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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationThu, 10 Oct 2013 04:44:40 -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/2013/Oct/10/t1381394692a08su1fhshy03rp.htm/, Retrieved Thu, 02 May 2024 13:02:09 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=214519, Retrieved Thu, 02 May 2024 13:02:09 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact121
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2013-10-10 08:44:40] [98a545f74f3e64fcb7a2edd9d5a425e5] [Current]
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Dataseries X:
104.78
105.56
107.95
107.11
107.47
107.06
99.71
99.6
107.19
107.26
113.24
113.52
110.48
111.41
115.5
118.32
118.42
117.5
110.23
109.19
118.41
118.3
116.1
114.11
113.41
114.33
116.61
123.64
123.77
123.39
116.03
114.95
123.4
123.53
114.45
114.26
114.35
112.77
115.31
114.93
116.38
115.07
105
103.43
114.52
115.04
117.16
115
116.22
112.92
116.56
114.32
113.22
111.56
103.87
102.85
112.27
112.76
118.55
122.73
115.44
116.97
119.84
116.37
117.23
115.58
109.82
108.46
116.54
117.49
122.87
127.1




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'George Udny Yule' @ yule.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 & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=214519&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]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=214519&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=214519&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'George Udny Yule' @ yule.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean113.8984722222220.685013754808677166.271803190337
Geometric Mean113.750201114076
Harmonic Mean113.599800730612
Quadratic Mean114.04463287459
Winsorized Mean ( 1 / 24 )113.853750.673478068553371169.053389139393
Winsorized Mean ( 2 / 24 )113.9373611111110.649291084253723175.479632901578
Winsorized Mean ( 3 / 24 )113.9569444444440.642633338035989177.328093174747
Winsorized Mean ( 4 / 24 )113.9741666666670.635564292479372179.327517318582
Winsorized Mean ( 5 / 24 )114.0366666666670.621712102960153183.423591279154
Winsorized Mean ( 6 / 24 )114.0116666666670.608846172667474187.258574965101
Winsorized Mean ( 7 / 24 )114.05250.594902799427623191.716193149089
Winsorized Mean ( 8 / 24 )113.8980555555560.501799642308254226.979148553454
Winsorized Mean ( 9 / 24 )113.7430555555560.475610086702456239.151899288279
Winsorized Mean ( 10 / 24 )113.7361111111110.470881019046657241.538958910216
Winsorized Mean ( 11 / 24 )113.7452777777780.468577533623325242.745905673775
Winsorized Mean ( 12 / 24 )113.7652777777780.459692137411608247.48145230057
Winsorized Mean ( 13 / 24 )113.8483333333330.442690150827938257.17385652337
Winsorized Mean ( 14 / 24 )113.7919444444440.403003426889716282.359743991914
Winsorized Mean ( 15 / 24 )113.9419444444440.374965289937115303.873311749878
Winsorized Mean ( 16 / 24 )114.0241666666670.342699443889162332.723524067186
Winsorized Mean ( 17 / 24 )114.1044444444440.323991506733436352.183443309592
Winsorized Mean ( 18 / 24 )114.1194444444440.307253781273338371.417542760595
Winsorized Mean ( 19 / 24 )114.2698611111110.254939734283251448.223033700002
Winsorized Mean ( 20 / 24 )114.2976388888890.246594845293202463.503763645135
Winsorized Mean ( 21 / 24 )114.4988888888890.214405550406723534.029500037135
Winsorized Mean ( 22 / 24 )114.5997222222220.186436810633635614.683987742212
Winsorized Mean ( 23 / 24 )114.5997222222220.185563576312176617.576598272873
Winsorized Mean ( 24 / 24 )114.5997222222220.171972922066781666.382363252051
Trimmed Mean ( 1 / 24 )113.9141428571430.646703809722513176.145773605418
Trimmed Mean ( 2 / 24 )113.9780882352940.614582995927256185.455974198129
Trimmed Mean ( 3 / 24 )114.0003030303030.592028946628073192.558664030867
Trimmed Mean ( 4 / 24 )114.01656250.568055511743459200.713768536571
Trimmed Mean ( 5 / 24 )114.0288709677420.541767682039955210.475587134288
Trimmed Mean ( 6 / 24 )114.0270.514449587939453221.648539863191
Trimmed Mean ( 7 / 24 )114.0301724137930.484859918362325235.181684637791
Trimmed Mean ( 8 / 24 )114.0260714285710.452185506595212252.166577135887
Trimmed Mean ( 9 / 24 )114.0474074074070.437346533745243260.771261705805
Trimmed Mean ( 10 / 24 )114.0942307692310.424950298411708268.488411928804
Trimmed Mean ( 11 / 24 )114.14580.410272093884544278.219751480641
Trimmed Mean ( 12 / 24 )114.2004166666670.391991523457045291.333893293182
Trimmed Mean ( 13 / 24 )114.2571739130430.37055470405846308.340907999964
Trimmed Mean ( 14 / 24 )114.3086363636360.347135604631785329.29101722333
