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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 computationTue, 13 Nov 2007 13:08:01 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2007/Nov/13/t1194984198o1yuh2ylfwfhrsp.htm/, Retrieved Tue, 30 Apr 2024 01:45:45 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=5380, Retrieved Tue, 30 Apr 2024 01:45:45 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact248
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2007-11-13 20:08:01] [bc15d8d2f79dc0888573b215bcd9118f] [Current]
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Dataseries X:
100,80
100,80
100,80
90,10
95,70
88,60
93,30
93,30
93,30
93,30
93,30
93,30
88,60
97,40
97,40
102,90
102,90
102,90
105,10
105,10
105,10
105,10
105,10
105,10
96,90
96,90
96,90
96,90
96,90
96,90
96,50
96,50
96,50
96,00
96,00
96,00
96,00
96,00
96,00
105,80
105,80
105,80
105,80
105,80
105,80
105,80
105,80
105,80
123,60
142,20
142,20
141,20
141,20
141,20
124,70
124,70
124,70
122,70
122,70
122,70
123,30
123,30
123,30
127,20
127,20
127,20
140,00
140,00
140,00
140,00
140,00
140,00
139,00
139,00
139,00
147,00
147,00
147,00
147,10
147,10




Summary of compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=5380&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]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=5380&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=5380&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 time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean113.448752.1246094158915353.3974617411712
Geometric Mean111.945316571588
Harmonic Mean110.525920332860
Quadratic Mean115.009661007239
Winsorized Mean ( 1 / 26 )113.448752.1246094158915353.3974617411712
Winsorized Mean ( 2 / 26 )113.483752.1187129211497353.5625892810515
Winsorized Mean ( 3 / 26 )113.603752.1029939806745054.0200072106548
Winsorized Mean ( 4 / 26 )113.603752.1029939806745054.0200072106548
Winsorized Mean ( 5 / 26 )113.303752.0459789552399655.3787465456658
Winsorized Mean ( 6 / 26 )113.303752.0459789552399655.3787465456658
Winsorized Mean ( 7 / 26 )113.216252.0305245345193055.7571445581191
Winsorized Mean ( 8 / 26 )113.216252.0305245345193055.7571445581191
Winsorized Mean ( 9 / 26 )113.486251.9985427790555856.7844987804707
Winsorized Mean ( 10 / 26 )113.373751.9683257228181557.5990796064368
Winsorized Mean ( 11 / 26 )113.373751.9683257228181557.5990796064368
Winsorized Mean ( 12 / 26 )113.373751.9683257228181557.5990796064368
Winsorized Mean ( 13 / 26 )113.373751.9683257228181557.5990796064368
Winsorized Mean ( 14 / 26 )113.373751.9683257228181557.5990796064368
Winsorized Mean ( 15 / 26 )113.373751.9683257228181557.5990796064368
Winsorized Mean ( 16 / 26 )113.273751.9231597679027558.8998126367462
Winsorized Mean ( 17 / 26 )113.273751.9231597679027558.8998126367462
Winsorized Mean ( 18 / 26 )113.273751.9231597679027558.8998126367462
Winsorized Mean ( 19 / 26 )110.566251.4694321470050675.2442024800886
Winsorized Mean ( 20 / 26 )110.566251.4694321470050675.2442024800886
Winsorized Mean ( 21 / 26 )110.566251.4694321470050675.2442024800886
Winsorized Mean ( 22 / 26 )109.878751.3731324414420180.0205039832934
Winsorized Mean ( 23 / 26 )109.878751.3731324414420180.0205039832934
Winsorized Mean ( 24 / 26 )109.878751.3731324414420180.0205039832934
