Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationTue, 14 Mar 2017 13:20:37 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2017/Mar/14/t148949771072x9t4uy1cprao3.htm/, Retrieved Tue, 14 May 2024 08:42:48 +0200
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Tue, 14 May 2024 08:42:48 +0200
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact0
Dataseries X:
93,55
94,11
94,47
94,38
94,42
94,39
94,42
94,34
94,59
94,63
94,84
94,98
95,19
95,76
96,08
96,04
96,2
96,31
96,3
96,29
96,46
96,66
96,83
97
97,1
97,33
97,31
97,16
97,4
97,4
97,52
97,77
98
98,2
98,48
98,53
98,71
99,03
99,52
99,65
99,98
99,94
100,12
100,17
100,38
100,75
100,84
100,91
100,9
101,15
101,4
101,39
101,55
101,73
101,7
101,65
101,73
101,53
101,58
101,58
101,71
101,71
101,98
101,99
101,95
102,11
102,28
102,32
102,18
102,14
102,29
102,33




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ jenkins.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 & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=0

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







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean98.65722222222220.333077614483532296.19889759088
Geometric Mean98.6171345409853
Harmonic Mean98.5768937767631
Quadratic Mean98.6971341332215
Winsorized Mean ( 1 / 24 )98.66486111111110.331463298648819297.664512219934
Winsorized Mean ( 2 / 24 )98.67041666666670.330125731104447298.887385532056
Winsorized Mean ( 3 / 24 )98.67166666666670.329754734103298299.227445316242
Winsorized Mean ( 4 / 24 )98.66666666666670.328806765272385300.074928765322
Winsorized Mean ( 5 / 24 )98.66597222222220.328009817720771300.801887296601
Winsorized Mean ( 6 / 24 )98.66347222222220.327638152521295301.135479683824
Winsorized Mean ( 7 / 24 )98.65666666666670.3250469449663303.51513279688
Winsorized Mean ( 8 / 24 )98.66888888888890.322489251774378305.960240057613
Winsorized Mean ( 9 / 24 )98.67013888888890.321059870211756307.326290338966
Winsorized Mean ( 10 / 24 )98.668750.311637538337813316.613815287694
Winsorized Mean ( 11 / 24 )98.69013888888890.307972158280646320.451496134776
Winsorized Mean ( 12 / 24 )98.72180555555550.30165190262868327.270621187089
Winsorized Mean ( 13 / 24 )98.82472222222220.285362930394126346.312403246391
Winsorized Mean ( 14 / 24 )98.87722222222220.2770377780139356.908804752474
Winsorized Mean ( 15 / 24 )98.87513888888890.274349422018912360.398568224696
Winsorized Mean ( 16 / 24 )98.886250.268348163756327368.499819845212
Winsorized Mean ( 17 / 24 )98.90750.265373975790023372.709869931859
Winsorized Mean ( 18 / 24 )98.90250.263965096894868374.680217814521
Winsorized Mean ( 19 / 24 )98.89986111111110.262854090345291376.253840985294
Winsorized Mean ( 20 / 24 )98.90541666666670.252053222506168392.398937348426
Winsorized Mean ( 21 / 24 )98.96083333333330.243780760267668405.94193415705
Winsorized Mean ( 22 / 24 )98.93944444444440.22673827653082436.359691703822
Winsorized Mean ( 23 / 24 )98.91708333333330.209264252295351472.689827566554
Winsorized Mean ( 24 / 24 )98.94708333333330.204545991160913483.740027226901
Trimmed Mean ( 1 / 24 )98.67771428571430.330482561498484298.586750956803
Trimmed Mean ( 2 / 24 )98.69132352941180.329079242267685299.901394112038
Trimmed Mean ( 3 / 24 )98.70272727272730.32798406248267300.937571556369
Trimmed Mean ( 4 / 24 )98.7143750.326567866117528302.278286512348
Trimmed Mean ( 5 / 24 )98.72822580645160.324919672308185303.854257592653
Trimmed Mean ( 6 / 24 )98.74316666666670.322885077915486305.815206153665
Trimmed Mean ( 7 / 24 )98.75965517241380.320229799285935308.402451591429
Trimmed Mean ( 8 / 24 )98.77857142857140.31733697405446311.273439607512
Trimmed Mean ( 9 / 24 )98.79685185185190.314095356010958314.544134324626
Trimmed Mean ( 10 / 24 )98.81634615384620.310104107080536318.655393132806
Trimmed Mean ( 11 / 24 )98.83760.306863734965106322.089542484514
Trimmed Mean ( 12 / 24 )98.85770833333330.303232180485862326.013248906946
Trimmed Mean ( 13 / 24 )98.87543478260870.299626612486797329.995503276485
Trimmed Mean ( 14 / 24 )98.88181818181820.298068176276861331.742285999602
Trimmed Mean ( 15 / 24 )98.8823809523810.297175986121867332.740145806502
Trimmed Mean ( 16 / 24 )98.883250.295872111037427334.209431410355
Trimmed Mean ( 17 / 24 )98.88289473684210.294678479920764335.56198187065
Trimmed Mean ( 18 / 24 )98.880.292895777552249337.594487794762
