8686594299774
Trimmed Mean ( 25 / 43 )55.3893754.6469326392703511.9195562534982
Trimmed Mean ( 26 / 43 )54.83333333333334.5927153175691211.9391970853434
Trimmed Mean ( 27 / 43 )54.26157894736844.5313354913513111.9747432188445
Trimmed Mean ( 28 / 43 )53.71067567567574.4720297149735212.0103575107827
Trimmed Mean ( 29 / 43 )53.16569444444444.4103871997165612.0546546225831
Trimmed Mean ( 30 / 43 )52.59457142857144.3375973097751612.1252775839852
Trimmed Mean ( 31 / 43 )52.04161764705884.2646142454430812.2031242808579
Trimmed Mean ( 32 / 43 )51.54121212121214.2017010847237112.2667488909677
Trimmed Mean ( 33 / 43 )51.021718754.1278536939654412.3603505677998
Trimmed Mean ( 34 / 43 )50.51467741935484.0513529917631112.4685944478443
Trimmed Mean ( 35 / 43 )49.9853.9613627990867912.6181323284813
Trimmed Mean ( 36 / 43 )49.54810344827593.8895803808164512.7386757946047
Trimmed Mean ( 37 / 43 )49.1853.8315921972769712.8367001151518
Trimmed Mean ( 38 / 43 )48.83851851851853.7709061632348112.9514011763749
Trimmed Mean ( 39 / 43 )48.56423076923083.7225167185549513.0460745890439
Trimmed Mean ( 40 / 43 )48.40143.6961365047899413.095133239066
Trimmed Mean ( 41 / 43 )48.22208333333333.6610311054635113.1717218303252
Trimmed Mean ( 42 / 43 )48.04608695652173.6182684154719713.2787514467068
Trimmed Mean ( 43 / 43 )47.88863636363643.5684240602653213.4201080238417
Median42.16
Midrange154.025
Midmean - Weighted Average at Xnp50.4107692307692
Midmean - Weighted Average at X(n+1)p51.5412121212121
Midmean - Empirical Distribution Function51.5412121212121
Midmean - Empirical Distribution Function - Averaging51.5412121212121
Midmean - Empirical Distribution Function - Interpolation51.02171875
Midmean - Closest Observation51.5412121212121
Midmean - True Basic - Statistics Graphics Toolkit51.5412121212121
Midmean - MS Excel (old versions)51.5412121212121
Number of observations130

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 75.6031538461538 & 6.7218625753749 & 11.2473519055747 \tabularnewline
Geometric Mean & 40.1346925720332 &  &  \tabularnewline
Harmonic Mean & 21.4236384347145 &  &  \tabularnewline
Quadratic Mean & 107.445335765180 &  &  \tabularnewline
Winsorized Mean ( 1 / 43 ) & 75.4709230769231 & 6.68861412284125 & 11.2834918700414 \tabularnewline
Winsorized Mean ( 2 / 43 ) & 75.1230769230769 & 6.60842779419621 & 11.3677684409374 \tabularnewline
Winsorized Mean ( 3 / 43 ) & 75.0349230769231 & 6.5892270169069 & 11.3875152403151 \tabularnewline
Winsorized Mean ( 4 / 43 ) & 75.0256923076923 & 6.58661657999281 & 11.3906269473142 \tabularnewline
Winsorized Mean ( 5 / 43 ) & 74.824923076923 & 6.54265504893843 & 11.4364768610357 \tabularnewline
Winsorized Mean ( 6 / 43 ) & 74.4386153846154 & 6.46233619957034 & 11.5188397950519 \tabularnewline
Winsorized Mean ( 7 / 43 ) & 74.0062307692308 & 6.37521075196471 & 11.608436747981 \tabularnewline
Winsorized Mean ( 8 / 43 ) & 72.5200769230769 & 6.09685699011994 & 11.8946658976251 \tabularnewline
Winsorized Mean ( 9 / 43 ) & 72.1053846153846 & 6.02292429044182 & 11.9718231772917 \tabularnewline
Winsorized Mean ( 10 / 43 ) & 71.7438461538462 & 5.96177047195059 & 12.0339832758393 \tabularnewline
Winsorized Mean ( 11 / 43 ) & 71.6118461538462 & 5.93417751270981 & 12.0676953125295 \tabularnewline
Winsorized Mean ( 12 / 43 ) & 71.0764615384615 & 5.84197032712932 & 12.1665221763267 \tabularnewline
Winsorized Mean ( 13 / 43 ) & 70.9184615384615 & 5.80385150784569 & 12.2192067530662 \tabularnewline
Winsorized Mean ( 14 / 43 ) & 70.7978461538462 & 5.78264629208388 & 12.2431569523394 \tabularnewline
Winsorized Mean ( 15 / 43 ) & 70.7828461538462 & 5.77693843047616 & 12.2526571826406 \tabularnewline
Winsorized Mean ( 16 / 43 ) & 70.4123846153846 & 5.71466207829455 & 12.3213557775927 \tabularnewline
Winsorized Mean ( 17 / 43 ) & 70.0226923076923 & 5.64961256267981 & 12.3942467790177 \tabularnewline
Winsorized Mean ( 18 / 43 ) & 68.8956153846154 & 5.4747506283394 & 12.5842472217795 \tabularnewline
Winsorized Mean ( 19 / 43 ) & 68.2686153846154 & 5.37794588158283 & 12.6941804339100 \tabularnewline
Winsorized Mean ( 20 / 43 ) & 68.104 & 5.34512852806316 & 12.7413213063892 \tabularnewline
Winsorized Mean ( 21 / 43 ) & 68.0119230769231 & 5.32436501861722 & 12.7737153330232 \tabularnewline
Winsorized Mean ( 22 / 43 ) & 67.3908461538462 & 5.22045846488573 & 12.9089900067467 \tabularnewline
Winsorized Mean ( 23 / 43 ) & 66.6212307692308 & 5.10807213208309 & 13.0423433825047 \tabularnewline
Winsorized Mean ( 24 / 43 ) & 65.6261538461538 & 4.9663923890257 & 13.2140492948501 \tabularnewline
Winsorized Mean ( 25 / 43 ) & 63.73 & 4.70702628102461 & 13.5393337948662 \tabularnewline
