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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 computationSat, 12 Oct 2013 15:56:18 -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/12/t1381608164sa711y2h06r4y28.htm/, Retrieved Sun, 28 Apr 2024 21:15:04 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=214991, Retrieved Sun, 28 Apr 2024 21:15:04 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact88
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [totale werklooshe...] [2013-10-12 19:56:18] [4a7f7842fc88d649abcd00dd10ef7b6c] [Current]
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Dataseries X:
125
123
117
114
111
112
144
150
149
134
123
116
117
111
105
102
95
93
124
130
124
115
106
105
105
101
95
93
84
87
116
120
117
109
105
107
109
109
108
107
99
103
131
137
135
124
118
121
121
118
113
107
100
102
130
136
133
120
112
109
110
106
102
98
92
92
120
127
124
114
108
106
111
110
104
100
96
98
122
134
133
125
118
116




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=214991&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]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=214991&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=214991&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'Gwilym Jenkins' @ jenkins.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean113.7142857142861.5102035278454275.2973249085967
Geometric Mean112.892201151082
Harmonic Mean112.078869926748
Quadratic Mean114.543607832293
Winsorized Mean ( 1 / 28 )113.7380952380951.4987199594372475.8901584795089
Winsorized Mean ( 2 / 28 )113.7380952380951.4431390540096978.8129840448011
Winsorized Mean ( 3 / 28 )113.4880952380951.3858863674246181.888456301789
Winsorized Mean ( 4 / 28 )113.4880952380951.3675501301480382.9864242167203
Winsorized Mean ( 5 / 28 )113.4285714285711.3559420360089183.6529648143649
Winsorized Mean ( 6 / 28 )113.51.3173344494224486.1588338859295
Winsorized Mean ( 7 / 28 )113.51.3173344494224486.1588338859295
Winsorized Mean ( 8 / 28 )113.51.283808429989188.4088290345342
Winsorized Mean ( 9 / 28 )113.7142857142861.2499651663042590.9739637389276
Winsorized Mean ( 10 / 28 )113.476190476191.2069881851930894.0159910993971
Winsorized Mean ( 11 / 28 )113.476190476191.1644076388038397.4540072519298
Winsorized Mean ( 12 / 28 )113.6190476190481.14345461529199.3647199457346
Winsorized Mean ( 13 / 28 )113.1547619047621.06696254783888106.053171345101
Winsorized Mean ( 14 / 28 )112.9880952380950.992006787440437113.898510240666
Winsorized Mean ( 15 / 28 )113.1666666666670.966571700876635117.080467557688
Winsorized Mean ( 16 / 28 )112.976190476190.939045332297148120.309623604455
Winsorized Mean ( 17 / 28 )112.976190476190.939045332297148120.309623604455
Winsorized Mean ( 18 / 28 )113.1904761904760.909482806896433124.455872427906
Winsorized Mean ( 19 / 28 )113.4166666666670.879616880126893128.938710965057
Winsorized Mean ( 20 / 28 )113.4166666666670.815302641599499139.109897208429
Winsorized Mean ( 21 / 28 )113.4166666666670.815302641599499139.109897208429
Winsorized Mean ( 22 / 28 )113.1547619047620.77882438724481145.28918682819
Winsorized Mean ( 23 / 28 )112.8809523809520.742026802512419152.125168523226
Winsorized Mean ( 24 / 28 )113.1666666666670.706261100996399160.233469614864
Winsorized Mean ( 25 / 28 )112.8690476190480.66719279910925169.170062641167
Winsorized Mean ( 26 / 28 )112.8690476190480.66719279910925169.170062641167
Winsorized Mean ( 27 / 28 )113.1904761904760.62814925233718180.196785667298
Winsorized Mean ( 28 / 28 )112.523809523810.543958681502488206.860949829872
Trimmed Mean ( 1 / 28 )113.6341463414631.4362402189790779.1191785606995