Winsorized Mean ( 25 / 26 )109.691251.3078610832702883.8707194541788
Winsorized Mean ( 26 / 26 )109.593751.2947659283961184.643677746262
Trimmed Mean ( 1 / 26 )113.3358974358972.1115021840047653.6754819836086
Trimmed Mean ( 2 / 26 )113.2171052631582.0952932953494854.0340130493637
Trimmed Mean ( 3 / 26 )113.0729729729732.0789323304450754.3899247306263
Trimmed Mean ( 4 / 26 )112.8763888888892.0651757959777854.6570365141463
Trimmed Mean ( 5 / 26 )112.6685714285712.0476594150770855.0231013023864
Trimmed Mean ( 6 / 26 )112.5191176470592.0422977399529655.094375049179
Trimmed Mean ( 7 / 26 )112.3606060606062.034148881638455.2371594207526
Trimmed Mean ( 8 / 26 )112.20781252.0262712851122755.3765003355821
Trimmed Mean ( 9 / 26 )112.0451612903232.0149358711589055.6073088449604
Trimmed Mean ( 10 / 26 )111.8316666666672.0052818555381855.7685526140927
Trimmed Mean ( 11 / 26 )111.6189655172411.9972886292928955.8852455675164
Trimmed Mean ( 12 / 26 )111.3910714285711.9849944826147856.1165647583256
Trimmed Mean ( 13 / 26 )111.1462962962961.9673464926045456.4955368635401
Trimmed Mean ( 14 / 26 )110.8826923076921.9429722553789357.0685927195945
Trimmed Mean ( 15 / 26 )110.5981.9100496627799357.9032064742407
Trimmed Mean ( 16 / 26 )110.2895833333331.8661035741613259.1015337307314
Trimmed Mean ( 17 / 26 )109.9652173913041.8173724659819260.5078042336744
Trimmed Mean ( 18 / 26 )109.6113636363641.7519310273582262.5660268153648
Trimmed Mean ( 19 / 26 )109.2238095238101.663493411855665.659297924103
Trimmed Mean ( 20 / 26 )109.08251.6581805270405365.7844536352668
Trimmed Mean ( 21 / 26 )108.9263157894741.6465260822569166.1552325002755
Trimmed Mean ( 22 / 26 )108.7527777777781.6261966832327966.8755378110742
Trimmed Mean ( 23 / 26 )108.6323529411761.6178577888993367.1457984048658
Trimmed Mean ( 24 / 26 )108.4968751.6002739456445867.7989386100379
Trimmed Mean ( 25 / 26 )108.3433333333331.5693375374703269.0376230393217
Trimmed Mean ( 26 / 26 )108.1892857142861.5385121246916270.3207234950918
Median105.8
Midrange117.85
Midmean - Weighted Average at Xnp109.223809523810
Midmean - Weighted Average at X(n+1)p109.223809523810
Midmean - Empirical Distribution Function109.223809523810
Midmean - Empirical Distribution Function - Averaging109.223809523810
Midmean - Empirical Distribution Function - Interpolation109.223809523810
Midmean - Closest Observation109.223809523810
Midmean - True Basic - Statistics Graphics Toolkit109.223809523810
Midmean - MS Excel (old versions)109.223809523810
Number of observations80

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 113.44875 & 2.12460941589153 & 53.3974617411712 \tabularnewline
Geometric Mean & 111.945316571588 &  &  \tabularnewline
Harmonic Mean & 110.525920332860 &  &  \tabularnewline
Quadratic Mean & 115.009661007239 &  &  \tabularnewline
Winsorized Mean ( 1 / 26 ) & 113.44875 & 2.12460941589153 & 53.3974617411712 \tabularnewline
Winsorized Mean ( 2 / 26 ) & 113.48375 & 2.11871292114973 & 53.5625892810515 \tabularnewline
Winsorized Mean ( 3 / 26 ) & 113.60375 & 2.10299398067450 & 54.0200072106548 \tabularnewline
Winsorized Mean ( 4 / 26 ) & 113.60375 & 2.10299398067450 & 54.0200072106548 \tabularnewline
Winsorized Mean ( 5 / 26 ) & 113.30375 & 2.04597895523996 & 55.3787465456658 \tabularnewline
Winsorized Mean ( 6 / 26 ) & 113.30375 & 2.04597895523996 & 55.3787465456658 \tabularnewline
