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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 computationWed, 03 Jun 2009 07:54:50 -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/2009/Jun/03/t12440374014ws4nrhy6psbrph.htm/, Retrieved Sat, 11 May 2024 13:39:16 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=41491, Retrieved Sat, 11 May 2024 13:39:16 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact101
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Van der Linden Ke...] [2009-06-03 13:54:50] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataseries X:
155
176
180
181
208
183
185
205
180
196
183
147
128
158
186
165
191
168
171
169
157
175
156
129
89
138
146
151
156
129
146
141
137
155
147
128
92
136
159
131
134
148
146
144
161
140
141
139
94
136
164
141
159
162
154
166
156
147
161
135
98
150
173
144
167
161
156
175
163
159
167
148
119
150
161
136
166
155
140
141




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\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' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41491&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' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41491&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41491&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' @ 72.249.127.135







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean153.3752.5623475564411659.8572194527046
Geometric Mean151.537718245749
Harmonic Mean149.499045072299
Quadratic Mean155.056683183925
Winsorized Mean ( 1 / 26 )153.3752.5407672891710360.3656228784499
Winsorized Mean ( 2 / 26 )153.22.4718926280396961.9768020108114
Winsorized Mean ( 3 / 26 )153.16252.38782803101464.1430195184361
Winsorized Mean ( 4 / 26 )153.96252.0694770749936074.396813504434
Winsorized Mean ( 5 / 26 )154.46251.9482988157150079.2807031211558
Winsorized Mean ( 6 / 26 )154.31251.9192226925687680.4036449743423
Winsorized Mean ( 7 / 26 )154.41.9042424321777881.0821129657432
Winsorized Mean ( 8 / 26 )154.21.8670527780299582.5900594854669
Winsorized Mean ( 9 / 26 )154.31251.8091359002839585.2962455588773
Winsorized Mean ( 10 / 26 )154.68751.7504604954704288.3696035416267
Winsorized Mean ( 11 / 26 )154.2751.6331199270728894.466424322257
Winsorized Mean ( 12 / 26 )154.2751.5859325212711097.2771526725177
Winsorized Mean ( 13 / 26 )154.2751.5859325212711097.2771526725177
Winsorized Mean ( 14 / 26 )153.9251.52933084978407100.648594136274
Winsorized Mean ( 15 / 26 )153.73751.44363988702783106.492970567969
Winsorized Mean ( 16 / 26 )153.53751.35524575635808113.291260481492
Winsorized Mean ( 17 / 26 )153.53751.29433328592882118.622847507024
Winsorized Mean ( 18 / 26 )153.53751.23118032155213124.707565018938
Winsorized Mean ( 19 / 26 )153.53751.23118032155213124.707565018938
Winsorized Mean ( 20 / 26 )153.53751.16243194301942132.083001436786
Winsorized Mean ( 21 / 26 )153.53751.16243194301942132.083001436786
Winsorized Mean ( 22 / 26 )153.26251.12561428376811136.158986439776
Winsorized Mean ( 23 / 26 )152.9751.08819543456011140.576770625617
Winsorized Mean ( 24 / 26 )153.5750.927903414604905165.507527596923
Winsorized Mean ( 25 / 26 )153.26250.888346449622534172.525595239473
Winsorized Mean ( 26 / 26 )153.58750.764251464266122200.964613325908
Trimmed Mean ( 1 / 26 )153.52.3920412772068764.171133442663
Trimmed Mean ( 2 / 26 )153.6315789473682.2135818481226269.4040652156893
Trimmed Mean ( 3 / 26 )153.8648648648652.0442462508030675.2672848510401
Trimmed Mean ( 4 / 26 )154.1251.8801052042451681.9767955814363
Trimmed Mean ( 5 / 26 )154.1714285714291.8097929406485485.187330057869
Trimmed Mean ( 6 / 26 )154.1029411764711.7644598526184687.3371762739639
Trimmed Mean ( 7 / 26 )154.0606060606061.7183879782419189.6541456360895
Trimmed Mean ( 8 / 26 )1541.6668154695477992.3917511047463