Trimmed Mean ( 15 / 24 )114.3719047619050.326378473593156350.427231008114
Trimmed Mean ( 16 / 24 )114.42350.306710535463167373.066741340358
Trimmed Mean ( 17 / 24 )114.4707894736840.28920560779771395.81109904948
Trimmed Mean ( 18 / 24 )114.5138888888890.270676189657063423.065985353103
Trimmed Mean ( 19 / 24 )114.5602941176470.249664118500612458.857663670906
Trimmed Mean ( 20 / 24 )114.59468750.237113856028631483.289713301964
Trimmed Mean ( 21 / 24 )114.6303333333330.221445867043509517.644943496783
Trimmed Mean ( 22 / 24 )114.6464285714290.21030980818664545.131154652024
Trimmed Mean ( 23 / 24 )114.6523076923080.203330959988736563.870389923203
Trimmed Mean ( 24 / 24 )114.6591666666670.192139853830359596.748484923381
Median114.725
Midrange113.35
Midmean - Weighted Average at Xnp114.398108108108
Midmean - Weighted Average at X(n+1)p114.513888888889
Midmean - Empirical Distribution Function114.398108108108
Midmean - Empirical Distribution Function - Averaging114.513888888889
Midmean - Empirical Distribution Function - Interpolation114.513888888889
Midmean - Closest Observation114.398108108108
Midmean - True Basic - Statistics Graphics Toolkit114.513888888889
Midmean - MS Excel (old versions)114.470789473684
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 113.898472222222 & 0.685013754808677 & 166.271803190337 \tabularnewline
Geometric Mean & 113.750201114076 &  &  \tabularnewline
Harmonic Mean & 113.599800730612 &  &  \tabularnewline
Quadratic Mean & 114.04463287459 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 113.85375 & 0.673478068553371 & 169.053389139393 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 113.937361111111 & 0.649291084253723 & 175.479632901578 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 113.956944444444 & 0.642633338035989 & 177.328093174747 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 113.974166666667 & 0.635564292479372 & 179.327517318582 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 114.036666666667 & 0.621712102960153 & 183.423591279154 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 114.011666666667 & 0.608846172667474 & 187.258574965101 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 114.0525 & 0.594902799427623 & 191.716193149089 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 113.898055555556 & 0.501799642308254 & 226.979148553454 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 113.743055555556 & 0.475610086702456 & 239.151899288279 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 113.736111111111 & 0.470881019046657 & 241.538958910216 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 113.745277777778 & 0.468577533623325 & 242.745905673775 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 113.765277777778 & 0.459692137411608 & 247.48145230057 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 113.848333333333 & 0.442690150827938 & 257.17385652337 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 113.791944444444 & 0.403003426889716 & 282.359743991914 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 113.941944444444 & 0.374965289937115 & 303.873311749878 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 114.024166666667 & 0.342699443889162 & 332.723524067186 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 114.104444444444 & 0.323991506733436 & 352.183443309592 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 114.119444444444 & 0.307253781273338 & 371.417542760595 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 114.269861111111 & 0.254939734283251 & 448.223033700002 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 114.297638888889 & 0.246594845293202 & 463.503763645135 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 114.498888888889 & 0.214405550406723 & 534.029500037135 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 114.599722222222 & 0.186436810633635 & 614.683987742212 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 114.599722222222 & 0.185563576312176 & 617.576598272873 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 114.599722222222 & 0.171972922066781 & 666.382363252051 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 113.914142857143 & 0.646703809722513 & 176.145773605418 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 113.978088235294 & 0.614582995927256 & 185.455974198129 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 114.000303030303 & 0.592028946628073 & 192.558664030867 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 114.0165625 & 0.568055511743459 & 200.713768536571 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 114.028870967742 & 