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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationThu, 11 Oct 2012 06:44:23 -0400
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/Oct/11/t1349952302g7y97e8m7boqhk0.htm/, Retrieved Sun, 28 Apr 2024 06:54:17 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=174913, Retrieved Sun, 28 Apr 2024 06:54:17 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact103
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Centrummaten cons...] [2012-10-11 10:44:23] [a6e34128b9d18a68d11d76dfebda1862] [Current]
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Dataseries X:
163,93
164,28
164,58
165,97
166,3
166,27
166,27
166,44
166,26
166,64
166,07
166,19
166,19
166,19
166,35
166,52
167,17
167,16
167,16
167,16
167,39
168,46
168,55
168,58
168,58
169,21
169,29
169,24
169,53
169,57
169,57
169,67
170,04
170,39
170,57
170,48
170,48
170,48
170,49
170,72
171,11
171,07
171,07
171,07
171,05
172,28
172,74
172,86
172,86
173,24
173,2
173,38
172,89
172,98
172,98
172,69
172,77
172,65
172,3
172,17
172,17
173,07
173,27
173,05
173,41
173,37
173,37
173,08
173,97
175,23
174,9
174,83




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' @ fisher.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 & 2 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=174913&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' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=174913&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=174913&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' @ fisher.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean170.0759722222220.34936957865997486.808189981967
Geometric Mean170.050413675988
Harmonic Mean170.024776355809
Quadratic Mean170.101447741079
Winsorized Mean ( 1 / 24 )170.076250.347271301304474489.750374883077
Winsorized Mean ( 2 / 24 )170.0826388888890.344976921562333493.026136701022
Winsorized Mean ( 3 / 24 )170.1047222222220.326804007982013520.509902166147
Winsorized Mean ( 4 / 24 )170.0791666666670.320952328399174529.920338995441
Winsorized Mean ( 5 / 24 )170.0854166666670.319199344206627532.850144443171
Winsorized Mean ( 6 / 24 )170.0845833333330.319078346640746533.049594633989
Winsorized Mean ( 7 / 24 )170.0845833333330.319078346640746533.049594633989
Winsorized Mean ( 8 / 24 )170.081250.316152779071128537.971706273488
Winsorized Mean ( 9 / 24 )170.078750.315409038241675539.232328116359
Winsorized Mean ( 10 / 24 )170.0731944444440.314628095182432540.553107140131
Winsorized Mean ( 11 / 24 )170.0594444444440.311312211441381546.266539488015
Winsorized Mean ( 12 / 24 )170.0661111111110.309671538060829549.182247022344
Winsorized Mean ( 13 / 24 )170.078750.30644613022783555.003745270183
Winsorized Mean ( 14 / 24 )170.0806944444440.302004086344174563.173487164723
Winsorized Mean ( 15 / 24 )170.1056944444440.297879820689318571.054776556552
Winsorized Mean ( 16 / 24 )170.201250.276721877622231615.062500523907
Winsorized Mean ( 17 / 24 )170.1941666666670.275754956738559617.193499183503
Winsorized Mean ( 18 / 24 )170.1941666666670.275754956738559617.193499183503
Winsorized Mean ( 19 / 24 )170.1730555555560.272132268919942625.332145397348
Winsorized Mean ( 20 / 24 )170.2258333333330.261592103098997650.730015611033
Winsorized Mean ( 21 / 24 )170.5233333333330.214323370266178795.635740150747
Winsorized Mean ( 22 / 24 )170.5386111111110.208874724301662816.463608420209
Winsorized Mean ( 23 / 24 )170.4363888888890.191963875052924887.856576357921
Winsorized Mean ( 24 / 24 )170.4297222222220.191053414949685892.052739633604
Trimmed Mean ( 1 / 24 )170.0901428571430.340385574384026499.698446871447
Trimmed Mean ( 2 / 24 )170.1048529411760.332174275731473512.095202334957
Trimmed Mean ( 3 / 24 )170.116969696970.323820144164563525.343999632454
Trimmed Mean ( 4 / 24 )170.12156250.321903226821348528.486664081859
Trimmed Mean ( 5 / 24 )170.1338709677420.3213553195423529.426029760641
Trimmed Mean ( 6 / 24 )170.14550.320867769815254530.266720456108
Trimmed Mean ( 7 / 24 )170.1581034482760.319942188601282531.840155848687
Trimmed Mean ( 8 / 24 )170.1716071428570.318447815944138534.378314507606
Trimmed Mean ( 9 / 24 )170.1866666666670.316904798469197537.027736685435
Trimmed Mean ( 10 / 24 )170.2032692307690.31476327875984540.734198415286
Trimmed Mean ( 11 / 24 )170.2220.311861298316664545.825983919161
Trimmed Mean ( 12 / 24 )170.2441666666670.308498829459332551.847042548047
Trimmed Mean ( 13 / 24 )170.2673913043480.304183620299028559.752004848145
Trimmed Mean ( 14 / 24 )170.2911363636360.298972556298343569.587852718174
