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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 computationMon, 21 Apr 2008 10:45:38 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/Apr/21/t1208796379sp3972pkxmqv67l.htm/, Retrieved Thu, 16 May 2024 11:14:39 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=10533, Retrieved Thu, 16 May 2024 11:14:39 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact186
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Mathieu Demoor Ce...] [2008-04-21 16:45:38] [8c69c5b6690db7c1e43065ff98235337] [Current]
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Dataseries X:
113
110
107
103
98
98
137
148
147
139
130
128
127
123
118
114
108
111
151
159
158
148
138
137
136
133
126
120
114
116
153
162
161
149
139
135
130
127
122
117
112
113
149
157
157
147
137
132
125
123
117
114
111
112
144
150
149
134
123
116
117
111
105
102
95
93
124
130
124
115
106
105




Summary of compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time7 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\begin{tabular}{lllllllll}
\hline
Summary of compuational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 7 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=10533&T=0

[TABLE]
[ROW][C]Summary of compuational 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]7 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=10533&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=10533&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 compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time7 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean126.9305555555562.1171043491226259.9547942018819
Geometric Mean125.682736830275
Harmonic Mean124.445463178237
Quadratic Mean128.177990397034
Winsorized Mean ( 1 / 24 )126.9444444444442.1078036029281260.2259357883702
Winsorized Mean ( 2 / 24 )126.9722222222222.0783717653304161.0921608637409
Winsorized Mean ( 3 / 24 )126.9305555555562.0694444444444461.3355704697987
Winsorized Mean ( 4 / 24 )127.0972222222222.0163804672389763.0323613460988
Winsorized Mean ( 5 / 24 )127.1666666666672.0043965759806263.443865445865
Winsorized Mean ( 6 / 24 )1271.9097394721087566.5012174984086
Winsorized Mean ( 7 / 24 )126.8055555555561.8734032208499167.6872731637708
Winsorized Mean ( 8 / 24 )126.8055555555561.8354276225087969.0877450031121
Winsorized Mean ( 9 / 24 )126.8055555555561.7937073637480770.6946730098644
Winsorized Mean ( 10 / 24 )126.9444444444441.7724514301766571.6208310609633
Winsorized Mean ( 11 / 24 )127.251.7279518754528673.6420972179276
Winsorized Mean ( 12 / 24 )127.251.6755339232652175.9459407136444
Winsorized Mean ( 13 / 24 )127.251.6755339232652175.9459407136444
Winsorized Mean ( 14 / 24 )127.0555555555561.641939681891777.3813782301511
Winsorized Mean ( 15 / 24 )127.2638888888891.6137119137786678.8640697278415
Winsorized Mean ( 16 / 24 )126.5972222222221.5017803365583084.2980954940126
Winsorized Mean ( 17 / 24 )125.6527777777781.2858565710724597.7191240489435
Winsorized Mean ( 18 / 24 )125.6527777777781.2858565710724597.7191240489435
Winsorized Mean ( 19 / 24 )125.6527777777781.21144123905115103.721727251248
Winsorized Mean ( 20 / 24 )125.3751.17209293096181106.96677429589
Winsorized Mean ( 21 / 24 )125.3751.17209293096181106.96677429589
Winsorized Mean ( 22 / 24 )125.6805555555561.13087734247709111.135443991002
Winsorized Mean ( 23 / 24 )125.6805555555561.04399062619250120.384754807541
Winsorized Mean ( 24 / 24 )125.3472222222220.998073206766434125.589206655816
Trimmed Mean ( 1 / 24 )126.9142857142862.0617529434064361.5564954667157
Trimmed Mean ( 2 / 24 )126.8823529411762.0069599498890463.2211683886326
Trimmed Mean ( 3 / 24 )126.8333333333331.9602796210480364.7016537699475
Trimmed Mean ( 4 / 24 )126.7968751.9082605111261466.4463128910905
Trimmed Mean ( 5 / 24 )126.7096774193551.8650090199548867.940517211236
Trimmed Mean ( 6 / 24 )126.61.8159992035638869.7136869617283
Trimmed Mean ( 7 / 24 )126.5172413793101.7830351610519970.956111322373
Trimmed Mean ( 8 / 24 )126.4642857142861.7514306370615672.2062769933383
Trimmed Mean ( 9 / 24 )126.4074074074071.7208221505656573.4575664114136
Trimmed Mean ( 10 / 24 )126.3461538461541.6914933595370574.695033908223
Trimmed Mean ( 11 / 24 )126.261.6583271630145476.1369667071499
Trimmed Mean ( 12 / 24 )126.1251.6247272002331177.628416623975
Trimmed Mean ( 13 / 24 )125.9782608695651.5920967642389979.1272639322156
Trimmed Mean ( 14 / 24 )125.8181818181821.5484674027335881.2533616116617
