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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationSat, 11 Oct 2014 11:46:26 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2014/Oct/11/t1413024427z912f1125rtqzjw.htm/, Retrieved Tue, 14 May 2024 06:41:01 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=240384, Retrieved Tue, 14 May 2024 06:41:01 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact121
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Centrummaten Leve...] [2014-10-11 10:46:26] [8bdab0fd537d5455eaa21dec7dfb1324] [Current]
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Dataseries X:
15071
14236
14771
14804
15597
15418
16903
16350
16393
15685
14556
14850
15391
13704
15409
15098
15254
15522
16669
16238
16246
15424
14952
15008
14929
13905
14994
14753
15031
15386
16160
16116
16219
16064
15436
15404
15112
14119
14775
14289
15121
15371
15782
16104
15674
15105
14223
14385
14558
13804
14672
14244
15089
14580
15218
15696
15129
15110
14204
13655
14534
12746
14074
13699
14184
14110
15820
15362
14993
14437
13694
13688




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net

\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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=240384&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]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=240384&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=240384&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 time1 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean15018.138888888997.6618421342711153.776936423553
Geometric Mean14995.444257164
Harmonic Mean14972.5877739339
Quadratic Mean15040.6676048638
Winsorized Mean ( 1 / 24 )15027.513888888993.4255706055868160.850116209943
Winsorized Mean ( 2 / 24 )15020.763888888991.4766885247218164.20318805954
Winsorized Mean ( 3 / 24 )15019.222222222291.0517192583377164.952648281234
Winsorized Mean ( 4 / 24 )15013.722222222289.8415994834215167.113256092382
Winsorized Mean ( 5 / 24 )15013.513888888989.6630123717714167.443781909067
Winsorized Mean ( 6 / 24 )15020.263888888987.6867378999975171.294590819638
Winsorized Mean ( 7 / 24 )15024.347222222284.719231953566177.342816687207
Winsorized Mean ( 8 / 24 )15038.236111111180.460428004028186.902263437603
Winsorized Mean ( 9 / 24 )15041.236111111179.426207849618189.373715783958
Winsorized Mean ( 10 / 24 )15036.930555555678.1821143689169192.332104048772
Winsorized Mean ( 11 / 24 )15009.583333333370.0273581402756214.338848871991
Winsorized Mean ( 12 / 24 )15006.583333333368.4538664143491219.221851436396
Winsorized Mean ( 13 / 24 )14994.486111111165.4741942052687229.013679253566
Winsorized Mean ( 14 / 24 )14994.87564.7337780886144231.639113964172
Winsorized Mean ( 15 / 24 )14994.2564.1156853445298233.862430377644
Winsorized Mean ( 16 / 24 )14987.138888888959.9668606498243249.923686624286
Winsorized Mean ( 17 / 24 )14992.097222222253.8057355956585278.633812106676
Winsorized Mean ( 18 / 24 )14983.597222222248.8503698099027306.724335568588
Winsorized Mean ( 19 / 24 )15006.027777777844.500562551271337.209844493284
Winsorized Mean ( 20 / 24 )15010.472222222243.3725309004058346.082460732808
Winsorized Mean ( 21 / 24 )15008.430555555642.9402486666206349.518948343266
Winsorized Mean ( 22 / 24 )15013.62541.7509731011201359.599402956124
Winsorized Mean ( 23 / 24 )15038.861111111136.9914938915273406.549169255251
Winsorized Mean ( 24 / 24 )15064.194444444433.0862239539016455.301108565096
Trimmed Mean ( 1 / 24 )15023.671428571491.0485905842723165.007182781878
Trimmed Mean ( 2 / 24 )15019.602941176588.2202107937631170.251270157227
Trimmed Mean ( 3 / 24 )15018.969696969786.0950983113364174.446280816804
Trimmed Mean ( 4 / 24 )15018.87583.7369141044149179.357875324524
Trimmed Mean ( 5 / 24 )15020.370967741981.342221336181184.65651319828
Trimmed Mean ( 6 / 24 )15022.016666666778.4889120661371191.390303053362
Trimmed Mean ( 7 / 24 )15022.379310344875.59376107592198.725120916495
Trimmed Mean ( 8 / 24 )15022.017857142972.8571297666782206.184595869343
Trimmed Mean ( 9 / 24 )15019.314814814870.5702232599078212.827933950261
Trimmed Mean ( 10 / 24 )15015.942307692367.9622067668019220.945478701367
Trimmed Mean ( 11 / 24 )15012.9264.9829920605604231.02845104468
Trimmed Mean ( 12 / 24 )15013.37563.1871349979988237.601768152259
Trimmed Mean ( 13 / 24 )15014.260869565261.2330184270193245.198771108434
Trimmed Mean ( 14 / 24 )15016.7559.3761357964137252.908846265927
Trimmed Mean ( 15 / 24 )15019.428571428657.0971434453021263.050437642592
Trimmed Mean ( 16 / 24 )15022.4554.2060758019445277.135907326852