Trimmed Mean ( 15 / 24 )170.3169047619050.292806018501997581.671461649765
Trimmed Mean ( 16 / 24 )170.342250.285323587667559597.01425806573
Trimmed Mean ( 17 / 24 )170.3589473684210.280177953376304608.038374595497
Trimmed Mean ( 18 / 24 )170.3783333333330.272944700486765624.22290313563
Trimmed Mean ( 19 / 24 )170.40.262539700758101649.044694985019
Trimmed Mean ( 20 / 24 )170.4268750.248510253853158685.794136690646
Trimmed Mean ( 21 / 24 )170.4510.231617674469019735.915341481417
Trimmed Mean ( 22 / 24 )170.4421428571430.223290896905734763.318815137804
Trimmed Mean ( 23 / 24 )170.430.212076183698942803.626305544699
Trimmed Mean ( 24 / 24 )170.4291666666670.201062320595593847.643487660028
Median170.48
Midrange169.58
Midmean - Weighted Average at Xnp170.276923076923
Midmean - Weighted Average at X(n+1)p170.276923076923
Midmean - Empirical Distribution Function170.276923076923
Midmean - Empirical Distribution Function - Averaging170.276923076923
Midmean - Empirical Distribution Function - Interpolation170.276923076923
Midmean - Closest Observation170.276923076923
Midmean - True Basic - Statistics Graphics Toolkit170.276923076923
Midmean - MS Excel (old versions)170.276923076923
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 170.075972222222 & 0.34936957865997 & 486.808189981967 \tabularnewline
Geometric Mean & 170.050413675988 &  &  \tabularnewline
Harmonic Mean & 170.024776355809 &  &  \tabularnewline
Quadratic Mean & 170.101447741079 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 170.07625 & 0.347271301304474 & 489.750374883077 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 170.082638888889 & 0.344976921562333 & 493.026136701022 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 170.104722222222 & 0.326804007982013 & 520.509902166147 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 170.079166666667 & 0.320952328399174 & 529.920338995441 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 170.085416666667 & 0.319199344206627 & 532.850144443171 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 170.084583333333 & 0.319078346640746 & 533.049594633989 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 170.084583333333 & 0.319078346640746 & 533.049594633989 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 170.08125 & 0.316152779071128 & 537.971706273488 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 170.07875 & 0.315409038241675 & 539.232328116359 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 170.073194444444 & 0.314628095182432 & 540.553107140131 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 170.059444444444 & 0.311312211441381 & 546.266539488015 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 170.066111111111 & 0.309671538060829 & 549.182247022344 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 170.07875 & 0.30644613022783 & 555.003745270183 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 170.080694444444 & 0.302004086344174 & 563.173487164723 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 170.105694444444 & 0.297879820689318 & 571.054776556552 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 170.20125 & 0.276721877622231 & 615.062500523907 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 170.194166666667 & 0.275754956738559 & 617.193499183503 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 170.194166666667 & 0.275754956738559 & 617.193499183503 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 170.173055555556 & 0.272132268919942 & 625.332145397348 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 170.225833333333 & 0.261592103098997 & 650.730015611033 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 170.523333333333 & 0.214323370266178 & 795.635740150747 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 170.538611111111 & 0.208874724301662 & 816.463608420209 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 170.436388888889 & 0.191963875052924 & 887.856576357921 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 170.429722222222 & 0.191053414949685 & 892.052739633604 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 170.090142857143 & 0.340385574384026 & 499.698446871447 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 170.104852941176 & 0.332174275731473 & 512.095202334957 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 170.11696969697 & 0.323820144164563 & 525.343999632454 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 170.1215625 & 0.321903226821348 & 528.486664081859 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 170.133870967742 & 0.3213553195423 & 529.426029760641 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 170.1455 & 0.320867769815254 & 530.266720456108 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 170.158103448276 & 0.319942188601282 & 531.840155848687 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 170.171607142857 & 0.318447815944138 & 534.378314507606 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 170.186666666667 & 0.316904798469197 & 537.027736685435 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 170.203269230769 & 0.31476327875984 & 540.734198415286 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 170.222 & 0.311861298316664 & 545.825983919161 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 170.244166666667 & 0.308498829459332 & 551.847042548047 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 170.267391304348 & 0.304183620299028 & 559.752004848145 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 170.291136363636 & 0.298972556298343 & 569.587852718174 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 170.316904761905 & 0.292806018501997 & 581.671461649765 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 170.34225 & 0.285323587667559 & 597.01425806573 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 170.358947368421 & 0.280177953376304 & 608.038374595497 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 170.378333333333 & 0.272944700486765 & 624.22290313563 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 170.4 & 0.262539700758101 & 649.044694985019 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 170.426875 & 0.248510253853158 & 685.794136690646 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 170.451 & 0.231617674469019 & 735.915341481417 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 170.442142857143 & 0.223290896905734 & 763.318815137804 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 170.43 & 0.212076183698942 & 803.626305544699 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 170.429166666667 & 0.201062320595593 & 847.643487660028 \tabularnewline
Median & 170.48 &  &  \tabularnewline
Midrange & 169.58 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 170.276923076923 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 170.276923076923 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 170.276923076923 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 170.276923076923 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 170.276923076923 &  &  \tabularnewline
Midmean - Closest Observation & 170.276923076923 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 170.276923076923 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 170.276923076923 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=174913&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]170.075972222222[/C][C]0.34936957865997[/C][C]486.808189981967[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]170.050413675988[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]170.024776355809[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]170.101447741079[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]170.07625[/C][C]0.347271301304474[/C][C]489.750374883077[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]170.082638888889[/C][C]0.344976921562333[/C][C]493.026136701022[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]170.104722222222[/C][C]0.326804007982013[/C][C]520.509902166147[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]170.079166666667[/C][C]0.320952328399174[/C][C]529.920338995441[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]170.085416666667[/C][C]0.319199344206627[/C][C]532.850144443171[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]170.084583333333[/C][C]0.319078346640746[/C][C]533.049594633989[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]170.084583333333[/C][C]0.319078346640746[/C][C]533.049594633989[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]170.08125[/C][C]0.316152779071128[/C][C]537.971706273488[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]170.07875[/C][C]0.315409038241675[/C][C]539.232328116359[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]170.073194444444[/C][C]0.314628095182432[/C][C]540.553107140131[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]170.059444444444[/C][C]0.311312211441381[/C][C]546.266539488015[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]170.066111111111[/C][C]0.309671538060829[/C][C]549.182247022344[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]170.07875[/C][C]