Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationWed, 19 Oct 2011 13:46:39 -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/2011/Oct/19/t1319046670u67pi7q7l6fdxsz.htm/, Retrieved Wed, 15 May 2024 08:06:48 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=132820, Retrieved Wed, 15 May 2024 08:06:48 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDG2011W52a
Estimated Impact94
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Centrummaten farm...] [2011-10-19 17:46:39] [459538fe31c621d37110fb87514358a8] [Current]
Feedback Forum

Post a new message
Dataseries X:
105,71
105,82
105,82
105,72
105,76
105,8
105,09
105,06
105,16
105,2
105,21
105,23
105,19
105,16
104,88
104,52
104,09
104,35
104,48
104,47
104,55
104,59
104,59
104,72
104,65
104,72
104,92
105,05
103,74
103,81
103,79
104,28
103,8
103,8
104,02
104,02
104,91
104,97
103,86
104,17
103,21
103,21
101,91
101,84
101,91
101,79
101,79
101,79
102,09
102,18
102,2
101,97
102,05
102,04
101,78
101,79
101,8
101,83
101,83
101,88
101,9




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'AstonUniversity' @ aston.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 & 'AstonUniversity' @ aston.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=132820&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]'AstonUniversity' @ aston.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=132820&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=132820&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'AstonUniversity' @ aston.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean103.8109836065570.180997645867919573.548805614369
Geometric Mean103.801487646146
Harmonic Mean103.791963744502
Quadratic Mean103.820450423939
Winsorized Mean ( 1 / 20 )103.8111475409840.180967058917225573.6466523914
Winsorized Mean ( 2 / 20 )103.8104918032790.180846284126843574.026125582252
Winsorized Mean ( 3 / 20 )103.8085245901640.180488686363502575.152529954674
Winsorized Mean ( 4 / 20 )103.8059016393440.180019940766921576.635572687728
Winsorized Mean ( 5 / 20 )103.8059016393440.179722216903167577.590814469388
Winsorized Mean ( 6 / 20 )103.7616393442620.171617852945462604.608655588042
Winsorized Mean ( 7 / 20 )103.7593442622950.171292238834203605.744574117718
Winsorized Mean ( 8 / 20 )103.7593442622950.170861665333281607.271057904668
Winsorized Mean ( 9 / 20 )103.7637704918030.16955569775512611.974542086246
Winsorized Mean ( 10 / 20 )103.7621311475410.168264544959382616.660694459363
Winsorized Mean ( 11 / 20 )103.763934426230.167932343696747617.891301592308
Winsorized Mean ( 12 / 20 )103.7501639344260.166052281549606624.804206038159
Winsorized Mean ( 13 / 20 )103.7565573770490.162845913499516637.145600692998
Winsorized Mean ( 14 / 20 )103.7703278688520.159619247646691650.111621240958
Winsorized Mean ( 15 / 20 )103.7531147540980.156585586678303662.596838923966
Winsorized Mean ( 16 / 20 )103.7504918032790.15300084399737678.104048923169
Winsorized Mean ( 17 / 20 )103.7727868852460.148128789619281700.557853419054
Winsorized Mean ( 18 / 20 )103.7698360655740.145943415152615711.027873077111
Winsorized Mean ( 19 / 20 )104.0345901639340.08516861250346061221.51326769245
Winsorized Mean ( 20 / 20 )104.0345901639340.08516861250346061221.51326769245
Trimmed Mean ( 1 / 20 )103.8113559322030.180703453276721574.484626883315
Trimmed Mean ( 2 / 20 )103.8115789473680.180173751679012576.174820027688
Trimmed Mean ( 3 / 20 )103.8121818181820.179392857627096578.686259817413
Trimmed Mean ( 4 / 20 )103.813584905660.178382324181865581.972375243972
Trimmed Mean ( 5 / 20 )103.8158823529410.177086480805192586.243974587457
Trimmed Mean ( 6 / 20 )103.8183673469390.175346194726312592.07653470315
Trimmed Mean ( 7 / 20 )103.8306382978720.175198949751466592.644182200663
Trimmed Mean ( 8 / 20 )103.8444444444440.174726497835948594.325678878681
Trimmed Mean ( 9 / 20 )103.8595348837210.173848036863213597.41563239762
Trimmed Mean ( 10 / 20 )103.8753658536590.172647991505406601.659856844649
Trimmed Mean ( 11 / 20 )103.8930769230770.170968959564108607.672159835073
Trimmed Mean ( 12 / 20 )103.9124324324320.168387247367153617.103931902046
Trimmed Mean ( 13 / 20 )103.9360.164883559627072630.359996078924
Trimmed Mean ( 14 / 20 )103.9615151515150.160497640648736647.744818748112
Trimmed Mean ( 15 / 20 )103.9883870967740.154859004046375671.503654160357
Trimmed Mean ( 16 / 20 )104.0213793103450.147015233400172707.555107756765
Trimmed Mean ( 17 / 20 )104.059629629630.135940829973865765.477374602136
Trimmed Mean ( 18 / 20 )104.10080.12023854068753865.785624182952
Trimmed Mean ( 19 / 20 )104.1495652173910.09324513627572721116.94367531857
Trimmed Mean ( 20 / 20 )104.1671428571430.08707999293791931196.22360249162
Median104.17
Midrange103.8
Midmean - Weighted Average at Xnp103.955666666667
Midmean - Weighted Average at X(n+1)p103.988387096774
Midmean - Empirical Distribution Function103.988387096774
Midmean - Empirical Distribution Function - Averaging103.988387096774
Midmean - Empirical Distribution Function - Interpolation103.988387096774
