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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationWed, 08 Oct 2014 16:56:38 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2014/Oct/08/t14127846260kj53wu8o6y4umy.htm/, Retrieved Sat, 11 May 2024 14:28:25 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=239764, Retrieved Sat, 11 May 2024 14:28:25 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact60
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2014-10-08 15:56:38] [5f87c1f524450f94c6870e724864065e] [Current]
- RM D    [Mean versus Median] [] [2014-10-08 16:34:11] [35cf553fdfdc66b14f70b75e31d8fd89]
- RMPD    [Mean Plot] [] [2014-10-08 17:32:14] [35cf553fdfdc66b14f70b75e31d8fd89]
- RMP     [Mean Plot] [] [2014-10-08 18:09:30] [35cf553fdfdc66b14f70b75e31d8fd89]
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Dataseries X:
102,9
103,2
103,1
103,6
104,2
104,9
104,5
103,9
102,8
100,8
99
97,8
96,4
96,1
96
95,6
95,7
95,7
95,5
95,1
95,1
94,6
95
95
95,8
96,1
96,5
96,8
97,7
98,9
100
101,1
102
103,8
104,9
106,3
108,9
110,4
111,3
112,2
112,9
113
113,4
112,4
112,4
112,2
112,6
112,7
113,8
114,1
114,7
115,3
115,6
116,2
117,5
118,5
119,3
120
120,1
119,8
119,9
119,8
119,3
119
118,9
119
119,3
119,2
118,6
117
117,4
117,4




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Sir Ronald Aylmer Fisher' @ fisher.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 & 1 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=239764&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]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=239764&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=239764&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 time1 seconds
R Server'Sir Ronald Aylmer Fisher' @ fisher.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean107.6458333333331.07026779424986100.578410292895
Geometric Mean107.26558243225
Harmonic Mean106.884227810918
Quadratic Mean108.022932878985
Winsorized Mean ( 1 / 24 )107.651.06910116840934100.692060939534
Winsorized Mean ( 2 / 24 )107.6472222222221.06865090572315100.731886948038
Winsorized Mean ( 3 / 24 )107.6472222222221.06728813362692100.860506952709
Winsorized Mean ( 4 / 24 )107.6472222222221.06728813362692100.860506952709
Winsorized Mean ( 5 / 24 )107.6402777777781.05726057368369101.810547425162
Winsorized Mean ( 6 / 24 )107.6486111111111.05591706549337101.947979276964
Winsorized Mean ( 7 / 24 )107.6583333333331.05435929042335102.107824449582
Winsorized Mean ( 8 / 24 )107.6472222222221.052636551612102.264378010978
Winsorized Mean ( 9 / 24 )107.6347222222221.04679845713865102.822774993798
Winsorized Mean ( 10 / 24 )107.66251.04239821729857103.283465199138
Winsorized Mean ( 11 / 24 )107.66251.03766025309863103.755058246185
Winsorized Mean ( 12 / 24 )107.61251.03009096317268104.468929295869
Winsorized Mean ( 13 / 24 )107.6486111111111.01890577921382105.6511929829
Winsorized Mean ( 14 / 24 )107.4736111111110.987373321554313108.847999804094
Winsorized Mean ( 15 / 24 )107.5152777777780.974664702432749110.310014828095
Winsorized Mean ( 16 / 24 )107.7152777777780.944232678435728114.077049267375
Winsorized Mean ( 17 / 24 )107.6444444444440.927169639415501116.100053181535
Winsorized Mean ( 18 / 24 )107.7194444444440.858551840751951125.466441665421
Winsorized Mean ( 19 / 24 )107.58750.832983347867607129.159244630062
Winsorized Mean ( 20 / 24 )107.7819444444440.782042004215346137.821170555393
Winsorized Mean ( 21 / 24 )107.8402777777780.726250633916268148.489065264225
Winsorized Mean ( 22 / 24 )107.7486111111110.689676255545347156.230710053823
Winsorized Mean ( 23 / 24 )107.9402777777780.638901455105377168.946677011363
Winsorized Mean ( 24 / 24 )108.0736111111110.587426927682094183.977965629793
Trimmed Mean ( 1 / 24 )107.6542857142861.0700470872832100.607054580762
Trimmed Mean ( 2 / 24 )107.6588235294121.0701682260373100.599906547458
Trimmed Mean ( 3 / 24 )107.6651515151521.06957389163635100.661723661218
Trimmed Mean ( 4 / 24 )107.6718751.06841483594002100.777218153534
Trimmed Mean ( 5 / 24 )107.6790322580651.06596581336639101.015464950051
Trimmed Mean ( 6 / 24 )107.6883333333331.06485215988443101.129844489418
Trimmed Mean ( 7 / 24 )107.6965517241381.06263027176821101.349034170589
Trimmed Mean ( 8 / 24 )107.7035714285711.05905484781783101.697822025453
Trimmed Mean ( 9 / 24 )107.7129629629631.0538042836211102.213441942785
Trimmed Mean ( 10 / 24 )107.7251.04732250374355102.857524415782
Trimmed Mean ( 11 / 24 )107.7341.0389029142832103.699776484247
Trimmed Mean ( 12 / 24 )107.743751.02804169966926104.804844039559