Trimmed Mean ( 2 / 28 )113.5251.3629332431621483.2946151761705
Trimmed Mean ( 3 / 28 )113.4102564102561.3125379524425386.4053158990251
Trimmed Mean ( 4 / 28 )113.3815789473681.2795239116340288.6123173755889
Trimmed Mean ( 5 / 28 )113.3513513513511.2473492712664190.8737864866571
Trimmed Mean ( 6 / 28 )113.3333333333331.2130291627198393.4300153833234
Trimmed Mean ( 7 / 28 )113.31.1829272040942995.7793510943459
Trimmed Mean ( 8 / 28 )113.2647058823531.1471263571664298.7377765097602
Trimmed Mean ( 9 / 28 )113.2272727272731.11229522974333101.796060703596
Trimmed Mean ( 10 / 28 )113.156251.07787515796162104.980849743295
Trimmed Mean ( 11 / 28 )113.1129032258061.04578043109092108.16123524879
Trimmed Mean ( 12 / 28 )113.0666666666671.01565894300806111.323458967239
Trimmed Mean ( 13 / 28 )1130.98291515506521114.964144583266
Trimmed Mean ( 14 / 28 )112.9821428571430.958384419600422117.888125627343
Trimmed Mean ( 15 / 28 )112.9814814814810.942249542519324119.906114445436
Trimmed Mean ( 16 / 28 )112.9615384615380.926386099569868121.93785994197
Trimmed Mean ( 17 / 28 )112.960.911137436708331123.976905622593
Trimmed Mean ( 18 / 28 )112.9583333333330.891229096585425126.744440645073
Trimmed Mean ( 19 / 28 )112.9347826086960.871115767340496129.64382788465
Trimmed Mean ( 20 / 28 )112.8863636363640.850454367485007132.736532320006
Trimmed Mean ( 21 / 28 )112.8333333333330.836116143360339134.949353901789
Trimmed Mean ( 22 / 28 )112.7750.816094121645669138.188717463847
Trimmed Mean ( 23 / 28 )112.7368421052630.79711804020685141.430549076531
Trimmed Mean ( 24 / 28 )112.7222222222220.779306886910343144.644201296774
Trimmed Mean ( 25 / 28 )112.6764705882350.76197579302352147.874081591405
Trimmed Mean ( 26 / 28 )112.656250.746779881579745150.856032384919
Trimmed Mean ( 27 / 28 )112.6333333333330.723152951712763155.753126730058
Trimmed Mean ( 28 / 28 )112.5714285714290.698502880180575161.161008444699
Median112
Midrange117
Midmean - Weighted Average at Xnp112.886363636364
Midmean - Weighted Average at X(n+1)p112.886363636364
Midmean - Empirical Distribution Function112.886363636364
Midmean - Empirical Distribution Function - Averaging112.886363636364
Midmean - Empirical Distribution Function - Interpolation112.886363636364
Midmean - Closest Observation112.886363636364
Midmean - True Basic - Statistics Graphics Toolkit112.886363636364
Midmean - MS Excel (old versions)112.886363636364
Number of observations84

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 113.714285714286 & 1.51020352784542 & 75.2973249085967 \tabularnewline
Geometric Mean & 112.892201151082 &  &  \tabularnewline
Harmonic Mean & 112.078869926748 &  &  \tabularnewline
Quadratic Mean & 114.543607832293 &  &  \tabularnewline
Winsorized Mean ( 1 / 28 ) & 113.738095238095 & 1.49871995943724 & 75.8901584795089 \tabularnewline
Winsorized Mean ( 2 / 28 ) & 113.738095238095 & 1.44313905400969 & 78.8129840448011 \tabularnewline
Winsorized Mean ( 3 / 28 ) & 113.488095238095 & 1.38588636742461 & 81.888456301789 \tabularnewline
Winsorized Mean ( 4 / 28 ) & 113.488095238095 & 1.36755013014803 & 82.9864242167203 \tabularnewline
Winsorized Mean ( 5 / 28 ) & 113.428571428571 & 1.35594203600891 & 83.6529648143649 \tabularnewline
Winsorized Mean ( 6 / 28 ) & 113.5 & 1.31733444942244 & 86.1588338859295 \tabularnewline
Winsorized Mean ( 7 / 28 ) & 113.5 & 1.31733444942244 & 86.1588338859295 \tabularnewline
Winsorized Mean ( 8 / 28 ) & 113.5 & 1.2838084299891 & 88.4088290345342 \tabularnewline
Winsorized Mean ( 9 / 28 ) & 113.714285714286 & 1.24996516630425 & 90.9739637389276 \tabularnewline
Winsorized Mean ( 10 / 28 ) & 113.47619047619 & 1.20698818519308 & 94.0159910993971 \tabularnewline
