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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 computationThu, 26 Feb 2015 16:46:48 +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/2015/Feb/26/t14249692625aox4v69x3iu30o.htm/, Retrieved Wed, 22 May 2024 05:27:03 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=277641, Retrieved Wed, 22 May 2024 05:27:03 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact74
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [eigen reeks de ce...] [2015-02-26 16:46:48] [24a1c9f91cd9dd71c8b0e9e460386711] [Current]
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Dataseries X:
12,8
12,1
11,4
11,4
10,6
10,4
10,9
11,6
13,3
15,2
17,4
19,1
19,9
19,4
18,2
15,8
13,5
12,1
10,3
8,8
8,2
6,8
5,9
4,9
3,9
3,6
2,8
4
4,2
4,2
4,8
4
3,8
4
3,7
4
4,6
4,6
4,6
4,5
4,1
4,1
4,4
4,2
4,4
3,2
2,8
1,7
-0,2
-2,9
-5,2
-5,3
-4,8
-2,2
-0,8
-1,1
-1,5
-2
-2,8
-3,4
-4,1
-5,5
-8,6
-7,6
-8,6
-8,7
-4,6
-4,3
-1,5
1,2
1,8
0





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net
R Framework error message
Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.

\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 & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
R Framework error message & 
Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.
\tabularnewline \hline \end{tabular} %Source: https://freestatistics.org/blog/index.php?pk=277641&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]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[ROW][C]R Framework error message[/C][C]
Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.
[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=277641&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=277641&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'Herman Ole Andreas Wold' @ wold.wessa.net
R Framework error message
Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean4.326388888888890.8490005932033315.09586085513222
Geometric MeanNaN
Harmonic Mean0
Quadratic Mean8.36029804093929
Winsorized Mean ( 1 / 24 )4.320833333333330.8469334758986745.10173875078977
Winsorized Mean ( 2 / 24 )4.31250.8448614296377345.10438735716595
Winsorized Mean ( 3 / 24 )4.316666666666670.8270892831587895.21910603191546
Winsorized Mean ( 4 / 24 )4.388888888888890.7946135062023945.52330013853427
Winsorized Mean ( 5 / 24 )4.291666666666670.7676120676389715.59093173178871
Winsorized Mean ( 6 / 24 )4.250.7557629398715285.62345647793004
Winsorized Mean ( 7 / 24 )4.123611111111110.7167962898813165.7528354559339
Winsorized Mean ( 8 / 24 )4.123611111111110.708848868056335.81733469141044
Winsorized Mean ( 9 / 24 )4.098611111111110.6911481824301565.93014814377421
Winsorized Mean ( 10 / 24 )4.029166666666670.6695169044675146.01802081438284
Winsorized Mean ( 11 / 24 )4.136111111111110.6516570474523776.34706726073331
Winsorized Mean ( 12 / 24 )4.136111111111110.6240557986980936.62779052728919
Winsorized Mean ( 13 / 24 )4.118055555555560.6151399906478566.69450144383961
Winsorized Mean ( 14 / 24 )4.234722222222220.5970393822457247.09286916098163
Winsorized Mean ( 15 / 24 )4.172222222222220.5733014724681977.2775362049217
Winsorized Mean ( 16 / 24 )4.216666666666670.5456722605762937.72747117878666
Winsorized Mean ( 17 / 24 )4.169444444444450.5379300110129497.75090506029432
Winsorized Mean ( 18 / 24 )4.244444444444440.5191628662808218.17555476348067
Winsorized Mean ( 19 / 24 )3.927777777777780.4442698209375268.84097364410018
Winsorized Mean ( 20 / 24 )3.927777777777780.3938554971929449.97263667962369
Winsorized Mean ( 21 / 24 )3.577777777777780.32509913151815511.005190204816
Winsorized Mean ( 22 / 24 )3.669444444444450.2309539894907515.8882054929448
Winsorized Mean ( 23 / 24 )3.509722222222220.16559703388037321.1943543913814
Winsorized Mean ( 24 / 24 )3.509722222222220.15656174343661222.4174957763115
Trimmed Mean ( 1 / 24 )4.290.823116206774645.21190077985495
Trimmed Mean ( 2 / 24 )4.257352941176470.7947763949029655.35666757150765
Trimmed Mean ( 3 / 24 )4.227272727272730.7621908841255155.54621265527573
Trimmed Mean ( 4 / 24 )4.193750.73141956384355.73371318913384
Trimmed Mean ( 5 / 24 )4.137096774193550.7066288603107365.85469545126459
Trimmed Mean ( 6 / 24 )4.10.6854583191884345.98139943046326
Trimmed Mean ( 7 / 24 )4.068965517241380.663070489211636.13655046249948
Trimmed Mean ( 8 / 24 )4.058928571428570.6461463023674136.28174850890128
Trimmed Mean ( 9 / 24 )4.048148148148150.6271113366195096.45523037419479
Trimmed Mean ( 10 / 24 )4.040384615384620.6076576421561526.64911347292222
Trimmed Mean ( 11 / 24 )4.0420.5883292844477286.87030223864222