Trimmed Mean ( 19 / 24 )98.87735294117650.289918640263279341.052071889495
Trimmed Mean ( 20 / 24 )98.87468750.28518386272627346.705057413798
Trimmed Mean ( 21 / 24 )98.8710.280539033692796352.4322398154
Trimmed Mean ( 22 / 24 )98.860.275146906407868359.298969741834
Trimmed Mean ( 23 / 24 )98.850.271366910289372364.266962005763
Trimmed Mean ( 24 / 24 )98.841250.269856585972538366.273254528087
Median98.62
Midrange97.94
Midmean - Weighted Average at Xnp98.81
Midmean - Weighted Average at X(n+1)p98.88
Midmean - Empirical Distribution Function98.81
Midmean - Empirical Distribution Function - Averaging98.88
Midmean - Empirical Distribution Function - Interpolation98.88
Midmean - Closest Observation98.81
Midmean - True Basic - Statistics Graphics Toolkit98.88
Midmean - MS Excel (old versions)98.9520512820513
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 98.6572222222222 & 0.333077614483532 & 296.19889759088 \tabularnewline
Geometric Mean & 98.6171345409853 &  &  \tabularnewline
Harmonic Mean & 98.5768937767631 &  &  \tabularnewline
Quadratic Mean & 98.6971341332215 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 98.6648611111111 & 0.331463298648819 & 297.664512219934 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 98.6704166666667 & 0.330125731104447 & 298.887385532056 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 98.6716666666667 & 0.329754734103298 & 299.227445316242 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 98.6666666666667 & 0.328806765272385 & 300.074928765322 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 98.6659722222222 & 0.328009817720771 & 300.801887296601 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 98.6634722222222 & 0.327638152521295 & 301.135479683824 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 98.6566666666667 & 0.3250469449663 & 303.51513279688 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 98.6688888888889 & 0.322489251774378 & 305.960240057613 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 98.6701388888889 & 0.321059870211756 & 307.326290338966 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 98.66875 & 0.311637538337813 & 316.613815287694 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 98.6901388888889 & 0.307972158280646 & 320.451496134776 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 98.7218055555555 & 0.30165190262868 & 327.270621187089 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 98.8247222222222 & 0.285362930394126 & 346.312403246391 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 98.8772222222222 & 0.2770377780139 & 356.908804752474 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 98.8751388888889 & 0.274349422018912 & 360.398568224696 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 98.88625 & 0.268348163756327 & 368.499819845212 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 98.9075 & 0.265373975790023 & 372.709869931859 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 98.9025 & 0.263965096894868 & 374.680217814521 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 98.8998611111111 & 0.262854090345291 & 376.253840985294 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 98.9054166666667 & 0.252053222506168 & 392.398937348426 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 98.9608333333333 & 0.243780760267668 & 405.94193415705 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 98.9394444444444 & 0.22673827653082 & 436.359691703822 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 98.9170833333333 & 0.209264252295351 & 472.689827566554 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 98.9470833333333 & 0.204545991160913 & 483.740027226901 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 98.6777142857143 & 0.330482561498484 & 298.586750956803 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 98.6913235294118 & 0.329079242267685 & 299.901394112038 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 98.7027272727273 & 0.32798406248267 & 300.937571556369 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 98.714375 & 0.326567866117528 & 302.278286512348 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 98.7282258064516 & 0.324919672308185 & 303.854257592653 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 98.7431666666667 & 0.322885077915486 & 305.815206153665 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 