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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationFri, 09 Oct 2015 08:59:24 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2015/Oct/09/t1444377599eq2ofc192hb4647.htm/, Retrieved Sat, 18 May 2024 22:55:33 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=281720, Retrieved Sat, 18 May 2024 22:55:33 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact98
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2015-10-09 07:59:24] [a231c0efc426ce58c731cc3abc4c2d25] [Current]
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Dataseries X:
85.74
86.62
86.66
87.39
87.59
88.8
88.64
89.55
89.04
88.49
89.5
89.46
90.33
90.27
91.5
92.53
93.14
93.01
92.84
92.88
93.05
93.17
93.67
94.9
95.72
96.08
97.52
98.26
98.48
98.09
98.03
98.14
98.71
98.69
98.72
98.47
99.49
99.84
100.9
101.31
100.09
99.28
99.57
101.04
101.87
101.39
100.3
99.95
99.87
100.51
100.27
100.04
99.23
99.32
99.95
100.23
101.02
99.83
99.61
100.12
99.83
100.03
100.07
100.46
100.43
100.68
101.8
101.21
100.63
100.55
99.76
98.8




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 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 & 1 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=281720&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=281720&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=281720&T=0

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Sir Ronald Aylmer Fisher' @ fisher.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean96.56888888888890.56339925703786171.404004677982
Geometric Mean96.4486490091076
Harmonic Mean96.324884835968
Quadratic Mean96.685505793555
Winsorized Mean ( 1 / 24 )96.58013888888890.560085663477056172.438155780157
Winsorized Mean ( 2 / 24 )96.56986111111110.558367719950683172.9502936159
Winsorized Mean ( 3 / 24 )96.59694444444440.550578996664805175.446112237465
Winsorized Mean ( 4 / 24 )96.60250.547317714275664176.501687192505
Winsorized Mean ( 5 / 24 )96.65319444444440.53192264381017181.705358042508
Winsorized Mean ( 6 / 24 )96.66402777777780.529043104487156182.71484300222
Winsorized Mean ( 7 / 24 )96.66791666666670.524398341342699184.340622472513
Winsorized Mean ( 8 / 24 )96.67013888888890.516076692275933187.317389713081
Winsorized Mean ( 9 / 24 )96.71638888888890.504608778935889191.666084551368
Winsorized Mean ( 10 / 24 )96.71083333333330.502279535720031192.543845519599
Winsorized Mean ( 11 / 24 )96.71236111111110.500080998644836193.393393016713
Winsorized Mean ( 12 / 24 )96.82402777777780.475421798543781203.659209725659
Winsorized Mean ( 13 / 24 )96.82944444444440.472738910002215204.826474816703
Winsorized Mean ( 14 / 24 )97.03166666666670.427184022826665227.142546260534
Winsorized Mean ( 15 / 24 )97.240.388559345058432250.257782335352
Winsorized Mean ( 16 / 24 )97.30.375945287448758258.814256351763
Winsorized Mean ( 17 / 24 )97.28347222222220.371545968723779261.834282730561
Winsorized Mean ( 18 / 24 )97.30847222222220.365335004993125266.354088418255
Winsorized Mean ( 19 / 24 )97.313750.363022136914089268.065608415031
Winsorized Mean ( 20 / 24 )97.33041666666670.358003802922379271.869784265307
Winsorized Mean ( 21 / 24 )97.336250.356251153115669273.223677028763
Winsorized Mean ( 22 / 24 )97.46458333333330.32863603081108296.573029721631
Winsorized Mean ( 23 / 24 )97.85750.265773132542062368.199370132016
Winsorized Mean ( 24 / 24 )98.10416666666670.220504095079416444.908592882749
Trimmed Mean ( 1 / 24 )96.64785714285710.552959546959626174.782870960927
Trimmed Mean ( 2 / 24 )96.71955882352940.544222848608433177.720503780463
Trimmed Mean ( 3 / 24 )96.80121212121210.534572025197366181.081701919349
Trimmed Mean ( 4 / 24 )96.87781250.52626121508758184.086931969474
Trimmed Mean ( 5 / 24 )96.95774193548390.51708987275656187.506557455111
Trimmed Mean ( 6 / 24 )97.03083333333330.510497281193016190.071204897655
Trimmed Mean ( 7 / 24 )97.1067241379310.502834337248095193.118721106787
Trimmed Mean ( 8 / 24 )97.18732142857140.494168098737498196.668545939865
Trimmed Mean ( 9 / 24 )97.27351851851850.484981874307923200.571451577091
Trimmed Mean ( 10 / 24 )97.35923076923080.475835602730693204.606864661896
Trimmed Mean ( 11 / 24 )97.45260.464266004856382209.906818463149
Trimmed Mean ( 12 / 24 )97.55354166666670.449483696087153217.034661136522
Trimmed Mean ( 13 / 24 )97.64869565217390.436210250318206223.856948755655
Trimmed Mean ( 14 / 24 )97.75181818181820.418968489776637233.315441535788
Trimmed Mean ( 15 / 24 )97.840.407683464468366239.990111268278
