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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationWed, 04 Dec 2013 04:44:18 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2013/Dec/04/t1386150266lz2u325ngqax9mc.htm/, Retrieved Thu, 28 Mar 2024 19:40:02 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=230463, Retrieved Thu, 28 Mar 2024 19:40:02 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact79
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Data Series] [] [2008-12-14 11:54:22] [d2d412c7f4d35ffbf5ee5ee89db327d4]
- RMPD  [Central Tendency] [] [2011-12-06 20:30:47] [b98453cac15ba1066b407e146608df68]
- R P       [Central Tendency] [WS 9] [2013-12-04 09:44:18] [964acef360ea028b18952da197fdc0b8] [Current]
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Dataseries X:
0.0589999409995141
-1.41417450501306
-18.3846475755861
4.24266776527226
-9.89940750475467
-1.41416601970523
-4.94968147844429
8.48527118362683
5.65684722004823
2.12135156036077
-12.7278137906086
-1.41417238368611
-5.65678640867546
5.71546709301464
11.430917448217
4.0824915417843
-5.71542749248443
-4.89893277693375
5.30722585896545
-8.98140023237252
-0.816480018948223
-3.67419274460486
2.44950292718234
-7.34841447478369
-12.2473676641251
13.5676795115537
-7.50550178552387
-10.1035605510469
4.61879420118808
-12.9903024874634
3.7527758629083
-14.1450008210891
-2.30938107887528
-11.2582591729112
-4.33008822361948
1.29908651985677e-05
16.454417696876
7.82621147962468
4.02491438422167
-8.72060773063855
-0.894411455568734
-0.223594253653449
-6.93176357788012
-2.01244265593132
-7.1553761680782
0.223617958497356
8.27342503551901
15.2051986751483
2.90688653528183
-12.7801213366766
-3.10373653589491
-7.1203466912372
-3.46888342810694
-8.3983624583384
2.55603701106735
0.182580385499283
10.5892565952768
15.7013138196074
6.75522353446613
5.11206123957597
8.76352852127385




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time5 seconds
R Server'Sir Maurice George Kendall' @ kendall.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 & 5 seconds \tabularnewline
R Server & 'Sir Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=230463&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]5 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Maurice George Kendall' @ kendall.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=230463&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=230463&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 time5 seconds
R Server'Sir Maurice George Kendall' @ kendall.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean-0.7693463525465171.02891120357779-0.74772861824354
Geometric MeanNaN
Harmonic Mean0.000792257219298152
Quadratic Mean8.00695882973367
Winsorized Mean ( 1 / 20 )-0.7121899119362151.00785492395399-0.706639313862921
Winsorized Mean ( 2 / 20 )-0.690597020488130.99537715778759-0.693804368610497
Winsorized Mean ( 3 / 20 )-0.7607939719376940.972634631806157-0.782199139387952
Winsorized Mean ( 4 / 20 )-0.8974795140536740.939363625668074-0.955412248814072
Winsorized Mean ( 5 / 20 )-0.9270872785173380.916401801393154-1.01166025329494
Winsorized Mean ( 6 / 20 )-1.009377729283470.860871324549968-1.17250708729454
Winsorized Mean ( 7 / 20 )-0.9088024999470650.829432893567807-1.09569141397063
Winsorized Mean ( 8 / 20 )-0.9098114313327160.8192936919046-1.11048265148691
Winsorized Mean ( 9 / 20 )-0.8403500633263160.782906124102636-1.07337270389796
Winsorized Mean ( 10 / 20 )-0.9731689884778870.744073808610639-1.30789308428289
Winsorized Mean ( 11 / 20 )-1.102556248488780.70258071542341-1.56929477892704
