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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 computationSun, 20 Apr 2008 13:40:25 -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/20/t1208720524wcsu622i55ewl80.htm/, Retrieved Sun, 12 May 2024 16:25:59 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=10442, Retrieved Sun, 12 May 2024 16:25:59 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact182
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [centrummaten PPI ...] [2008-04-20 19:40:25] [fbc596b5f40baab1386d720ab747ae76] [Current]
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Dataseries X:
121.3
124.0
122.9
120.1
118.3
118.1
118.4
116.6
116.4
116.7
117.7
119.5
123.3
124.6
125.4
127.0
126.8
131.8
128.1
130.1
133.5
142.7
140.0
137.9
132.6
133.7
137.0
141.1
145.3
146.1
141.8
140.0
137.4
139.5
140.3
142.7
143.3
146.0
147.2
146.1
147.1
141.7
138.8
138.3
140.2
143.1
142.0
142.4
141.2
138.0
137.9
136.8
135.9
138.8
139.5
138.0
139.7
137.5
137.8
137.4
141.7
145.3
148.9
151.3
151.4
149.2
143.8
143.6
144.3
142.0
140.8
141.8




Summary of compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 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 & 3 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=10442&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]3 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=10442&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=10442&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 time3 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean136.0763888888891.13352575875331120.047019521242
Geometric Mean135.728284820847
Harmonic Mean135.367325563126
Quadratic Mean136.411180402813
Winsorized Mean ( 1 / 24 )136.0777777777781.13258609414487120.147844372503
Winsorized Mean ( 2 / 24 )136.0222222222221.12156138059710121.279338407503
Winsorized Mean ( 3 / 24 )136.0513888888891.10959852785528122.613166360143
Winsorized Mean ( 4 / 24 )135.9791666666671.08988617210852124.764558122247
Winsorized Mean ( 5 / 24 )135.9861111111111.08568416937527125.253839879936
Winsorized Mean ( 6 / 24 )135.9111111111111.07218269243665126.761150007224
Winsorized Mean ( 7 / 24 )136.0180555555561.04800713777765129.787336987025
Winsorized Mean ( 8 / 24 )136.0736111111111.03183291237453131.875625868503
Winsorized Mean ( 9 / 24 )136.1361111111110.987958220693318137.795413064709
Winsorized Mean ( 10 / 24 )136.3583333333330.942073741419588144.742738639396
Winsorized Mean ( 11 / 24 )136.2666666666670.910072311354205149.731691610197
Winsorized Mean ( 12 / 24 )136.30.876631053026238155.481601443932
Winsorized Mean ( 13 / 24 )136.3722222222220.851035506188959160.242694024499
Winsorized Mean ( 14 / 24 )136.4694444444440.814043499337793167.643921431053
Winsorized Mean ( 15 / 24 )136.7194444444440.754116607652789181.297485106432
Winsorized Mean ( 16 / 24 )136.6750.73545560916458185.837184864566
Winsorized Mean ( 17 / 24 )136.9347222222220.68788464761768199.066402625007
Winsorized Mean ( 18 / 24 )137.3597222222220.590279434776281232.702876179791
Winsorized Mean ( 19 / 24 )137.7027777777780.501379053696903274.648046747128
Winsorized Mean ( 20 / 24 )137.9250.465015312652783296.603135955193
Winsorized Mean ( 21 / 24 )138.1291666666670.416020332035187332.025038273812
Winsorized Mean ( 22 / 24 )138.1902777777780.406477096016688339.970638277007
Winsorized Mean ( 23 / 24 )138.8611111111110.297600968226484466.601677873015
Winsorized Mean ( 24 / 24 )139.1611111111110.257056556770183541.36378725218
Trimmed Mean ( 1 / 24 )136.1385714285711.10953572977185122.698681777977
Trimmed Mean ( 2 / 24 )136.2029411764711.08203457307612125.876699844496
Trimmed Mean ( 3 / 24 )136.3015151515151.05603271392837129.069406045655
Trimmed Mean ( 4 / 24 )136.39531251.03016610832986132.401281110994
Trimmed Mean ( 5 / 24 )136.5161290322581.00587432086883135.718872825326
Trimmed Mean ( 6 / 24 )136.6433333333330.977392376107888139.803968880406
Trimmed Mean ( 7 / 24 )136.7948275862070.945932235626217144.613770875085
Trimmed Mean ( 8 / 24 )136.93750.913700064814247149.871391360620
Trimmed Mean ( 9 / 24 )137.0814814814810.877663955444651156.189029560900
Trimmed Mean ( 10 / 24 )137.2269230769230.843501086448759162.687310403671
Trimmed Mean ( 11 / 24 )137.3520.812068359442826169.138470182781
Trimmed Mean ( 12 / 24 )137.50.778956384944234176.518227024795
Trimmed Mean ( 13 / 24 )137.6565217391300.74399789733946185.022729541832
Trimmed Mean ( 14 / 24 )137.8181818181820.7044353047633195.643490447275
Trimmed Mean ( 15 / 24 )137.9833333333330.661474408681905208.599654835154
