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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, 22 Oct 2012 14:03:49 -0400
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/Oct/22/t13509291522gfq84xgf2g9hfk.htm/, Retrieved Fri, 03 May 2024 18:28:07 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=181980, Retrieved Fri, 03 May 2024 18:28:07 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact45
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Werkloosheid in B...] [2012-10-22 18:03:49] [ad1fc76d648632443dce4152f75a8e3a] [Current]
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Dataseries X:
125
123
117
114
111
112
144
150
149
134
123
116
117
111
105
102
95
93
124
130
124
115
106
105
105
101
95
93
84
87
116
120
117
109
105
107
109
109
108
107
99
103
131
137
135
124
118
121
121
118
113
107
100
102
130
136
133
120
112
109
110
106
102
98
92
92
120
127
124
114
108
106




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

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=181980&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=181980&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=181980&T=0

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

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







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean113.6805555555561.6568757471063868.6113945201327
Geometric Mean112.835008848456
Harmonic Mean111.999031305487
Quadratic Mean114.534626011331
Winsorized Mean ( 1 / 24 )113.7083333333331.6426006018168969.2245779086894
Winsorized Mean ( 2 / 24 )113.7083333333331.573255237478572.2758333324077
Winsorized Mean ( 3 / 24 )113.4166666666671.5012709795338875.5470985670294
Winsorized Mean ( 4 / 24 )113.4166666666671.4781599926957476.7282751712333
Winsorized Mean ( 5 / 24 )113.3472222222221.4634514109352377.4519887543015
Winsorized Mean ( 6 / 24 )113.4305555555561.4146044627210480.1853511315582
Winsorized Mean ( 7 / 24 )113.3333333333331.3949944048889181.2428587069198
Winsorized Mean ( 8 / 24 )113.4444444444441.292643336477687.7615976836858
Winsorized Mean ( 9 / 24 )113.4444444444441.2482991384287390.8792139256301
Winsorized Mean ( 10 / 24 )113.5833333333331.2261416385083392.6347574914055
Winsorized Mean ( 11 / 24 )113.2777777777781.11947167532516101.188605549019
Winsorized Mean ( 12 / 24 )113.1111111111111.03830312459458108.938428895971
Winsorized Mean ( 13 / 24 )112.9305555555561.00979676693873111.834934764064
Winsorized Mean ( 14 / 24 )112.9305555555561.00979676693873111.834934764064
Winsorized Mean ( 15 / 24 )113.1388888888890.97870630083815115.600450096212
Winsorized Mean ( 16 / 24 )113.5833333333330.916880043454163123.880254722778
Winsorized Mean ( 17 / 24 )113.3472222222220.879731722653452128.842940755102
Winsorized Mean ( 18 / 24 )113.3472222222220.879731722653452128.842940755102
Winsorized Mean ( 19 / 24 )112.8194444444440.800852047454903140.874266105685
Winsorized Mean ( 20 / 24 )113.0972222222220.763547369950895148.120767188938
Winsorized Mean ( 21 / 24 )112.8055555555560.72179323963719156.285137295353
Winsorized Mean ( 22 / 24 )112.8055555555560.72179323963719156.285137295353
Winsorized Mean ( 23 / 24 )113.1250.68030000631453166.286930692307
Winsorized Mean ( 24 / 24 )112.4583333333330.588404350074189191.12423849204
Trimmed Mean ( 1 / 24 )113.5857142857141.5652135709309672.5688279192185
Trimmed Mean ( 2 / 24 )113.4558823529411.4719254236619477.0799121538908
Trimmed Mean ( 3 / 24 )113.3181818181821.4056428223462680.6166260850208
Trimmed Mean ( 4 / 24 )113.281251.3603054537784483.2763330363379
Trimmed Mean ( 5 / 24 )113.2419354838711.3143405196212486.1587494209678
Trimmed Mean ( 6 / 24 )113.2166666666671.2633673206226889.6150033474551
Trimmed Mean ( 7 / 24 )113.1724137931031.2157312112968493.0899961615533
Trimmed Mean ( 8 / 24 )113.1428571428571.1625734361467897.3210410843863
Trimmed Mean ( 9 / 24 )113.0925925925931.12380646168516100.633513374722
Trimmed Mean ( 10 / 24 )113.0384615384621.08637577366905104.050977827582
Trimmed Mean ( 11 / 24 )112.961.04430818814981108.167302796055
Trimmed Mean ( 12 / 24 )112.9166666666671.01663178640317111.069384389568
Trimmed Mean ( 13 / 24 )112.8913043478260.999143720769541112.988053671475
Trimmed Mean ( 14 / 24 )112.8863636363640.981981379827875114.957743553295
Trimmed Mean ( 15 / 24 )112.8809523809520.958610578057019117.754753561918
Trimmed Mean ( 16 / 24 )112.850.93407708461347120.814440113043
Trimmed Mean ( 17 / 24 )112.7631578947370.914117356409565123.357419158568
Trimmed Mean ( 18 / 24 )112.6944444444440.895154012149514125.893916482409