Trimmed Mean ( 13 / 24 )107.7608695652171.01459150658075106.211089750179
Trimmed Mean ( 14 / 24 )107.7750.998530235964493107.933636977851
Trimmed Mean ( 15 / 24 )107.8119047619050.983216901201261109.652208612549
Trimmed Mean ( 16 / 24 )107.84750.964577677615363111.807998985236
Trimmed Mean ( 17 / 24 )107.8631578947370.945607657240285114.067559699686
Trimmed Mean ( 18 / 24 )107.8888888888890.922572127156461116.943581659488
Trimmed Mean ( 19 / 24 )107.9088235294120.906771590543274119.00331313287
Trimmed Mean ( 20 / 24 )107.9468750.888989372453168121.426507835657
Trimmed Mean ( 21 / 24 )107.9666666666670.875428740062378123.330045868695
Trimmed Mean ( 22 / 24 )107.9821428571430.868344736412172124.354001733578
Trimmed Mean ( 23 / 24 )108.0115384615380.864003684519867125.012821584854
Trimmed Mean ( 24 / 24 )108.0208333333330.867675955647995124.49444130633
Median107.6
Midrange107.35
Midmean - Weighted Average at Xnp107.616216216216
Midmean - Weighted Average at X(n+1)p107.888888888889
Midmean - Empirical Distribution Function107.616216216216
Midmean - Empirical Distribution Function - Averaging107.888888888889
Midmean - Empirical Distribution Function - Interpolation107.888888888889
Midmean - Closest Observation107.616216216216
Midmean - True Basic - Statistics Graphics Toolkit107.888888888889
Midmean - MS Excel (old versions)107.863157894737
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 107.645833333333 & 1.07026779424986 & 100.578410292895 \tabularnewline
Geometric Mean & 107.26558243225 &  &  \tabularnewline
Harmonic Mean & 106.884227810918 &  &  \tabularnewline
Quadratic Mean & 108.022932878985 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 107.65 & 1.06910116840934 & 100.692060939534 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 107.647222222222 & 1.06865090572315 & 100.731886948038 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 107.647222222222 & 1.06728813362692 & 100.860506952709 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 107.647222222222 & 1.06728813362692 & 100.860506952709 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 107.640277777778 & 1.05726057368369 & 101.810547425162 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 107.648611111111 & 1.05591706549337 & 101.947979276964 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 107.658333333333 & 1.05435929042335 & 102.107824449582 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 107.647222222222 & 1.052636551612 & 102.264378010978 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 107.634722222222 & 1.04679845713865 & 102.822774993798 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 107.6625 & 1.04239821729857 & 103.283465199138 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 107.6625 & 1.03766025309863 & 103.755058246185 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 107.6125 & 1.03009096317268 & 104.468929295869 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 107.648611111111 & 1.01890577921382 & 105.6511929829 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 107.473611111111 & 0.987373321554313 & 108.847999804094 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 107.515277777778 & 0.974664702432749 & 110.310014828095 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 107.715277777778 & 0.944232678435728 & 114.077049267375 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 107.644444444444 & 0.927169639415501 & 116.100053181535 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 107.719444444444 & 0.858551840751951 & 125.466441665421 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 107.5875 & 0.832983347867607 & 129.159244630062 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 107.781944444444 & 0.782042004215346 & 137.821170555393 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 107.840277777778 & 0.726250633916268 & 148.489065264225 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 107.748611111111 & 0.689676255545347 & 156.230710053823 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 107.940277777778 & 0.638901455105377 & 168.946677011363 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 108.073611111111 & 0.587426927682094 & 183.977965629793 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 107.654285714286 & 1.0700470872832 & 100.607054580762 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 107.658823529412 & 1.0701682260373 & 100.599906547458 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 107.665151515152 & 1.06957389163635 & 100.661723661218 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 107.671875 & 