Winsorized Mean ( 26 / 43 ) & 63.524 & 4.67827940023793 & 13.5784964012131 \tabularnewline
Winsorized Mean ( 27 / 43 ) & 62.7285384615385 & 4.56973792206349 & 13.7269444181195 \tabularnewline
Winsorized Mean ( 28 / 43 ) & 62.1620769230769 & 4.49550817451394 & 13.8275973505037 \tabularnewline
Winsorized Mean ( 29 / 43 ) & 62.084 & 4.48079740645949 & 13.8555695266428 \tabularnewline
Winsorized Mean ( 30 / 43 ) & 61.2716923076923 & 4.37460681887857 & 14.0062169800666 \tabularnewline
Winsorized Mean ( 31 / 43 ) & 59.9172307692308 & 4.19479238018817 & 14.2837178431565 \tabularnewline
Winsorized Mean ( 32 / 43 ) & 59.7252307692308 & 4.16988377681791 & 14.3229965068254 \tabularnewline
Winsorized Mean ( 33 / 43 ) & 59.0017692307692 & 4.07563838368059 & 14.4766938762331 \tabularnewline
Winsorized Mean ( 34 / 43 ) & 58.8265384615385 & 4.04476662648779 & 14.5438646759750 \tabularnewline
Winsorized Mean ( 35 / 43 ) & 56.8073076923077 & 3.80536528584543 & 14.9282140938243 \tabularnewline
Winsorized Mean ( 36 / 43 ) & 55.179 & 3.60845659478151 & 15.2915792529690 \tabularnewline
Winsorized Mean ( 37 / 43 ) & 54.5101538461538 & 3.52658410251849 & 15.4569272308651 \tabularnewline
Winsorized Mean ( 38 / 43 ) & 53.0076923076923 & 3.35091067915982 & 15.8188914546009 \tabularnewline
Winsorized Mean ( 39 / 43 ) & 51.0066923076923 & 3.12517648568018 & 16.3212197907572 \tabularnewline
Winsorized Mean ( 40 / 43 ) & 51.0497692307692 & 3.10631020959779 & 16.4342148034788 \tabularnewline
Winsorized Mean ( 41 / 43 ) & 50.7753846153846 & 3.06909617891692 & 16.5440838785649 \tabularnewline
Winsorized Mean ( 42 / 43 ) & 50.2843076923077 & 3.01796618864156 & 16.6616537592628 \tabularnewline
Winsorized Mean ( 43 / 43 ) & 50.2214615384615 & 2.97026303044433 & 16.9080855882817 \tabularnewline
Trimmed Mean ( 1 / 43 ) & 74.3778125 & 6.57165665454721 & 11.3179699442354 \tabularnewline
Trimmed Mean ( 2 / 43 ) & 73.25 & 6.44153480774303 & 11.3715134958131 \tabularnewline
Trimmed Mean ( 3 / 43 ) & 72.2681451612903 & 6.34354615889328 & 11.3923889495113 \tabularnewline
Trimmed Mean ( 4 / 43 ) & 71.2854098360656 & 6.24206157077941 & 11.4201708886964 \tabularnewline
Trimmed Mean ( 5 / 43 ) & 70.2724166666667 & 6.12948339541103 & 11.4646556868524 \tabularnewline
Trimmed Mean ( 6 / 43 ) & 69.2693220338983 & 6.01545159796051 & 11.5152322158794 \tabularnewline
Trimmed Mean ( 7 / 43 ) & 68.3037931034483 & 5.90676614499692 & 11.5636528392617 \tabularnewline
Trimmed Mean ( 8 / 43 ) & 67.3748245614035 & 5.80333644543954 & 11.6096706084220 \tabularnewline
Trimmed Mean ( 9 / 43 ) & 66.6283035714286 & 5.74043483678037 & 11.6068391099094 \tabularnewline
Trimmed Mean ( 10 / 43 ) & 65.9090909090909 & 5.68202000775822 & 11.5995879667968 \tabularnewline
Trimmed Mean ( 11 / 43 ) & 65.2067592592593 & 5.62554969711857 & 11.5911800215112 \tabularnewline
Trimmed Mean ( 12 / 43 ) & 64.492641509434 & 5.56535936944643 & 11.5882258859142 \tabularnewline
Trimmed Mean ( 13 / 43 ) & 63.8068269230769 & 5.51024583760984 & 11.5796697286294 \tabularnewline
Trimmed Mean ( 14 / 43 ) & 63.1096078431373 & 5.45232933916374 & 11.5747974704728 \tabularnewline
Trimmed Mean ( 15 / 43 ) & 62.3957 & 5.38870200494338 & 11.5789850585096 \tabularnewline
Trimmed Mean ( 16 / 43 ) & 61.6539795918367 & 5.31629330802202 & 11.5971742000773 \tabularnewline
Trimmed Mean ( 17 / 43 ) & 60.9127083333333 & 5.24147763893498 & 11.6212855475828 \tabularnewline
Trimmed Mean ( 18 / 43 ) & 60.1715957446809 & 5.1639833711661 & 11.6521668293237 \tabularnewline
Trimmed Mean ( 19 / 43 ) & 59.4867391304348 & 5.09763808771362 & 11.6694708621646 \tabularnewline
Trimmed Mean ( 20 / 43 ) & 58.8191111111111 & 5.03308358297075 & 11.6864959902759 \tabularnewline
Trimmed Mean ( 21 / 43 ) & 58.1332954545455 & 4.96192623719082 & 11.715872561511 \tabularnewline
Trimmed Mean ( 22 / 43 ) & 57.4222093023256 & 4.8814396252902 & 11.7633759116527 \tabularnewline
Trimmed Mean ( 23 / 43 ) & 56.7209523809524 & 4.80098266864159 & 11.8144463947839 \tabularnewline
Trimmed Mean ( 24 / 43 ) & 56.0385365853659 & 4.72155570020199 & 11.8686594299774 \tabularnewline
Trimmed Mean ( 25 / 43 ) & 55.389375 & 4.64693263927035 & 11.9195562534982 \tabularnewline
Trimmed Mean ( 26 / 43 ) & 54.8333333333333 & 4.59271531756912 & 11.9391970853434 \tabularnewline
Trimmed Mean ( 27 / 43 ) & 54.2615789473684 & 4.53133549135131 & 11.9747432188445 \tabularnewline
Trimmed Mean ( 28 / 43 ) & 53.7106756756757 & 4.47202971497352 & 12.0103575107827 \tabularnewline
Trimmed Mean ( 29 / 43 ) & 53.1656944444444 & 4.41038719971656 & 12.0546546225831 \tabularnewline
Trimmed Mean ( 30 / 43 ) & 52.5945714285714 & 4.33759730977516 & 12.1252775839852 \tabularnewline
Trimmed Mean ( 31 / 43 ) & 52.0416176470588 & 4.26461424544308 & 12.2031242808579 \tabularnewline