Trimmed Mean ( 12 / 24 )4.029166666666670.5679451446682567.0942884264292
Trimmed Mean ( 13 / 24 )4.015217391304350.5483217028087227.32274022847683
Trimmed Mean ( 14 / 24 )4.002272727272730.5249432531131777.62420071795807
Trimmed Mean ( 15 / 24 )3.973809523809520.4986283103817557.96948236005118
Trimmed Mean ( 16 / 24 )3.950.4699017900664918.40601181672681
Trimmed Mean ( 17 / 24 )3.918421052631580.4386202222124318.93351663739256
Trimmed Mean ( 18 / 24 )3.888888888888890.3975076674468219.78317956447758
Trimmed Mean ( 19 / 24 )3.847058823529410.34435181026910311.171884999016
Trimmed Mean ( 20 / 24 )3.83750.29599987739753312.9645323969042
Trimmed Mean ( 21 / 24 )3.826666666666670.24348680406705715.7161152175327
Trimmed Mean ( 22 / 24 )3.857142857142860.19268559879991820.0178055919377
Trimmed Mean ( 23 / 24 )3.880769230769230.16086489608643524.1244008182124
Trimmed Mean ( 24 / 24 )3.929166666666670.14096961933295927.8724358146013
Median4.05
Midrange5.6
Midmean - Weighted Average at Xnp3.60526315789474
Midmean - Weighted Average at X(n+1)p3.88888888888889
Midmean - Empirical Distribution Function3.60526315789474
Midmean - Empirical Distribution Function - Averaging3.88888888888889
Midmean - Empirical Distribution Function - Interpolation3.88888888888889
Midmean - Closest Observation3.60526315789474
Midmean - True Basic - Statistics Graphics Toolkit3.88888888888889
Midmean - MS Excel (old versions)3.77948717948718
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 4.32638888888889 & 0.849000593203331 & 5.09586085513222 \tabularnewline
Geometric Mean & NaN &  &  \tabularnewline
Harmonic Mean & 0 &  &  \tabularnewline
Quadratic Mean & 8.36029804093929 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 4.32083333333333 & 0.846933475898674 & 5.10173875078977 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 4.3125 & 0.844861429637734 & 5.10438735716595 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 4.31666666666667 & 0.827089283158789 & 5.21910603191546 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 4.38888888888889 & 0.794613506202394 & 5.52330013853427 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 4.29166666666667 & 0.767612067638971 & 5.59093173178871 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 4.25 & 0.755762939871528 & 5.62345647793004 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 4.12361111111111 & 0.716796289881316 & 5.7528354559339 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 4.12361111111111 & 0.70884886805633 & 5.81733469141044 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 4.09861111111111 & 0.691148182430156 & 5.93014814377421 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 4.02916666666667 & 0.669516904467514 & 6.01802081438284 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 4.13611111111111 & 0.651657047452377 & 6.34706726073331 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 4.13611111111111 & 0.624055798698093 & 6.62779052728919 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 4.11805555555556 & 0.615139990647856 & 6.69450144383961 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 4.23472222222222 & 0.597039382245724 & 7.09286916098163 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 4.17222222222222 & 0.573301472468197 & 7.2775362049217 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 4.21666666666667 & 0.545672260576293 & 7.72747117878666 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 4.16944444444445 & 0.537930011012949 & 7.75090506029432 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 4.24444444444444 & 0.519162866280821 & 8.17555476348067 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 3.92777777777778 & 0.444269820937526 & 8.84097364410018 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 3.92777777777778 & 0.393855497192944 & 9.97263667962369 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 3.57777777777778 & 0.325099131518155 & 11.005190204816 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 3.66944444444445 & 0.23095398949075 & 15.8882054929448 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 3.50972222222222 & 0.165597033880373 & 21.1943543913814 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 3.50972222222222 & 0.156561743436612 & 22.4174957763115 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 4.29 & 0.82311620677464 & 5.21190077985495 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 4.25735294117647 & 0.794776394902965 & 5.35666757150765 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 4.22727272727273 & 0.762190884125515 & 5.54621265527573 