Trimmed Mean ( 16 / 24 )97.9120.401837159262434243.66089034602
Trimmed Mean ( 17 / 24 )97.98447368421050.396104914721273247.370002346876
Trimmed Mean ( 18 / 24 )98.06694444444440.388054941995402252.714071724427
Trimmed Mean ( 19 / 24 )98.15617647058820.37739491099166260.088765406689
Trimmed Mean ( 20 / 24 )98.25593750.36165609761002271.683342681951
Trimmed Mean ( 21 / 24 )98.3670.339070789069185290.107562111252
Trimmed Mean ( 22 / 24 )98.49321428571430.303860980801776324.139065258815
Trimmed Mean ( 23 / 24 )98.62269230769230.260121603333345379.140721277608
Trimmed Mean ( 24 / 24 )98.72250.225710833667289437.384853868037
Median98.76
Midrange93.805
Midmean - Weighted Average at Xnp97.9267567567568
Midmean - Weighted Average at X(n+1)p98.0669444444445
Midmean - Empirical Distribution Function97.9267567567568
Midmean - Empirical Distribution Function - Averaging98.0669444444445
Midmean - Empirical Distribution Function - Interpolation98.0669444444445
Midmean - Closest Observation97.9267567567568
Midmean - True Basic - Statistics Graphics Toolkit98.0669444444445
Midmean - MS Excel (old versions)97.9844736842105
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 96.5688888888889 & 0.56339925703786 & 171.404004677982 \tabularnewline
Geometric Mean & 96.4486490091076 &  &  \tabularnewline
Harmonic Mean & 96.324884835968 &  &  \tabularnewline
Quadratic Mean & 96.685505793555 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 96.5801388888889 & 0.560085663477056 & 172.438155780157 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 96.5698611111111 & 0.558367719950683 & 172.9502936159 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 96.5969444444444 & 0.550578996664805 & 175.446112237465 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 96.6025 & 0.547317714275664 & 176.501687192505 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 96.6531944444444 & 0.53192264381017 & 181.705358042508 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 96.6640277777778 & 0.529043104487156 & 182.71484300222 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 96.6679166666667 & 0.524398341342699 & 184.340622472513 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 96.6701388888889 & 0.516076692275933 & 187.317389713081 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 96.7163888888889 & 0.504608778935889 & 191.666084551368 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 96.7108333333333 & 0.502279535720031 & 192.543845519599 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 96.7123611111111 & 0.500080998644836 & 193.393393016713 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 96.8240277777778 & 0.475421798543781 & 203.659209725659 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 96.8294444444444 & 0.472738910002215 & 204.826474816703 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 97.0316666666667 & 0.427184022826665 & 227.142546260534 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 97.24 & 0.388559345058432 & 250.257782335352 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 97.3 & 0.375945287448758 & 258.814256351763 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 97.2834722222222 & 0.371545968723779 & 261.834282730561 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 97.3084722222222 & 0.365335004993125 & 266.354088418255 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 97.31375 & 0.363022136914089 & 268.065608415031 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 97.3304166666667 & 0.358003802922379 & 271.869784265307 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 97.33625 & 0.356251153115669 & 273.223677028763 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 97.4645833333333 & 0.32863603081108 & 296.573029721631 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 97.8575 & 0.265773132542062 & 368.199370132016 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 98.1041666666667 & 0.220504095079416 & 444.908592882749 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 96.6478571428571 & 0.552959546959626 & 174.782870960927 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 96.7195588235294 & 0.544222848608433 & 177.720503780463 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 96.8012121212121 & 0.534572025197366 & 181.081701919349 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 96.8778125 & 0.52626121508758 & 184.086931969474 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 96.9577419354839 & 0.51708987275656 & 187.506557455111 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 