Trimmed Mean ( 19 / 24 )112.6176470588240.867325992742581129.844658180616
Trimmed Mean ( 20 / 24 )112.593750.849406072148784132.555857194623
Trimmed Mean ( 21 / 24 )112.5333333333330.831469179325718135.34275969747
Trimmed Mean ( 22 / 24 )112.50.815686162285419137.920692052435
Trimmed Mean ( 23 / 24 )112.4615384615380.788827307279647142.568008769085
Trimmed Mean ( 24 / 24 )112.3750.758556266005134148.143262452781
Median112
Midrange117
Midmean - Weighted Average at Xnp112.564102564103
Midmean - Weighted Average at X(n+1)p112.564102564103
Midmean - Empirical Distribution Function112.564102564103
Midmean - Empirical Distribution Function - Averaging112.564102564103
Midmean - Empirical Distribution Function - Interpolation112.564102564103
Midmean - Closest Observation112.564102564103
Midmean - True Basic - Statistics Graphics Toolkit112.564102564103
Midmean - MS Excel (old versions)112.564102564103
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 113.680555555556 & 1.65687574710638 & 68.6113945201327 \tabularnewline
Geometric Mean & 112.835008848456 &  &  \tabularnewline
Harmonic Mean & 111.999031305487 &  &  \tabularnewline
Quadratic Mean & 114.534626011331 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 113.708333333333 & 1.64260060181689 & 69.2245779086894 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 113.708333333333 & 1.5732552374785 & 72.2758333324077 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 113.416666666667 & 1.50127097953388 & 75.5470985670294 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 113.416666666667 & 1.47815999269574 & 76.7282751712333 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 113.347222222222 & 1.46345141093523 & 77.4519887543015 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 113.430555555556 & 1.41460446272104 & 80.1853511315582 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 113.333333333333 & 1.39499440488891 & 81.2428587069198 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 113.444444444444 & 1.2926433364776 & 87.7615976836858 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 113.444444444444 & 1.24829913842873 & 90.8792139256301 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 113.583333333333 & 1.22614163850833 & 92.6347574914055 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 113.277777777778 & 1.11947167532516 & 101.188605549019 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 113.111111111111 & 1.03830312459458 & 108.938428895971 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 112.930555555556 & 1.00979676693873 & 111.834934764064 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 112.930555555556 & 1.00979676693873 & 111.834934764064 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 113.138888888889 & 0.97870630083815 & 115.600450096212 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 113.583333333333 & 0.916880043454163 & 123.880254722778 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 113.347222222222 & 0.879731722653452 & 128.842940755102 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 113.347222222222 & 0.879731722653452 & 128.842940755102 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 112.819444444444 & 0.800852047454903 & 140.874266105685 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 113.097222222222 & 0.763547369950895 & 148.120767188938 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 112.805555555556 & 0.72179323963719 & 156.285137295353 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 112.805555555556 & 0.72179323963719 & 156.285137295353 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 113.125 & 0.68030000631453 & 166.286930692307 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 112.458333333333 & 0.588404350074189 & 191.12423849204 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 113.585714285714 & 1.56521357093096 & 72.5688279192185 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 113.455882352941 & 1.47192542366194 & 77.0799121538908 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 113.318181818182 & 1.40564282234626 & 80.6166260850208 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 113.28125 & 1.36030545377844 & 83.2763330363379 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 113.241935483871 & 1.31434051962124 & 86.1587494209678 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 113.216666666667 & 1.26336732062268 & 89.6150033474551 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 113.172413793103 & 1.21573121129684 & 93.0899961615533 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 113.142857142857 & 1.16257343614678 & 97.3210410843863 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 113.092592592593 & 1.12380646168516 & 100.633513374722 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 113.038461538462 & 1.08637577366905 & 104.050977827582 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 112.96 & 1.04430818814981 & 108.167302796055 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 112.916666666667 & 1.01663178640317 & 111.069384389568 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 112.891304347826 & 0.999143720769541 & 112.988053671475 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 112.886363636364 & 0.981981379827875 & 114.957743553295 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 112.880952380952 & 0.958610578057019 & 117.754753561918 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 112.85 & 0.93407708461347 & 120.814440113043 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 112.763157894737 & 0.914117356409565 & 123.357419158568 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 112.694444444444 & 0.895154012149514 & 125.893916482409 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 112.617647058824 & 0.867325992742581 & 129.844658180616 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 112.59375 & 0.849406072148784 & 132.555857194623 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 112.533333333333 & 0.831469179325718 & 135.34275969747 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 112.5 & 0.815686162285419 & 137.920692052435 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 112.461538461538 & 0.788827307279647 & 142.568008769085 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 112.375 & 0.758556266005134 & 148.143262452781 \tabularnewline
Median & 112 &  &  \tabularnewline
Midrange & 117 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 112.564102564103 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 112.564102564103 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 112.564102564103 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 112.564102564103 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 112.564102564103 &  &  \tabularnewline
Midmean - Closest Observation & 112.564102564103 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 112.564102564103 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 112.564102564103 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=181980&T=1

[TABLE]
[ROW][C]Central Tendency - Ungrouped Data[/C][/ROW]
[ROW][C]Measure[/C][C]Value[/C][C]S.E.[/C][C]Value/S.E.[/C][/ROW]
[ROW][C]Arithmetic Mean[/C][C]113.680555555556[/C][C]1.65687574710638[/C][C]68.6113945201327[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]112.835008848456[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]111.999031305487[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]114.534626011331[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]113.708333333333[/C][C]1.64260060181689[/C][C]69.2245779086894[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]113.708333333333[/C][C]1.5732552374785[/C][C]72.2758333324077[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]113.416666666667[/C][C]1.50127097953388[/C][C]75.5470985670294[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]113.416666666667[/C][C]1.47815999269574[/C][C]76.7282751712333[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]113.347222222222[/C][C]1.46345141093523[/C][C]77.4519887543015[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]113.430555555556[/C][C]1.41460446272104[/C][C]80.1853511315582[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]113.333333333333[/C][C]1.39499440488891[/C][C]81.2428587069198[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]113.444444444444[/C][C]1.2926433364776[/C][C]87.7615976836858[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]113.444444444444[/C][C]1.24829913842873[/C][C]90.8792139256301[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]113.583333333333[/C][C]1.22614163850833[/C][C]92.6347574914055[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]113.277777777778[/C][C]1.11947167532516[/C][C]101.188605549019[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]113.111111111111[/C][C]1.03830312459458[/C][C]108.938428895971[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]112.930555555556[/C][C]1.00979676693873[/C][C]111.834934764064[