Trimmed Mean ( 16 / 24 )138.1350.620840517941563222.496754010185
Trimmed Mean ( 17 / 24 )138.3078947368420.56907478476347243.039928037452
Trimmed Mean ( 18 / 24 )138.4694444444440.512460907443532270.204892574566
Trimmed Mean ( 19 / 24 )138.60.467118446963681296.712752195754
Trimmed Mean ( 20 / 24 )138.706250.433778817486516319.762617279743
Trimmed Mean ( 21 / 24 )138.80.398647137491146348.177591023296
Trimmed Mean ( 22 / 24 )138.8821428571430.36547619047619380.003257328991
Trimmed Mean ( 23 / 24 )138.9692307692310.317236588770018438.061798949607
Trimmed Mean ( 24 / 24 )138.9833333333330.296517630696742468.718615506126
Median138.8
Midrange133.9
Midmean - Weighted Average at Xnp138.189189189189
Midmean - Weighted Average at X(n+1)p138.469444444444
Midmean - Empirical Distribution Function138.189189189189
Midmean - Empirical Distribution Function - Averaging138.469444444444
Midmean - Empirical Distribution Function - Interpolation138.469444444444
Midmean - Closest Observation138.189189189189
Midmean - True Basic - Statistics Graphics Toolkit138.469444444444
Midmean - MS Excel (old versions)138.420512820513
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 136.076388888889 & 1.13352575875331 & 120.047019521242 \tabularnewline
Geometric Mean & 135.728284820847 &  &  \tabularnewline
Harmonic Mean & 135.367325563126 &  &  \tabularnewline
Quadratic Mean & 136.411180402813 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 136.077777777778 & 1.13258609414487 & 120.147844372503 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 136.022222222222 & 1.12156138059710 & 121.279338407503 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 136.051388888889 & 1.10959852785528 & 122.613166360143 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 135.979166666667 & 1.08988617210852 & 124.764558122247 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 135.986111111111 & 1.08568416937527 & 125.253839879936 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 135.911111111111 & 1.07218269243665 & 126.761150007224 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 136.018055555556 & 1.04800713777765 & 129.787336987025 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 136.073611111111 & 1.03183291237453 & 131.875625868503 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 136.136111111111 & 0.987958220693318 & 137.795413064709 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 136.358333333333 & 0.942073741419588 & 144.742738639396 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 136.266666666667 & 0.910072311354205 & 149.731691610197 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 136.3 & 0.876631053026238 & 155.481601443932 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 136.372222222222 & 0.851035506188959 & 160.242694024499 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 136.469444444444 & 0.814043499337793 & 167.643921431053 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 136.719444444444 & 0.754116607652789 & 181.297485106432 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 136.675 & 0.73545560916458 & 185.837184864566 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 136.934722222222 & 0.68788464761768 & 199.066402625007 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 137.359722222222 & 0.590279434776281 & 232.702876179791 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 137.702777777778 & 0.501379053696903 & 274.648046747128 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 137.925 & 0.465015312652783 & 296.603135955193 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 138.129166666667 & 0.416020332035187 & 332.025038273812 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 138.190277777778 & 0.406477096016688 & 339.970638277007 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 138.861111111111 & 0.297600968226484 & 466.601677873015 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 139.161111111111 & 0.257056556770183 & 541.36378725218 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 136.138571428571 & 1.10953572977185 & 122.698681777977 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 136.202941176471 & 1.08203457307612 & 125.876699844496 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 136.301515151515 & 1.05603271392837 & 129.069406045655 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 136.3953125 & 1.03016610832986 & 132.401281110994 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 136.516129032258 & 1.00587432086883 & 135.718872825326 