Winsorized Mean ( 12 / 20 )-0.9384433042563670.671162689138062-1.39823521099118
Winsorized Mean ( 13 / 20 )-0.9794751510506910.653639356286528-1.49849476111003
Winsorized Mean ( 14 / 20 )-0.979963157240460.639328224295555-1.53280133740417
Winsorized Mean ( 15 / 20 )-1.092644524833960.618972486368883-1.76525540132455
Winsorized Mean ( 16 / 20 )-1.141836215996910.595935979678967-1.9160383915937
Winsorized Mean ( 17 / 20 )-0.8474965823504890.535959589413665-1.5812695566799
Winsorized Mean ( 18 / 20 )-0.8471826369007490.5307410589904-1.59622592326341
Winsorized Mean ( 19 / 20 )-0.7117012964181560.485061204207413-1.46724019617498
Winsorized Mean ( 20 / 20 )-0.9724031410463290.44096762984277-2.20515764704327
Trimmed Mean ( 1 / 20 )-0.7627101292648710.977199113828589-0.780506366073782
Trimmed Mean ( 2 / 20 )-0.8167756250025560.939493638215347-0.869378558596837
Trimmed Mean ( 3 / 20 )-0.886747396596920.901223571963845-0.983937198474092
Trimmed Mean ( 4 / 20 )-0.9350691507114660.86492260505468-1.08110152890772
Trimmed Mean ( 5 / 20 )-0.9463091891238450.833077500979644-1.13591975297742
Trimmed Mean ( 6 / 20 )-0.9510950525809760.800977795779019-1.18741750095077
Trimmed Mean ( 7 / 20 )-0.9384878069112860.777916426579654-1.20641212197772
Trimmed Mean ( 8 / 20 )-0.9442363901646750.757299694188864-1.24684639041884
Trimmed Mean ( 9 / 20 )-0.9503408160040630.733011213444526-1.29648878294545
Trimmed Mean ( 10 / 20 )-0.9685235691567530.710905589696749-1.36238001669096
Trimmed Mean ( 11 / 20 )-0.9677969779296020.691710695709801-1.39913548240929
Trimmed Mean ( 12 / 20 )-0.9475996425386680.676275775783999-1.4012029950949
Trimmed Mean ( 13 / 20 )-0.9489294916701450.662668343734782-1.43198253038919
Trimmed Mean ( 14 / 20 )-0.9445861694738430.647306772429683-1.459255811473
Trimmed Mean ( 15 / 20 )-0.939613827875310.628372826259688-1.49531263703468
Trimmed Mean ( 16 / 20 )-0.9181543508305340.605904879274421-1.51534404530631
Trimmed Mean ( 17 / 20 )-0.8865696430176890.578924131070574-1.53140903174688
Trimmed Mean ( 18 / 20 )-0.8921777764310990.558669979365387-1.59696745732526
Trimmed Mean ( 19 / 20 )-0.8988074950575520.526730135899563-1.70639087038858
Trimmed Mean ( 20 / 20 )-0.9274127033708430.493585025884706-1.87893200712185
Median-0.894411455568734
Midrange-0.96511493935505
Midmean - Weighted Average at Xnp-1.12489409551076
Midmean - Weighted Average at X(n+1)p-0.939613827875309
Midmean - Empirical Distribution Function-0.939613827875309
Midmean - Empirical Distribution Function - Averaging-0.939613827875309
Midmean - Empirical Distribution Function - Interpolation-0.939613827875309
Midmean - Closest Observation-1.13385640100665
Midmean - True Basic - Statistics Graphics Toolkit-0.939613827875309
Midmean - MS Excel (old versions)-0.939613827875309
Number of observations61

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & -0.769346352546517 & 1.02891120357779 & -0.74772861824354 \tabularnewline
Geometric Mean & NaN &  &  \tabularnewline
Harmonic Mean & 0.000792257219298152 &  &  \tabularnewline
Quadratic Mean & 8.00695882973367 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & -0.712189911936215 & 1.00785492395399 & -0.706639313862921 \tabularnewline
Winsorized Mean ( 2 / 20 ) & -0.69059702048813 & 0.99537715778759 & -0.693804368610497 \tabularnewline
Winsorized Mean ( 3 / 20 ) & -0.760793971937694 & 0.972634631806157 & -0.782199139387952 \tabularnewline
Winsorized Mean ( 4 / 20 ) & -0.897479514053674 & 0.939363625668074 & -0.955412248814072 \tabularnewline
Winsorized Mean ( 5 / 20 ) & -0.927087278517338 & 0.916401801393154 & -1.01166025329494 \tabularnewline