Trimmed Mean ( 9 / 26 )153.9677419354841.6136592622567895.4152747960883
Trimmed Mean ( 10 / 26 )153.9166666666671.5625004708097298.506636984822
Trimmed Mean ( 11 / 26 )153.8103448275861.51269219835502101.679869172888
Trimmed Mean ( 12 / 26 )153.751.47693302787607104.100861107496
Trimmed Mean ( 13 / 26 )153.6851851851851.44206159059834106.573246376681
Trimmed Mean ( 14 / 26 )153.6153846153851.39816563895777109.869231752752
Trimmed Mean ( 15 / 26 )153.581.35498776257747113.344197078104
Trimmed Mean ( 16 / 26 )153.56251.31814473438244116.498967066728
Trimmed Mean ( 17 / 26 )153.5652173913041.28899173191302119.135921192756
Trimmed Mean ( 18 / 26 )153.5681818181821.26315393014457121.575192186281
Trimmed Mean ( 19 / 26 )153.5714285714291.24153012312369123.695289958042
Trimmed Mean ( 20 / 26 )153.5751.21152981274894126.761222368553
Trimmed Mean ( 21 / 26 )153.5789473684211.18587681094452129.506662033554
Trimmed Mean ( 22 / 26 )153.5833333333331.14944776250605133.614887377299
Trimmed Mean ( 23 / 26 )153.6176470588241.10743292138604138.715080699027
Trimmed Mean ( 24 / 26 )153.68751.05726890634435145.362735135563
Trimmed Mean ( 25 / 26 )153.71.03296248443633148.795336051213
Trimmed Mean ( 26 / 26 )153.751.0060991252036152.817944224816
Median155
Midrange148.5
Midmean - Weighted Average at Xnp152.928571428571
Midmean - Weighted Average at X(n+1)p153.575
Midmean - Empirical Distribution Function152.928571428571
Midmean - Empirical Distribution Function - Averaging153.575
Midmean - Empirical Distribution Function - Interpolation153.575
Midmean - Closest Observation152.928571428571
Midmean - True Basic - Statistics Graphics Toolkit153.575
Midmean - MS Excel (old versions)153.568181818182
Number of observations80

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 153.375 & 2.56234755644116 & 59.8572194527046 \tabularnewline
Geometric Mean & 151.537718245749 &  &  \tabularnewline
Harmonic Mean & 149.499045072299 &  &  \tabularnewline
Quadratic Mean & 155.056683183925 &  &  \tabularnewline
Winsorized Mean ( 1 / 26 ) & 153.375 & 2.54076728917103 & 60.3656228784499 \tabularnewline
Winsorized Mean ( 2 / 26 ) & 153.2 & 2.47189262803969 & 61.9768020108114 \tabularnewline
Winsorized Mean ( 3 / 26 ) & 153.1625 & 2.387828031014 & 64.1430195184361 \tabularnewline
Winsorized Mean ( 4 / 26 ) & 153.9625 & 2.06947707499360 & 74.396813504434 \tabularnewline
Winsorized Mean ( 5 / 26 ) & 154.4625 & 1.94829881571500 & 79.2807031211558 \tabularnewline
Winsorized Mean ( 6 / 26 ) & 154.3125 & 1.91922269256876 & 80.4036449743423 \tabularnewline
Winsorized Mean ( 7 / 26 ) & 154.4 & 1.90424243217778 & 81.0821129657432 \tabularnewline
Winsorized Mean ( 8 / 26 ) & 154.2 & 1.86705277802995 & 82.5900594854669 \tabularnewline
Winsorized Mean ( 9 / 26 ) & 154.3125 & 1.80913590028395 & 85.2962455588773 \tabularnewline
Winsorized Mean ( 10 / 26 ) & 154.6875 & 1.75046049547042 & 88.3696035416267 \tabularnewline
Winsorized Mean ( 11 / 26 ) & 154.275 & 1.63311992707288 & 94.466424322257 \tabularnewline
Winsorized Mean ( 12 / 26 ) & 154.275 & 1.58593252127110 & 97.2771526725177 \tabularnewline
Winsorized Mean ( 13 / 26 ) & 154.275 & 1.58593252127110 & 97.2771526725177 \tabularnewline
Winsorized Mean ( 14 / 26 ) & 153.925 & 1.52933084978407 & 100.648594136274 \tabularnewline
Winsorized Mean ( 15 / 26 ) & 153.7375 & 1.44363988702783 & 106.492970567969 \tabularnewline
Winsorized Mean ( 16 / 26 ) & 153.5375 & 1.35524575635808 & 113.291260481492 \tabularnewline
Winsorized Mean ( 17 / 26 ) & 153.5375 & 1.29433328592882 & 118.622847507024 \tabularnewline
Winsorized Mean ( 18 / 26 ) & 153.5375 & 1.23118032155213 & 124.707565018938 \tabularnewline
Winsorized Mean ( 19 / 26 ) & 153.5375 & 1.23118032155213 & 124.707565018938 \tabularnewline
Winsorized Mean ( 20 / 26 ) & 153.5375 & 1.16243194301942 & 132.083001436786 \tabularnewline