Winsorized Mean ( 11 / 28 ) & 113.47619047619 & 1.16440763880383 & 97.4540072519298 \tabularnewline
Winsorized Mean ( 12 / 28 ) & 113.619047619048 & 1.143454615291 & 99.3647199457346 \tabularnewline
Winsorized Mean ( 13 / 28 ) & 113.154761904762 & 1.06696254783888 & 106.053171345101 \tabularnewline
Winsorized Mean ( 14 / 28 ) & 112.988095238095 & 0.992006787440437 & 113.898510240666 \tabularnewline
Winsorized Mean ( 15 / 28 ) & 113.166666666667 & 0.966571700876635 & 117.080467557688 \tabularnewline
Winsorized Mean ( 16 / 28 ) & 112.97619047619 & 0.939045332297148 & 120.309623604455 \tabularnewline
Winsorized Mean ( 17 / 28 ) & 112.97619047619 & 0.939045332297148 & 120.309623604455 \tabularnewline
Winsorized Mean ( 18 / 28 ) & 113.190476190476 & 0.909482806896433 & 124.455872427906 \tabularnewline
Winsorized Mean ( 19 / 28 ) & 113.416666666667 & 0.879616880126893 & 128.938710965057 \tabularnewline
Winsorized Mean ( 20 / 28 ) & 113.416666666667 & 0.815302641599499 & 139.109897208429 \tabularnewline
Winsorized Mean ( 21 / 28 ) & 113.416666666667 & 0.815302641599499 & 139.109897208429 \tabularnewline
Winsorized Mean ( 22 / 28 ) & 113.154761904762 & 0.77882438724481 & 145.28918682819 \tabularnewline
Winsorized Mean ( 23 / 28 ) & 112.880952380952 & 0.742026802512419 & 152.125168523226 \tabularnewline
Winsorized Mean ( 24 / 28 ) & 113.166666666667 & 0.706261100996399 & 160.233469614864 \tabularnewline
Winsorized Mean ( 25 / 28 ) & 112.869047619048 & 0.66719279910925 & 169.170062641167 \tabularnewline
Winsorized Mean ( 26 / 28 ) & 112.869047619048 & 0.66719279910925 & 169.170062641167 \tabularnewline
Winsorized Mean ( 27 / 28 ) & 113.190476190476 & 0.62814925233718 & 180.196785667298 \tabularnewline
Winsorized Mean ( 28 / 28 ) & 112.52380952381 & 0.543958681502488 & 206.860949829872 \tabularnewline
Trimmed Mean ( 1 / 28 ) & 113.634146341463 & 1.43624021897907 & 79.1191785606995 \tabularnewline
Trimmed Mean ( 2 / 28 ) & 113.525 & 1.36293324316214 & 83.2946151761705 \tabularnewline
Trimmed Mean ( 3 / 28 ) & 113.410256410256 & 1.31253795244253 & 86.4053158990251 \tabularnewline
Trimmed Mean ( 4 / 28 ) & 113.381578947368 & 1.27952391163402 & 88.6123173755889 \tabularnewline
Trimmed Mean ( 5 / 28 ) & 113.351351351351 & 1.24734927126641 & 90.8737864866571 \tabularnewline
Trimmed Mean ( 6 / 28 ) & 113.333333333333 & 1.21302916271983 & 93.4300153833234 \tabularnewline
Trimmed Mean ( 7 / 28 ) & 113.3 & 1.18292720409429 & 95.7793510943459 \tabularnewline
Trimmed Mean ( 8 / 28 ) & 113.264705882353 & 1.14712635716642 & 98.7377765097602 \tabularnewline
Trimmed Mean ( 9 / 28 ) & 113.227272727273 & 1.11229522974333 & 101.796060703596 \tabularnewline
Trimmed Mean ( 10 / 28 ) & 113.15625 & 1.07787515796162 & 104.980849743295 \tabularnewline
Trimmed Mean ( 11 / 28 ) & 113.112903225806 & 1.04578043109092 & 108.16123524879 \tabularnewline
Trimmed Mean ( 12 / 28 ) & 113.066666666667 & 1.01565894300806 & 111.323458967239 \tabularnewline
Trimmed Mean ( 13 / 28 ) & 113 & 0.98291515506521 & 114.964144583266 \tabularnewline
Trimmed Mean ( 14 / 28 ) & 112.982142857143 & 0.958384419600422 & 117.888125627343 \tabularnewline
Trimmed Mean ( 15 / 28 ) & 112.981481481481 & 0.942249542519324 & 119.906114445436 \tabularnewline
Trimmed Mean ( 16 / 28 ) & 112.961538461538 & 0.926386099569868 & 121.93785994197 \tabularnewline
Trimmed Mean ( 17 / 28 ) & 112.96 & 0.911137436708331 & 123.976905622593 \tabularnewline
Trimmed Mean ( 18 / 28 ) & 112.958333333333 & 0.891229096585425 & 126.744440645073 \tabularnewline
Trimmed Mean ( 19 / 28 ) & 112.934782608696 & 0.871115767340496 & 129.64382788465 \tabularnewline