Midmean - Closest Observation103.9275
Midmean - True Basic - Statistics Graphics Toolkit103.988387096774
Midmean - MS Excel (old versions)103.988387096774
Number of observations61

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 103.810983606557 & 0.180997645867919 & 573.548805614369 \tabularnewline
Geometric Mean & 103.801487646146 &  &  \tabularnewline
Harmonic Mean & 103.791963744502 &  &  \tabularnewline
Quadratic Mean & 103.820450423939 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 103.811147540984 & 0.180967058917225 & 573.6466523914 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 103.810491803279 & 0.180846284126843 & 574.026125582252 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 103.808524590164 & 0.180488686363502 & 575.152529954674 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 103.805901639344 & 0.180019940766921 & 576.635572687728 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 103.805901639344 & 0.179722216903167 & 577.590814469388 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 103.761639344262 & 0.171617852945462 & 604.608655588042 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 103.759344262295 & 0.171292238834203 & 605.744574117718 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 103.759344262295 & 0.170861665333281 & 607.271057904668 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 103.763770491803 & 0.16955569775512 & 611.974542086246 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 103.762131147541 & 0.168264544959382 & 616.660694459363 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 103.76393442623 & 0.167932343696747 & 617.891301592308 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 103.750163934426 & 0.166052281549606 & 624.804206038159 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 103.756557377049 & 0.162845913499516 & 637.145600692998 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 103.770327868852 & 0.159619247646691 & 650.111621240958 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 103.753114754098 & 0.156585586678303 & 662.596838923966 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 103.750491803279 & 0.15300084399737 & 678.104048923169 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 103.772786885246 & 0.148128789619281 & 700.557853419054 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 103.769836065574 & 0.145943415152615 & 711.027873077111 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 104.034590163934 & 0.0851686125034606 & 1221.51326769245 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 104.034590163934 & 0.0851686125034606 & 1221.51326769245 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 103.811355932203 & 0.180703453276721 & 574.484626883315 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 103.811578947368 & 0.180173751679012 & 576.174820027688 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 103.812181818182 & 0.179392857627096 & 578.686259817413 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 103.81358490566 & 0.178382324181865 & 581.972375243972 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 103.815882352941 & 0.177086480805192 & 586.243974587457 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 103.818367346939 & 0.175346194726312 & 592.07653470315 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 103.830638297872 & 0.175198949751466 & 592.644182200663 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 103.844444444444 & 0.174726497835948 & 594.325678878681 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 103.859534883721 & 0.173848036863213 & 597.41563239762 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 103.875365853659 & 0.172647991505406 & 601.659856844649 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 103.893076923077 & 0.170968959564108 & 607.672159835073 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 103.912432432432 & 0.168387247367153 & 617.103931902046 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 103.936 & 0.164883559627072 & 630.359996078924 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 103.961515151515 & 0.160497640648736 & 647.744818748112 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 103.988387096774 & 0.154859004046375 & 671.503654160357 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 104.021379310345 & 0.147015233400172 & 707.555107756765 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 104.05962962963 & 0.135940829973865 & 765.477374602136 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 104.1008 & 0.12023854068753 & 865.785624182952 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 104.149565217391 & 0.0932451362757272 & 1116.94367531857 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 104.167142857143 & 0.0870799929379193 & 1196.22360249162 \tabularnewline
Median & 104.17 &  &  \tabularnewline