Trimmed Mean ( 32 / 43 ) & 51.5412121212121 & 4.20170108472371 & 12.2667488909677 \tabularnewline
Trimmed Mean ( 33 / 43 ) & 51.02171875 & 4.12785369396544 & 12.3603505677998 \tabularnewline
Trimmed Mean ( 34 / 43 ) & 50.5146774193548 & 4.05135299176311 & 12.4685944478443 \tabularnewline
Trimmed Mean ( 35 / 43 ) & 49.985 & 3.96136279908679 & 12.6181323284813 \tabularnewline
Trimmed Mean ( 36 / 43 ) & 49.5481034482759 & 3.88958038081645 & 12.7386757946047 \tabularnewline
Trimmed Mean ( 37 / 43 ) & 49.185 & 3.83159219727697 & 12.8367001151518 \tabularnewline
Trimmed Mean ( 38 / 43 ) & 48.8385185185185 & 3.77090616323481 & 12.9514011763749 \tabularnewline
Trimmed Mean ( 39 / 43 ) & 48.5642307692308 & 3.72251671855495 & 13.0460745890439 \tabularnewline
Trimmed Mean ( 40 / 43 ) & 48.4014 & 3.69613650478994 & 13.095133239066 \tabularnewline
Trimmed Mean ( 41 / 43 ) & 48.2220833333333 & 3.66103110546351 & 13.1717218303252 \tabularnewline
Trimmed Mean ( 42 / 43 ) & 48.0460869565217 & 3.61826841547197 & 13.2787514467068 \tabularnewline
Trimmed Mean ( 43 / 43 ) & 47.8886363636364 & 3.56842406026532 & 13.4201080238417 \tabularnewline
Median & 42.16 &  &  \tabularnewline
Midrange & 154.025 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 50.4107692307692 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 51.5412121212121 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 51.5412121212121 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 51.5412121212121 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 51.02171875 &  &  \tabularnewline
Midmean - Closest Observation & 51.5412121212121 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 51.5412121212121 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 51.5412121212121 &  &  \tabularnewline
Number of observations & 130 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=108058&T=1

[TABLE]
[ROW][C]Central Tendency - Ungrouped Data[/C][/ROW]
[ROW][C]Measure[/C][C]Value[/C][C]S.E.[/C][C]Value/S.E.[/C][/ROW]
[ROW][C]Arithmetic Mean[/C][C]75.6031538461538[/C][C]6.7218625753749[/C][C]11.2473519055747[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]40.1346925720332[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]21.4236384347145[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]107.445335765180[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 43 )[/C][C]75.4709230769231[/C][C]6.68861412284125[/C][C]11.2834918700414[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 43 )[/C][C]75.1230769230769[/C][C]6.60842779419621[/C][C]11.3677684409374[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 43 )[/C][C]75.0349230769231[/C][C]6.5892270169069[/C][C]11.3875152403151[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 43 )[/C][C]75.0256923076923[/C][C]6.58661657999281[/C][C]11.3906269473142[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 43 )[/C][C]74.824923076923[/C][C]6.54265504893843[/C][C]11.4364768610357[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 43 )[/C][C]74.4386153846154[/C][C]6.46233619957034[/C][C]11.5188397950519[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 43 )[/C][C]74.0062307692308[/C][C]6.37521075196471[/C][C]11.608436747981[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 43 )[/C][C]72.5200769230769[/C][C]6.09685699011994[/C][C]11.8946658976251[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 43 )[/C][C]72.1053846153846[/C][C]6.02292429044182[/C][C]11.9718231772917[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 43 )[/C][C]71.7438461538462[/C][C]5.96177047195059[/C][C]12.0339832758393[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 43 )[/C][C]71.6118461538462[/C][C]5.93417751270981[/C][C]12.0676953125295[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 43 )[/C][C]71.0764615384615[/C][C]5.84197032712932[/C][C]12.1665221763267[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 43 )[/C][C]70.9184615384615[/C][C]5.80385150784569[/C][C]12.2192067530662[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 43 )[/C][C]70.7978461538462[/C][C]5.78264629208388[/C][C]12.2431569523394[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 43 )[/C][C]70.7828461538462[/C][C]5.77693843047616[/C][C]12.2526571826406[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 43 )[/C][C]70.4123846153846[/C][C]5.71466207829455[/C][C]12.3213557775927[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 43 )[/C][C]70.0226923076923[/C][C]5.64961256267981[/C][C]12.3942467790177[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 43 )[/C][C]68.8956153846154[/C][C]5.4747506283394[/C][C]12.5842472217795[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 43 )[/C][C]68.2686153846154[/C][C]5.37794588158283[/C][C]12.6941804339100[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 43 )[/C][C]68.104[/C][C]5.34512852806316[/C][C]12.7413213063892[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 43 )[/C][C]68.0119230769231[/C][C]5.32436501861722[/C][C]12.7737153330232[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 43 )[/C][C]67.3908461538462[/C][C]5.22045846488573[/C][C]12.9089900067467[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 43 )[/C][C]66.6212307692308[/C][C]5.10807213208309[/C][C]13.0423433825047[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 43 )[/C][C]65.6261538461538[/C][C]4.9663923890257[/C][C]13.2140492948501[/C][/ROW]
[ROW][C]Winsorized Mean ( 25 / 43 )[/C][C]63.73[/C][C]4.70702628102461[/C][C]13.5393337948662[/C][/ROW]
[ROW][C]Winsorized Mean ( 26 / 43 )[/C][C]63.524[/C][C]4.67827940023793[/C][C]13.5784964012131[/C][/ROW]
[ROW][C]Winsorized Mean ( 27 / 43 )[/C][C]62.7285384615385[/C][C]4.56973792206349[/C][C]13.7269444181195[/C][/ROW]
[ROW][C]Winsorized Mean ( 28 / 43 )[/C][C]62.1620769230769[/C][C]4.49550817451394[/C][C]13.8275973505037[/C][/ROW]
[ROW][C]Winsorized Mean ( 29 / 43 )[/C][C]62.084[/C][C]4.48079740645949[/C][C]13.8555695266428[/C][/ROW]
[ROW][C]Winsorized Mean ( 30 / 43 )[/C][C]61.2716923076923[/C][C]4.37460681887857[/C][C]14.0062169800666[/C][/ROW]
[ROW][C]Winsorized Mean ( 31 / 43 )[/C][C]59.9172307692308[/C][C]4.19479238018817[/C][C]14.2837178431565[/C][/ROW]
[ROW][C]Winsorized Mean ( 32 / 43 )[/C][C]59.7252307692308[/C][C]4.16988377681791[/C][C]14.3229965068254[/C][/ROW]
[ROW][C]Winsorized Mean ( 33 / 43 )[/C][C]59.0017692307692[/C][C]4.07563838368059[/C][C]14.4766938762331[/C][/ROW]
[ROW][C]Winsorized Mean ( 34 / 43 )[/C][C]58.8265384615385[/C][C]4.04476662648779[/C][C]14.5438646759750[/C][/ROW]
[ROW][C]Winsorized Mean ( 35 / 43 )[/C][C]56.8073076923077[/C][C]3.80536528584543[/C][C]14.9282140938243[/C][/ROW]
[ROW][C]Winsorized Mean ( 36 / 43 )[/C][C]55.179[/C][C]3.60845659478151[/C][C]15.2915792529690[/C][/ROW]
[ROW][C]Winsorized Mean ( 37 / 43 )[/C][C]54.5101538461538[/C][C]3.52658410251849[/C][C]15.4569272308651[/C][/ROW]
[ROW][C]Winsorized Mean ( 38 / 43 )[/C][C]53.0076923076923[/C][C]3.35091067915982[/C][C]15.8188914546009[/C][/ROW]
[ROW][C]Winsorized Mean ( 39 / 43 )[/C][C]51.0066923076923[/C][C]3.12517648568018[/C][C]16.3212197907572[/C][/ROW]
[ROW][C]Winsorized Mean ( 40 / 43 )[/C][C]51.0497692307692[/C][C]3.10631020959779[/C][C]16.4342148034788[/C][/ROW]
[ROW][C]Winsorized Mean ( 41 / 43 )[/C][C]50.7753846153846[/C][C]3.06909617891692[/C][C]16.5440838785649[/C][/ROW]
[ROW][C]Winsorized Mean ( 42 / 43 )[/C][C]50.2843076923077[/C][C]3.01796618864156[/C][C]16.6616537592628[/C][/ROW]
[ROW][C]Winsorized Mean ( 43 / 43 )[/C][C]50.2214615384615[/C][C]2.97026303044433[/C][C]16.9080855882817[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 43 )[/C][C]74.3778125[/C][C]6.57165665454721[/C][C]11.3179699442354[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 43 )[/C][C]73.25[/C][C]6.44153480774303[/C][C]11.3715134958131[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 43 )[/C][C]72.2681451612903[/C][C]6.34354615889328[/C][C]11.3923889495113[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 43 )[/C][C]71.2854098360656[/C][C]6.24206157077941[/C][C]11.4201708886964[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 43 )[/C][C]70.2724166666667[/C][C]6.12948339541103[/C][C]11.4646556868524[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 43 )[/C][C]69.2693220338983[/C][C]6.01545159796051[/C][C]11.5152322158794[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 43 )[/C][C]68.3037931034483[/C][C]5.90676614499692[/C][C]11.5636528392617[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 43 )[/C][C]67.3748245614035[/C][C]5.80333644543954[/C][C]11.6096706084220[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 43 )[/C][C]66.6283035714286[/C][C]5.74043483678037[/C][C]11.6068391099094[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 43 )[/C][C]65.9090909090909[/C][C]5.68202000775822[/C][C]11.5995879667968[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 43 )[/C][C]65.2067592592593[/C][C]5.62554969711857[/C][C]11.5911800215112[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 43 )[/C][C]64.492641509434[/C][C]5.56535936944643[/C][C]11.5882258859142[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 43 )[/C][C]63.8068269230769[/C][C]5.51024583760984[/C][C]11.5796697286294[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 43 )[/C][C]63.1096078431373[/C][C]5.45232933916374[/C][C]11.5747974704728[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 43 )[/C][C]62.3957[/C][C]5.38870200494338[/C][C]11.5789850585096[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 43 )[/C][C]61.6539795918367[/C][C]5.31629330802202[/C][C]11.5971742000773[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 43 )[/C][C]60.9127083333333[/C][C]5.24147763893498[/C][C]11.6212855475828[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 43 )[/C][C]60.1715957446809[/C][C]5.1639833711661[/C][C]11.6521668293237[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 43 )[/C][C]59.4867391304348[/C][C]5.09763808771362[/C][C]11.6694708621646[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 43 )[/C][C]58.8191111111111[/C][C]5.03308358297075[/C][C]11.6864959902759[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 43 )[/C][C]58.1332954545455[/C][C]4.96192623719082[/C][C]11.715872561511[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 43 )[/C][C]57.4222093023256[/C][C]4.8814396252902[/C][C]11.7633759116527[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 43 )[/C][C]56.7209523809524[/C][C]4.80098266864159[/C][C]11.8144463947839[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 43 )[/C][C]56.0385365853659[/C][C]4.72155570020199[/C][C]11.8686594299774[/C][/ROW]
[ROW][C]Trimmed Mean ( 25 / 43 )[/C][C]55.389375[/C][C]4.64693263927035[/C][C]11.9195562534982[/C][/ROW]
[ROW][C]Trimmed Mean ( 26 / 43 )[/C][C]54.8333333333333[/C][C]4.59271531756912[/C][C]11.9391970853434[/C][/ROW]
[ROW][C]Trimmed Mean ( 27 / 43 )[/C][C]54.2615789473684[/C][C]4.53133549135131[/C][C]11.9747432188445[/C][/ROW]
[ROW][C]Trimmed Mean ( 28 / 43 )[/C][C]53.7106756756757[/C][C]4.47202971497352[/C][C]12.0103575107827[/C][/ROW]
[ROW][C]Trimmed Mean ( 29 / 43 )[/C][C]53.1656944444444[/C][C]4.41038719971656[/C][C]12.0546546225831[/C][/ROW]
[ROW][C]Trimmed Mean ( 30 / 43 )[/C][C]52.5945714285714[/C][C]4.33759730977516[/C][C]12.1252775839852[/C][/ROW]
[ROW][C]Trimmed Mean ( 31 / 43 )[/C][C]52.0416176470588[/C][C]4.26461424544308[/C][C]12.2031242808579[/C][/ROW]
[ROW][C]Trimmed Mean ( 32 / 43 )[/C][C]51.5412121212121[/C][C]4.20170108472371[/C][C]12.2667488909677[/C][/ROW]
[ROW][C]Trimmed Mean ( 33 / 43 )[/C][C]51.02171875[/C][C]4.12785369396544[/C][C]12.3603505677998[/C][/ROW]
[ROW][C]Trimmed Mean ( 34 / 43 )[/C][C]50.5146774193548[/C][C]4.05135299176311[/C][C]12.4685944478443[/C][/ROW]
[ROW][C]Trimmed Mean ( 35 / 43 )[/C][C]49.985[/C][C]3.96136279908679[/C][C]12.6181323284813[/C][/ROW]
[ROW][C]Trimmed Mean ( 36 / 43 )[/C][C]49.5481034482759[/C][C]3.88958038081645[/C][C]12.7386757946047[/C][/ROW]
[ROW][C]Trimmed Mean ( 37 / 43 )[/C][C]49.185[/C][C]3.83159219727697[/C][C]12.8367001151518[/C][/ROW]
[ROW][C]Trimmed Mean ( 38 / 43 )[/C][C]48.8385185185185[/C][C]3.77090616323481[/C][C]12.9514011763749[/C][/ROW]
[ROW][C]Trimmed Mean ( 39 / 43 )[/C][C]48.5642307692308[/C][C]3.72251671855495[/C][C]13.0460745890439[/C][/ROW]
[ROW][C]Trimmed Mean ( 40 / 43 )[/C][C]48.4014[/C][C]3.69613650478994[/C][C]13.095133239066[/C][/ROW]
[ROW][C]Trimmed Mean ( 41 / 43 )[/C][C]48.2220833333333[/C][C]3.66103110546351[/C][C]13.1717218303252[/C][/ROW]
[ROW][C]Trimmed Mean ( 42 / 43 )[/C][C]48.0460869565217[/C][C]3.61826841547197[/C][C]13.2787514467068[/C][/ROW]
[ROW][C]Trimmed Mean ( 43 / 43 )[/C][C]47.8886363636364[/C][C]3.56842406026532[/C][C]13.4201080238417[/C][/ROW]
[ROW][C]Median[/C][C]42.16[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]154.025[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]50.4107692307692[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]51.5412121212121[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]51.5412121212121[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]51.5412121212121[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]51.02171875[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]51.5412121212121[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]51.5412121212121[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]51.5412121212121[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]130[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=108058&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=108058&T=1

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean75.60315384615386.721862575374911.2473519055747
Geometric Mean40.1346925720332
Harmonic Mean21.4236384347145
Quadratic Mean107.445335765180
Winsorized Mean ( 1 / 43 )75.47092307692316.6886141228412511.2834918700414
Winsorized Mean ( 2 / 43 )75.12307692307696.6084277941962111.3677684409374
Winsorized Mean ( 3 / 43 )75.03492307692316.589227016906911.3875152403151
Winsorized Mean ( 4 / 43 )75.02569230769236.5866165799928111.3906269473142
Winsorized Mean ( 5 / 43 )74.8249230769236.5426550489384311.4364768610357