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 4.19375 & 0.7314195638435 & 5.73371318913384 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 4.13709677419355 & 0.706628860310736 & 5.85469545126459 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 4.1 & 0.685458319188434 & 5.98139943046326 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 4.06896551724138 & 0.66307048921163 & 6.13655046249948 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 4.05892857142857 & 0.646146302367413 & 6.28174850890128 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 4.04814814814815 & 0.627111336619509 & 6.45523037419479 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 4.04038461538462 & 0.607657642156152 & 6.64911347292222 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 4.042 & 0.588329284447728 & 6.87030223864222 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 4.02916666666667 & 0.567945144668256 & 7.0942884264292 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 4.01521739130435 & 0.548321702808722 & 7.32274022847683 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 4.00227272727273 & 0.524943253113177 & 7.62420071795807 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 3.97380952380952 & 0.498628310381755 & 7.96948236005118 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 3.95 & 0.469901790066491 & 8.40601181672681 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 3.91842105263158 & 0.438620222212431 & 8.93351663739256 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 3.88888888888889 & 0.397507667446821 & 9.78317956447758 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 3.84705882352941 & 0.344351810269103 & 11.171884999016 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 3.8375 & 0.295999877397533 & 12.9645323969042 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 3.82666666666667 & 0.243486804067057 & 15.7161152175327 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 3.85714285714286 & 0.192685598799918 & 20.0178055919377 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 3.88076923076923 & 0.160864896086435 & 24.1244008182124 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 3.92916666666667 & 0.140969619332959 & 27.8724358146013 \tabularnewline
Median & 4.05 &  &  \tabularnewline
Midrange & 5.6 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 3.60526315789474 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 3.88888888888889 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 3.60526315789474 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 3.88888888888889 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 3.88888888888889 &  &  \tabularnewline
Midmean - Closest Observation & 3.60526315789474 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 3.88888888888889 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 3.77948717948718 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=277641&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]4.32638888888889[/C][C]0.849000593203331[/C][C]5.09586085513222[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]NaN[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]0[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]8.36029804093929[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]4.32083333333333[/C][C]0.846933475898674[/C][C]5.10173875078977[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]4.3125[/C][C]0.844861429637734[/C][C]5.10438735716595[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]4.31666666666667[/C][C]0.827089283158789[/C][C]5.21910603191546[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]4.38888888888889[/C][C]0.794613506202394[/C][C]5.52330013853427[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]4.29166666666667[/C][C]0.767612067638971[/C][C]5.59093173178871[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]4.25[/C][C]0.755762939871528[/C][C]5.62345647793004[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]4.12361111111111[/C][C]0.716796289881316[/C][C]5.7528354559339[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]4.12361111111111[/C][C]0.70884886805633[/C][C]5.81733469141044[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]4.09861111111111[/C][C]0.691148182430156[/C][C]5.93014814377421[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]4.02916666666667[/C][C]0.669516904467514[/C][C]6.01802081438284[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]4.13611111111111[/C][C]0.651657047452377[/C][C]6.34706726073331[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]4.13611111111111[/C][C]0.624055798698093[/