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]112.930555555556[/C][C]1.00979676693873[/C][C]111.834934764064[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]113.138888888889[/C][C]0.97870630083815[/C][C]115.600450096212[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]113.583333333333[/C][C]0.916880043454163[/C][C]123.880254722778[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]113.347222222222[/C][C]0.879731722653452[/C][C]128.842940755102[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]113.347222222222[/C][C]0.879731722653452[/C][C]128.842940755102[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]112.819444444444[/C][C]0.800852047454903[/C][C]140.874266105685[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]113.097222222222[/C][C]0.763547369950895[/C][C]148.120767188938[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]112.805555555556[/C][C]0.72179323963719[/C][C]156.285137295353[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]112.805555555556[/C][C]0.72179323963719[/C][C]156.285137295353[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]113.125[/C][C]0.68030000631453[/C][C]166.286930692307[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]112.458333333333[/C][C]0.588404350074189[/C][C]191.12423849204[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]113.585714285714[/C][C]1.56521357093096[/C][C]72.5688279192185[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]113.455882352941[/C][C]1.47192542366194[/C][C]77.0799121538908[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]113.318181818182[/C][C]1.40564282234626[/C][C]80.6166260850208[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]113.28125[/C][C]1.36030545377844[/C][C]83.2763330363379[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]113.241935483871[/C][C]1.31434051962124[/C][C]86.1587494209678[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]113.216666666667[/C][C]1.26336732062268[/C][C]89.6150033474551[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]113.172413793103[/C][C]1.21573121129684[/C][C]93.0899961615533[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]113.142857142857[/C][C]1.16257343614678[/C][C]97.3210410843863[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]113.092592592593[/C][C]1.12380646168516[/C][C]100.633513374722[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]113.038461538462[/C][C]1.08637577366905[/C][C]104.050977827582[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]112.96[/C][C]1.04430818814981[/C][C]108.167302796055[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]112.916666666667[/C][C]1.01663178640317[/C][C]111.069384389568[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]112.891304347826[/C][C]0.999143720769541[/C][C]112.988053671475[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]112.886363636364[/C][C]0.981981379827875[/C][C]114.957743553295[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]112.880952380952[/C][C]0.958610578057019[/C][C]117.754753561918[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]112.85[/C][C]0.93407708461347[/C][C]120.814440113043[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]112.763157894737[/C][C]0.914117356409565[/C][C]123.357419158568[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]112.694444444444[/C][C]0.895154012149514[/C][C]125.893916482409[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]112.617647058824[/C][C]0.867325992742581[/C][C]129.844658180616[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]112.59375[/C][C]0.849406072148784[/C][C]132.555857194623[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]112.533333333333[/C][C]0.831469179325718[/C][C]135.34275969747[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]112.5[/C][C]0.815686162285419[/C][C]137.920692052435[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]112.461538461538[/C][C]0.788827307279647[/C][C]142.568008769085[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]112.375[/C][C]0.758556266005134[/C][C]148.143262452781[/C][/ROW]
[ROW][C]Median[/C][C]112[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]117[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]112.564102564103[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]112.564102564103[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]112.564102564103[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]112.564102564103[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]112.564102564103[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]112.564102564103[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]112.564102564103[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]112.564102564103[/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=181980&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=181980&T=1