0.30644613022783[/C][C]555.003745270183[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]170.080694444444[/C][C]0.302004086344174[/C][C]563.173487164723[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]170.105694444444[/C][C]0.297879820689318[/C][C]571.054776556552[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]170.20125[/C][C]0.276721877622231[/C][C]615.062500523907[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]170.194166666667[/C][C]0.275754956738559[/C][C]617.193499183503[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]170.194166666667[/C][C]0.275754956738559[/C][C]617.193499183503[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]170.173055555556[/C][C]0.272132268919942[/C][C]625.332145397348[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]170.225833333333[/C][C]0.261592103098997[/C][C]650.730015611033[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]170.523333333333[/C][C]0.214323370266178[/C][C]795.635740150747[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]170.538611111111[/C][C]0.208874724301662[/C][C]816.463608420209[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]170.436388888889[/C][C]0.191963875052924[/C][C]887.856576357921[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]170.429722222222[/C][C]0.191053414949685[/C][C]892.052739633604[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]170.090142857143[/C][C]0.340385574384026[/C][C]499.698446871447[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]170.104852941176[/C][C]0.332174275731473[/C][C]512.095202334957[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]170.11696969697[/C][C]0.323820144164563[/C][C]525.343999632454[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]170.1215625[/C][C]0.321903226821348[/C][C]528.486664081859[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]170.133870967742[/C][C]0.3213553195423[/C][C]529.426029760641[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]170.1455[/C][C]0.320867769815254[/C][C]530.266720456108[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]170.158103448276[/C][C]0.319942188601282[/C][C]531.840155848687[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]170.171607142857[/C][C]0.318447815944138[/C][C]534.378314507606[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]170.186666666667[/C][C]0.316904798469197[/C][C]537.027736685435[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]170.203269230769[/C][C]0.31476327875984[/C][C]540.734198415286[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]170.222[/C][C]0.311861298316664[/C][C]545.825983919161[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]170.244166666667[/C][C]0.308498829459332[/C][C]551.847042548047[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]170.267391304348[/C][C]0.304183620299028[/C][C]559.752004848145[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]170.291136363636[/C][C]0.298972556298343[/C][C]569.587852718174[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]170.316904761905[/C][C]0.292806018501997[/C][C]581.671461649765[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]170.34225[/C][C]0.285323587667559[/C][C]597.01425806573[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]170.358947368421[/C][C]0.280177953376304[/C][C]608.038374595497[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]170.378333333333[/C][C]0.272944700486765[/C][C]624.22290313563[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]170.4[/C][C]0.262539700758101[/C][C]649.044694985019[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]170.426875[/C][C]0.248510253853158[/C][C]685.794136690646[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]170.451[/C][C]0.231617674469019[/C][C]735.915341481417[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]170.442142857143[/C][C]0.223290896905734[/C][C]763.318815137804[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]170.43[/C][C]0.212076183698942[/C][C]803.626305544699[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]170.429166666667[/C][C]0.201062320595593[/C][C]847.643487660028[/C][/ROW]
[ROW][C]Median[/C][C]170.48[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]169.58[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]170.276923076923[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]170.276923076923[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]170.276923076923[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]170.276923076923[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]170.276923076923[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]170.276923076923[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]170.276923076923[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]170.276923076923[/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=174913&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=174913&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 Mean170.0759722222220.34936957865997486.808189981967