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 136.643333333333 & 0.977392376107888 & 139.803968880406 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 136.794827586207 & 0.945932235626217 & 144.613770875085 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 136.9375 & 0.913700064814247 & 149.871391360620 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 137.081481481481 & 0.877663955444651 & 156.189029560900 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 137.226923076923 & 0.843501086448759 & 162.687310403671 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 137.352 & 0.812068359442826 & 169.138470182781 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 137.5 & 0.778956384944234 & 176.518227024795 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 137.656521739130 & 0.74399789733946 & 185.022729541832 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 137.818181818182 & 0.7044353047633 & 195.643490447275 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 137.983333333333 & 0.661474408681905 & 208.599654835154 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 138.135 & 0.620840517941563 & 222.496754010185 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 138.307894736842 & 0.56907478476347 & 243.039928037452 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 138.469444444444 & 0.512460907443532 & 270.204892574566 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 138.6 & 0.467118446963681 & 296.712752195754 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 138.70625 & 0.433778817486516 & 319.762617279743 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 138.8 & 0.398647137491146 & 348.177591023296 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 138.882142857143 & 0.36547619047619 & 380.003257328991 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 138.969230769231 & 0.317236588770018 & 438.061798949607 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 138.983333333333 & 0.296517630696742 & 468.718615506126 \tabularnewline
Median & 138.8 &  &  \tabularnewline
Midrange & 133.9 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 138.189189189189 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 138.469444444444 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 138.189189189189 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 138.469444444444 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 138.469444444444 &  &  \tabularnewline
Midmean - Closest Observation & 138.189189189189 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 138.469444444444 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 138.420512820513 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=10442&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]136.076388888889[/C][C]1.13352575875331[/C][C]120.047019521242[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]135.728284820847[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]135.367325563126[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]136.411180402813[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]136.077777777778[/C][C]1.13258609414487[/C][C]120.147844372503[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]136.022222222222[/C][C]1.12156138059710[/C][C]121.279338407503[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]136.051388888889[/C][C]1.10959852785528[/C][C]122.613166360143[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]135.979166666667[/C][C]1.08988617210852[/C][C]124.764558122247[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]135.986111111111[/C][C]1.08568416937527[/C][C]125.253839879936[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]135.911111111111[/C][C]1.07218269243665[/C][C]126.761150007224[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]136.018055555556[/C][C]1.04800713777765[/C][C]129.787336987025[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]136.073611111111[/C][C]1.03183291237453[/C][C]131.875625868503[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]136.136111111111[/C][C]0.987958220693318[/C][C]137.795413064709[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]136.358333333333[/C][C]0.942073741419588[/C][C]144.742738639396[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]136.266666666667[/C][C]0.910072311354205[/C][C]149.731691610197[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]136.3[/C][C]0.876631053026238[/C][C]155.481601443932[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]136.372222222222[/C][C]0.851035506