1.06841483594002 & 100.777218153534 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 107.679032258065 & 1.06596581336639 & 101.015464950051 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 107.688333333333 & 1.06485215988443 & 101.129844489418 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 107.696551724138 & 1.06263027176821 & 101.349034170589 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 107.703571428571 & 1.05905484781783 & 101.697822025453 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 107.712962962963 & 1.0538042836211 & 102.213441942785 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 107.725 & 1.04732250374355 & 102.857524415782 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 107.734 & 1.0389029142832 & 103.699776484247 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 107.74375 & 1.02804169966926 & 104.804844039559 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 107.760869565217 & 1.01459150658075 & 106.211089750179 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 107.775 & 0.998530235964493 & 107.933636977851 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 107.811904761905 & 0.983216901201261 & 109.652208612549 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 107.8475 & 0.964577677615363 & 111.807998985236 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 107.863157894737 & 0.945607657240285 & 114.067559699686 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 107.888888888889 & 0.922572127156461 & 116.943581659488 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 107.908823529412 & 0.906771590543274 & 119.00331313287 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 107.946875 & 0.888989372453168 & 121.426507835657 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 107.966666666667 & 0.875428740062378 & 123.330045868695 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 107.982142857143 & 0.868344736412172 & 124.354001733578 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 108.011538461538 & 0.864003684519867 & 125.012821584854 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 108.020833333333 & 0.867675955647995 & 124.49444130633 \tabularnewline
Median & 107.6 &  &  \tabularnewline
Midrange & 107.35 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 107.616216216216 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 107.888888888889 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 107.616216216216 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 107.888888888889 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 107.888888888889 &  &  \tabularnewline
Midmean - Closest Observation & 107.616216216216 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 107.888888888889 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 107.863157894737 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=239764&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]107.645833333333[/C][C]1.07026779424986[/C][C]100.578410292895[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]107.26558243225[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]106.884227810918[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]108.022932878985[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]107.65[/C][C]1.06910116840934[/C][C]100.692060939534[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]107.647222222222[/C][C]1.06865090572315[/C][C]100.731886948038[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]107.647222222222[/C][C]1.06728813362692[/C][C]100.860506952709[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]107.647222222222[/C][C]1.06728813362692[/C][C]100.860506952709[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]107.640277777778[/C][C]1.05726057368369[/C][C]101.810547425162[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]107.648611111111[/C][C]1.05591706549337[/C][C]101.947979276964[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]107.658333333333[/C][C]1.05435929042335[/C][C]102.107824449582[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]107.647222222222[/C][C]1.052636551612[/C][C]102.264378010978[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]107.634722222222[/C][C]1.04679845713865[/C][C]102.822774993798[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]107.6625[/C][C]1.04239821729857[/C][C]103.283465199138[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]107.6625[/C][C]1.03766025309863[/C][C]103.755058246185[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]107.6125[/C][C]1.03009096317268[/C][C]104.468929295869[