Winsorized Mean ( 7 / 26 ) & 113.21625 & 2.03052453451930 & 55.7571445581191 \tabularnewline
Winsorized Mean ( 8 / 26 ) & 113.21625 & 2.03052453451930 & 55.7571445581191 \tabularnewline
Winsorized Mean ( 9 / 26 ) & 113.48625 & 1.99854277905558 & 56.7844987804707 \tabularnewline
Winsorized Mean ( 10 / 26 ) & 113.37375 & 1.96832572281815 & 57.5990796064368 \tabularnewline
Winsorized Mean ( 11 / 26 ) & 113.37375 & 1.96832572281815 & 57.5990796064368 \tabularnewline
Winsorized Mean ( 12 / 26 ) & 113.37375 & 1.96832572281815 & 57.5990796064368 \tabularnewline
Winsorized Mean ( 13 / 26 ) & 113.37375 & 1.96832572281815 & 57.5990796064368 \tabularnewline
Winsorized Mean ( 14 / 26 ) & 113.37375 & 1.96832572281815 & 57.5990796064368 \tabularnewline
Winsorized Mean ( 15 / 26 ) & 113.37375 & 1.96832572281815 & 57.5990796064368 \tabularnewline
Winsorized Mean ( 16 / 26 ) & 113.27375 & 1.92315976790275 & 58.8998126367462 \tabularnewline
Winsorized Mean ( 17 / 26 ) & 113.27375 & 1.92315976790275 & 58.8998126367462 \tabularnewline
Winsorized Mean ( 18 / 26 ) & 113.27375 & 1.92315976790275 & 58.8998126367462 \tabularnewline
Winsorized Mean ( 19 / 26 ) & 110.56625 & 1.46943214700506 & 75.2442024800886 \tabularnewline
Winsorized Mean ( 20 / 26 ) & 110.56625 & 1.46943214700506 & 75.2442024800886 \tabularnewline
Winsorized Mean ( 21 / 26 ) & 110.56625 & 1.46943214700506 & 75.2442024800886 \tabularnewline
Winsorized Mean ( 22 / 26 ) & 109.87875 & 1.37313244144201 & 80.0205039832934 \tabularnewline
Winsorized Mean ( 23 / 26 ) & 109.87875 & 1.37313244144201 & 80.0205039832934 \tabularnewline
Winsorized Mean ( 24 / 26 ) & 109.87875 & 1.37313244144201 & 80.0205039832934 \tabularnewline
Winsorized Mean ( 25 / 26 ) & 109.69125 & 1.30786108327028 & 83.8707194541788 \tabularnewline
Winsorized Mean ( 26 / 26 ) & 109.59375 & 1.29476592839611 & 84.643677746262 \tabularnewline
Trimmed Mean ( 1 / 26 ) & 113.335897435897 & 2.11150218400476 & 53.6754819836086 \tabularnewline
Trimmed Mean ( 2 / 26 ) & 113.217105263158 & 2.09529329534948 & 54.0340130493637 \tabularnewline
Trimmed Mean ( 3 / 26 ) & 113.072972972973 & 2.07893233044507 & 54.3899247306263 \tabularnewline
Trimmed Mean ( 4 / 26 ) & 112.876388888889 & 2.06517579597778 & 54.6570365141463 \tabularnewline
Trimmed Mean ( 5 / 26 ) & 112.668571428571 & 2.04765941507708 & 55.0231013023864 \tabularnewline
Trimmed Mean ( 6 / 26 ) & 112.519117647059 & 2.04229773995296 & 55.094375049179 \tabularnewline
Trimmed Mean ( 7 / 26 ) & 112.360606060606 & 2.0341488816384 & 55.2371594207526 \tabularnewline
Trimmed Mean ( 8 / 26 ) & 112.2078125 & 2.02627128511227 & 55.3765003355821 \tabularnewline
Trimmed Mean ( 9 / 26 ) & 112.045161290323 & 2.01493587115890 & 55.6073088449604 \tabularnewline
Trimmed Mean ( 10 / 26 ) & 111.831666666667 & 2.00528185553818 & 55.7685526140927 \tabularnewline
Trimmed Mean ( 11 / 26 ) & 111.618965517241 & 1.99728862929289 & 55.8852455675164 \tabularnewline
Trimmed Mean ( 12 / 26 ) & 111.391071428571 & 1.98499448261478 & 56.1165647583256 \tabularnewline
Trimmed Mean ( 13 / 26 ) & 111.146296296296 & 1.96734649260454 & 56.4955368635401 \tabularnewline
Trimmed Mean ( 14 / 26 ) & 110.882692307692 & 1.94297225537893 & 57.0685927195945 \tabularnewline
Trimmed Mean ( 15 / 26 ) & 110.598 & 1.91004966277993 & 57.9032064742407 \tabularnewline