Trimmed Mean ( 15 / 24 )125.6666666666671.4986120821171383.8553673537277
Trimmed Mean ( 16 / 24 )125.4751.4375850030609187.2817953253812
Trimmed Mean ( 17 / 24 )125.3421052631581.385392352819690.4740848381739
Trimmed Mean ( 18 / 24 )125.3055555555561.3684769917305791.5657013692974
Trimmed Mean ( 19 / 24 )125.2647058823531.3419787605672393.3432849782254
Trimmed Mean ( 20 / 24 )125.218751.3211480642461394.7802546805776
Trimmed Mean ( 21 / 24 )125.21.29845177480596.4225259877691
Trimmed Mean ( 22 / 24 )125.1785714285711.2609872375655199.27029211671
Trimmed Mean ( 23 / 24 )125.1153846153851.21443487721900103.023543676458
Trimmed Mean ( 24 / 24 )125.0416666666671.17102575911139106.779603859057
Median124.5
Midrange127.5
Midmean - Weighted Average at Xnp125.342105263158
Midmean - Weighted Average at X(n+1)p125.342105263158
Midmean - Empirical Distribution Function125.342105263158
Midmean - Empirical Distribution Function - Averaging125.342105263158
Midmean - Empirical Distribution Function - Interpolation125.342105263158
Midmean - Closest Observation125.342105263158
Midmean - True Basic - Statistics Graphics Toolkit125.342105263158
Midmean - MS Excel (old versions)125.342105263158
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 126.930555555556 & 2.11710434912262 & 59.9547942018819 \tabularnewline
Geometric Mean & 125.682736830275 &  &  \tabularnewline
Harmonic Mean & 124.445463178237 &  &  \tabularnewline
Quadratic Mean & 128.177990397034 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 126.944444444444 & 2.10780360292812 & 60.2259357883702 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 126.972222222222 & 2.07837176533041 & 61.0921608637409 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 126.930555555556 & 2.06944444444444 & 61.3355704697987 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 127.097222222222 & 2.01638046723897 & 63.0323613460988 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 127.166666666667 & 2.00439657598062 & 63.443865445865 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 127 & 1.90973947210875 & 66.5012174984086 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 126.805555555556 & 1.87340322084991 & 67.6872731637708 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 126.805555555556 & 1.83542762250879 & 69.0877450031121 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 126.805555555556 & 1.79370736374807 & 70.6946730098644 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 126.944444444444 & 1.77245143017665 & 71.6208310609633 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 127.25 & 1.72795187545286 & 73.6420972179276 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 127.25 & 1.67553392326521 & 75.9459407136444 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 127.25 & 1.67553392326521 & 75.9459407136444 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 127.055555555556 & 1.6419396818917 & 77.3813782301511 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 127.263888888889 & 1.61371191377866 & 78.8640697278415 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 126.597222222222 & 1.50178033655830 & 84.2980954940126 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 125.652777777778 & 1.28585657107245 & 97.7191240489435 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 125.652777777778 & 1.28585657107245 & 97.7191240489435 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 125.652777777778 & 1.21144123905115 & 103.721727251248 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 125.375 & 1.17209293096181 & 106.96677429589 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 125.375 & 1.17209293096181 & 106.96677429589 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 125.680555555556 & 1.13087734247709 & 111.135443991002 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 125.680555555556 & 1.04399062619250 & 120.384754807541 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 125.347222222222 & 0.998073206766434 & 125.589206655816 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 126.914285714286 & 2.06175294340643 & 61.5564954667157 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 126.882352941176 & 2.00695994988904 & 63.2211683886326 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 126.833333333333 & 1.96027962104803 & 64.7016537699475 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 126.796875 & 1.90826051112614 & 66.4463128910905 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 126.709677419355 & 1.86500901995488 & 67.940517211236 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 126.6 & 1.81599920356388 & 69.7136869617283 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 126.517241379310 & 1.78303516105199 & 70.956111322373 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 126.464285714286 & 1.75143063706156 & 72.2062769933383 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 126.407407407407 & 1.72082215056565 & 73.4575664114136 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 126.346153846154 & 1.69149335953705 & 74.695033908223 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 126.26 & 1.65832716301454 & 76.1369667071499 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 126.125 & 1.62472720023311 & 77.628416623975 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 125.978260869565 & 1.59209676423899 & 79.1272639322156 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 125.818181818182 & 1.54846740273358 & 81.2533616116617 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 125.666666666667 & 1.49861208211713 & 83.8553673537277 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 125.475 & 1.43758500306091 & 87.2817953253812 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 125.342105263158 & 1.3853923528196 & 90.4740848381739 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 125.305555555556 & 1.36847699173057 & 91.5657013692974 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 125.264705882353 & 1.34197876056723 & 93.3432849782254 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 125.21875 & 1.32114806424613 & 94.7802546805776 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 125.2 & 1.298451774805 & 96.4225259877691 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 125.178571428571 & 1.26098723756551 & 99.27029211671 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 125.115384615385 & 1.21443487721900 & 103.023543676458 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 125.041666666667 & 1.17102575911139 & 106.779603859057 \tabularnewline
Median & 124.5 &  &  \tabularnewline
Midrange & 127.5 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 125.342105263158 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 125.342105263158 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 125.342105263158 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 125.342105263158 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 125.342105263158 &  &  \tabularnewline
Midmean - Closest Observation & 125.342105263158 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 125.342105263158 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 125.342105263158 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=10533&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]126.930555555556[/C][C]2.11710434912262[/C][C]59.9547942018819[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]125.682736830275[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]124.445463178237[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]128.177990397034[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]126.944444444444[/C][C]2.10780360292812[/C][C]60.2259357883702[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]126.972222222222[/C][C]2.07837176533041[/C][C]61.0921608637409[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]126.930555555556[/C][C]2.06944444444444[/C][C]61.3355704697987[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]127.097222222222[/C][C]2.01638046723897[/C][C]63.0323613460988[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]127.166666666667[/C][C]2.00439657598062[/C][C]63.443865445865[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]127[/C][C]1.90973947210875[/C][C]66.5012174984086[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]126.805555555556[/C][C]1.87340322084991[/C][C]67.6872731637708[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]126.805555555556[/C][C]1.83542762250879[/C][C]69.0877450031121[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]126.805555555556[/C][C]1.79370736374807[/C][C]70.6946730098644[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]126.944444444444[/C][C]1.77245143017665[/C][C]71.6208310609633[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]127.25[/C][C]1.72795187545286[/C][C]73.6420972179276[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]127.25[/C][C]1.67553392326521[/C][C]75.9459407136444[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]127.25