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]107.648611111111[/C][C]1.01890577921382[/C][C]105.6511929829[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]107.473611111111[/C][C]0.987373321554313[/C][C]108.847999804094[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]107.515277777778[/C][C]0.974664702432749[/C][C]110.310014828095[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]107.715277777778[/C][C]0.944232678435728[/C][C]114.077049267375[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]107.644444444444[/C][C]0.927169639415501[/C][C]116.100053181535[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]107.719444444444[/C][C]0.858551840751951[/C][C]125.466441665421[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]107.5875[/C][C]0.832983347867607[/C][C]129.159244630062[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]107.781944444444[/C][C]0.782042004215346[/C][C]137.821170555393[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]107.840277777778[/C][C]0.726250633916268[/C][C]148.489065264225[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]107.748611111111[/C][C]0.689676255545347[/C][C]156.230710053823[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]107.940277777778[/C][C]0.638901455105377[/C][C]168.946677011363[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]108.073611111111[/C][C]0.587426927682094[/C][C]183.977965629793[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]107.654285714286[/C][C]1.0700470872832[/C][C]100.607054580762[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]107.658823529412[/C][C]1.0701682260373[/C][C]100.599906547458[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]107.665151515152[/C][C]1.06957389163635[/C][C]100.661723661218[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]107.671875[/C][C]1.06841483594002[/C][C]100.777218153534[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]107.679032258065[/C][C]1.06596581336639[/C][C]101.015464950051[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]107.688333333333[/C][C]1.06485215988443[/C][C]101.129844489418[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]107.696551724138[/C][C]1.06263027176821[/C][C]101.349034170589[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]107.703571428571[/C][C]1.05905484781783[/C][C]101.697822025453[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]107.712962962963[/C][C]1.0538042836211[/C][C]102.213441942785[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]107.725[/C][C]1.04732250374355[/C][C]102.857524415782[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]107.734[/C][C]1.0389029142832[/C][C]103.699776484247[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]107.74375[/C][C]1.02804169966926[/C][C]104.804844039559[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]107.760869565217[/C][C]1.01459150658075[/C][C]106.211089750179[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]107.775[/C][C]0.998530235964493[/C][C]107.933636977851[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]107.811904761905[/C][C]0.983216901201261[/C][C]109.652208612549[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]107.8475[/C][C]0.964577677615363[/C][C]111.807998985236[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]107.863157894737[/C][C]0.945607657240285[/C][C]114.067559699686[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]107.888888888889[/C][C]0.922572127156461[/C][C]116.943581659488[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]107.908823529412[/C][C]0.906771590543274[/C][C]119.00331313287[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]107.946875[/C][C]0.888989372453168[/C][C]121.426507835657[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]107.966666666667[/C][C]0.875428740062378[/C][C]123.330045868695[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]107.982142857143[/C][C]0.868344736412172[/C][C]124.354001733578[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]108.011538461538[/C][C]0.864003684519867[/C][C]125.012821584854[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]108.020833333333[/C][C]0.867675955647995[/C][C]124.49444130633[/C][/ROW]