188959[/C][C]160.242694024499[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]136.469444444444[/C][C]0.814043499337793[/C][C]167.643921431053[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]136.719444444444[/C][C]0.754116607652789[/C][C]181.297485106432[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]136.675[/C][C]0.73545560916458[/C][C]185.837184864566[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]136.934722222222[/C][C]0.68788464761768[/C][C]199.066402625007[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]137.359722222222[/C][C]0.590279434776281[/C][C]232.702876179791[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]137.702777777778[/C][C]0.501379053696903[/C][C]274.648046747128[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]137.925[/C][C]0.465015312652783[/C][C]296.603135955193[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]138.129166666667[/C][C]0.416020332035187[/C][C]332.025038273812[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]138.190277777778[/C][C]0.406477096016688[/C][C]339.970638277007[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]138.861111111111[/C][C]0.297600968226484[/C][C]466.601677873015[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]139.161111111111[/C][C]0.257056556770183[/C][C]541.36378725218[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]136.138571428571[/C][C]1.10953572977185[/C][C]122.698681777977[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]136.202941176471[/C][C]1.08203457307612[/C][C]125.876699844496[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]136.301515151515[/C][C]1.05603271392837[/C][C]129.069406045655[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]136.3953125[/C][C]1.03016610832986[/C][C]132.401281110994[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]136.516129032258[/C][C]1.00587432086883[/C][C]135.718872825326[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]136.643333333333[/C][C]0.977392376107888[/C][C]139.803968880406[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]136.794827586207[/C][C]0.945932235626217[/C][C]144.613770875085[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]136.9375[/C][C]0.913700064814247[/C][C]149.871391360620[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]137.081481481481[/C][C]0.877663955444651[/C][C]156.189029560900[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]137.226923076923[/C][C]0.843501086448759[/C][C]162.687310403671[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]137.352[/C][C]0.812068359442826[/C][C]169.138470182781[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]137.5[/C][C]0.778956384944234[/C][C]176.518227024795[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]137.656521739130[/C][C]0.74399789733946[/C][C]185.022729541832[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]137.818181818182[/C][C]0.7044353047633[/C][C]195.643490447275[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]137.983333333333[/C][C]0.661474408681905[/C][C]208.599654835154[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]138.135[/C][C]0.620840517941563[/C][C]222.496754010185[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]138.307894736842[/C][C]0.56907478476347[/C][C]243.039928037452[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]138.469444444444[/C][C]0.512460907443532[/C][C]270.204892574566[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]138.6[/C][C]0.467118446963681[/C][C]296.712752195754[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]138.70625[/C][C]0.433778817486516[/C][C]319.762617279743[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]138.8[/C][C]0.398647137491146[/C][C]348.177591023296[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]138.882142857143[/C][C]0.36547619047619[/C][C]380.003257328991[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]138.969230769231[/C][C]0.317236588770018[/C][C]438.061798949607[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]138.983333333333[/C][C]0.296517630696742[/C][C]468.718615506126[/C][/ROW]
[ROW][C]Median[/C][C]138.8[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]133.9[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]138.189189189189[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]138.469444444444[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]138.189189189189[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]138.469444444444[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]138.469444444444[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]138.189189189189[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]138.469444444444[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]138.420512820513[/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=10442&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=10442&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 Mean136.0763888888891.13352575875331120.047019521242