0.541767682039955 & 210.475587134288 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 114.027 & 0.514449587939453 & 221.648539863191 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 114.030172413793 & 0.484859918362325 & 235.181684637791 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 114.026071428571 & 0.452185506595212 & 252.166577135887 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 114.047407407407 & 0.437346533745243 & 260.771261705805 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 114.094230769231 & 0.424950298411708 & 268.488411928804 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 114.1458 & 0.410272093884544 & 278.219751480641 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 114.200416666667 & 0.391991523457045 & 291.333893293182 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 114.257173913043 & 0.37055470405846 & 308.340907999964 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 114.308636363636 & 0.347135604631785 & 329.29101722333 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 114.371904761905 & 0.326378473593156 & 350.427231008114 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 114.4235 & 0.306710535463167 & 373.066741340358 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 114.470789473684 & 0.28920560779771 & 395.81109904948 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 114.513888888889 & 0.270676189657063 & 423.065985353103 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 114.560294117647 & 0.249664118500612 & 458.857663670906 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 114.5946875 & 0.237113856028631 & 483.289713301964 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 114.630333333333 & 0.221445867043509 & 517.644943496783 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 114.646428571429 & 0.21030980818664 & 545.131154652024 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 114.652307692308 & 0.203330959988736 & 563.870389923203 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 114.659166666667 & 0.192139853830359 & 596.748484923381 \tabularnewline
Median & 114.725 &  &  \tabularnewline
Midrange & 113.35 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 114.398108108108 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 114.513888888889 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 114.398108108108 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 114.513888888889 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 114.513888888889 &  &  \tabularnewline
Midmean - Closest Observation & 114.398108108108 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 114.513888888889 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 114.470789473684 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=214519&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]113.898472222222[/C][C]0.685013754808677[/C][C]166.271803190337[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]113.750201114076[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]113.599800730612[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]114.04463287459[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]113.85375[/C][C]0.673478068553371[/C][C]169.053389139393[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]113.937361111111[/C][C]0.649291084253723[/C][C]175.479632901578[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]113.956944444444[/C][C]0.642633338035989[/C][C]177.328093174747[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]113.974166666667[/C][C]0.635564292479372[/C][C]179.327517318582[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]114.036666666667[/C][C]0.621712102960153[/C][C]183.423591279154[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]114.011666666667[/C][C]0.608846172667474[/C][C]187.258574965101[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]114.0525[/C][C]0.594902799427623[/C][C]191.716193149089[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]113.898055555556[/C][C]0.501799642308254[/C][C]226.979148553454[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]113.743055555556[/C][C]0.475610086702456[/C][C]239.151899288279[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]113.736111111111[/C][C]0.470881019046657[/C][C]241.538958910216[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]113.745277777778[/C][C]0.468577533623325[/C][C]242.745905673775[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]113.765277777778[/C][C]0.459692137411608[/C][C]247.48145230057[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]113.848333333333[/C][C]0.442690150