Trimmed Mean ( 16 / 26 ) & 110.289583333333 & 1.86610357416132 & 59.1015337307314 \tabularnewline
Trimmed Mean ( 17 / 26 ) & 109.965217391304 & 1.81737246598192 & 60.5078042336744 \tabularnewline
Trimmed Mean ( 18 / 26 ) & 109.611363636364 & 1.75193102735822 & 62.5660268153648 \tabularnewline
Trimmed Mean ( 19 / 26 ) & 109.223809523810 & 1.6634934118556 & 65.659297924103 \tabularnewline
Trimmed Mean ( 20 / 26 ) & 109.0825 & 1.65818052704053 & 65.7844536352668 \tabularnewline
Trimmed Mean ( 21 / 26 ) & 108.926315789474 & 1.64652608225691 & 66.1552325002755 \tabularnewline
Trimmed Mean ( 22 / 26 ) & 108.752777777778 & 1.62619668323279 & 66.8755378110742 \tabularnewline
Trimmed Mean ( 23 / 26 ) & 108.632352941176 & 1.61785778889933 & 67.1457984048658 \tabularnewline
Trimmed Mean ( 24 / 26 ) & 108.496875 & 1.60027394564458 & 67.7989386100379 \tabularnewline
Trimmed Mean ( 25 / 26 ) & 108.343333333333 & 1.56933753747032 & 69.0376230393217 \tabularnewline
Trimmed Mean ( 26 / 26 ) & 108.189285714286 & 1.53851212469162 & 70.3207234950918 \tabularnewline
Median & 105.8 &  &  \tabularnewline
Midrange & 117.85 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 109.223809523810 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 109.223809523810 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 109.223809523810 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 109.223809523810 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 109.223809523810 &  &  \tabularnewline
Midmean - Closest Observation & 109.223809523810 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 109.223809523810 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 109.223809523810 &  &  \tabularnewline
Number of observations & 80 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=5380&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]113.44875[/C][C]2.12460941589153[/C][C]53.3974617411712[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]111.945316571588[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]110.525920332860[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]115.009661007239[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 26 )[/C][C]113.44875[/C][C]2.12460941589153[/C][C]53.3974617411712[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 26 )[/C][C]113.48375[/C][C]2.11871292114973[/C][C]53.5625892810515[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 26 )[/C][C]113.60375[/C][C]2.10299398067450[/C][C]54.0200072106548[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 26 )[/C][C]113.60375[/C][C]2.10299398067450[/C][C]54.0200072106548[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 26 )[/C][C]113.30375[/C][C]2.04597895523996[/C][C]55.3787465456658[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 26 )[/C][C]113.30375[/C][C]2.04597895523996[/C][C]55.3787465456658[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 26 )[/C][C]113.21625[/C][C]2.03052453451930[/C][C]55.7571445581191[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 26 )[/C][C]113.21625[/C][C]2.03052453451930[/C][C]55.7571445581191[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 26 )[/C][C]113.48625[/C][C]1.99854277905558[/C][C]56.7844987804707[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 26 )[/C][C]113.37375[/C][C]1.96832572281815[/C][C]57.5990796064368[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 