97.0308333333333 & 0.510497281193016 & 190.071204897655 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 97.106724137931 & 0.502834337248095 & 193.118721106787 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 97.1873214285714 & 0.494168098737498 & 196.668545939865 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 97.2735185185185 & 0.484981874307923 & 200.571451577091 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 97.3592307692308 & 0.475835602730693 & 204.606864661896 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 97.4526 & 0.464266004856382 & 209.906818463149 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 97.5535416666667 & 0.449483696087153 & 217.034661136522 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 97.6486956521739 & 0.436210250318206 & 223.856948755655 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 97.7518181818182 & 0.418968489776637 & 233.315441535788 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 97.84 & 0.407683464468366 & 239.990111268278 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 97.912 & 0.401837159262434 & 243.66089034602 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 97.9844736842105 & 0.396104914721273 & 247.370002346876 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 98.0669444444444 & 0.388054941995402 & 252.714071724427 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 98.1561764705882 & 0.37739491099166 & 260.088765406689 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 98.2559375 & 0.36165609761002 & 271.683342681951 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 98.367 & 0.339070789069185 & 290.107562111252 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 98.4932142857143 & 0.303860980801776 & 324.139065258815 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 98.6226923076923 & 0.260121603333345 & 379.140721277608 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 98.7225 & 0.225710833667289 & 437.384853868037 \tabularnewline
Median & 98.76 &  &  \tabularnewline
Midrange & 93.805 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 97.9267567567568 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 98.0669444444445 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 97.9267567567568 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 98.0669444444445 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 98.0669444444445 &  &  \tabularnewline
Midmean - Closest Observation & 97.9267567567568 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 98.0669444444445 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 97.9844736842105 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=281720&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]96.5688888888889[/C][C]0.56339925703786[/C][C]171.404004677982[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]96.4486490091076[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]96.324884835968[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]96.685505793555[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]96.5801388888889[/C][C]0.560085663477056[/C][C]172.438155780157[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]96.5698611111111[/C][C]0.558367719950683[/C][C]172.9502936159[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]96.5969444444444[/C][C]0.550578996664805[/C][C]175.446112237465[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]96.6025[/C][C]0.547317714275664[/C][C]176.501687192505[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]96.6531944444444[/C][C]0.53192264381017[/C][C]181.705358042508[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]96.6640277777778[/C][C]0.529043104487156[/C][C]182.71484300222[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]96.6679166666667[/C][C]0.524398341342699[/C][C]184.340622472513[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]96.6701388888889[/C][C]0.516076692275933[/C][C]187.317389713081[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]96.7163888888889[/C][C]0.504608778935889[/C][C]191.666084551368[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]96.7108333333333[/C][C]0.502279535720031[/C][C]192.543845519599[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]96.7123611111111[/C][C]0.500080998644836[/C][C]193.393393016713[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]96.8240277777778[/C][C]0.475421798543781[/C][C]203.659209725659[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]96.8294444444444[/C][C]0.472738910002215[/C][C