98.7596551724138 & 0.320229799285935 & 308.402451591429 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 98.7785714285714 & 0.31733697405446 & 311.273439607512 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 98.7968518518519 & 0.314095356010958 & 314.544134324626 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 98.8163461538462 & 0.310104107080536 & 318.655393132806 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 98.8376 & 0.306863734965106 & 322.089542484514 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 98.8577083333333 & 0.303232180485862 & 326.013248906946 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 98.8754347826087 & 0.299626612486797 & 329.995503276485 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 98.8818181818182 & 0.298068176276861 & 331.742285999602 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 98.882380952381 & 0.297175986121867 & 332.740145806502 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 98.88325 & 0.295872111037427 & 334.209431410355 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 98.8828947368421 & 0.294678479920764 & 335.56198187065 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 98.88 & 0.292895777552249 & 337.594487794762 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 98.8773529411765 & 0.289918640263279 & 341.052071889495 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 98.8746875 & 0.28518386272627 & 346.705057413798 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 98.871 & 0.280539033692796 & 352.4322398154 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 98.86 & 0.275146906407868 & 359.298969741834 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 98.85 & 0.271366910289372 & 364.266962005763 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 98.84125 & 0.269856585972538 & 366.273254528087 \tabularnewline
Median & 98.62 &  &  \tabularnewline
Midrange & 97.94 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 98.81 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 98.88 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 98.81 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 98.88 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 98.88 &  &  \tabularnewline
Midmean - Closest Observation & 98.81 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 98.88 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 98.9520512820513 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]98.6572222222222[/C][C]0.333077614483532[/C][C]296.19889759088[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]98.6171345409853[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]98.5768937767631[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]98.6971341332215[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]98.6648611111111[/C][C]0.331463298648819[/C][C]297.664512219934[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]98.6704166666667[/C][C]0.330125731104447[/C][C]298.887385532056[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]98.6716666666667[/C][C]0.329754734103298[/C][C]299.227445316242[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]98.6666666666667[/C][C]0.328806765272385[/C][C]300.074928765322[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]98.6659722222222[/C][C]0.328009817720771[/C][C]300.801887296601[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]98.6634722222222[/C][C]0.327638152521295[/C][C]301.135479683824[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]98.6566666666667[/C][C]0.3250469449663[/C][C]303.51513279688[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]98.6688888888889[/C][C]0.322489251774378[/C][C]305.960240057613[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]98.6701388888889[/C][C]0.321059870211756[/C][C]307.326290338966[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]98.66875[/C][C]0.311637538337813[/C][C]316.613815287694[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]98.6901388888889[/C][C]0.307972158280646[/C][C]320.451496134776[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]98.7218055555555[/C][C]0.30165190262868[/C][C]327.270621187089[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]98.8247222222222[/C][C]0.285362930394126[/C][C]346.312403246391[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]98.8772222222222[/C][C]0.2770377780139[/C][C]356.908804752474[