Winsorized Mean ( 6 / 20 ) & -1.00937772928347 & 0.860871324549968 & -1.17250708729454 \tabularnewline
Winsorized Mean ( 7 / 20 ) & -0.908802499947065 & 0.829432893567807 & -1.09569141397063 \tabularnewline
Winsorized Mean ( 8 / 20 ) & -0.909811431332716 & 0.8192936919046 & -1.11048265148691 \tabularnewline
Winsorized Mean ( 9 / 20 ) & -0.840350063326316 & 0.782906124102636 & -1.07337270389796 \tabularnewline
Winsorized Mean ( 10 / 20 ) & -0.973168988477887 & 0.744073808610639 & -1.30789308428289 \tabularnewline
Winsorized Mean ( 11 / 20 ) & -1.10255624848878 & 0.70258071542341 & -1.56929477892704 \tabularnewline
Winsorized Mean ( 12 / 20 ) & -0.938443304256367 & 0.671162689138062 & -1.39823521099118 \tabularnewline
Winsorized Mean ( 13 / 20 ) & -0.979475151050691 & 0.653639356286528 & -1.49849476111003 \tabularnewline
Winsorized Mean ( 14 / 20 ) & -0.97996315724046 & 0.639328224295555 & -1.53280133740417 \tabularnewline
Winsorized Mean ( 15 / 20 ) & -1.09264452483396 & 0.618972486368883 & -1.76525540132455 \tabularnewline
Winsorized Mean ( 16 / 20 ) & -1.14183621599691 & 0.595935979678967 & -1.9160383915937 \tabularnewline
Winsorized Mean ( 17 / 20 ) & -0.847496582350489 & 0.535959589413665 & -1.5812695566799 \tabularnewline
Winsorized Mean ( 18 / 20 ) & -0.847182636900749 & 0.5307410589904 & -1.59622592326341 \tabularnewline
Winsorized Mean ( 19 / 20 ) & -0.711701296418156 & 0.485061204207413 & -1.46724019617498 \tabularnewline
Winsorized Mean ( 20 / 20 ) & -0.972403141046329 & 0.44096762984277 & -2.20515764704327 \tabularnewline
Trimmed Mean ( 1 / 20 ) & -0.762710129264871 & 0.977199113828589 & -0.780506366073782 \tabularnewline
Trimmed Mean ( 2 / 20 ) & -0.816775625002556 & 0.939493638215347 & -0.869378558596837 \tabularnewline
Trimmed Mean ( 3 / 20 ) & -0.88674739659692 & 0.901223571963845 & -0.983937198474092 \tabularnewline
Trimmed Mean ( 4 / 20 ) & -0.935069150711466 & 0.86492260505468 & -1.08110152890772 \tabularnewline
Trimmed Mean ( 5 / 20 ) & -0.946309189123845 & 0.833077500979644 & -1.13591975297742 \tabularnewline
Trimmed Mean ( 6 / 20 ) & -0.951095052580976 & 0.800977795779019 & -1.18741750095077 \tabularnewline
Trimmed Mean ( 7 / 20 ) & -0.938487806911286 & 0.777916426579654 & -1.20641212197772 \tabularnewline
Trimmed Mean ( 8 / 20 ) & -0.944236390164675 & 0.757299694188864 & -1.24684639041884 \tabularnewline
Trimmed Mean ( 9 / 20 ) & -0.950340816004063 & 0.733011213444526 & -1.29648878294545 \tabularnewline
Trimmed Mean ( 10 / 20 ) & -0.968523569156753 & 0.710905589696749 & -1.36238001669096 \tabularnewline
Trimmed Mean ( 11 / 20 ) & -0.967796977929602 & 0.691710695709801 & -1.39913548240929 \tabularnewline
Trimmed Mean ( 12 / 20 ) & -0.947599642538668 & 0.676275775783999 & -1.4012029950949 \tabularnewline
Trimmed Mean ( 13 / 20 ) & -0.948929491670145 & 0.662668343734782 & -1.43198253038919 \tabularnewline
Trimmed Mean ( 14 / 20 ) & -0.944586169473843 & 0.647306772429683 & -1.459255811473 \tabularnewline
Trimmed Mean ( 15 / 20 ) & -0.93961382787531 & 0.628372826259688 & -1.49531263703468 \tabularnewline
Trimmed Mean ( 16 / 20 ) & -0.918154350830534 & 0.605904879274421 & -1.51534404530631 \tabularnewline
Trimmed Mean ( 17 / 20 ) & -0.886569643017689 & 0.578924131070574 & -1.53140903174688 \tabularnewline
Trimmed Mean ( 18 / 20 ) & -0.892177776431099 & 0.558669979365387 & -1.59696745732526 \tabularnewline
Trimmed Mean ( 19 / 20 ) & -0.898807495057552 & 0.526730135899563 & -1.70639087038858 \tabularnewline
Trimmed Mean ( 20 / 20 ) & -0.927412703370843 & 0.493585025884706 & -1.87893200712185 \tabularnewline