Winsorized Mean ( 6 / 43 )74.43861538461546.4623361995703411.5188397950519
Winsorized Mean ( 7 / 43 )74.00623076923086.3752107519647111.608436747981
Winsorized Mean ( 8 / 43 )72.52007692307696.0968569901199411.8946658976251
Winsorized Mean ( 9 / 43 )72.10538461538466.0229242904418211.9718231772917
Winsorized Mean ( 10 / 43 )71.74384615384625.9617704719505912.0339832758393
Winsorized Mean ( 11 / 43 )71.61184615384625.9341775127098112.0676953125295
Winsorized Mean ( 12 / 43 )71.07646153846155.8419703271293212.1665221763267
Winsorized Mean ( 13 / 43 )70.91846153846155.8038515078456912.2192067530662
Winsorized Mean ( 14 / 43 )70.79784615384625.7826462920838812.2431569523394
Winsorized Mean ( 15 / 43 )70.78284615384625.7769384304761612.2526571826406
Winsorized Mean ( 16 / 43 )70.41238461538465.7146620782945512.3213557775927
Winsorized Mean ( 17 / 43 )70.02269230769235.6496125626798112.3942467790177
Winsorized Mean ( 18 / 43 )68.89561538461545.474750628339412.5842472217795
Winsorized Mean ( 19 / 43 )68.26861538461545.3779458815828312.6941804339100
Winsorized Mean ( 20 / 43 )68.1045.3451285280631612.7413213063892
Winsorized Mean ( 21 / 43 )68.01192307692315.3243650186172212.7737153330232
Winsorized Mean ( 22 / 43 )67.39084615384625.2204584648857312.9089900067467
Winsorized Mean ( 23 / 43 )66.62123076923085.1080721320830913.0423433825047
Winsorized Mean ( 24 / 43 )65.62615384615384.966392389025713.2140492948501
Winsorized Mean ( 25 / 43 )63.734.7070262810246113.5393337948662
Winsorized Mean ( 26 / 43 )63.5244.6782794002379313.5784964012131
Winsorized Mean ( 27 / 43 )62.72853846153854.5697379220634913.7269444181195
Winsorized Mean ( 28 / 43 )62.16207692307694.4955081745139413.8275973505037
Winsorized Mean ( 29 / 43 )62.0844.4807974064594913.8555695266428
Winsorized Mean ( 30 / 43 )61.27169230769234.3746068188785714.0062169800666
Winsorized Mean ( 31 / 43 )59.91723076923084.1947923801881714.2837178431565
Winsorized Mean ( 32 / 43 )59.72523076923084.1698837768179114.3229965068254
Winsorized Mean ( 33 / 43 )59.00176923076924.0756383836805914.4766938762331
Winsorized Mean ( 34 / 43 )58.82653846153854.0447666264877914.5438646759750
Winsorized Mean ( 35 / 43 )56.80730769230773.8053652858454314.9282140938243
Winsorized Mean ( 36 / 43 )55.1793.6084565947815115.2915792529690
Winsorized Mean ( 37 / 43 )54.51015384615383.5265841025184915.4569272308651
Winsorized Mean ( 38 / 43 )53.00769230769233.3509106791598215.8188914546009
Winsorized Mean ( 39 / 43 )51.00669230769233.1251764856801816.3212197907572
Winsorized Mean ( 40 / 43 )51.04976923076923.1063102095977916.4342148034788
Winsorized Mean ( 41 / 43 )50.77538461538463.0690961789169216.5440838785649
Winsorized Mean ( 42 / 43 )50.28430769230773.0179661886415616.6616537592628
Winsorized Mean ( 43 / 43 )50.22146153846152.9702630304443316.9080855882817
Trimmed Mean ( 1 / 43 )74.37781256.5716566545472111.3179699442354
Trimmed Mean ( 2 / 43 )73.256.4415348077430311.3715134958131
Trimmed Mean ( 3 / 43 )72.26814516129036.3435461588932811.3923889495113
Trimmed Mean ( 4 / 43 )71.28540983606566.2420615707794111.4201708886964
Trimmed Mean ( 5 / 43 )70.27241666666676.1294833954110311.4646556868524
Trimmed Mean ( 6 / 43 )69.26932203389836.0154515979605111.5152322158794
Trimmed Mean ( 7 / 43 )68.30379310344835.9067661449969211.5636528392617
Trimmed Mean ( 8 / 43 )67.37482456140355.8033364454395411.6096706084220
Trimmed Mean ( 9 / 43 )66.62830357142865.7404348367803711.6068391099094
Trimmed Mean ( 10 / 43 )65.90909090909095.6820200077582211.5995879667968
Trimmed Mean ( 11 / 43 )65.20675925925935.6255496971185711.5911800215112
Trimmed Mean ( 12 / 43 )64.4926415094345.5653593694464311.5882258859142
Trimmed Mean ( 13 / 43 )63.80682692307695.5102458376098411.5796697286294
Trimmed Mean ( 14 / 43 )63.10960784313735.4523293391637411.5747974704728
Trimmed Mean ( 15 / 43 )62.39575.3887020049433811.5789850585096
Trimmed Mean ( 16 / 43 )61.65397959183675.3162933080220211.5971742000773
Trimmed Mean ( 17 / 43 )60.91270833333335.2414776389349811.6212855475828
Trimmed Mean ( 18 / 43 )60.17159574468095.163983371166111.6521668293237
Trimmed Mean ( 19 / 43 )59.48673913043485.0976380877136211.6694708621646
Trimmed Mean ( 20 / 43 )58.81911111111115.0330835829707511.6864959902759
Trimmed Mean ( 21 / 43 )58.13329545454554.9619262371908211.715872561511
Trimmed Mean ( 22 / 43 )57.42220930232564.881439625290211.7633759116527
Trimmed Mean ( 23 / 43 )56.72095238095244.8009826686415911.8144463947839
Trimmed Mean ( 24 / 43 )56.03853658536594.7215557002019911.8686594299774
Trimmed Mean ( 25 / 43 )55.3893754.6469326392703511.9195562534982
Trimmed Mean ( 26 / 43 )54.83333333333334.5927153175691211.9391970853434