C][C]6.62779052728919[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]4.11805555555556[/C][C]0.615139990647856[/C][C]6.69450144383961[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]4.23472222222222[/C][C]0.597039382245724[/C][C]7.09286916098163[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]4.17222222222222[/C][C]0.573301472468197[/C][C]7.2775362049217[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]4.21666666666667[/C][C]0.545672260576293[/C][C]7.72747117878666[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]4.16944444444445[/C][C]0.537930011012949[/C][C]7.75090506029432[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]4.24444444444444[/C][C]0.519162866280821[/C][C]8.17555476348067[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]3.92777777777778[/C][C]0.444269820937526[/C][C]8.84097364410018[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]3.92777777777778[/C][C]0.393855497192944[/C][C]9.97263667962369[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]3.57777777777778[/C][C]0.325099131518155[/C][C]11.005190204816[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]3.66944444444445[/C][C]0.23095398949075[/C][C]15.8882054929448[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]3.50972222222222[/C][C]0.165597033880373[/C][C]21.1943543913814[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]3.50972222222222[/C][C]0.156561743436612[/C][C]22.4174957763115[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]4.29[/C][C]0.82311620677464[/C][C]5.21190077985495[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]4.25735294117647[/C][C]0.794776394902965[/C][C]5.35666757150765[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]4.22727272727273[/C][C]0.762190884125515[/C][C]5.54621265527573[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]4.19375[/C][C]0.7314195638435[/C][C]5.73371318913384[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]4.13709677419355[/C][C]0.706628860310736[/C][C]5.85469545126459[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]4.1[/C][C]0.685458319188434[/C][C]5.98139943046326[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]4.06896551724138[/C][C]0.66307048921163[/C][C]6.13655046249948[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]4.05892857142857[/C][C]0.646146302367413[/C][C]6.28174850890128[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]4.04814814814815[/C][C]0.627111336619509[/C][C]6.45523037419479[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]4.04038461538462[/C][C]0.607657642156152[/C][C]6.64911347292222[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]4.042[/C][C]0.588329284447728[/C][C]6.87030223864222[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]4.02916666666667[/C][C]0.567945144668256[/C][C]7.0942884264292[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]4.01521739130435[/C][C]0.548321702808722[/C][C]7.32274022847683[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]4.00227272727273[/C][C]0.524943253113177[/C][C]7.62420071795807[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]3.97380952380952[/C][C]0.498628310381755[/C][C]7.96948236005118[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]3.95[/C][C]0.469901790066491[/C][C]8.40601181672681[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]3.91842105263158[/C][C]0.438620222212431[/C][C]8.93351663739256[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]3.88888888888889[/C][C]0.397507667446821[/C][C]9.78317956447758[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]3.84705882352941[/C][C]0.344351810269103[/C][C]11.171884999016[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]3.8375[/C][C]0.295999877397533[/C][C]12.9645323969042[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]3.82666666666667[/C][C]0.243486804067057[/C][C]15.7161152175327[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]3.85714285714286[/C][C]0.192685598799918[/C][C]20.0178055919377[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]3.88076923076923[/C][C]0.160864896086435[/C][C]24.1244008182124[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]3.92916666666667[/C][C]0.140969619332959[/C][C]27.8724358146013[/C][/ROW]