Winsorized Mean ( 21 / 26 ) & 153.5375 & 1.16243194301942 & 132.083001436786 \tabularnewline
Winsorized Mean ( 22 / 26 ) & 153.2625 & 1.12561428376811 & 136.158986439776 \tabularnewline
Winsorized Mean ( 23 / 26 ) & 152.975 & 1.08819543456011 & 140.576770625617 \tabularnewline
Winsorized Mean ( 24 / 26 ) & 153.575 & 0.927903414604905 & 165.507527596923 \tabularnewline
Winsorized Mean ( 25 / 26 ) & 153.2625 & 0.888346449622534 & 172.525595239473 \tabularnewline
Winsorized Mean ( 26 / 26 ) & 153.5875 & 0.764251464266122 & 200.964613325908 \tabularnewline
Trimmed Mean ( 1 / 26 ) & 153.5 & 2.39204127720687 & 64.171133442663 \tabularnewline
Trimmed Mean ( 2 / 26 ) & 153.631578947368 & 2.21358184812262 & 69.4040652156893 \tabularnewline
Trimmed Mean ( 3 / 26 ) & 153.864864864865 & 2.04424625080306 & 75.2672848510401 \tabularnewline
Trimmed Mean ( 4 / 26 ) & 154.125 & 1.88010520424516 & 81.9767955814363 \tabularnewline
Trimmed Mean ( 5 / 26 ) & 154.171428571429 & 1.80979294064854 & 85.187330057869 \tabularnewline
Trimmed Mean ( 6 / 26 ) & 154.102941176471 & 1.76445985261846 & 87.3371762739639 \tabularnewline
Trimmed Mean ( 7 / 26 ) & 154.060606060606 & 1.71838797824191 & 89.6541456360895 \tabularnewline
Trimmed Mean ( 8 / 26 ) & 154 & 1.66681546954779 & 92.3917511047463 \tabularnewline
Trimmed Mean ( 9 / 26 ) & 153.967741935484 & 1.61365926225678 & 95.4152747960883 \tabularnewline
Trimmed Mean ( 10 / 26 ) & 153.916666666667 & 1.56250047080972 & 98.506636984822 \tabularnewline
Trimmed Mean ( 11 / 26 ) & 153.810344827586 & 1.51269219835502 & 101.679869172888 \tabularnewline
Trimmed Mean ( 12 / 26 ) & 153.75 & 1.47693302787607 & 104.100861107496 \tabularnewline
Trimmed Mean ( 13 / 26 ) & 153.685185185185 & 1.44206159059834 & 106.573246376681 \tabularnewline
Trimmed Mean ( 14 / 26 ) & 153.615384615385 & 1.39816563895777 & 109.869231752752 \tabularnewline
Trimmed Mean ( 15 / 26 ) & 153.58 & 1.35498776257747 & 113.344197078104 \tabularnewline
Trimmed Mean ( 16 / 26 ) & 153.5625 & 1.31814473438244 & 116.498967066728 \tabularnewline
Trimmed Mean ( 17 / 26 ) & 153.565217391304 & 1.28899173191302 & 119.135921192756 \tabularnewline
Trimmed Mean ( 18 / 26 ) & 153.568181818182 & 1.26315393014457 & 121.575192186281 \tabularnewline
Trimmed Mean ( 19 / 26 ) & 153.571428571429 & 1.24153012312369 & 123.695289958042 \tabularnewline
Trimmed Mean ( 20 / 26 ) & 153.575 & 1.21152981274894 & 126.761222368553 \tabularnewline
Trimmed Mean ( 21 / 26 ) & 153.578947368421 & 1.18587681094452 & 129.506662033554 \tabularnewline
Trimmed Mean ( 22 / 26 ) & 153.583333333333 & 1.14944776250605 & 133.614887377299 \tabularnewline
Trimmed Mean ( 23 / 26 ) & 153.617647058824 & 1.10743292138604 & 138.715080699027 \tabularnewline
Trimmed Mean ( 24 / 26 ) & 153.6875 & 1.05726890634435 & 145.362735135563 \tabularnewline
Trimmed Mean ( 25 / 26 ) & 153.7 & 1.03296248443633 & 148.795336051213 \tabularnewline
Trimmed Mean ( 26 / 26 ) & 153.75 & 1.0060991252036 & 152.817944224816 \tabularnewline
Median & 155 &  &  \tabularnewline
Midrange & 148.5 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 152.928571428571 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 153.575 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 152.928571428571 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 153.575 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 153.575 &  &  \tabularnewline
Midmean - Closest Observation & 152.928571428571 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 153.575 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 153.568181818182 &  &  \tabularnewline