Midrange & 103.8 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 103.955666666667 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 103.988387096774 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 103.988387096774 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 103.988387096774 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 103.988387096774 &  &  \tabularnewline
Midmean - Closest Observation & 103.9275 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 103.988387096774 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 103.988387096774 &  &  \tabularnewline
Number of observations & 61 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=132820&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]103.810983606557[/C][C]0.180997645867919[/C][C]573.548805614369[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]103.801487646146[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]103.791963744502[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]103.820450423939[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]103.811147540984[/C][C]0.180967058917225[/C][C]573.6466523914[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]103.810491803279[/C][C]0.180846284126843[/C][C]574.026125582252[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]103.808524590164[/C][C]0.180488686363502[/C][C]575.152529954674[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]103.805901639344[/C][C]0.180019940766921[/C][C]576.635572687728[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]103.805901639344[/C][C]0.179722216903167[/C][C]577.590814469388[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]103.761639344262[/C][C]0.171617852945462[/C][C]604.608655588042[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]103.759344262295[/C][C]0.171292238834203[/C][C]605.744574117718[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]103.759344262295[/C][C]0.170861665333281[/C][C]607.271057904668[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]103.763770491803[/C][C]0.16955569775512[/C][C]611.974542086246[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]103.762131147541[/C][C]0.168264544959382[/C][C]616.660694459363[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]103.76393442623[/C][C]0.167932343696747[/C][C]617.891301592308[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]103.750163934426[/C][C]0.166052281549606[/C][C]624.804206038159[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]103.756557377049[/C][C]0.162845913499516[/C][C]637.145600692998[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]103.770327868852[/C][C]0.159619247646691[/C][C]650.111621240958[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]103.753114754098[/C][C]0.156585586678303[/C][C]662.596838923966[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]103.750491803279[/C][C]0.15300084399737[/C][C]678.104048923169[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]103.772786885246[/C][C]0.148128789619281[/C][C]700.557853419054[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]103.769836065574[/C][C]0.145943415152615[/C][C]711.027873077111[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]104.034590163934[/C][C]0.0851686125034606[/C][C]1221.51326769245[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]104.034590163934[/C][C]0.0851686125034606[/C][C]1221.51326769245[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]103.811355932203[/C][C]0.180703453276721[/C][C]574.484626883315[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]103.811578947368[/C][C]0.180173751679012[/C][C]576.174820027688[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]103.812181818182[/C][C]0.179392857627096[/C][C]578.686259817413[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]103.81358490566[/C][C]0.178382324181865[/C][C]581.972375243972[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]103.815882352941[/C][C]0.177086480805192[/C][C]586.243974587457[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]103.818367346939[/C][C]0.175346194726312[/C][C]592.07653470315[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]103.830638297872[/C][C]0.175198949751466[/C][C]592.644182200663[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]103.844444444444[/C][C]0.174726497835948[/C][C]594.325678878681[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]103.859534883721[/C][C]0.173848036863213[/C][C]597.41563239762[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]103.875365853659[/C][C]0.172647991505406[/C][C]601.659856844649[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]103.893076923077[/C][C]0.170968959564108[/C][C]607.672159835073[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]103.912432432432[/C][C]0.168387247367153[/C][C]617.103931902046[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]103.936[/C][C]0.164883559627072[/C][C]630.359996078924[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]103.961515151515[/C][C]0.160497640648736[/C][C]647.744818748112[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]103.988387096774[/C][C]0.154859004046375[/C][C]671.503654160357[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]104.021379310345[/C][C]0.147015233400172[/C][C]707.555107756765[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]104.05962962963[/C][C]0.135940829973865[/C][C]765.477374602136[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]104.1008[/C][C]0.12023854068753[/C][C]865.785624182952[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]104.149565217391[/C][C]0.0932451362757272[/C][C]1116.94367531857[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]104.167142857143[/C][C]0.0870799929379193[/C][C]1196.22360249162[/C][/ROW]