]204.826474816703[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]97.0316666666667[/C][C]0.427184022826665[/C][C]227.142546260534[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]97.24[/C][C]0.388559345058432[/C][C]250.257782335352[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]97.3[/C][C]0.375945287448758[/C][C]258.814256351763[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]97.2834722222222[/C][C]0.371545968723779[/C][C]261.834282730561[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]97.3084722222222[/C][C]0.365335004993125[/C][C]266.354088418255[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]97.31375[/C][C]0.363022136914089[/C][C]268.065608415031[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]97.3304166666667[/C][C]0.358003802922379[/C][C]271.869784265307[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]97.33625[/C][C]0.356251153115669[/C][C]273.223677028763[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]97.4645833333333[/C][C]0.32863603081108[/C][C]296.573029721631[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]97.8575[/C][C]0.265773132542062[/C][C]368.199370132016[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]98.1041666666667[/C][C]0.220504095079416[/C][C]444.908592882749[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]96.6478571428571[/C][C]0.552959546959626[/C][C]174.782870960927[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]96.7195588235294[/C][C]0.544222848608433[/C][C]177.720503780463[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]96.8012121212121[/C][C]0.534572025197366[/C][C]181.081701919349[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]96.8778125[/C][C]0.52626121508758[/C][C]184.086931969474[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]96.9577419354839[/C][C]0.51708987275656[/C][C]187.506557455111[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]97.0308333333333[/C][C]0.510497281193016[/C][C]190.071204897655[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]97.106724137931[/C][C]0.502834337248095[/C][C]193.118721106787[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]97.1873214285714[/C][C]0.494168098737498[/C][C]196.668545939865[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]97.2735185185185[/C][C]0.484981874307923[/C][C]200.571451577091[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]97.3592307692308[/C][C]0.475835602730693[/C][C]204.606864661896[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]97.4526[/C][C]0.464266004856382[/C][C]209.906818463149[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]97.5535416666667[/C][C]0.449483696087153[/C][C]217.034661136522[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]97.6486956521739[/C][C]0.436210250318206[/C][C]223.856948755655[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]97.7518181818182[/C][C]0.418968489776637[/C][C]233.315441535788[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]97.84[/C][C]0.407683464468366[/C][C]239.990111268278[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]97.912[/C][C]0.401837159262434[/C][C]243.66089034602[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]97.9844736842105[/C][C]0.396104914721273[/C][C]247.370002346876[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]98.0669444444444[/C][C]0.388054941995402[/C][C]252.714071724427[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]98.1561764705882[/C][C]0.37739491099166[/C][C]260.088765406689[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]98.2559375[/C][C]0.36165609761002[/C][C]271.683342681951[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]98.367[/C][C]0.339070789069185[/C][C]290.107562111252[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]98.4932142857143[/C][C]0.303860980801776[/C][C]324.139065258815[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]98.6226923076923[/C][C]0.260121603333345[/C][C]379.140721277608[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]98.7225[/C][C]0.225710833667289[/C][C]437.384853868037[/C][/ROW]
[ROW][C]Median[/C][C]98.76[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]93.805[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]97.9267567567568[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]98.0669444444445[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]97.9267567567568[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]98.0669444444445[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]98.0669444444445[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]97.9267567567568[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]98.0669444444445[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]97.9844736842105[/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=281720&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=281720&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 Mean96.56888888888890.56339925703786171.404004677982