Number of observations & 80 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41491&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]153.375[/C][C]2.56234755644116[/C][C]59.8572194527046[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]151.537718245749[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]149.499045072299[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]155.056683183925[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 26 )[/C][C]153.375[/C][C]2.54076728917103[/C][C]60.3656228784499[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 26 )[/C][C]153.2[/C][C]2.47189262803969[/C][C]61.9768020108114[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 26 )[/C][C]153.1625[/C][C]2.387828031014[/C][C]64.1430195184361[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 26 )[/C][C]153.9625[/C][C]2.06947707499360[/C][C]74.396813504434[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 26 )[/C][C]154.4625[/C][C]1.94829881571500[/C][C]79.2807031211558[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 26 )[/C][C]154.3125[/C][C]1.91922269256876[/C][C]80.4036449743423[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 26 )[/C][C]154.4[/C][C]1.90424243217778[/C][C]81.0821129657432[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 26 )[/C][C]154.2[/C][C]1.86705277802995[/C][C]82.5900594854669[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 26 )[/C][C]154.3125[/C][C]1.80913590028395[/C][C]85.2962455588773[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 26 )[/C][C]154.6875[/C][C]1.75046049547042[/C][C]88.3696035416267[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 26 )[/C][C]154.275[/C][C]1.63311992707288[/C][C]94.466424322257[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 26 )[/C][C]154.275[/C][C]1.58593252127110[/C][C]97.2771526725177[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 26 )[/C][C]154.275[/C][C]1.58593252127110[/C][C]97.2771526725177[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 26 )[/C][C]153.925[/C][C]1.52933084978407[/C][C]100.648594136274[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 26 )[/C][C]153.7375[/C][C]1.44363988702783[/C][C]106.492970567969[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 26 )[/C][C]153.5375[/C][C]1.35524575635808[/C][C]113.291260481492[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 26 )[/C][C]153.5375[/C][C]1.29433328592882[/C][C]118.622847507024[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 26 )[/C][C]153.5375[/C][C]1.23118032155213[/C][C]124.707565018938[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 26 )[/C][C]153.5375[/C][C]1.23118032155213[/C][C]124.707565018938[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 26 )[/C][C]153.5375[/C][C]1.16243194301942[/C][C]132.083001436786[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 26 )[/C][C]153.5375[/C][C]1.16243194301942[/C][C]132.083001436786[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 26 )[/C][C]153.2625[/C][C]1.12561428376811[/C][C]136.158986439776[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 26 )[/C][C]152.975[/C][C]1.08819543456011[/C][C]140.576770625617[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 26 )[/C][C]153.575[/C][C]0.927903414604905[/C][C]165.507527596923[/C][/ROW]
[ROW][C]Winsorized Mean ( 25 / 26 )[/C][C]153.2625[/C][C]0.888346449622534[/C][C]172.525595239473[/C][/ROW]
[ROW][C]Winsorized Mean ( 26 / 26 )[/C][C]153.5875[/C][C]0.764251464266122[/C][C]200.964613325908[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 26 )[/C][C]153.5[/C][C]2.39204127720687[/C][C]64.171133442663[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 26 )[/C][C]153.631578947368[/C][C]2.21358184812262[/C][C]69.4040652156893[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 26 )[/C][C]153.864864864865[/C][C]2.04424625080306[/C][C]75.2672848510401[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 26 )[/C][C]154.125[/C][C]1.88010520424516[/C][C]81.9767955814363[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 26 )[/C][C]154.171428571429[/C][C]1.80979294064854[/C][C]85.187330057869[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 26 )[/C][C]154.102941176471[/C][C]1.76445985261846[/C][C]87.3371762739639[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 26 )[/C][C]154.060606060606[/C][C]1.71838797824191[/C][C]89.6541456360895[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 26 )[/C][C]154[/C][C]1.66681546954779[/C][C]92.3917511047463[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 26 )[/C][C]153.967741935484[/C][C]1.61365926225678[/C][C]95.4152747960883[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 26 )[/C][C]153.916666666667[/C][C]1.56250047080972[/C][C]98.506636984822[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 26 )[/C][C]153.810344827586[/C][C]1.51269219835502[/C][C]101.679869172888[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 26 )[/C][C]153.75[/C][C]1.47693302787607[/C][C]104.100861107496[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 26 )[/C][C]153.685185185185[/C][C]1.44206159059834[/C][C]106.573246376681[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 26 )[/C][C]153.615384615385[/C][C]1.39816563895777[/C][C]109.869231752752[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 26 )[/C][C]153.58[/C][C]1.35498776257747[/C][C]113.344197078104[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 26 )[/C][C]153.5625[/C][C]1.31814473438244[/C][C]116.498967066728[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 26 )[/C][C]153.565217391304[/C][C]1.28899173191302[/C][C]119.135921192756[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 26 )[/C][C]153.568181818182[/C][C]1.26315393014457[/C][C]121.575192186281[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 26 )[/C][C]153.571428571429[/C][C]1.24153012312369[/C][C]123.695289958042[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 26 )[/C][C]153.575[/C][C]1.21152981274894[/C][C]126.761222368553[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 26 )[/C][C]153.578947368421[/C][C]1.18587681094452[/C][C]129.506662033554[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 26 )[/C][C]153.583333333333[/C][C]1.14944776250605[/C][C]133.614887377299[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 26 )[/C][C]153.617647058824[/C][C]1.10743292138604[/C][C]138.715080699027[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 26 )[/C][C]153.6875[/C][C]1.05726890634435[/C][C]145.362735135563[/C][/ROW]
[ROW][C]Trimmed Mean ( 25 / 26 )[/C][C]153.7[/C][C]1.03296248443633[/C][C]148.795336051213[/C][/ROW]
[ROW][C]Trimmed Mean ( 26 / 26 )[/C][C]153.75[/C][C]1.0060991252036[/C][C]152.817944224816[/C][/ROW]
[ROW][C]Median[/C][C]155[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]148.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]152.928571428571[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]153.575[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]152.928571428571[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]153.575[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]153.575[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]152.928571428571[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]153.575[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]153.568181818182[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]80[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41491&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41491&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 Mean153.3752.5623475564411659.8572194527046
Geometric Mean151.537718245749
Harmonic Mean149.499045072299
Quadratic Mean155.056683183925
Winsorized Mean ( 1 / 26 )153.3752.5407672891710360.3656228784499
Winsorized Mean ( 2 / 26 )153.22.4718926280396961.9768020108114
Winsorized Mean ( 3 / 26 )153.16252.38782803101464.1430195184361
Winsorized Mean ( 4 / 26 )153.96252.0694770749936074.396813504434