[ROW][C]Median[/C][C]4.05[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]5.6[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]3.60526315789474[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]3.88888888888889[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]3.60526315789474[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]3.88888888888889[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]3.88888888888889[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]3.60526315789474[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]3.88888888888889[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]3.77948717948718[/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=277641&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=277641&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 Mean4.326388888888890.8490005932033315.09586085513222
Geometric MeanNaN
Harmonic Mean0
Quadratic Mean8.36029804093929
Winsorized Mean ( 1 / 24 )4.320833333333330.8469334758986745.10173875078977
Winsorized Mean ( 2 / 24 )4.31250.8448614296377345.10438735716595
Winsorized Mean ( 3 / 24 )4.316666666666670.8270892831587895.21910603191546
Winsorized Mean ( 4 / 24 )4.388888888888890.7946135062023945.52330013853427
Winsorized Mean ( 5 / 24 )4.291666666666670.7676120676389715.59093173178871
Winsorized Mean ( 6 / 24 )4.250.7557629398715285.62345647793004
Winsorized Mean ( 7 / 24 )4.123611111111110.7167962898813165.7528354559339
Winsorized Mean ( 8 / 24 )4.123611111111110.708848868056335.81733469141044
Winsorized Mean ( 9 / 24 )4.098611111111110.6911481824301565.93014814377421
Winsorized Mean ( 10 / 24 )4.029166666666670.6695169044675146.01802081438284
Winsorized Mean ( 11 / 24 )4.136111111111110.6516570474523776.34706726073331
Winsorized Mean ( 12 / 24 )4.136111111111110.6240557986980936.62779052728919
Winsorized Mean ( 13 / 24 )4.118055555555560.6151399906478566.69450144383961
Winsorized Mean ( 14 / 24 )4.234722222222220.5970393822457247.09286916098163
Winsorized Mean ( 15 / 24 )4.172222222222220.5733014724681977.2775362049217
Winsorized Mean ( 16 / 24 )4.216666666666670.5456722605762937.72747117878666
Winsorized Mean ( 17 / 24 )4.169444444444450.5379300110129497.75090506029432
Winsorized Mean ( 18 / 24 )4.244444444444440.5191628662808218.17555476348067
Winsorized Mean ( 19 / 24 )3.927777777777780.4442698209375268.84097364410018
Winsorized Mean ( 20 / 24 )3.927777777777780.3938554971929449.97263667962369
Winsorized Mean ( 21 / 24 )3.577777777777780.32509913151815511.005190204816
Winsorized Mean ( 22 / 24 )3.669444444444450.2309539894907515.8882054929448
Winsorized Mean ( 23 / 24 )3.509722222222220.16559703388037321.1943543913814
Winsorized Mean ( 24 / 24 )3.509722222222220.15656174343661222.4174957763115
Trimmed Mean ( 1 / 24 )4.290.823116206774645.21190077985495
Trimmed Mean ( 2 / 24 )4.257352941176470.7947763949029655.35666757150765
Trimmed Mean ( 3 / 24 )4.227272727272730.7621908841255155.54621265527573
Trimmed Mean ( 4 / 24 )4.193750.73141956384355.73371318913384
Trimmed Mean ( 5 / 24 )4.137096774193550.7066288603107365.85469545126459
Trimmed Mean ( 6 / 24 )4.10.6854583191884345.98139943046326
Trimmed Mean ( 7 / 24 )4.068965517241380.663070489211636.13655046249948
Trimmed Mean ( 8 / 24 )4.058928571428570.6461463023674136.28174850890128
Trimmed Mean ( 9 / 24 )4.048148148148150.6271113366195096.45523037419479
Trimmed Mean ( 10 / 24 )4.040384615384620.6076576421561526.64911347292222
Trimmed Mean ( 11 / 24 )4.0420.5883292844477286.87030223864222
Trimmed Mean ( 12 / 24 )4.029166666666670.5679451446682567.0942884264292
Trimmed Mean ( 13 / 24 )4.015217391304350.5483217028087227.32274022847683
Trimmed Mean ( 14 / 24 )4.002272727272730.5249432531131777.62420071795807
Trimmed Mean ( 15 / 24 )3.973809523809520.4986283103817557.96948236005118
Trimmed Mean ( 16 / 24 )3.950.4699017900664918.40601181672681
Trimmed Mean ( 17 / 24 )3.918421052631580.4386202222124318.93351663739256
Trimmed Mean ( 18 / 24 )3.888888888888890.3975076674468219.78317956447758
Trimmed Mean ( 19 / 24 )3.847058823529410.34435181026910311.171884999016
Trimmed Mean ( 20 / 24 )3.83750.29599987739753312.9645323969042
Trimmed Mean ( 21 / 24 )3.826666666666670.24348680406705715.7161152175327
Trimmed Mean ( 22 / 24 )3.857142857142860.19268559879991820.0178055919377
Trimmed Mean ( 23 / 24 )3.880769230769230.16086489608643524.1244008182124
Trimmed Mean ( 24 / 24 )3.929166666666670.14096961933295927.8724358146013
Median4.05
Midrange5.6
Midmean - Weighted Average at Xnp3.60526315789474
Midmean - Weighted Average at X(n+1)p3.88888888888889
Midmean - Empirical Distribution Function3.60526315789474
Midmean - Empirical Distribution Function - Averaging3.88888888888889
Midmean - Empirical Distribution Function - Interpolation3.88888888888889
Midmean - Closest Observation3.60526315789474
Midmean - True Basic - Statistics Graphics Toolkit3.88888888888889
Midmean - MS Excel (old versions)3.77948717948718
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')