Geometric Mean170.050413675988
Harmonic Mean170.024776355809
Quadratic Mean170.101447741079
Winsorized Mean ( 1 / 24 )170.076250.347271301304474489.750374883077
Winsorized Mean ( 2 / 24 )170.0826388888890.344976921562333493.026136701022
Winsorized Mean ( 3 / 24 )170.1047222222220.326804007982013520.509902166147
Winsorized Mean ( 4 / 24 )170.0791666666670.320952328399174529.920338995441
Winsorized Mean ( 5 / 24 )170.0854166666670.319199344206627532.850144443171
Winsorized Mean ( 6 / 24 )170.0845833333330.319078346640746533.049594633989
Winsorized Mean ( 7 / 24 )170.0845833333330.319078346640746533.049594633989
Winsorized Mean ( 8 / 24 )170.081250.316152779071128537.971706273488
Winsorized Mean ( 9 / 24 )170.078750.315409038241675539.232328116359
Winsorized Mean ( 10 / 24 )170.0731944444440.314628095182432540.553107140131
Winsorized Mean ( 11 / 24 )170.0594444444440.311312211441381546.266539488015
Winsorized Mean ( 12 / 24 )170.0661111111110.309671538060829549.182247022344
Winsorized Mean ( 13 / 24 )170.078750.30644613022783555.003745270183
Winsorized Mean ( 14 / 24 )170.0806944444440.302004086344174563.173487164723
Winsorized Mean ( 15 / 24 )170.1056944444440.297879820689318571.054776556552
Winsorized Mean ( 16 / 24 )170.201250.276721877622231615.062500523907
Winsorized Mean ( 17 / 24 )170.1941666666670.275754956738559617.193499183503
Winsorized Mean ( 18 / 24 )170.1941666666670.275754956738559617.193499183503
Winsorized Mean ( 19 / 24 )170.1730555555560.272132268919942625.332145397348
Winsorized Mean ( 20 / 24 )170.2258333333330.261592103098997650.730015611033
Winsorized Mean ( 21 / 24 )170.5233333333330.214323370266178795.635740150747
Winsorized Mean ( 22 / 24 )170.5386111111110.208874724301662816.463608420209
Winsorized Mean ( 23 / 24 )170.4363888888890.191963875052924887.856576357921
Winsorized Mean ( 24 / 24 )170.4297222222220.191053414949685892.052739633604
Trimmed Mean ( 1 / 24 )170.0901428571430.340385574384026499.698446871447
Trimmed Mean ( 2 / 24 )170.1048529411760.332174275731473512.095202334957
Trimmed Mean ( 3 / 24 )170.116969696970.323820144164563525.343999632454
Trimmed Mean ( 4 / 24 )170.12156250.321903226821348528.486664081859
Trimmed Mean ( 5 / 24 )170.1338709677420.3213553195423529.426029760641
Trimmed Mean ( 6 / 24 )170.14550.320867769815254530.266720456108
Trimmed Mean ( 7 / 24 )170.1581034482760.319942188601282531.840155848687
Trimmed Mean ( 8 / 24 )170.1716071428570.318447815944138534.378314507606
Trimmed Mean ( 9 / 24 )170.1866666666670.316904798469197537.027736685435
Trimmed Mean ( 10 / 24 )170.2032692307690.31476327875984540.734198415286
Trimmed Mean ( 11 / 24 )170.2220.311861298316664545.825983919161
Trimmed Mean ( 12 / 24 )170.2441666666670.308498829459332551.847042548047
Trimmed Mean ( 13 / 24 )170.2673913043480.304183620299028559.752004848145
Trimmed Mean ( 14 / 24 )170.2911363636360.298972556298343569.587852718174
Trimmed Mean ( 15 / 24 )170.3169047619050.292806018501997581.671461649765
Trimmed Mean ( 16 / 24 )170.342250.285323587667559597.01425806573
Trimmed Mean ( 17 / 24 )170.3589473684210.280177953376304608.038374595497
Trimmed Mean ( 18 / 24 )170.3783333333330.272944700486765624.22290313563
Trimmed Mean ( 19 / 24 )170.40.262539700758101649.044694985019
Trimmed Mean ( 20 / 24 )170.4268750.248510253853158685.794136690646
Trimmed Mean ( 21 / 24 )170.4510.231617674469019735.915341481417
Trimmed Mean ( 22 / 24 )170.4421428571430.223290896905734763.318815137804
Trimmed Mean ( 23 / 24 )170.430.212076183698942803.626305544699
Trimmed Mean ( 24 / 24 )170.4291666666670.201062320595593847.643487660028
Median170.48
Midrange169.58
Midmean - Weighted Average at Xnp170.276923076923
Midmean - Weighted Average at X(n+1)p170.276923076923
Midmean - Empirical Distribution Function170.276923076923
Midmean - Empirical Distribution Function - Averaging170.276923076923
Midmean - Empirical Distribution Function - Interpolation170.276923076923
Midmean - Closest Observation170.276923076923
Midmean - True Basic - Statistics Graphics Toolkit170.276923076923
Midmean - MS Excel (old versions)170.276923076923
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')