[ROW][C]Median[/C][C]104.17[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]103.8[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]103.955666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]103.988387096774[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]103.988387096774[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]103.988387096774[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]103.988387096774[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]103.9275[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]103.988387096774[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]103.988387096774[/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=132820&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=132820&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 Mean103.8109836065570.180997645867919573.548805614369
Geometric Mean103.801487646146
Harmonic Mean103.791963744502
Quadratic Mean103.820450423939
Winsorized Mean ( 1 / 20 )103.8111475409840.180967058917225573.6466523914
Winsorized Mean ( 2 / 20 )103.8104918032790.180846284126843574.026125582252
Winsorized Mean ( 3 / 20 )103.8085245901640.180488686363502575.152529954674
Winsorized Mean ( 4 / 20 )103.8059016393440.180019940766921576.635572687728
Winsorized Mean ( 5 / 20 )103.8059016393440.179722216903167577.590814469388
Winsorized Mean ( 6 / 20 )103.7616393442620.171617852945462604.608655588042
Winsorized Mean ( 7 / 20 )103.7593442622950.171292238834203605.744574117718
Winsorized Mean ( 8 / 20 )103.7593442622950.170861665333281607.271057904668
Winsorized Mean ( 9 / 20 )103.7637704918030.16955569775512611.974542086246
Winsorized Mean ( 10 / 20 )103.7621311475410.168264544959382616.660694459363
Winsorized Mean ( 11 / 20 )103.763934426230.167932343696747617.891301592308
Winsorized Mean ( 12 / 20 )103.7501639344260.166052281549606624.804206038159
Winsorized Mean ( 13 / 20 )103.7565573770490.162845913499516637.145600692998
Winsorized Mean ( 14 / 20 )103.7703278688520.159619247646691650.111621240958
Winsorized Mean ( 15 / 20 )103.7531147540980.156585586678303662.596838923966
Winsorized Mean ( 16 / 20 )103.7504918032790.15300084399737678.104048923169
Winsorized Mean ( 17 / 20 )103.7727868852460.148128789619281700.557853419054
Winsorized Mean ( 18 / 20 )103.7698360655740.145943415152615711.027873077111
Winsorized Mean ( 19 / 20 )104.0345901639340.08516861250346061221.51326769245
Winsorized Mean ( 20 / 20 )104.0345901639340.08516861250346061221.51326769245
Trimmed Mean ( 1 / 20 )103.8113559322030.180703453276721574.484626883315
Trimmed Mean ( 2 / 20 )103.8115789473680.180173751679012576.174820027688
Trimmed Mean ( 3 / 20 )103.8121818181820.179392857627096578.686259817413
Trimmed Mean ( 4 / 20 )103.813584905660.178382324181865581.972375243972
Trimmed Mean ( 5 / 20 )103.8158823529410.177086480805192586.243974587457
Trimmed Mean ( 6 / 20 )103.8183673469390.175346194726312592.07653470315
Trimmed Mean ( 7 / 20 )103.8306382978720.175198949751466592.644182200663
Trimmed Mean ( 8 / 20 )103.8444444444440.174726497835948594.325678878681
Trimmed Mean ( 9 / 20 )103.8595348837210.173848036863213597.41563239762
Trimmed Mean ( 10 / 20 )103.8753658536590.172647991505406601.659856844649
Trimmed Mean ( 11 / 20 )103.8930769230770.170968959564108607.672159835073
Trimmed Mean ( 12 / 20 )103.9124324324320.168387247367153617.103931902046
Trimmed Mean ( 13 / 20 )103.9360.164883559627072630.359996078924
Trimmed Mean ( 14 / 20 )103.9615151515150.160497640648736647.744818748112
Trimmed Mean ( 15 / 20 )103.9883870967740.154859004046375671.503654160357
Trimmed Mean ( 16 / 20 )104.0213793103450.147015233400172707.555107756765
Trimmed Mean ( 17 / 20 )104.059629629630.135940829973865765.477374602136
Trimmed Mean ( 18 / 20 )104.10080.12023854068753865.785624182952
Trimmed Mean ( 19 / 20 )104.1495652173910.09324513627572721116.94367531857
Trimmed Mean ( 20 / 20 )104.1671428571430.08707999293791931196.22360249162
Median104.17
Midrange103.8
Midmean - Weighted Average at Xnp103.955666666667
Midmean - Weighted Average at X(n+1)p103.988387096774
Midmean - Empirical Distribution Function103.988387096774
Midmean - Empirical Distribution Function - Averaging103.988387096774
Midmean - Empirical Distribution Function - Interpolation103.988387096774
Midmean - Closest Observation103.9275
Midmean - True Basic - Statistics Graphics Toolkit103.988387096774
Midmean - MS Excel (old versions)103.988387096774
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')