Trimmed Mean ( 17 / 24 )15026.631578947451.4029685845743292.330034484755
Trimmed Mean ( 18 / 24 )15030.694444444449.2591917044132305.134816962452
Trimmed Mean ( 19 / 24 )15036.235294117647.5754407730273316.050362325647
Trimmed Mean ( 20 / 24 )15039.812546.408825753976324.072248234195
Trimmed Mean ( 21 / 24 )15043.333333333344.9658448498984334.550221029981
Trimmed Mean ( 22 / 24 )15047.607142857142.8684569501278351.018166116014
Trimmed Mean ( 23 / 24 )15051.884615384640.0606588878983375.727335326768
Trimmed Mean ( 24 / 24 )15053.583333333337.6813449340472399.496975484322
Median15080
Midrange14824.5
Midmean - Weighted Average at Xnp15013.2432432432
Midmean - Weighted Average at X(n+1)p15030.6944444444
Midmean - Empirical Distribution Function15013.2432432432
Midmean - Empirical Distribution Function - Averaging15030.6944444444
Midmean - Empirical Distribution Function - Interpolation15030.6944444444
Midmean - Closest Observation15013.2432432432
Midmean - True Basic - Statistics Graphics Toolkit15030.6944444444
Midmean - MS Excel (old versions)15026.6315789474
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 15018.1388888889 & 97.6618421342711 & 153.776936423553 \tabularnewline
Geometric Mean & 14995.444257164 &  &  \tabularnewline
Harmonic Mean & 14972.5877739339 &  &  \tabularnewline
Quadratic Mean & 15040.6676048638 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 15027.5138888889 & 93.4255706055868 & 160.850116209943 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 15020.7638888889 & 91.4766885247218 & 164.20318805954 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 15019.2222222222 & 91.0517192583377 & 164.952648281234 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 15013.7222222222 & 89.8415994834215 & 167.113256092382 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 15013.5138888889 & 89.6630123717714 & 167.443781909067 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 15020.2638888889 & 87.6867378999975 & 171.294590819638 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 15024.3472222222 & 84.719231953566 & 177.342816687207 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 15038.2361111111 & 80.460428004028 & 186.902263437603 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 15041.2361111111 & 79.426207849618 & 189.373715783958 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 15036.9305555556 & 78.1821143689169 & 192.332104048772 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 15009.5833333333 & 70.0273581402756 & 214.338848871991 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 15006.5833333333 & 68.4538664143491 & 219.221851436396 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 14994.4861111111 & 65.4741942052687 & 229.013679253566 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 14994.875 & 64.7337780886144 & 231.639113964172 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 14994.25 & 64.1156853445298 & 233.862430377644 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 14987.1388888889 & 59.9668606498243 & 249.923686624286 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 14992.0972222222 & 53.8057355956585 & 278.633812106676 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 14983.5972222222 & 48.8503698099027 & 306.724335568588 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 15006.0277777778 & 44.500562551271 & 337.209844493284 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 15010.4722222222 & 43.3725309004058 & 346.082460732808 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 15008.4305555556 & 42.9402486666206 & 349.518948343266 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 15013.625 & 41.7509731011201 & 359.599402956124 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 15038.8611111111 & 36.9914938915273 & 406.549169255251 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 15064.1944444444 & 33.0862239539016 & 455.301108565096 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 15023.6714285714 & 91.0485905842723 & 165.007182781878 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 15019.6029411765 & 88.2202107937631 & 170.251270157227 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 15018.9696969697 & 86.0950983113364 & 174.446280816804 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 15018.875 & 83.7369141044149 & 179.357875324524 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 15020.3709677419 & 81.342221336181 & 184.65651319828 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 