Winsorized Mean ( 5 / 26 )154.46251.9482988157150079.2807031211558
Winsorized Mean ( 6 / 26 )154.31251.9192226925687680.4036449743423
Winsorized Mean ( 7 / 26 )154.41.9042424321777881.0821129657432
Winsorized Mean ( 8 / 26 )154.21.8670527780299582.5900594854669
Winsorized Mean ( 9 / 26 )154.31251.8091359002839585.2962455588773
Winsorized Mean ( 10 / 26 )154.68751.7504604954704288.3696035416267
Winsorized Mean ( 11 / 26 )154.2751.6331199270728894.466424322257
Winsorized Mean ( 12 / 26 )154.2751.5859325212711097.2771526725177
Winsorized Mean ( 13 / 26 )154.2751.5859325212711097.2771526725177
Winsorized Mean ( 14 / 26 )153.9251.52933084978407100.648594136274
Winsorized Mean ( 15 / 26 )153.73751.44363988702783106.492970567969
Winsorized Mean ( 16 / 26 )153.53751.35524575635808113.291260481492
Winsorized Mean ( 17 / 26 )153.53751.29433328592882118.622847507024
Winsorized Mean ( 18 / 26 )153.53751.23118032155213124.707565018938
Winsorized Mean ( 19 / 26 )153.53751.23118032155213124.707565018938
Winsorized Mean ( 20 / 26 )153.53751.16243194301942132.083001436786
Winsorized Mean ( 21 / 26 )153.53751.16243194301942132.083001436786
Winsorized Mean ( 22 / 26 )153.26251.12561428376811136.158986439776
Winsorized Mean ( 23 / 26 )152.9751.08819543456011140.576770625617
Winsorized Mean ( 24 / 26 )153.5750.927903414604905165.507527596923
Winsorized Mean ( 25 / 26 )153.26250.888346449622534172.525595239473
Winsorized Mean ( 26 / 26 )153.58750.764251464266122200.964613325908
Trimmed Mean ( 1 / 26 )153.52.3920412772068764.171133442663
Trimmed Mean ( 2 / 26 )153.6315789473682.2135818481226269.4040652156893
Trimmed Mean ( 3 / 26 )153.8648648648652.0442462508030675.2672848510401
Trimmed Mean ( 4 / 26 )154.1251.8801052042451681.9767955814363
Trimmed Mean ( 5 / 26 )154.1714285714291.8097929406485485.187330057869
Trimmed Mean ( 6 / 26 )154.1029411764711.7644598526184687.3371762739639
Trimmed Mean ( 7 / 26 )154.0606060606061.7183879782419189.6541456360895
Trimmed Mean ( 8 / 26 )1541.6668154695477992.3917511047463
Trimmed Mean ( 9 / 26 )153.9677419354841.6136592622567895.4152747960883
Trimmed Mean ( 10 / 26 )153.9166666666671.5625004708097298.506636984822
Trimmed Mean ( 11 / 26 )153.8103448275861.51269219835502101.679869172888
Trimmed Mean ( 12 / 26 )153.751.47693302787607104.100861107496
Trimmed Mean ( 13 / 26 )153.6851851851851.44206159059834106.573246376681
Trimmed Mean ( 14 / 26 )153.6153846153851.39816563895777109.869231752752
Trimmed Mean ( 15 / 26 )153.581.35498776257747113.344197078104
Trimmed Mean ( 16 / 26 )153.56251.31814473438244116.498967066728
Trimmed Mean ( 17 / 26 )153.5652173913041.28899173191302119.135921192756
Trimmed Mean ( 18 / 26 )153.5681818181821.26315393014457121.575192186281
Trimmed Mean ( 19 / 26 )153.5714285714291.24153012312369123.695289958042
Trimmed Mean ( 20 / 26 )153.5751.21152981274894126.761222368553
Trimmed Mean ( 21 / 26 )153.5789473684211.18587681094452129.506662033554
Trimmed Mean ( 22 / 26 )153.5833333333331.14944776250605133.614887377299
Trimmed Mean ( 23 / 26 )153.6176470588241.10743292138604138.715080699027
Trimmed Mean ( 24 / 26 )153.68751.05726890634435145.362735135563
Trimmed Mean ( 25 / 26 )153.71.03296248443633148.795336051213
Trimmed Mean ( 26 / 26 )153.751.0060991252036152.817944224816
Median155
Midrange148.5
Midmean - Weighted Average at Xnp152.928571428571
Midmean - Weighted Average at X(n+1)p153.575
Midmean - Empirical Distribution Function152.928571428571
Midmean - Empirical Distribution Function - Averaging153.575
Midmean - Empirical Distribution Function - Interpolation153.575
Midmean - Closest Observation152.928571428571
Midmean - True Basic - Statistics Graphics Toolkit153.575
Midmean - MS Excel (old versions)153.568181818182
Number of observations80



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')