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]98.8751388888889[/C][C]0.274349422018912[/C][C]360.398568224696[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]98.88625[/C][C]0.268348163756327[/C][C]368.499819845212[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]98.9075[/C][C]0.265373975790023[/C][C]372.709869931859[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]98.9025[/C][C]0.263965096894868[/C][C]374.680217814521[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]98.8998611111111[/C][C]0.262854090345291[/C][C]376.253840985294[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]98.9054166666667[/C][C]0.252053222506168[/C][C]392.398937348426[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]98.9608333333333[/C][C]0.243780760267668[/C][C]405.94193415705[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]98.9394444444444[/C][C]0.22673827653082[/C][C]436.359691703822[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]98.9170833333333[/C][C]0.209264252295351[/C][C]472.689827566554[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]98.9470833333333[/C][C]0.204545991160913[/C][C]483.740027226901[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]98.6777142857143[/C][C]0.330482561498484[/C][C]298.586750956803[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]98.6913235294118[/C][C]0.329079242267685[/C][C]299.901394112038[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]98.7027272727273[/C][C]0.32798406248267[/C][C]300.937571556369[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]98.714375[/C][C]0.326567866117528[/C][C]302.278286512348[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]98.7282258064516[/C][C]0.324919672308185[/C][C]303.854257592653[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]98.7431666666667[/C][C]0.322885077915486[/C][C]305.815206153665[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]98.7596551724138[/C][C]0.320229799285935[/C][C]308.402451591429[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]98.7785714285714[/C][C]0.31733697405446[/C][C]311.273439607512[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]98.7968518518519[/C][C]0.314095356010958[/C][C]314.544134324626[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]98.8163461538462[/C][C]0.310104107080536[/C][C]318.655393132806[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]98.8376[/C][C]0.306863734965106[/C][C]322.089542484514[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]98.8577083333333[/C][C]0.303232180485862[/C][C]326.013248906946[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]98.8754347826087[/C][C]0.299626612486797[/C][C]329.995503276485[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]98.8818181818182[/C][C]0.298068176276861[/C][C]331.742285999602[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]98.882380952381[/C][C]0.297175986121867[/C][C]332.740145806502[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]98.88325[/C][C]0.295872111037427[/C][C]334.209431410355[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]98.8828947368421[/C][C]0.294678479920764[/C][C]335.56198187065[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]98.88[/C][C]0.292895777552249[/C][C]337.594487794762[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]98.8773529411765[/C][C]0.289918640263279[/C][C]341.052071889495[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]98.8746875[/C][C]0.28518386272627[/C][C]346.705057413798[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]98.871[/C][C]0.280539033692796[/C][C]352.4322398154[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]98.86[/C][C]0.275146906407868[/C][C]359.298969741834[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]98.85[/C][C]0.271366910289372[/C][C]364.266962005763[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]98.84125[/C][C]0.269856585972538[/C][C]366.273254528087[/C][/ROW]
[ROW][C]Median[/C][C]98.62[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]97.94[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]98.81[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]98.88[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]98.81[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]98.88[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]98.88[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]98.81[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]98.88[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]98.9520512820513[/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=&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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 Mean98.65722222222220.333077614483532296.19889759088