Median & -0.894411455568734 &  &  \tabularnewline
Midrange & -0.96511493935505 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & -1.12489409551076 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & -0.939613827875309 &  &  \tabularnewline
Midmean - Empirical Distribution Function & -0.939613827875309 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & -0.939613827875309 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & -0.939613827875309 &  &  \tabularnewline
Midmean - Closest Observation & -1.13385640100665 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & -0.939613827875309 &  &  \tabularnewline
Midmean - MS Excel (old versions) & -0.939613827875309 &  &  \tabularnewline
Number of observations & 61 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=230463&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]-0.769346352546517[/C][C]1.02891120357779[/C][C]-0.74772861824354[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]NaN[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]0.000792257219298152[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]8.00695882973367[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]-0.712189911936215[/C][C]1.00785492395399[/C][C]-0.706639313862921[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]-0.69059702048813[/C][C]0.99537715778759[/C][C]-0.693804368610497[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]-0.760793971937694[/C][C]0.972634631806157[/C][C]-0.782199139387952[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]-0.897479514053674[/C][C]0.939363625668074[/C][C]-0.955412248814072[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]-0.927087278517338[/C][C]0.916401801393154[/C][C]-1.01166025329494[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]-1.00937772928347[/C][C]0.860871324549968[/C][C]-1.17250708729454[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]-0.908802499947065[/C][C]0.829432893567807[/C][C]-1.09569141397063[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]-0.909811431332716[/C][C]0.8192936919046[/C][C]-1.11048265148691[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]-0.840350063326316[/C][C]0.782906124102636[/C][C]-1.07337270389796[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]-0.973168988477887[/C][C]0.744073808610639[/C][C]-1.30789308428289[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]-1.10255624848878[/C][C]0.70258071542341[/C][C]-1.56929477892704[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]-0.938443304256367[/C][C]0.671162689138062[/C][C]-1.39823521099118[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]-0.979475151050691[/C][C]0.653639356286528[/C][C]-1.49849476111003[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]-0.97996315724046[/C][C]0.639328224295555[/C][C]-1.53280133740417[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]-1.09264452483396[/C][C]0.618972486368883[/C][C]-1.76525540132455[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]-1.14183621599691[/C][C]0.595935979678967[/C][C]-1.9160383915937[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]-0.847496582350489[/C][C]0.535959589413665[/C][C]-1.5812695566799[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]-0.847182636900749[/C][C]0.5307410589904[/C][C]-1.59622592326341[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]-0.711701296418156[/C][C]0.485061204207413[/C][C]-1.46724019617498[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]-0.972403141046329[/C][C]0.44096762984277[/C][C]-2.20515764704327[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