Trimmed Mean ( 27 / 43 )54.26157894736844.5313354913513111.9747432188445
Trimmed Mean ( 28 / 43 )53.71067567567574.4720297149735212.0103575107827
Trimmed Mean ( 29 / 43 )53.16569444444444.4103871997165612.0546546225831
Trimmed Mean ( 30 / 43 )52.59457142857144.3375973097751612.1252775839852
Trimmed Mean ( 31 / 43 )52.04161764705884.2646142454430812.2031242808579
Trimmed Mean ( 32 / 43 )51.54121212121214.2017010847237112.2667488909677
Trimmed Mean ( 33 / 43 )51.021718754.1278536939654412.3603505677998
Trimmed Mean ( 34 / 43 )50.51467741935484.0513529917631112.4685944478443
Trimmed Mean ( 35 / 43 )49.9853.9613627990867912.6181323284813
Trimmed Mean ( 36 / 43 )49.54810344827593.8895803808164512.7386757946047
Trimmed Mean ( 37 / 43 )49.1853.8315921972769712.8367001151518
Trimmed Mean ( 38 / 43 )48.83851851851853.7709061632348112.9514011763749
Trimmed Mean ( 39 / 43 )48.56423076923083.7225167185549513.0460745890439
Trimmed Mean ( 40 / 43 )48.40143.6961365047899413.095133239066
Trimmed Mean ( 41 / 43 )48.22208333333333.6610311054635113.1717218303252
Trimmed Mean ( 42 / 43 )48.04608695652173.6182684154719713.2787514467068
Trimmed Mean ( 43 / 43 )47.88863636363643.5684240602653213.4201080238417
Median42.16
Midrange154.025
Midmean - Weighted Average at Xnp50.4107692307692
Midmean - Weighted Average at X(n+1)p51.5412121212121
Midmean - Empirical Distribution Function51.5412121212121
Midmean - Empirical Distribution Function - Averaging51.5412121212121
Midmean - Empirical Distribution Function - Interpolation51.02171875
Midmean - Closest Observation51.5412121212121
Midmean - True Basic - Statistics Graphics Toolkit51.5412121212121
Midmean - MS Excel (old versions)51.5412121212121
Number of observations130



Parameters (Session):
Parameters (R input):
R code (references can be found in the software module):
geomean <- function(x) {
return(exp(mean(log(x))))
}
harmean <- function(x) {
return(1/mean(1/x))
}
quamean <- function(x) {
return(sqrt(mean(x*x)))
}
winmean <- function(x) {
x <-sort(x[!is.na(x)])
n<-length(x)
denom <- 3
nodenom <- n/denom
if (nodenom>40) denom <- n/40
sqrtn = sqrt(n)
roundnodenom = floor(nodenom)
win <- array(NA,dim=c(roundnodenom,2))
for (j in 1:roundnodenom) {
win[j,1] <- (j*x[j+1]+sum(x[(j+1):(n-j)])+j*x[n-j])/n
win[j,2] <- sd(c(rep(x[j+1],j),x[(j+1):(n-j)],rep(x[n-j],j)))/sqrtn
}
return(win)
}
trimean <- function(x) {
x <-sort(x[!is.na(x)])
n<-length(x)
denom <- 3
nodenom <- n/denom
if (nodenom>40) denom <- n/40
sqrtn = sqrt(n)
roundnodenom = floor(nodenom)
tri <- array(NA,dim=c(roundnodenom,2))
for (j in 1:roundnodenom) {
tri[j,1] <- mean(x,trim=j/n)
tri[j,2] <- sd(x[(j+1):(n-j)]) / sqrt(n-j*2)
}
return(tri)
}
midrange <- function(x) {
return((max(x)+min(x))/2)
}
q1 <- function(data,n,p,i,f) {
np <- n*p;
i <<- floor(np)
f <<- np - i
qvalue <- (1-f)*data[i] + f*data[i+1]
}
q2 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
qvalue <- (1-f)*data[i] + f*data[i+1]
}
q3 <- function(data,n,p,i,f) {
np <- n*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
qvalue <- data[i+1]
}
}
q4 <- function(data,n,p,i,f) {
np <- n*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- (data[i]+data[i+1])/2
} else {
qvalue <- data[i+1]
}
}
q5 <- function(data,n,p,i,f) {
np <- (n-1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i+1]
} else {
qvalue <- data[i+1] + f*(data[i+2]-data[i+1])
}
}
q6 <- function(data,n,p,i,f) {
np <- n*p+0.5
i <<- floor(np)
f <<- np - i
qvalue <- data[i]
}
q7 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
qvalue <- f*data[i] + (1-f)*data[i+1]
}
}
q8 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
if (f == 0.5) {
qvalue <- (data[i]+data[i+1])/2
} else {
if (f < 0.5) {
qvalue <- data[i]
} else {
qvalue <- data[i+1]
}
}
}
}
midmean <- function(x,def) {
x <-sort(x[!is.na(x)])
n<-length(x)
if (def==1) {
qvalue1 <- q1(x,n,0.25,i,f)
qvalue3 <- q1(x,n,0.75,i,f)
}
if (def==2) {
qvalue1 <- q2(x,n,0.25,i,f)
qvalue3 <- q2(x,n,0.75,i,f)
}
if (def==3) {
qvalue1 <- q3(x,n,0.25,i,f)
qvalue3 <- q3(x,n,0.75,i,f)
}
if (def==4) {
qvalue1 <- q4(x,n,0.25,i,f)
qvalue3 <- q4(x,n,0.75,i,f)
}
if (def==5) {
qvalue1 <- q5(x,n,0.25,i,f)
qvalue3 <- q5(x,n,0.75,i,f)
}
if (def==6) {
qvalue1 <- q6(x,n,0.25,i,f)
qvalue3 <- q6(x,n,0.75,i,f)
}
if (def==7) {
qvalue1 <- q7(x,n,0.25,i,f)
qvalue3 <- q7(x,n,0.75,i,f)
}
if (def==8) {
qvalue1 <- q8(x,n,0.25,i,f)
qvalue3 <- q8(x,n,0.75,i,f)
}
midm <- 0
myn <- 0
roundno4 <- round(n/4)
round3no4 <- round(3*n/4)
for (i in 1:n) {
if ((x[i]>=qvalue1) & (x[i]<=qvalue3)){
midm = midm + x[i]
myn = myn + 1
}
}
midm = midm / myn
return(midm)
}
(arm <- mean(x))
sqrtn <- sqrt(length(x))
(armse <- sd(x) / sqrtn)
(armose <- arm / armse)
(geo <- geomean(x))
(har <- harmean(x))
(qua <- quamean(x))
(win <- winmean(x))