15022.0166666667 & 78.4889120661371 & 191.390303053362 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 15022.3793103448 & 75.59376107592 & 198.725120916495 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 15022.0178571429 & 72.8571297666782 & 206.184595869343 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 15019.3148148148 & 70.5702232599078 & 212.827933950261 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 15015.9423076923 & 67.9622067668019 & 220.945478701367 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 15012.92 & 64.9829920605604 & 231.02845104468 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 15013.375 & 63.1871349979988 & 237.601768152259 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 15014.2608695652 & 61.2330184270193 & 245.198771108434 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 15016.75 & 59.3761357964137 & 252.908846265927 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 15019.4285714286 & 57.0971434453021 & 263.050437642592 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 15022.45 & 54.2060758019445 & 277.135907326852 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 15026.6315789474 & 51.4029685845743 & 292.330034484755 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 15030.6944444444 & 49.2591917044132 & 305.134816962452 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 15036.2352941176 & 47.5754407730273 & 316.050362325647 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 15039.8125 & 46.408825753976 & 324.072248234195 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 15043.3333333333 & 44.9658448498984 & 334.550221029981 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 15047.6071428571 & 42.8684569501278 & 351.018166116014 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 15051.8846153846 & 40.0606588878983 & 375.727335326768 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 15053.5833333333 & 37.6813449340472 & 399.496975484322 \tabularnewline
Median & 15080 &  &  \tabularnewline
Midrange & 14824.5 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 15013.2432432432 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 15030.6944444444 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 15013.2432432432 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 15030.6944444444 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 15030.6944444444 &  &  \tabularnewline
Midmean - Closest Observation & 15013.2432432432 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 15030.6944444444 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 15026.6315789474 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=240384&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]15018.1388888889[/C][C]97.6618421342711[/C][C]153.776936423553[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]14995.444257164[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]14972.5877739339[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]15040.6676048638[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]15027.5138888889[/C][C]93.4255706055868[/C][C]160.850116209943[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]15020.7638888889[/C][C]91.4766885247218[/C][C]164.20318805954[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]15019.2222222222[/C][C]91.0517192583377[/C][C]164.952648281234[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]15013.7222222222[/C][C]89.8415994834215[/C][C]167.113256092382[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]15013.5138888889[/C][C]89.6630123717714[/C][C]167.443781909067[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]15020.2638888889[/C][C]87.6867378999975[/C][C]171.294590819638[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]15024.3472222222[/C][C]84.719231953566[/C][C]177.342816687207[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]15038.2361111111[/C][C]80.460428004028[/C][C]186.902263437603[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]15041.2361111111[/C][C]79.426207849618[/C][C]189.373715783958[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]15036.9305555556[/C][C]78.1821143689169[/C][C]192.332104048772[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]15009.5833333333[/C][C]70.0273581402756[/C][C]214.338848871991[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]15006.5833333333[/C][C]68.4538664143491[/C][C]219.221851436396[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]14994.4861111111[/C][C]65.4741942052687[/C][C]229.013679253566[