]-0.762710129264871[/C][C]0.977199113828589[/C][C]-0.780506366073782[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]-0.816775625002556[/C][C]0.939493638215347[/C][C]-0.869378558596837[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]-0.88674739659692[/C][C]0.901223571963845[/C][C]-0.983937198474092[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]-0.935069150711466[/C][C]0.86492260505468[/C][C]-1.08110152890772[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]-0.946309189123845[/C][C]0.833077500979644[/C][C]-1.13591975297742[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]-0.951095052580976[/C][C]0.800977795779019[/C][C]-1.18741750095077[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]-0.938487806911286[/C][C]0.777916426579654[/C][C]-1.20641212197772[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]-0.944236390164675[/C][C]0.757299694188864[/C][C]-1.24684639041884[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]-0.950340816004063[/C][C]0.733011213444526[/C][C]-1.29648878294545[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]-0.968523569156753[/C][C]0.710905589696749[/C][C]-1.36238001669096[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]-0.967796977929602[/C][C]0.691710695709801[/C][C]-1.39913548240929[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]-0.947599642538668[/C][C]0.676275775783999[/C][C]-1.4012029950949[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]-0.948929491670145[/C][C]0.662668343734782[/C][C]-1.43198253038919[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]-0.944586169473843[/C][C]0.647306772429683[/C][C]-1.459255811473[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]-0.93961382787531[/C][C]0.628372826259688[/C][C]-1.49531263703468[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]-0.918154350830534[/C][C]0.605904879274421[/C][C]-1.51534404530631[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]-0.886569643017689[/C][C]0.578924131070574[/C][C]-1.53140903174688[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]-0.892177776431099[/C][C]0.558669979365387[/C][C]-1.59696745732526[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]-0.898807495057552[/C][C]0.526730135899563[/C][C]-1.70639087038858[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]-0.927412703370843[/C][C]0.493585025884706[/C][C]-1.87893200712185[/C][/ROW]
[ROW][C]Median[/C][C]-0.894411455568734[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]-0.96511493935505[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]-1.12489409551076[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]-0.939613827875309[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]-0.939613827875309[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]-0.939613827875309[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]-0.939613827875309[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]-1.13385640100665[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]-0.939613827875309[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]-0.939613827875309[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]61[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=230463&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=230463&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 Mean-0.7693463525465171.02891120357779-0.74772861824354
Geometric MeanNaN
Harmonic Mean0.000792257219298152
Quadratic Mean8.00695882973367
Winsorized Mean ( 1 / 20 )-0.7121899119362151.00785492395399-0.706639313862921
Winsorized Mean ( 2 / 20 )-0.690597020488130.99537715778759-0.693804368610497