26 )[/C][C]113.37375[/C][C]1.96832572281815[/C][C]57.5990796064368[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 26 )[/C][C]113.37375[/C][C]1.96832572281815[/C][C]57.5990796064368[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 26 )[/C][C]113.37375[/C][C]1.96832572281815[/C][C]57.5990796064368[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 26 )[/C][C]113.37375[/C][C]1.96832572281815[/C][C]57.5990796064368[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 26 )[/C][C]113.37375[/C][C]1.96832572281815[/C][C]57.5990796064368[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 26 )[/C][C]113.27375[/C][C]1.92315976790275[/C][C]58.8998126367462[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 26 )[/C][C]113.27375[/C][C]1.92315976790275[/C][C]58.8998126367462[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 26 )[/C][C]113.27375[/C][C]1.92315976790275[/C][C]58.8998126367462[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 26 )[/C][C]110.56625[/C][C]1.46943214700506[/C][C]75.2442024800886[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 26 )[/C][C]110.56625[/C][C]1.46943214700506[/C][C]75.2442024800886[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 26 )[/C][C]110.56625[/C][C]1.46943214700506[/C][C]75.2442024800886[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 26 )[/C][C]109.87875[/C][C]1.37313244144201[/C][C]80.0205039832934[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 26 )[/C][C]109.87875[/C][C]1.37313244144201[/C][C]80.0205039832934[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 26 )[/C][C]109.87875[/C][C]1.37313244144201[/C][C]80.0205039832934[/C][/ROW]
[ROW][C]Winsorized Mean ( 25 / 26 )[/C][C]109.69125[/C][C]1.30786108327028[/C][C]83.8707194541788[/C][/ROW]
[ROW][C]Winsorized Mean ( 26 / 26 )[/C][C]109.59375[/C][C]1.29476592839611[/C][C]84.643677746262[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 26 )[/C][C]113.335897435897[/C][C]2.11150218400476[/C][C]53.6754819836086[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 26 )[/C][C]113.217105263158[/C][C]2.09529329534948[/C][C]54.0340130493637[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 26 )[/C][C]113.072972972973[/C][C]2.07893233044507[/C][C]54.3899247306263[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 26 )[/C][C]112.876388888889[/C][C]2.06517579597778[/C][C]54.6570365141463[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 26 )[/C][C]112.668571428571[/C][C]2.04765941507708[/C][C]55.0231013023864[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 26 )[/C][C]112.519117647059[/C][C]2.04229773995296[/C][C]55.094375049179[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 26 )[/C][C]112.360606060606[/C][C]2.0341488816384[/C][C]55.2371594207526[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 26 )[/C][C]112.2078125[/C][C]2.02627128511227[/C][C]55.3765003355821[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 26 )[/C][C]112.045161290323[/C][C]2.01493587115890[/C][C]55.6073088449604[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 26 )[/C][C]111.831666666667[/C][C]2.00528185553818[/C][C]55.7685526140927[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 26 )[/C][C]111.618965517241[/C][C]1.99728862929289[/C][C]55.8852455675164[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 