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean113.6805555555561.6568757471063868.6113945201327
Geometric Mean112.835008848456
Harmonic Mean111.999031305487
Quadratic Mean114.534626011331
Winsorized Mean ( 1 / 24 )113.7083333333331.6426006018168969.2245779086894
Winsorized Mean ( 2 / 24 )113.7083333333331.573255237478572.2758333324077
Winsorized Mean ( 3 / 24 )113.4166666666671.5012709795338875.5470985670294
Winsorized Mean ( 4 / 24 )113.4166666666671.4781599926957476.7282751712333
Winsorized Mean ( 5 / 24 )113.3472222222221.4634514109352377.4519887543015
Winsorized Mean ( 6 / 24 )113.4305555555561.4146044627210480.1853511315582
Winsorized Mean ( 7 / 24 )113.3333333333331.3949944048889181.2428587069198
Winsorized Mean ( 8 / 24 )113.4444444444441.292643336477687.7615976836858
Winsorized Mean ( 9 / 24 )113.4444444444441.2482991384287390.8792139256301
Winsorized Mean ( 10 / 24 )113.5833333333331.2261416385083392.6347574914055
Winsorized Mean ( 11 / 24 )113.2777777777781.11947167532516101.188605549019
Winsorized Mean ( 12 / 24 )113.1111111111111.03830312459458108.938428895971
Winsorized Mean ( 13 / 24 )112.9305555555561.00979676693873111.834934764064
Winsorized Mean ( 14 / 24 )112.9305555555561.00979676693873111.834934764064
Winsorized Mean ( 15 / 24 )113.1388888888890.97870630083815115.600450096212
Winsorized Mean ( 16 / 24 )113.5833333333330.916880043454163123.880254722778
Winsorized Mean ( 17 / 24 )113.3472222222220.879731722653452128.842940755102
Winsorized Mean ( 18 / 24 )113.3472222222220.879731722653452128.842940755102
Winsorized Mean ( 19 / 24 )112.8194444444440.800852047454903140.874266105685
Winsorized Mean ( 20 / 24 )113.0972222222220.763547369950895148.120767188938
Winsorized Mean ( 21 / 24 )112.8055555555560.72179323963719156.285137295353
Winsorized Mean ( 22 / 24 )112.8055555555560.72179323963719156.285137295353
Winsorized Mean ( 23 / 24 )113.1250.68030000631453166.286930692307
Winsorized Mean ( 24 / 24 )112.4583333333330.588404350074189191.12423849204
Trimmed Mean ( 1 / 24 )113.5857142857141.5652135709309672.5688279192185
Trimmed Mean ( 2 / 24 )113.4558823529411.4719254236619477.0799121538908
Trimmed Mean ( 3 / 24 )113.3181818181821.4056428223462680.6166260850208
Trimmed Mean ( 4 / 24 )113.281251.3603054537784483.2763330363379
Trimmed Mean ( 5 / 24 )113.2419354838711.3143405196212486.1587494209678
Trimmed Mean ( 6 / 24 )113.2166666666671.2633673206226889.6150033474551
Trimmed Mean ( 7 / 24 )113.1724137931031.2157312112968493.0899961615533
Trimmed Mean ( 8 / 24 )113.1428571428571.1625734361467897.3210410843863
Trimmed Mean ( 9 / 24 )113.0925925925931.12380646168516100.633513374722
Trimmed Mean ( 10 / 24 )113.0384615384621.08637577366905104.050977827582
Trimmed Mean ( 11 / 24 )112.961.04430818814981108.167302796055
Trimmed Mean ( 12 / 24 )112.9166666666671.01663178640317111.069384389568
Trimmed Mean ( 13 / 24 )112.8913043478260.999143720769541112.988053671475
Trimmed Mean ( 14 / 24 )112.8863636363640.981981379827875114.957743553295
Trimmed Mean ( 15 / 24 )112.8809523809520.958610578057019117.754753561918
Trimmed Mean ( 16 / 24 )112.850.93407708461347120.814440113043
Trimmed Mean ( 17 / 24 )112.7631578947370.914117356409565123.357419158568
Trimmed Mean ( 18 / 24 )112.6944444444440.895154012149514125.893916482409
Trimmed Mean ( 19 / 24 )112.6176470588240.867325992742581129.844658180616
Trimmed Mean ( 20 / 24 )112.593750.849406072148784132.555857194623
Trimmed Mean ( 21 / 24 )112.5333333333330.831469179325718135.34275969747
Trimmed Mean ( 22 / 24 )112.50.815686162285419137.920692052435
Trimmed Mean ( 23 / 24 )112.4615384615380.788827307279647142.568008769085
Trimmed Mean ( 24 / 24 )112.3750.758556266005134148.143262452781
Median112
Midrange117
Midmean - Weighted Average at Xnp112.564102564103
Midmean - Weighted Average at X(n+1)p112.564102564103
Midmean - Empirical Distribution Function112.564102564103
Midmean - Empirical Distribution Function - Averaging112.564102564103
Midmean - Empirical Distribution Function - Interpolation112.564102564103
Midmean - Closest Observation112.564102564103
Midmean - True Basic - Statistics Graphics Toolkit112.564102564103
Midmean - MS Excel (old versions)112.564102564103
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')