Geometric Mean135.728284820847
Harmonic Mean135.367325563126
Quadratic Mean136.411180402813
Winsorized Mean ( 1 / 24 )136.0777777777781.13258609414487120.147844372503
Winsorized Mean ( 2 / 24 )136.0222222222221.12156138059710121.279338407503
Winsorized Mean ( 3 / 24 )136.0513888888891.10959852785528122.613166360143
Winsorized Mean ( 4 / 24 )135.9791666666671.08988617210852124.764558122247
Winsorized Mean ( 5 / 24 )135.9861111111111.08568416937527125.253839879936
Winsorized Mean ( 6 / 24 )135.9111111111111.07218269243665126.761150007224
Winsorized Mean ( 7 / 24 )136.0180555555561.04800713777765129.787336987025
Winsorized Mean ( 8 / 24 )136.0736111111111.03183291237453131.875625868503
Winsorized Mean ( 9 / 24 )136.1361111111110.987958220693318137.795413064709
Winsorized Mean ( 10 / 24 )136.3583333333330.942073741419588144.742738639396
Winsorized Mean ( 11 / 24 )136.2666666666670.910072311354205149.731691610197
Winsorized Mean ( 12 / 24 )136.30.876631053026238155.481601443932
Winsorized Mean ( 13 / 24 )136.3722222222220.851035506188959160.242694024499
Winsorized Mean ( 14 / 24 )136.4694444444440.814043499337793167.643921431053
Winsorized Mean ( 15 / 24 )136.7194444444440.754116607652789181.297485106432
Winsorized Mean ( 16 / 24 )136.6750.73545560916458185.837184864566
Winsorized Mean ( 17 / 24 )136.9347222222220.68788464761768199.066402625007
Winsorized Mean ( 18 / 24 )137.3597222222220.590279434776281232.702876179791
Winsorized Mean ( 19 / 24 )137.7027777777780.501379053696903274.648046747128
Winsorized Mean ( 20 / 24 )137.9250.465015312652783296.603135955193
Winsorized Mean ( 21 / 24 )138.1291666666670.416020332035187332.025038273812
Winsorized Mean ( 22 / 24 )138.1902777777780.406477096016688339.970638277007
Winsorized Mean ( 23 / 24 )138.8611111111110.297600968226484466.601677873015
Winsorized Mean ( 24 / 24 )139.1611111111110.257056556770183541.36378725218
Trimmed Mean ( 1 / 24 )136.1385714285711.10953572977185122.698681777977
Trimmed Mean ( 2 / 24 )136.2029411764711.08203457307612125.876699844496
Trimmed Mean ( 3 / 24 )136.3015151515151.05603271392837129.069406045655
Trimmed Mean ( 4 / 24 )136.39531251.03016610832986132.401281110994
Trimmed Mean ( 5 / 24 )136.5161290322581.00587432086883135.718872825326
Trimmed Mean ( 6 / 24 )136.6433333333330.977392376107888139.803968880406
Trimmed Mean ( 7 / 24 )136.7948275862070.945932235626217144.613770875085
Trimmed Mean ( 8 / 24 )136.93750.913700064814247149.871391360620
Trimmed Mean ( 9 / 24 )137.0814814814810.877663955444651156.189029560900
Trimmed Mean ( 10 / 24 )137.2269230769230.843501086448759162.687310403671
Trimmed Mean ( 11 / 24 )137.3520.812068359442826169.138470182781
Trimmed Mean ( 12 / 24 )137.50.778956384944234176.518227024795
Trimmed Mean ( 13 / 24 )137.6565217391300.74399789733946185.022729541832
Trimmed Mean ( 14 / 24 )137.8181818181820.7044353047633195.643490447275
Trimmed Mean ( 15 / 24 )137.9833333333330.661474408681905208.599654835154
Trimmed Mean ( 16 / 24 )138.1350.620840517941563222.496754010185
Trimmed Mean ( 17 / 24 )138.3078947368420.56907478476347243.039928037452
Trimmed Mean ( 18 / 24 )138.4694444444440.512460907443532270.204892574566
Trimmed Mean ( 19 / 24 )138.60.467118446963681296.712752195754
Trimmed Mean ( 20 / 24 )138.706250.433778817486516319.762617279743
Trimmed Mean ( 21 / 24 )138.80.398647137491146348.177591023296
Trimmed Mean ( 22 / 24 )138.8821428571430.36547619047619380.003257328991
Trimmed Mean ( 23 / 24 )138.9692307692310.317236588770018438.061798949607
Trimmed Mean ( 24 / 24 )138.9833333333330.296517630696742468.718615506126
Median138.8
Midrange133.9
Midmean - Weighted Average at Xnp138.189189189189
Midmean - Weighted Average at X(n+1)p138.469444444444
Midmean - Empirical Distribution Function138.189189189189
Midmean - Empirical Distribution Function - Averaging138.469444444444
Midmean - Empirical Distribution Function - Interpolation138.469444444444
Midmean - Closest Observation138.189189189189
Midmean - True Basic - Statistics Graphics Toolkit138.469444444444
Midmean - MS Excel (old versions)138.420512820513
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')