26 )[/C][C]111.391071428571[/C][C]1.98499448261478[/C][C]56.1165647583256[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 26 )[/C][C]111.146296296296[/C][C]1.96734649260454[/C][C]56.4955368635401[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 26 )[/C][C]110.882692307692[/C][C]1.94297225537893[/C][C]57.0685927195945[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 26 )[/C][C]110.598[/C][C]1.91004966277993[/C][C]57.9032064742407[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 26 )[/C][C]110.289583333333[/C][C]1.86610357416132[/C][C]59.1015337307314[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 26 )[/C][C]109.965217391304[/C][C]1.81737246598192[/C][C]60.5078042336744[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 26 )[/C][C]109.611363636364[/C][C]1.75193102735822[/C][C]62.5660268153648[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 26 )[/C][C]109.223809523810[/C][C]1.6634934118556[/C][C]65.659297924103[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 26 )[/C][C]109.0825[/C][C]1.65818052704053[/C][C]65.7844536352668[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 26 )[/C][C]108.926315789474[/C][C]1.64652608225691[/C][C]66.1552325002755[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 26 )[/C][C]108.752777777778[/C][C]1.62619668323279[/C][C]66.8755378110742[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 26 )[/C][C]108.632352941176[/C][C]1.61785778889933[/C][C]67.1457984048658[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 26 )[/C][C]108.496875[/C][C]1.60027394564458[/C][C]67.7989386100379[/C][/ROW]
[ROW][C]Trimmed Mean ( 25 / 26 )[/C][C]108.343333333333[/C][C]1.56933753747032[/C][C]69.0376230393217[/C][/ROW]
[ROW][C]Trimmed Mean ( 26 / 26 )[/C][C]108.189285714286[/C][C]1.53851212469162[/C][C]70.3207234950918[/C][/ROW]
[ROW][C]Median[/C][C]105.8[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]117.85[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]109.223809523810[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]109.223809523810[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]109.223809523810[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]109.223809523810[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]109.223809523810[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]109.223809523810[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]109.223809523810[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]109.223809523810[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]80[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=5380&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=5380&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 Mean113.448752.1246094158915353.3974617411712
Geometric Mean111.945316571588
Harmonic Mean110.525920332860
Quadratic Mean115.009661007239
Winsorized Mean ( 1 / 26 )113.448752.1246094158915353.3974617411712
Winsorized Mean ( 2 / 26 )113.483752.1187129211497353.5625892810515
Winsorized Mean ( 3 / 26 )113.603752.1029939806745054.0200072106548
Winsorized Mean ( 4 / 26 )113.603752.1029939806745054.0200072106548
Winsorized Mean ( 5 / 26 )113.303752.0459789552399655.3787465456658
Winsorized Mean ( 6 / 26 )113.303752.0459789552399655.3787465456658
Winsorized Mean ( 7 / 26 )113.216252.0305245345193055.7571445581191