827938[/C][C]257.17385652337[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]113.791944444444[/C][C]0.403003426889716[/C][C]282.359743991914[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]113.941944444444[/C][C]0.374965289937115[/C][C]303.873311749878[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]114.024166666667[/C][C]0.342699443889162[/C][C]332.723524067186[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]114.104444444444[/C][C]0.323991506733436[/C][C]352.183443309592[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]114.119444444444[/C][C]0.307253781273338[/C][C]371.417542760595[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]114.269861111111[/C][C]0.254939734283251[/C][C]448.223033700002[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]114.297638888889[/C][C]0.246594845293202[/C][C]463.503763645135[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]114.498888888889[/C][C]0.214405550406723[/C][C]534.029500037135[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]114.599722222222[/C][C]0.186436810633635[/C][C]614.683987742212[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]114.599722222222[/C][C]0.185563576312176[/C][C]617.576598272873[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]114.599722222222[/C][C]0.171972922066781[/C][C]666.382363252051[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]113.914142857143[/C][C]0.646703809722513[/C][C]176.145773605418[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]113.978088235294[/C][C]0.614582995927256[/C][C]185.455974198129[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]114.000303030303[/C][C]0.592028946628073[/C][C]192.558664030867[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]114.0165625[/C][C]0.568055511743459[/C][C]200.713768536571[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]114.028870967742[/C][C]0.541767682039955[/C][C]210.475587134288[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]114.027[/C][C]0.514449587939453[/C][C]221.648539863191[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]114.030172413793[/C][C]0.484859918362325[/C][C]235.181684637791[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]114.026071428571[/C][C]0.452185506595212[/C][C]252.166577135887[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]114.047407407407[/C][C]0.437346533745243[/C][C]260.771261705805[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]114.094230769231[/C][C]0.424950298411708[/C][C]268.488411928804[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]114.1458[/C][C]0.410272093884544[/C][C]278.219751480641[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]114.200416666667[/C][C]0.391991523457045[/C][C]291.333893293182[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]114.257173913043[/C][C]0.37055470405846[/C][C]308.340907999964[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]114.308636363636[/C][C]0.347135604631785[/C][C]329.29101722333[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]114.371904761905[/C][C]0.326378473593156[/C][C]350.427231008114[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]114.4235[/C][C]0.306710535463167[/C][C]373.066741340358[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]114.470789473684[/C][C]0.28920560779771[/C][C]395.81109904948[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]114.513888888889[/C][C]0.270676189657063[/C][C]423.065985353103[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]114.560294117647[/C][C]0.249664118500612[/C][C]458.857663670906[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]114.5946875[/C][C]0.237113856028631[/C][C]483.289713301964[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]114.630333333333[/C][C]0.221445867043509[/C][C]517.644943496783[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]114.646428571429[/C][C]0.21030980818664[/C][C]545.131154652024[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]114.652307692308[/C][C]0.203330959988736[/C][C]563.870389923203[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]114.659166666667[/C][C]0.192139853830359[/C][C]596.748484923381[/C][/ROW]
[ROW][C]Median[/C][C]114.725[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]113.35[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]114.398108108108[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]114.513888888889[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]114.398108108108[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]114.513888888889[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]114.513888888889[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]114.398108108108[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]114.513888888889[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]114.470789473684[/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=214519&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=214519&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 Mean113.8984722222220.685013754808677166.271803190337