(tri <- trimean(x))
(midr <- midrange(x))
midm <- array(NA,dim=8)
for (j in 1:8) midm[j] <- midmean(x,j)
midm
bitmap(file='test1.png')
lb <- win[,1] - 2*win[,2]
ub <- win[,1] + 2*win[,2]
if ((ylimmin == '') | (ylimmax == '')) plot(win[,1],type='b',main=main, xlab='j', pch=19, ylab='Winsorized Mean(j/n)', ylim=c(min(lb),max(ub))) else plot(win[,1],type='l',main=main, xlab='j', pch=19, ylab='Winsorized Mean(j/n)', ylim=c(ylimmin,ylimmax))
lines(ub,lty=3)
lines(lb,lty=3)
grid()
dev.off()
bitmap(file='test2.png')
lb <- tri[,1] - 2*tri[,2]
ub <- tri[,1] + 2*tri[,2]
if ((ylimmin == '') | (ylimmax == '')) plot(tri[,1],type='b',main=main, xlab='j', pch=19, ylab='Trimmed Mean(j/n)', ylim=c(min(lb),max(ub))) else plot(tri[,1],type='l',main=main, xlab='j', pch=19, ylab='Trimmed Mean(j/n)', ylim=c(ylimmin,ylimmax))
lines(ub,lty=3)
lines(lb,lty=3)
grid()
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Central Tendency - Ungrouped Data',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Measure',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.element(a,'S.E.',header=TRUE)
a<-table.element(a,'Value/S.E.',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('arithmetic_mean.htm', 'Arithmetic Mean', 'click to view the definition of the Arithmetic Mean'),header=TRUE)
a<-table.element(a,arm)
a<-table.element(a,hyperlink('arithmetic_mean_standard_error.htm', armse, 'click to view the definition of the Standard Error of the Arithmetic Mean'))
a<-table.element(a,armose)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('geometric_mean.htm', 'Geometric Mean', 'click to view the definition of the Geometric Mean'),header=TRUE)
a<-table.element(a,geo)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('harmonic_mean.htm', 'Harmonic Mean', 'click to view the definition of the Harmonic Mean'),header=TRUE)
a<-table.element(a,har)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('quadratic_mean.htm', 'Quadratic Mean', 'click to view the definition of the Quadratic Mean'),header=TRUE)
a<-table.element(a,qua)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
for (j in 1:length(win[,1])) {
a<-table.row.start(a)
mylabel <- paste('Winsorized Mean (',j)
mylabel <- paste(mylabel,'/')
mylabel <- paste(mylabel,length(win[,1]))
mylabel <- paste(mylabel,')')
a<-table.element(a,hyperlink('winsorized_mean.htm', mylabel, 'click to view the definition of the Winsorized Mean'),header=TRUE)
a<-table.element(a,win[j,1])
a<-table.element(a,win[j,2])
a<-table.element(a,win[j,1]/win[j,2])
a<-table.row.end(a)
}
for (j in 1:length(tri[,1])) {
a<-table.row.start(a)
mylabel <- paste('Trimmed Mean (',j)
mylabel <- paste(mylabel,'/')
mylabel <- paste(mylabel,length(tri[,1]))
mylabel <- paste(mylabel,')')
a<-table.element(a,hyperlink('arithmetic_mean.htm', mylabel, 'click to view the definition of the Trimmed Mean'),header=TRUE)
a<-table.element(a,tri[j,1])
a<-table.element(a,tri[j,2])
a<-table.element(a,tri[j,1]/tri[j,2])
a<-table.row.end(a)
}
a<-table.row.start(a)
a<-table.element(a,hyperlink('median_1.htm', 'Median', 'click to view the definition of the Median'),header=TRUE)
a<-table.element(a,median(x))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('midrange.htm', 'Midrange', 'click to view the definition of the Midrange'),header=TRUE)
a<-table.element(a,midr)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_1.htm','Weighted Average at Xnp',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[1])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_2.htm','Weighted Average at X(n+1)p',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[2])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_3.htm','Empirical Distribution Function',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[3])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_4.htm','Empirical Distribution Function - Averaging',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[4])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_5.htm','Empirical Distribution Function - Interpolation',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[5])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_6.htm','Closest Observation',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[6])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_7.htm','True Basic - Statistics Graphics Toolkit',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[7])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_8.htm','MS Excel (old versions)',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[8])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Number of observations',header=TRUE)
a<-table.element(a,length(x))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')