Winsorized Mean ( 8 / 26 )113.216252.0305245345193055.7571445581191
Winsorized Mean ( 9 / 26 )113.486251.9985427790555856.7844987804707
Winsorized Mean ( 10 / 26 )113.373751.9683257228181557.5990796064368
Winsorized Mean ( 11 / 26 )113.373751.9683257228181557.5990796064368
Winsorized Mean ( 12 / 26 )113.373751.9683257228181557.5990796064368
Winsorized Mean ( 13 / 26 )113.373751.9683257228181557.5990796064368
Winsorized Mean ( 14 / 26 )113.373751.9683257228181557.5990796064368
Winsorized Mean ( 15 / 26 )113.373751.9683257228181557.5990796064368
Winsorized Mean ( 16 / 26 )113.273751.9231597679027558.8998126367462
Winsorized Mean ( 17 / 26 )113.273751.9231597679027558.8998126367462
Winsorized Mean ( 18 / 26 )113.273751.9231597679027558.8998126367462
Winsorized Mean ( 19 / 26 )110.566251.4694321470050675.2442024800886
Winsorized Mean ( 20 / 26 )110.566251.4694321470050675.2442024800886
Winsorized Mean ( 21 / 26 )110.566251.4694321470050675.2442024800886
Winsorized Mean ( 22 / 26 )109.878751.3731324414420180.0205039832934
Winsorized Mean ( 23 / 26 )109.878751.3731324414420180.0205039832934
Winsorized Mean ( 24 / 26 )109.878751.3731324414420180.0205039832934
Winsorized Mean ( 25 / 26 )109.691251.3078610832702883.8707194541788
Winsorized Mean ( 26 / 26 )109.593751.2947659283961184.643677746262
Trimmed Mean ( 1 / 26 )113.3358974358972.1115021840047653.6754819836086
Trimmed Mean ( 2 / 26 )113.2171052631582.0952932953494854.0340130493637
Trimmed Mean ( 3 / 26 )113.0729729729732.0789323304450754.3899247306263
Trimmed Mean ( 4 / 26 )112.8763888888892.0651757959777854.6570365141463
Trimmed Mean ( 5 / 26 )112.6685714285712.0476594150770855.0231013023864
Trimmed Mean ( 6 / 26 )112.5191176470592.0422977399529655.094375049179
Trimmed Mean ( 7 / 26 )112.3606060606062.034148881638455.2371594207526
Trimmed Mean ( 8 / 26 )112.20781252.0262712851122755.3765003355821
Trimmed Mean ( 9 / 26 )112.0451612903232.0149358711589055.6073088449604
Trimmed Mean ( 10 / 26 )111.8316666666672.0052818555381855.7685526140927
Trimmed Mean ( 11 / 26 )111.6189655172411.9972886292928955.8852455675164
Trimmed Mean ( 12 / 26 )111.3910714285711.9849944826147856.1165647583256
Trimmed Mean ( 13 / 26 )111.1462962962961.9673464926045456.4955368635401
Trimmed Mean ( 14 / 26 )110.8826923076921.9429722553789357.0685927195945
Trimmed Mean ( 15 / 26 )110.5981.9100496627799357.9032064742407
Trimmed Mean ( 16 / 26 )110.2895833333331.8661035741613259.1015337307314
Trimmed Mean ( 17 / 26 )109.9652173913041.8173724659819260.5078042336744
Trimmed Mean ( 18 / 26 )109.6113636363641.7519310273582262.5660268153648
Trimmed Mean ( 19 / 26 )109.2238095238101.663493411855665.659297924103
Trimmed Mean ( 20 / 26 )109.08251.6581805270405365.7844536352668
Trimmed Mean ( 21 / 26 )108.9263157894741.6465260822569166.1552325002755
Trimmed Mean ( 22 / 26 )108.7527777777781.6261966832327966.8755378110742
Trimmed Mean ( 23 / 26 )108.6323529411761.6178577888993367.1457984048658
Trimmed Mean ( 24 / 26 )108.4968751.6002739456445867.7989386100379
Trimmed Mean ( 25 / 26 )108.3433333333331.5693375374703269.0376230393217
Trimmed Mean ( 26 / 26 )108.1892857142861.5385121246916270.3207234950918
Median105.8
Midrange117.85
Midmean - Weighted Average at Xnp109.223809523810
Midmean - Weighted Average at X(n+1)p109.223809523810
Midmean - Empirical Distribution Function109.223809523810