[ROW][C]Median[/C][C]107.6[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]107.35[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]107.616216216216[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]107.888888888889[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]107.616216216216[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]107.888888888889[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]107.888888888889[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]107.616216216216[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]107.888888888889[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]107.863157894737[/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=239764&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=239764&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 Mean107.6458333333331.07026779424986100.578410292895
Geometric Mean107.26558243225
Harmonic Mean106.884227810918
Quadratic Mean108.022932878985
Winsorized Mean ( 1 / 24 )107.651.06910116840934100.692060939534
Winsorized Mean ( 2 / 24 )107.6472222222221.06865090572315100.731886948038
Winsorized Mean ( 3 / 24 )107.6472222222221.06728813362692100.860506952709
Winsorized Mean ( 4 / 24 )107.6472222222221.06728813362692100.860506952709
Winsorized Mean ( 5 / 24 )107.6402777777781.05726057368369101.810547425162
Winsorized Mean ( 6 / 24 )107.6486111111111.05591706549337101.947979276964
Winsorized Mean ( 7 / 24 )107.6583333333331.05435929042335102.107824449582
Winsorized Mean ( 8 / 24 )107.6472222222221.052636551612102.264378010978
Winsorized Mean ( 9 / 24 )107.6347222222221.04679845713865102.822774993798
Winsorized Mean ( 10 / 24 )107.66251.04239821729857103.283465199138
Winsorized Mean ( 11 / 24 )107.66251.03766025309863103.755058246185
Winsorized Mean ( 12 / 24 )107.61251.03009096317268104.468929295869
Winsorized Mean ( 13 / 24 )107.6486111111111.01890577921382105.6511929829
Winsorized Mean ( 14 / 24 )107.4736111111110.987373321554313108.847999804094
Winsorized Mean ( 15 / 24 )107.5152777777780.974664702432749110.310014828095
Winsorized Mean ( 16 / 24 )107.7152777777780.944232678435728114.077049267375
Winsorized Mean ( 17 / 24 )107.6444444444440.927169639415501116.100053181535
Winsorized Mean ( 18 / 24 )107.7194444444440.858551840751951125.466441665421
Winsorized Mean ( 19 / 24 )107.58750.832983347867607129.159244630062
Winsorized Mean ( 20 / 24 )107.7819444444440.782042004215346137.821170555393
Winsorized Mean ( 21 / 24 )107.8402777777780.726250633916268148.489065264225
Winsorized Mean ( 22 / 24 )107.7486111111110.689676255545347156.230710053823
Winsorized Mean ( 23 / 24 )107.9402777777780.638901455105377168.946677011363
Winsorized Mean ( 24 / 24 )108.0736111111110.587426927682094183.977965629793
Trimmed Mean ( 1 / 24 )107.6542857142861.0700470872832100.607054580762
Trimmed Mean ( 2 / 24 )107.6588235294121.0701682260373100.599906547458
Trimmed Mean ( 3 / 24 )107.6651515151521.06957389163635100.661723661218
Trimmed Mean ( 4 / 24 )107.6718751.06841483594002100.777218153534
Trimmed Mean ( 5 / 24 )107.6790322580651.06596581336639101.015464950051
Trimmed Mean ( 6 / 24 )107.6883333333331.06485215988443101.129844489418
Trimmed Mean ( 7 / 24 )107.6965517241381.06263027176821101.349034170589
Trimmed Mean ( 8 / 24 )107.7035714285711.05905484781783101.697822025453
Trimmed Mean ( 9 / 24 )107.7129629629631.0538042836211102.213441942785
Trimmed Mean ( 10 / 24 )107.7251.04732250374355102.857524415782
Trimmed Mean ( 11 / 24 )107.7341.0389029142832103.699776484247
Trimmed Mean ( 12 / 24 )107.743751.02804169966926104.804844039559
Trimmed Mean ( 13 / 24 )107.7608695652171.01459150658075106.211089750179
Trimmed Mean ( 14 / 24 )107.7750.998530235964493107.933636977851
Trimmed Mean ( 15 / 24 )107.8119047619050.983216901201261109.652208612549
Trimmed Mean ( 16 / 24 )107.84750.964577677615363111.807998985236
Trimmed Mean ( 17 / 24 )107.8631578947370.945607657240285114.067559699686
Trimmed Mean ( 18 / 24 )107.8888888888890.922572127156461116.943581659488
Trimmed Mean ( 19 / 24 )107.9088235294120.906771590543274119.00331313287
Trimmed Mean ( 20 / 24 )107.9468750.888989372453168121.426507835657
Trimmed Mean ( 21 / 24 )107.9666666666670.875428740062378123.330045868695
Trimmed Mean ( 22 / 24 )107.9821428571430.868344736412172124.354001733578
Trimmed Mean ( 23 / 24 )108.0115384615380.864003684519867125.012821584854
Trimmed Mean ( 24 / 24 )108.0208333333330.867675955647995124.49444130633
Median107.6
Midrange107.35
Midmean - Weighted Average at Xnp107.616216216216
Midmean - Weighted Average at X(n+1)p107.888888888889
Midmean - Empirical Distribution Function107.616216216216
Midmean - Empirical Distribution Function - Averaging107.888888888889
Midmean - Empirical Distribution Function - Interpolation107.888888888889
Midmean - Closest Observation107.616216216216
Midmean - True Basic - Statistics Graphics Toolkit107.888888888889
Midmean - MS Excel (old versions)107.863157894737
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')