Geometric Mean96.4486490091076
Harmonic Mean96.324884835968
Quadratic Mean96.685505793555
Winsorized Mean ( 1 / 24 )96.58013888888890.560085663477056172.438155780157
Winsorized Mean ( 2 / 24 )96.56986111111110.558367719950683172.9502936159
Winsorized Mean ( 3 / 24 )96.59694444444440.550578996664805175.446112237465
Winsorized Mean ( 4 / 24 )96.60250.547317714275664176.501687192505
Winsorized Mean ( 5 / 24 )96.65319444444440.53192264381017181.705358042508
Winsorized Mean ( 6 / 24 )96.66402777777780.529043104487156182.71484300222
Winsorized Mean ( 7 / 24 )96.66791666666670.524398341342699184.340622472513
Winsorized Mean ( 8 / 24 )96.67013888888890.516076692275933187.317389713081
Winsorized Mean ( 9 / 24 )96.71638888888890.504608778935889191.666084551368
Winsorized Mean ( 10 / 24 )96.71083333333330.502279535720031192.543845519599
Winsorized Mean ( 11 / 24 )96.71236111111110.500080998644836193.393393016713
Winsorized Mean ( 12 / 24 )96.82402777777780.475421798543781203.659209725659
Winsorized Mean ( 13 / 24 )96.82944444444440.472738910002215204.826474816703
Winsorized Mean ( 14 / 24 )97.03166666666670.427184022826665227.142546260534
Winsorized Mean ( 15 / 24 )97.240.388559345058432250.257782335352
Winsorized Mean ( 16 / 24 )97.30.375945287448758258.814256351763
Winsorized Mean ( 17 / 24 )97.28347222222220.371545968723779261.834282730561
Winsorized Mean ( 18 / 24 )97.30847222222220.365335004993125266.354088418255
Winsorized Mean ( 19 / 24 )97.313750.363022136914089268.065608415031
Winsorized Mean ( 20 / 24 )97.33041666666670.358003802922379271.869784265307
Winsorized Mean ( 21 / 24 )97.336250.356251153115669273.223677028763
Winsorized Mean ( 22 / 24 )97.46458333333330.32863603081108296.573029721631
Winsorized Mean ( 23 / 24 )97.85750.265773132542062368.199370132016
Winsorized Mean ( 24 / 24 )98.10416666666670.220504095079416444.908592882749
Trimmed Mean ( 1 / 24 )96.64785714285710.552959546959626174.782870960927
Trimmed Mean ( 2 / 24 )96.71955882352940.544222848608433177.720503780463
Trimmed Mean ( 3 / 24 )96.80121212121210.534572025197366181.081701919349
Trimmed Mean ( 4 / 24 )96.87781250.52626121508758184.086931969474
Trimmed Mean ( 5 / 24 )96.95774193548390.51708987275656187.506557455111
Trimmed Mean ( 6 / 24 )97.03083333333330.510497281193016190.071204897655
Trimmed Mean ( 7 / 24 )97.1067241379310.502834337248095193.118721106787
Trimmed Mean ( 8 / 24 )97.18732142857140.494168098737498196.668545939865
Trimmed Mean ( 9 / 24 )97.27351851851850.484981874307923200.571451577091
Trimmed Mean ( 10 / 24 )97.35923076923080.475835602730693204.606864661896
Trimmed Mean ( 11 / 24 )97.45260.464266004856382209.906818463149
Trimmed Mean ( 12 / 24 )97.55354166666670.449483696087153217.034661136522
Trimmed Mean ( 13 / 24 )97.64869565217390.436210250318206223.856948755655
Trimmed Mean ( 14 / 24 )97.75181818181820.418968489776637233.315441535788
Trimmed Mean ( 15 / 24 )97.840.407683464468366239.990111268278
Trimmed Mean ( 16 / 24 )97.9120.401837159262434243.66089034602
Trimmed Mean ( 17 / 24 )97.98447368421050.396104914721273247.370002346876
Trimmed Mean ( 18 / 24 )98.06694444444440.388054941995402252.714071724427
Trimmed Mean ( 19 / 24 )98.15617647058820.37739491099166260.088765406689
Trimmed Mean ( 20 / 24 )98.25593750.36165609761002271.683342681951
Trimmed Mean ( 21 / 24 )98.3670.339070789069185290.107562111252
Trimmed Mean ( 22 / 24 )98.49321428571430.303860980801776324.139065258815
Trimmed Mean ( 23 / 24 )98.62269230769230.260121603333345379.140721277608
Trimmed Mean ( 24 / 24 )98.72250.225710833667289437.384853868037
Median98.76
Midrange93.805
Midmean - Weighted Average at Xnp97.9267567567568
Midmean - Weighted Average at X(n+1)p98.0669444444445
Midmean - Empirical Distribution Function97.9267567567568
Midmean - Empirical Distribution Function - Averaging98.0669444444445
Midmean - Empirical Distribution Function - Interpolation98.0669444444445
Midmean - Closest Observation97.9267567567568
Midmean - True Basic - Statistics Graphics Toolkit98.0669444444445
Midmean - MS Excel (old versions)97.9844736842105
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')