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]14994.875[/C][C]64.7337780886144[/C][C]231.639113964172[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]14994.25[/C][C]64.1156853445298[/C][C]233.862430377644[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]14987.1388888889[/C][C]59.9668606498243[/C][C]249.923686624286[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]14992.0972222222[/C][C]53.8057355956585[/C][C]278.633812106676[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]14983.5972222222[/C][C]48.8503698099027[/C][C]306.724335568588[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]15006.0277777778[/C][C]44.500562551271[/C][C]337.209844493284[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]15010.4722222222[/C][C]43.3725309004058[/C][C]346.082460732808[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]15008.4305555556[/C][C]42.9402486666206[/C][C]349.518948343266[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]15013.625[/C][C]41.7509731011201[/C][C]359.599402956124[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]15038.8611111111[/C][C]36.9914938915273[/C][C]406.549169255251[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]15064.1944444444[/C][C]33.0862239539016[/C][C]455.301108565096[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]15023.6714285714[/C][C]91.0485905842723[/C][C]165.007182781878[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]15019.6029411765[/C][C]88.2202107937631[/C][C]170.251270157227[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]15018.9696969697[/C][C]86.0950983113364[/C][C]174.446280816804[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]15018.875[/C][C]83.7369141044149[/C][C]179.357875324524[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]15020.3709677419[/C][C]81.342221336181[/C][C]184.65651319828[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]15022.0166666667[/C][C]78.4889120661371[/C][C]191.390303053362[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]15022.3793103448[/C][C]75.59376107592[/C][C]198.725120916495[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]15022.0178571429[/C][C]72.8571297666782[/C][C]206.184595869343[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]15019.3148148148[/C][C]70.5702232599078[/C][C]212.827933950261[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]15015.9423076923[/C][C]67.9622067668019[/C][C]220.945478701367[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]15012.92[/C][C]64.9829920605604[/C][C]231.02845104468[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]15013.375[/C][C]63.1871349979988[/C][C]237.601768152259[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]15014.2608695652[/C][C]61.2330184270193[/C][C]245.198771108434[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]15016.75[/C][C]59.3761357964137[/C][C]252.908846265927[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]15019.4285714286[/C][C]57.0971434453021[/C][C]263.050437642592[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]15022.45[/C][C]54.2060758019445[/C][C]277.135907326852[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]15026.6315789474[/C][C]51.4029685845743[/C][C]292.330034484755[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]15030.6944444444[/C][C]49.2591917044132[/C][C]305.134816962452[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]15036.2352941176[/C][C]47.5754407730273[/C][C]316.050362325647[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]15039.8125[/C][C]46.408825753976[/C][C]324.072248234195[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]15043.3333333333[/C][C]44.9658448498984[/C][C]334.550221029981[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]15047.6071428571[/C][C]42.8684569501278[/C][C]351.018166116014[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]15051.8846153846[/C][C]40.0606588878983[/C][C]375.727335326768[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]15053.5833333333[/C][C]37.6813449340472[/C][C]399.496975484322[/C][/ROW]
[ROW][C]Median[/C][C]15080[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]14824.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]15013.2432432432[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]15030.6944444444[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]15013.2432432432[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]15030.6944444444[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]15030.6944444444[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]15013.2432432432[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]15030.6944444444[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]15026.6315789474[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]72[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=240384&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=240384&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 Mean15018.138888888997.6618421342711153.776936423553