Trimmed Mean ( 20 / 28 ) & 112.886363636364 & 0.850454367485007 & 132.736532320006 \tabularnewline
Trimmed Mean ( 21 / 28 ) & 112.833333333333 & 0.836116143360339 & 134.949353901789 \tabularnewline
Trimmed Mean ( 22 / 28 ) & 112.775 & 0.816094121645669 & 138.188717463847 \tabularnewline
Trimmed Mean ( 23 / 28 ) & 112.736842105263 & 0.79711804020685 & 141.430549076531 \tabularnewline
Trimmed Mean ( 24 / 28 ) & 112.722222222222 & 0.779306886910343 & 144.644201296774 \tabularnewline
Trimmed Mean ( 25 / 28 ) & 112.676470588235 & 0.76197579302352 & 147.874081591405 \tabularnewline
Trimmed Mean ( 26 / 28 ) & 112.65625 & 0.746779881579745 & 150.856032384919 \tabularnewline
Trimmed Mean ( 27 / 28 ) & 112.633333333333 & 0.723152951712763 & 155.753126730058 \tabularnewline
Trimmed Mean ( 28 / 28 ) & 112.571428571429 & 0.698502880180575 & 161.161008444699 \tabularnewline
Median & 112 &  &  \tabularnewline
Midrange & 117 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 112.886363636364 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 112.886363636364 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 112.886363636364 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 112.886363636364 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 112.886363636364 &  &  \tabularnewline
Midmean - Closest Observation & 112.886363636364 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 112.886363636364 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 112.886363636364 &  &  \tabularnewline
Number of observations & 84 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=214991&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]113.714285714286[/C][C]1.51020352784542[/C][C]75.2973249085967[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]112.892201151082[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]112.078869926748[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]114.543607832293[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 28 )[/C][C]113.738095238095[/C][C]1.49871995943724[/C][C]75.8901584795089[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 28 )[/C][C]113.738095238095[/C][C]1.44313905400969[/C][C]78.8129840448011[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 28 )[/C][C]113.488095238095[/C][C]1.38588636742461[/C][C]81.888456301789[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 28 )[/C][C]113.488095238095[/C][C]1.36755013014803[/C][C]82.9864242167203[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 28 )[/C][C]113.428571428571[/C][C]1.35594203600891[/C][C]83.6529648143649[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 28 )[/C][C]113.5[/C][C]1.31733444942244[/C][C]86.1588338859295[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 28 )[/C][C]113.5[/C][C]1.31733444942244[/C][C]86.1588338859295[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 28 )[/C][C]113.5[/C][C]1.2838084299891[/C][C]88.4088290345342[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 28 )[/C][C]113.714285714286[/C][C]1.24996516630425[/C][C]90.9739637389276[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 28 )[/C][C]113.47619047619[/C][C]1.20698818519308[/C][C]94.0159910993971[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 28 )[/C][C]113.47619047619[/C][C]1.16440763880383[/C][C]97.4540072519298[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 28 )[/C][C]113.619047619048[/C][C]1.143454615291[/C][C]99.3647199457346[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 28 )[/C][C]113.154761904762[/C][C]1.06696254783888[/C][C]106.053171345101[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 28 )[/C][C]112.988095238095[/C][C]0.992006787440437[/C][C]113.898510240666[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 28 )[/C][C]113.166666666667[/C][C]0.966571700876635[/C][C]117.080467557688[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 28 )[/C][C]112.97619047619[/C][C]0.939045332297148[/C][C]120.309623604455[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 28 )[/C][C]112.97619047619[/C][C]0.939045332297148[/C][C]120.309623604455[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 28 )[/C][C]113.190476190476[/C][C]0.909482806896433[/C][C]124.455872427906[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 28 )[/C][C]113.416666666667[/C][C]0.879616880126893[/C][C]128.938710965057[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 28 )[/C][C]113.416666666667[/C][C]0.815302641599499[/C][C]139.109897208429[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 28 )[/C][C]113.416666666667[/C][C]0.815302641599499[/C][C]139.109897208429[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 28 )[/C][C]113.154761904762[/C][C]0.77882438724481[/C][C]145.28918682819[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 28 )[/C][C]112.880952380952[/C][C]0.742026802512419[/C][C]152.125168523226[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 28 )[/C][C]113.166666666667[/C][C]0.706261100996399[/C][C]160.233469614864[/C][/ROW]
[ROW][C]Winsorized Mean ( 25 / 28 )[/C][C]112.869047619048[/C][C]0.66719279910925[/C][C]169.170062641167[/C][/ROW]
[ROW][C]Winsorized Mean ( 26 / 28 )[/C][C]112.869047619048[/C][C]0.66719279910925[/C][C]169.170062641167[/C][/ROW]
[ROW][C]Winsorized Mean ( 27 / 28 )[/C][C]113.190476190476[/C][C]0.62814925233718[/C][C]180.196785667298[/C][/ROW]
[ROW][C]Winsorized Mean ( 28 / 28 )[/C][C]112.52380952381[/C][C]0.543958681502488[/C][C]206.860949829872[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 28 )[/C][C]113.634146341463[/C][C]1.43624021897907[/C][C]79.1191785606995[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 28 )[/C][C]113.525[/C][C]1.36293324316214[/C][C]83.2946151761705[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 28 )[/C][C]113.410256410256[/C][C]1.31253795244253[/C][C]86.4053158990251[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 28 )[/C][C]113.381578947368[/C][C]1.27952391163402[/C][C]88.6123173755889[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 28 )[/C][C]113.351351351351[/C][C]1.24734927126641[/C][C]90.8737864866571[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 28 )[/C][C]113.333333333333[/C][C]1.21302916271983[/C][C]93.4300153833234[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 28 )[/C][C]113.3[/C][C]1.18292720409429[/C][C]95.7793510943459[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 28 )[/C][C]113.264705882353[/C][C]1.14712635716642[/C][C]98.7377765097602[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 28 )[/C][C]113.227272727273[/C][C]1.11229522974333[/C][C]101.796060703596[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 28 )[/C][C]113.15625[/C][C]1.07787515796162[/C][C]104.980849743295[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 28 )[/C][C]113.112903225806[/C][C]1.04578043109092[/C][C]108.16123524879[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 28 )[/C][C]113.066666666667[/C][C]1.01565894300806[/C][C]111.323458967239[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 28 )[/C][C]113[/C][C]0.98291515506521[/C][C]114.964144583266[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 28 )[/C][C]112.982142857143[/C][C]0.958384419600422[/C][C]117.888125627343[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 28 )[/C][C]112.981481481481[/C][C]0.942249542519324[/C][C]119.906114445436[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 28 )[/C][C]112.961538461538[/C][C]0.926386099569868[/C][C]121.93785994197[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 28 )[/C][C]112.96[/C][C]0.911137436708331[/C][C]123.976905622593[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 28 )[/C][C]112.958333333333[/C][C]0.891229096585425[/C][C]126.744440645073[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 28 )[/C][C]112.934782608696[/C][C]0.871115767340496[/C][C]129.64382788465[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 28 )[/C][C]112.886363636364[/C][C]0.850454367485007[/C][C]132.736532320006[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 28 )[/C][C]112.833333333333[/C][C]0.836116143360339[/C][C]134.949353901789[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 28 )[/C][C]112.775[/C][C]0.816094121645669[/C][C]138.188717463847[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 28 )[/C][C]112.736842105263[/C][C]0.79711804020685[/C][C]141.430549076531[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 28 )[/C][C]112.722222222222[/C][C]0.779306886910343[/C][C]144.644201296774[/C][/ROW]
[ROW][C]Trimmed Mean ( 25 / 28 )[/C][C]112.676470588235[/C][C]0.76197579302352[/C][C]147.874081591405[/C][/ROW]
[ROW][C]Trimmed Mean ( 26 / 28 )[/C][C]112.65625[/C][C]0.746779881579745[/C][C]150.856032384919[/C][/ROW]
[ROW][C]Trimmed Mean ( 27 / 28 )[/C][C]112.633333333333[/C][C]0.723152951712763[/C][C]155.753126730058[/C][/ROW]
[ROW][C]Trimmed Mean ( 28 / 28 )[/C][C]112.571428571429[/C][C]0.698502880180575[/C][C]161.161008444699[/C][/ROW]
[ROW][C]Median[/C][C]112[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]117[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]112.886363636364[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]112.886363636364[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]112.886363636364[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]112.886363636364[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]112.886363636364[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]112.886363636364[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]112.886363636364[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]112.886363636364[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]84[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=214991&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=214991&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 Mean113.7142857142861.5102035278454275.2973249085967
Geometric Mean112.892201151082
Harmonic Mean112.078869926748
Quadratic Mean114.543607832293
Winsorized Mean ( 1 / 28 )113.7380952380951.4987199594372475.8901584795089
Winsorized Mean ( 2 / 28 )113.7380952380951.4431390540096978.8129840448011
Winsorized Mean ( 3 / 28 )113.4880952380951.3858863674246181.888456301789
Winsorized Mean ( 4 / 28 )113.4880952380951.3675501301480382.9864242167203
Winsorized Mean ( 5 / 28 )113.4285714285711.3559420360089183.6529648143649
Winsorized Mean ( 6 / 28 )113.51.3173344494224486.1588338859295
Winsorized Mean ( 7 / 28 )113.51.3173344494224486.1588338859295
Winsorized Mean ( 8 / 28 )113.51.283808429989188.4088290345342
Winsorized Mean ( 9 / 28 )113.7142857142861.2499651663042590.9739637389276
Winsorized Mean ( 10 / 28 )113.476190476191.2069881851930894.0159910993971
Winsorized Mean ( 11 / 28 )113.476190476191.1644076388038397.4540072519298
Winsorized Mean ( 12 / 28 )113.6190476190481.14345461529199.3647199457346
Winsorized Mean ( 13 / 28 )113.1547619047621.06696254783888106.053171345101
Winsorized Mean ( 14 / 28 )112.9880952380950.992006787440437113.898510240666