Geometric Mean98.6171345409853
Harmonic Mean98.5768937767631
Quadratic Mean98.6971341332215
Winsorized Mean ( 1 / 24 )98.66486111111110.331463298648819297.664512219934
Winsorized Mean ( 2 / 24 )98.67041666666670.330125731104447298.887385532056
Winsorized Mean ( 3 / 24 )98.67166666666670.329754734103298299.227445316242
Winsorized Mean ( 4 / 24 )98.66666666666670.328806765272385300.074928765322
Winsorized Mean ( 5 / 24 )98.66597222222220.328009817720771300.801887296601
Winsorized Mean ( 6 / 24 )98.66347222222220.327638152521295301.135479683824
Winsorized Mean ( 7 / 24 )98.65666666666670.3250469449663303.51513279688
Winsorized Mean ( 8 / 24 )98.66888888888890.322489251774378305.960240057613
Winsorized Mean ( 9 / 24 )98.67013888888890.321059870211756307.326290338966
Winsorized Mean ( 10 / 24 )98.668750.311637538337813316.613815287694
Winsorized Mean ( 11 / 24 )98.69013888888890.307972158280646320.451496134776
Winsorized Mean ( 12 / 24 )98.72180555555550.30165190262868327.270621187089
Winsorized Mean ( 13 / 24 )98.82472222222220.285362930394126346.312403246391
Winsorized Mean ( 14 / 24 )98.87722222222220.2770377780139356.908804752474
Winsorized Mean ( 15 / 24 )98.87513888888890.274349422018912360.398568224696
Winsorized Mean ( 16 / 24 )98.886250.268348163756327368.499819845212
Winsorized Mean ( 17 / 24 )98.90750.265373975790023372.709869931859
Winsorized Mean ( 18 / 24 )98.90250.263965096894868374.680217814521
Winsorized Mean ( 19 / 24 )98.89986111111110.262854090345291376.253840985294
Winsorized Mean ( 20 / 24 )98.90541666666670.252053222506168392.398937348426
Winsorized Mean ( 21 / 24 )98.96083333333330.243780760267668405.94193415705
Winsorized Mean ( 22 / 24 )98.93944444444440.22673827653082436.359691703822
Winsorized Mean ( 23 / 24 )98.91708333333330.209264252295351472.689827566554
Winsorized Mean ( 24 / 24 )98.94708333333330.204545991160913483.740027226901
Trimmed Mean ( 1 / 24 )98.67771428571430.330482561498484298.586750956803
Trimmed Mean ( 2 / 24 )98.69132352941180.329079242267685299.901394112038
Trimmed Mean ( 3 / 24 )98.70272727272730.32798406248267300.937571556369
Trimmed Mean ( 4 / 24 )98.7143750.326567866117528302.278286512348
Trimmed Mean ( 5 / 24 )98.72822580645160.324919672308185303.854257592653
Trimmed Mean ( 6 / 24 )98.74316666666670.322885077915486305.815206153665
Trimmed Mean ( 7 / 24 )98.75965517241380.320229799285935308.402451591429
Trimmed Mean ( 8 / 24 )98.77857142857140.31733697405446311.273439607512
Trimmed Mean ( 9 / 24 )98.79685185185190.314095356010958314.544134324626
Trimmed Mean ( 10 / 24 )98.81634615384620.310104107080536318.655393132806
Trimmed Mean ( 11 / 24 )98.83760.306863734965106322.089542484514
Trimmed Mean ( 12 / 24 )98.85770833333330.303232180485862326.013248906946
Trimmed Mean ( 13 / 24 )98.87543478260870.299626612486797329.995503276485
Trimmed Mean ( 14 / 24 )98.88181818181820.298068176276861331.742285999602
Trimmed Mean ( 15 / 24 )98.8823809523810.297175986121867332.740145806502
Trimmed Mean ( 16 / 24 )98.883250.295872111037427334.209431410355
Trimmed Mean ( 17 / 24 )98.88289473684210.294678479920764335.56198187065
Trimmed Mean ( 18 / 24 )98.880.292895777552249337.594487794762
Trimmed Mean ( 19 / 24 )98.87735294117650.289918640263279341.052071889495
Trimmed Mean ( 20 / 24 )98.87468750.28518386272627346.705057413798
Trimmed Mean ( 21 / 24 )98.8710.280539033692796352.4322398154
Trimmed Mean ( 22 / 24 )98.860.275146906407868359.298969741834
Trimmed Mean ( 23 / 24 )98.850.271366910289372364.266962005763
Trimmed Mean ( 24 / 24 )98.841250.269856585972538366.273254528087
Median98.62
Midrange97.94
Midmean - Weighted Average at Xnp98.81
Midmean - Weighted Average at X(n+1)p98.88
Midmean - Empirical Distribution Function98.81
Midmean - Empirical Distribution Function - Averaging98.88
Midmean - Empirical Distribution Function - Interpolation98.88
Midmean - Closest Observation98.81
Midmean - True Basic - Statistics Graphics Toolkit98.88
Midmean - MS Excel (old versions)98.9520512820513
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')