[/C][C]1.67553392326521[/C][C]75.9459407136444[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]127.055555555556[/C][C]1.6419396818917[/C][C]77.3813782301511[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]127.263888888889[/C][C]1.61371191377866[/C][C]78.8640697278415[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]126.597222222222[/C][C]1.50178033655830[/C][C]84.2980954940126[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]125.652777777778[/C][C]1.28585657107245[/C][C]97.7191240489435[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]125.652777777778[/C][C]1.28585657107245[/C][C]97.7191240489435[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]125.652777777778[/C][C]1.21144123905115[/C][C]103.721727251248[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]125.375[/C][C]1.17209293096181[/C][C]106.96677429589[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]125.375[/C][C]1.17209293096181[/C][C]106.96677429589[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]125.680555555556[/C][C]1.13087734247709[/C][C]111.135443991002[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]125.680555555556[/C][C]1.04399062619250[/C][C]120.384754807541[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]125.347222222222[/C][C]0.998073206766434[/C][C]125.589206655816[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]126.914285714286[/C][C]2.06175294340643[/C][C]61.5564954667157[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]126.882352941176[/C][C]2.00695994988904[/C][C]63.2211683886326[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]126.833333333333[/C][C]1.96027962104803[/C][C]64.7016537699475[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]126.796875[/C][C]1.90826051112614[/C][C]66.4463128910905[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]126.709677419355[/C][C]1.86500901995488[/C][C]67.940517211236[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]126.6[/C][C]1.81599920356388[/C][C]69.7136869617283[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]126.517241379310[/C][C]1.78303516105199[/C][C]70.956111322373[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]126.464285714286[/C][C]1.75143063706156[/C][C]72.2062769933383[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]126.407407407407[/C][C]1.72082215056565[/C][C]73.4575664114136[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]126.346153846154[/C][C]1.69149335953705[/C][C]74.695033908223[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]126.26[/C][C]1.65832716301454[/C][C]76.1369667071499[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]126.125[/C][C]1.62472720023311[/C][C]77.628416623975[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]125.978260869565[/C][C]1.59209676423899[/C][C]79.1272639322156[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]125.818181818182[/C][C]1.54846740273358[/C][C]81.2533616116617[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]125.666666666667[/C][C]1.49861208211713[/C][C]83.8553673537277[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]125.475[/C][C]1.43758500306091[/C][C]87.2817953253812[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]125.342105263158[/C][C]1.3853923528196[/C][C]90.4740848381739[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]125.305555555556[/C][C]1.36847699173057[/C][C]91.5657013692974[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]125.264705882353[/C][C]1.34197876056723[/C][C]93.3432849782254[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]125.21875[/C][C]1.32114806424613[/C][C]94.7802546805776[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]125.2[/C][C]1.298451774805[/C][C]96.4225259877691[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]125.178571428571[/C][C]1.26098723756551[/C][C]99.27029211671[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]125.115384615385[/C][C]1.21443487721900[/C][C]103.023543676458[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]125.041666666667[/C][C]1.17102575911139[/C][C]106.779603859057[/C][/ROW]
[ROW][C]Median[/C][C]124.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]127.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]125.342105263158[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]125.342105263158[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]125.342105263158[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]125.342105263158[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]125.342105263158[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]125.342105263158[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]125.342105263158[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]125.342105263158[/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=10533&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=10533&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 Mean126.9305555555562.1171043491226259.9547942018819