Winsorized Mean ( 3 / 20 )-0.7607939719376940.972634631806157-0.782199139387952
Winsorized Mean ( 4 / 20 )-0.8974795140536740.939363625668074-0.955412248814072
Winsorized Mean ( 5 / 20 )-0.9270872785173380.916401801393154-1.01166025329494
Winsorized Mean ( 6 / 20 )-1.009377729283470.860871324549968-1.17250708729454
Winsorized Mean ( 7 / 20 )-0.9088024999470650.829432893567807-1.09569141397063
Winsorized Mean ( 8 / 20 )-0.9098114313327160.8192936919046-1.11048265148691
Winsorized Mean ( 9 / 20 )-0.8403500633263160.782906124102636-1.07337270389796
Winsorized Mean ( 10 / 20 )-0.9731689884778870.744073808610639-1.30789308428289
Winsorized Mean ( 11 / 20 )-1.102556248488780.70258071542341-1.56929477892704
Winsorized Mean ( 12 / 20 )-0.9384433042563670.671162689138062-1.39823521099118
Winsorized Mean ( 13 / 20 )-0.9794751510506910.653639356286528-1.49849476111003
Winsorized Mean ( 14 / 20 )-0.979963157240460.639328224295555-1.53280133740417
Winsorized Mean ( 15 / 20 )-1.092644524833960.618972486368883-1.76525540132455
Winsorized Mean ( 16 / 20 )-1.141836215996910.595935979678967-1.9160383915937
Winsorized Mean ( 17 / 20 )-0.8474965823504890.535959589413665-1.5812695566799
Winsorized Mean ( 18 / 20 )-0.8471826369007490.5307410589904-1.59622592326341
Winsorized Mean ( 19 / 20 )-0.7117012964181560.485061204207413-1.46724019617498
Winsorized Mean ( 20 / 20 )-0.9724031410463290.44096762984277-2.20515764704327
Trimmed Mean ( 1 / 20 )-0.7627101292648710.977199113828589-0.780506366073782
Trimmed Mean ( 2 / 20 )-0.8167756250025560.939493638215347-0.869378558596837
Trimmed Mean ( 3 / 20 )-0.886747396596920.901223571963845-0.983937198474092
Trimmed Mean ( 4 / 20 )-0.9350691507114660.86492260505468-1.08110152890772
Trimmed Mean ( 5 / 20 )-0.9463091891238450.833077500979644-1.13591975297742
Trimmed Mean ( 6 / 20 )-0.9510950525809760.800977795779019-1.18741750095077
Trimmed Mean ( 7 / 20 )-0.9384878069112860.777916426579654-1.20641212197772
Trimmed Mean ( 8 / 20 )-0.9442363901646750.757299694188864-1.24684639041884
Trimmed Mean ( 9 / 20 )-0.9503408160040630.733011213444526-1.29648878294545
Trimmed Mean ( 10 / 20 )-0.9685235691567530.710905589696749-1.36238001669096
Trimmed Mean ( 11 / 20 )-0.9677969779296020.691710695709801-1.39913548240929
Trimmed Mean ( 12 / 20 )-0.9475996425386680.676275775783999-1.4012029950949
Trimmed Mean ( 13 / 20 )-0.9489294916701450.662668343734782-1.43198253038919
Trimmed Mean ( 14 / 20 )-0.9445861694738430.647306772429683-1.459255811473
Trimmed Mean ( 15 / 20 )-0.939613827875310.628372826259688-1.49531263703468
Trimmed Mean ( 16 / 20 )-0.9181543508305340.605904879274421-1.51534404530631
Trimmed Mean ( 17 / 20 )-0.8865696430176890.578924131070574-1.53140903174688
Trimmed Mean ( 18 / 20 )-0.8921777764310990.558669979365387-1.59696745732526
Trimmed Mean ( 19 / 20 )-0.8988074950575520.526730135899563-1.70639087038858
Trimmed Mean ( 20 / 20 )-0.9274127033708430.493585025884706-1.87893200712185
Median-0.894411455568734
Midrange-0.96511493935505
Midmean - Weighted Average at Xnp-1.12489409551076
Midmean - Weighted Average at X(n+1)p-0.939613827875309
Midmean - Empirical Distribution Function-0.939613827875309
Midmean - Empirical Distribution Function - Averaging-0.939613827875309
Midmean - Empirical Distribution Function - Interpolation-0.939613827875309
Midmean - Closest Observation-1.13385640100665
Midmean - True Basic - Statistics Graphics Toolkit-0.939613827875309
Midmean - MS Excel (old versions)-0.939613827875309
Number of observations61



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')