Geometric Mean14995.444257164
Harmonic Mean14972.5877739339
Quadratic Mean15040.6676048638
Winsorized Mean ( 1 / 24 )15027.513888888993.4255706055868160.850116209943
Winsorized Mean ( 2 / 24 )15020.763888888991.4766885247218164.20318805954
Winsorized Mean ( 3 / 24 )15019.222222222291.0517192583377164.952648281234
Winsorized Mean ( 4 / 24 )15013.722222222289.8415994834215167.113256092382
Winsorized Mean ( 5 / 24 )15013.513888888989.6630123717714167.443781909067
Winsorized Mean ( 6 / 24 )15020.263888888987.6867378999975171.294590819638
Winsorized Mean ( 7 / 24 )15024.347222222284.719231953566177.342816687207
Winsorized Mean ( 8 / 24 )15038.236111111180.460428004028186.902263437603
Winsorized Mean ( 9 / 24 )15041.236111111179.426207849618189.373715783958
Winsorized Mean ( 10 / 24 )15036.930555555678.1821143689169192.332104048772
Winsorized Mean ( 11 / 24 )15009.583333333370.0273581402756214.338848871991
Winsorized Mean ( 12 / 24 )15006.583333333368.4538664143491219.221851436396
Winsorized Mean ( 13 / 24 )14994.486111111165.4741942052687229.013679253566
Winsorized Mean ( 14 / 24 )14994.87564.7337780886144231.639113964172
Winsorized Mean ( 15 / 24 )14994.2564.1156853445298233.862430377644
Winsorized Mean ( 16 / 24 )14987.138888888959.9668606498243249.923686624286
Winsorized Mean ( 17 / 24 )14992.097222222253.8057355956585278.633812106676
Winsorized Mean ( 18 / 24 )14983.597222222248.8503698099027306.724335568588
Winsorized Mean ( 19 / 24 )15006.027777777844.500562551271337.209844493284
Winsorized Mean ( 20 / 24 )15010.472222222243.3725309004058346.082460732808
Winsorized Mean ( 21 / 24 )15008.430555555642.9402486666206349.518948343266
Winsorized Mean ( 22 / 24 )15013.62541.7509731011201359.599402956124
Winsorized Mean ( 23 / 24 )15038.861111111136.9914938915273406.549169255251
Winsorized Mean ( 24 / 24 )15064.194444444433.0862239539016455.301108565096
Trimmed Mean ( 1 / 24 )15023.671428571491.0485905842723165.007182781878
Trimmed Mean ( 2 / 24 )15019.602941176588.2202107937631170.251270157227
Trimmed Mean ( 3 / 24 )15018.969696969786.0950983113364174.446280816804
Trimmed Mean ( 4 / 24 )15018.87583.7369141044149179.357875324524
Trimmed Mean ( 5 / 24 )15020.370967741981.342221336181184.65651319828
Trimmed Mean ( 6 / 24 )15022.016666666778.4889120661371191.390303053362
Trimmed Mean ( 7 / 24 )15022.379310344875.59376107592198.725120916495
Trimmed Mean ( 8 / 24 )15022.017857142972.8571297666782206.184595869343
Trimmed Mean ( 9 / 24 )15019.314814814870.5702232599078212.827933950261
Trimmed Mean ( 10 / 24 )15015.942307692367.9622067668019220.945478701367
Trimmed Mean ( 11 / 24 )15012.9264.9829920605604231.02845104468
Trimmed Mean ( 12 / 24 )15013.37563.1871349979988237.601768152259
Trimmed Mean ( 13 / 24 )15014.260869565261.2330184270193245.198771108434
Trimmed Mean ( 14 / 24 )15016.7559.3761357964137252.908846265927
Trimmed Mean ( 15 / 24 )15019.428571428657.0971434453021263.050437642592
Trimmed Mean ( 16 / 24 )15022.4554.2060758019445277.135907326852
Trimmed Mean ( 17 / 24 )15026.631578947451.4029685845743292.330034484755
Trimmed Mean ( 18 / 24 )15030.694444444449.2591917044132305.134816962452
Trimmed Mean ( 19 / 24 )15036.235294117647.5754407730273316.050362325647
Trimmed Mean ( 20 / 24 )15039.812546.408825753976324.072248234195
Trimmed Mean ( 21 / 24 )15043.333333333344.9658448498984334.550221029981
Trimmed Mean ( 22 / 24 )15047.607142857142.8684569501278351.018166116014
Trimmed Mean ( 23 / 24 )15051.884615384640.0606588878983375.727335326768
Trimmed Mean ( 24 / 24 )15053.583333333337.6813449340472399.496975484322
Median15080
Midrange14824.5
Midmean - Weighted Average at Xnp15013.2432432432
Midmean - Weighted Average at X(n+1)p15030.6944444444
Midmean - Empirical Distribution Function15013.2432432432
Midmean - Empirical Distribution Function - Averaging15030.6944444444
Midmean - Empirical Distribution Function - Interpolation15030.6944444444
Midmean - Closest Observation15013.2432432432
Midmean - True Basic - Statistics Graphics Toolkit15030.6944444444
Midmean - MS Excel (old versions)15026.6315789474
Number of observations72



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')