Geometric Mean125.682736830275
Harmonic Mean124.445463178237
Quadratic Mean128.177990397034
Winsorized Mean ( 1 / 24 )126.9444444444442.1078036029281260.2259357883702
Winsorized Mean ( 2 / 24 )126.9722222222222.0783717653304161.0921608637409
Winsorized Mean ( 3 / 24 )126.9305555555562.0694444444444461.3355704697987
Winsorized Mean ( 4 / 24 )127.0972222222222.0163804672389763.0323613460988
Winsorized Mean ( 5 / 24 )127.1666666666672.0043965759806263.443865445865
Winsorized Mean ( 6 / 24 )1271.9097394721087566.5012174984086
Winsorized Mean ( 7 / 24 )126.8055555555561.8734032208499167.6872731637708
Winsorized Mean ( 8 / 24 )126.8055555555561.8354276225087969.0877450031121
Winsorized Mean ( 9 / 24 )126.8055555555561.7937073637480770.6946730098644
Winsorized Mean ( 10 / 24 )126.9444444444441.7724514301766571.6208310609633
Winsorized Mean ( 11 / 24 )127.251.7279518754528673.6420972179276
Winsorized Mean ( 12 / 24 )127.251.6755339232652175.9459407136444
Winsorized Mean ( 13 / 24 )127.251.6755339232652175.9459407136444
Winsorized Mean ( 14 / 24 )127.0555555555561.641939681891777.3813782301511
Winsorized Mean ( 15 / 24 )127.2638888888891.6137119137786678.8640697278415
Winsorized Mean ( 16 / 24 )126.5972222222221.5017803365583084.2980954940126
Winsorized Mean ( 17 / 24 )125.6527777777781.2858565710724597.7191240489435
Winsorized Mean ( 18 / 24 )125.6527777777781.2858565710724597.7191240489435
Winsorized Mean ( 19 / 24 )125.6527777777781.21144123905115103.721727251248
Winsorized Mean ( 20 / 24 )125.3751.17209293096181106.96677429589
Winsorized Mean ( 21 / 24 )125.3751.17209293096181106.96677429589
Winsorized Mean ( 22 / 24 )125.6805555555561.13087734247709111.135443991002
Winsorized Mean ( 23 / 24 )125.6805555555561.04399062619250120.384754807541
Winsorized Mean ( 24 / 24 )125.3472222222220.998073206766434125.589206655816
Trimmed Mean ( 1 / 24 )126.9142857142862.0617529434064361.5564954667157
Trimmed Mean ( 2 / 24 )126.8823529411762.0069599498890463.2211683886326
Trimmed Mean ( 3 / 24 )126.8333333333331.9602796210480364.7016537699475
Trimmed Mean ( 4 / 24 )126.7968751.9082605111261466.4463128910905
Trimmed Mean ( 5 / 24 )126.7096774193551.8650090199548867.940517211236
Trimmed Mean ( 6 / 24 )126.61.8159992035638869.7136869617283
Trimmed Mean ( 7 / 24 )126.5172413793101.7830351610519970.956111322373
Trimmed Mean ( 8 / 24 )126.4642857142861.7514306370615672.2062769933383
Trimmed Mean ( 9 / 24 )126.4074074074071.7208221505656573.4575664114136
Trimmed Mean ( 10 / 24 )126.3461538461541.6914933595370574.695033908223
Trimmed Mean ( 11 / 24 )126.261.6583271630145476.1369667071499
Trimmed Mean ( 12 / 24 )126.1251.6247272002331177.628416623975
Trimmed Mean ( 13 / 24 )125.9782608695651.5920967642389979.1272639322156
Trimmed Mean ( 14 / 24 )125.8181818181821.5484674027335881.2533616116617
Trimmed Mean ( 15 / 24 )125.6666666666671.4986120821171383.8553673537277
Trimmed Mean ( 16 / 24 )125.4751.4375850030609187.2817953253812
Trimmed Mean ( 17 / 24 )125.3421052631581.385392352819690.4740848381739
Trimmed Mean ( 18 / 24 )125.3055555555561.3684769917305791.5657013692974
Trimmed Mean ( 19 / 24 )125.2647058823531.3419787605672393.3432849782254
Trimmed Mean ( 20 / 24 )125.218751.3211480642461394.7802546805776
Trimmed Mean ( 21 / 24 )125.21.29845177480596.4225259877691
Trimmed Mean ( 22 / 24 )125.1785714285711.2609872375655199.27029211671
Trimmed Mean ( 23 / 24 )125.1153846153851.21443487721900103.023543676458
Trimmed Mean ( 24 / 24 )125.0416666666671.17102575911139106.779603859057
Median124.5
Midrange127.5
Midmean - Weighted Average at Xnp125.342105263158
Midmean - Weighted Average at X(n+1)p125.342105263158
Midmean - Empirical Distribution Function125.342105263158
Midmean - Empirical Distribution Function - Averaging125.342105263158
Midmean - Empirical Distribution Function - Interpolation125.342105263158
Midmean - Closest Observation125.342105263158
Midmean - True Basic - Statistics Graphics Toolkit125.342105263158
Midmean - MS Excel (old versions)125.342105263158
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')