Geometric Mean113.750201114076
Harmonic Mean113.599800730612
Quadratic Mean114.04463287459
Winsorized Mean ( 1 / 24 )113.853750.673478068553371169.053389139393
Winsorized Mean ( 2 / 24 )113.9373611111110.649291084253723175.479632901578
Winsorized Mean ( 3 / 24 )113.9569444444440.642633338035989177.328093174747
Winsorized Mean ( 4 / 24 )113.9741666666670.635564292479372179.327517318582
Winsorized Mean ( 5 / 24 )114.0366666666670.621712102960153183.423591279154
Winsorized Mean ( 6 / 24 )114.0116666666670.608846172667474187.258574965101
Winsorized Mean ( 7 / 24 )114.05250.594902799427623191.716193149089
Winsorized Mean ( 8 / 24 )113.8980555555560.501799642308254226.979148553454
Winsorized Mean ( 9 / 24 )113.7430555555560.475610086702456239.151899288279
Winsorized Mean ( 10 / 24 )113.7361111111110.470881019046657241.538958910216
Winsorized Mean ( 11 / 24 )113.7452777777780.468577533623325242.745905673775
Winsorized Mean ( 12 / 24 )113.7652777777780.459692137411608247.48145230057
Winsorized Mean ( 13 / 24 )113.8483333333330.442690150827938257.17385652337
Winsorized Mean ( 14 / 24 )113.7919444444440.403003426889716282.359743991914
Winsorized Mean ( 15 / 24 )113.9419444444440.374965289937115303.873311749878
Winsorized Mean ( 16 / 24 )114.0241666666670.342699443889162332.723524067186
Winsorized Mean ( 17 / 24 )114.1044444444440.323991506733436352.183443309592
Winsorized Mean ( 18 / 24 )114.1194444444440.307253781273338371.417542760595
Winsorized Mean ( 19 / 24 )114.2698611111110.254939734283251448.223033700002
Winsorized Mean ( 20 / 24 )114.2976388888890.246594845293202463.503763645135
Winsorized Mean ( 21 / 24 )114.4988888888890.214405550406723534.029500037135
Winsorized Mean ( 22 / 24 )114.5997222222220.186436810633635614.683987742212
Winsorized Mean ( 23 / 24 )114.5997222222220.185563576312176617.576598272873
Winsorized Mean ( 24 / 24 )114.5997222222220.171972922066781666.382363252051
Trimmed Mean ( 1 / 24 )113.9141428571430.646703809722513176.145773605418
Trimmed Mean ( 2 / 24 )113.9780882352940.614582995927256185.455974198129
Trimmed Mean ( 3 / 24 )114.0003030303030.592028946628073192.558664030867
Trimmed Mean ( 4 / 24 )114.01656250.568055511743459200.713768536571
Trimmed Mean ( 5 / 24 )114.0288709677420.541767682039955210.475587134288
Trimmed Mean ( 6 / 24 )114.0270.514449587939453221.648539863191
Trimmed Mean ( 7 / 24 )114.0301724137930.484859918362325235.181684637791
Trimmed Mean ( 8 / 24 )114.0260714285710.452185506595212252.166577135887
Trimmed Mean ( 9 / 24 )114.0474074074070.437346533745243260.771261705805
Trimmed Mean ( 10 / 24 )114.0942307692310.424950298411708268.488411928804
Trimmed Mean ( 11 / 24 )114.14580.410272093884544278.219751480641
Trimmed Mean ( 12 / 24 )114.2004166666670.391991523457045291.333893293182
Trimmed Mean ( 13 / 24 )114.2571739130430.37055470405846308.340907999964
Trimmed Mean ( 14 / 24 )114.3086363636360.347135604631785329.29101722333
Trimmed Mean ( 15 / 24 )114.3719047619050.326378473593156350.427231008114
Trimmed Mean ( 16 / 24 )114.42350.306710535463167373.066741340358
Trimmed Mean ( 17 / 24 )114.4707894736840.28920560779771395.81109904948
Trimmed Mean ( 18 / 24 )114.5138888888890.270676189657063423.065985353103
Trimmed Mean ( 19 / 24 )114.5602941176470.249664118500612458.857663670906
Trimmed Mean ( 20 / 24 )114.59468750.237113856028631483.289713301964
Trimmed Mean ( 21 / 24 )114.6303333333330.221445867043509517.644943496783
Trimmed Mean ( 22 / 24 )114.6464285714290.21030980818664545.131154652024
Trimmed Mean ( 23 / 24 )114.6523076923080.203330959988736563.870389923203
Trimmed Mean ( 24 / 24 )114.6591666666670.192139853830359596.748484923381
Median114.725
Midrange113.35
Midmean - Weighted Average at Xnp114.398108108108
Midmean - Weighted Average at X(n+1)p114.513888888889
Midmean - Empirical Distribution Function114.398108108108
Midmean - Empirical Distribution Function - Averaging114.513888888889
Midmean - Empirical Distribution Function - Interpolation114.513888888889
Midmean - Closest Observation114.398108108108
Midmean - True Basic - Statistics Graphics Toolkit114.513888888889
Midmean - MS Excel (old versions)114.470789473684
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')