Winsorized Mean ( 15 / 28 )113.1666666666670.966571700876635117.080467557688
Winsorized Mean ( 16 / 28 )112.976190476190.939045332297148120.309623604455
Winsorized Mean ( 17 / 28 )112.976190476190.939045332297148120.309623604455
Winsorized Mean ( 18 / 28 )113.1904761904760.909482806896433124.455872427906
Winsorized Mean ( 19 / 28 )113.4166666666670.879616880126893128.938710965057
Winsorized Mean ( 20 / 28 )113.4166666666670.815302641599499139.109897208429
Winsorized Mean ( 21 / 28 )113.4166666666670.815302641599499139.109897208429
Winsorized Mean ( 22 / 28 )113.1547619047620.77882438724481145.28918682819
Winsorized Mean ( 23 / 28 )112.8809523809520.742026802512419152.125168523226
Winsorized Mean ( 24 / 28 )113.1666666666670.706261100996399160.233469614864
Winsorized Mean ( 25 / 28 )112.8690476190480.66719279910925169.170062641167
Winsorized Mean ( 26 / 28 )112.8690476190480.66719279910925169.170062641167
Winsorized Mean ( 27 / 28 )113.1904761904760.62814925233718180.196785667298
Winsorized Mean ( 28 / 28 )112.523809523810.543958681502488206.860949829872
Trimmed Mean ( 1 / 28 )113.6341463414631.4362402189790779.1191785606995
Trimmed Mean ( 2 / 28 )113.5251.3629332431621483.2946151761705
Trimmed Mean ( 3 / 28 )113.4102564102561.3125379524425386.4053158990251
Trimmed Mean ( 4 / 28 )113.3815789473681.2795239116340288.6123173755889
Trimmed Mean ( 5 / 28 )113.3513513513511.2473492712664190.8737864866571
Trimmed Mean ( 6 / 28 )113.3333333333331.2130291627198393.4300153833234
Trimmed Mean ( 7 / 28 )113.31.1829272040942995.7793510943459
Trimmed Mean ( 8 / 28 )113.2647058823531.1471263571664298.7377765097602
Trimmed Mean ( 9 / 28 )113.2272727272731.11229522974333101.796060703596
Trimmed Mean ( 10 / 28 )113.156251.07787515796162104.980849743295
Trimmed Mean ( 11 / 28 )113.1129032258061.04578043109092108.16123524879
Trimmed Mean ( 12 / 28 )113.0666666666671.01565894300806111.323458967239
Trimmed Mean ( 13 / 28 )1130.98291515506521114.964144583266
Trimmed Mean ( 14 / 28 )112.9821428571430.958384419600422117.888125627343
Trimmed Mean ( 15 / 28 )112.9814814814810.942249542519324119.906114445436
Trimmed Mean ( 16 / 28 )112.9615384615380.926386099569868121.93785994197
Trimmed Mean ( 17 / 28 )112.960.911137436708331123.976905622593
Trimmed Mean ( 18 / 28 )112.9583333333330.891229096585425126.744440645073
Trimmed Mean ( 19 / 28 )112.9347826086960.871115767340496129.64382788465
Trimmed Mean ( 20 / 28 )112.8863636363640.850454367485007132.736532320006
Trimmed Mean ( 21 / 28 )112.8333333333330.836116143360339134.949353901789
Trimmed Mean ( 22 / 28 )112.7750.816094121645669138.188717463847
Trimmed Mean ( 23 / 28 )112.7368421052630.79711804020685141.430549076531
Trimmed Mean ( 24 / 28 )112.7222222222220.779306886910343144.644201296774
Trimmed Mean ( 25 / 28 )112.6764705882350.76197579302352147.874081591405
Trimmed Mean ( 26 / 28 )112.656250.746779881579745150.856032384919
Trimmed Mean ( 27 / 28 )112.6333333333330.723152951712763155.753126730058
Trimmed Mean ( 28 / 28 )112.5714285714290.698502880180575161.161008444699
Median112
Midrange117
Midmean - Weighted Average at Xnp112.886363636364
Midmean - Weighted Average at X(n+1)p112.886363636364
Midmean - Empirical Distribution Function112.886363636364
Midmean - Empirical Distribution Function - Averaging112.886363636364
Midmean - Empirical Distribution Function - Interpolation112.886363636364
Midmean - Closest Observation112.886363636364
Midmean - True Basic - Statistics Graphics Toolkit112.886363636364
Midmean - MS Excel (old versions)112.886363636364
Number of observations84



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')