Midmean - Empirical Distribution Function - Averaging109.223809523810
Midmean - Empirical Distribution Function - Interpolation109.223809523810
Midmean - Closest Observation109.223809523810
Midmean - True Basic - Statistics Graphics Toolkit109.223809523810
Midmean - MS Excel (old versions)109.223809523810
Number of observations80



Parameters (Session):
Parameters (R input):
R code (references can be found in the software module):
geomean <- function(x) {
return(exp(mean(log(x))))
}
harmean <- function(x) {
return(1/mean(1/x))
}
quamean <- function(x) {
return(sqrt(mean(x*x)))
}
winmean <- function(x) {
x <-sort(x[!is.na(x)])
n<-length(x)
denom <- 3
nodenom <- n/denom
if (nodenom>40) denom <- n/40
sqrtn = sqrt(n)
roundnodenom = floor(nodenom)
win <- array(NA,dim=c(roundnodenom,2))
for (j in 1:roundnodenom) {
win[j,1] <- (j*x[j+1]+sum(x[(j+1):(n-j)])+j*x[n-j])/n
win[j,2] <- sd(c(rep(x[j+1],j),x[(j+1):(n-j)],rep(x[n-j],j)))/sqrtn
}
return(win)
}
trimean <- function(x) {
x <-sort(x[!is.na(x)])
n<-length(x)
denom <- 3
nodenom <- n/denom
if (nodenom>40) denom <- n/40
sqrtn = sqrt(n)
roundnodenom = floor(nodenom)
tri <- array(NA,dim=c(roundnodenom,2))
for (j in 1:roundnodenom) {
tri[j,1] <- mean(x,trim=j/n)
tri[j,2] <- sd(x[(j+1):(n-j)]) / sqrt(n-j*2)
}
return(tri)
}
midrange <- function(x) {
return((max(x)+min(x))/2)
}
q1 <- function(data,n,p,i,f) {
np <- n*p;
i <<- floor(np)
f <<- np - i
qvalue <- (1-f)*data[i] + f*data[i+1]
}
q2 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
qvalue <- (1-f)*data[i] + f*data[i+1]
}
q3 <- function(data,n,p,i,f) {
np <- n*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
qvalue <- data[i+1]
}
}
q4 <- function(data,n,p,i,f) {
np <- n*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- (data[i]+data[i+1])/2
} else {
qvalue <- data[i+1]
}
}
q5 <- function(data,n,p,i,f) {
np <- (n-1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i+1]
} else {
qvalue <- data[i+1] + f*(data[i+2]-data[i+1])
}
}
q6 <- function(data,n,p,i,f) {
np <- n*p+0.5
i <<- floor(np)
f <<- np - i
qvalue <- data[i]
}
q7 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
qvalue <- f*data[i] + (1-f)*data[i+1]
}
}
q8 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
if (f == 0.5) {
qvalue <- (data[i]+data[i+1])/2
} else {
if (f < 0.5) {
qvalue <- data[i]
} else {
qvalue <- data[i+1]
}
}
}
}
midmean <- function(x,def) {
x <-sort(x[!is.na(x)])
n<-length(x)
if (def==1) {
qvalue1 <- q1(x,n,0.25,i,f)
qvalue3 <- q1(x,n,0.75,i,f)
}
if (def==2) {
qvalue1 <- q2(x,n,0.25,i,f)
qvalue3 <- q2(x,n,0.75,i,f)
}
if (def==3) {
qvalue1 <- q3(x,n,0.25,i,f)
qvalue3 <- q3(x,n,0.75,i,f)
}
if (def==4) {
qvalue1 <- q4(x,n,0.25,i,f)
qvalue3 <- q4(x,n,0.75,i,f)
}
if (def==5) {
qvalue1 <- q5(x,n,0.25,i,f)
qvalue3 <- q5(x,n,0.75,i,f)
}
if (def==6) {
qvalue1 <- q6(x,n,0.25,i,f)
qvalue3 <- q6(x,n,0.75,i,f)
}
if (def==7) {
qvalue1 <- q7(x,n,0.25,i,f)
qvalue3 <- q7(x,n,0.75,i,f)
}
if (def==8) {
qvalue1 <- q8(x,n,0.25,i,f)
qvalue3 <- q8(x,n,0.75,i,f)
}
midm <- 0
myn <- 0
roundno4 <- round(n/4)
round3no4 <- round(3*n/4)
for (i in 1:n) {
if ((x[i]>=qvalue1) & (x[i]<=qvalue3)){
midm = midm + x[i]
myn = myn + 1
}
}
midm = midm / myn
return(midm)
}
(arm <- mean(x))
sqrtn <- sqrt(length(x))
(armse <- sd(x) / sqrtn)
(armose <- arm / armse)
(geo <- geomean(x))
(har <- harmean(x))
(qua <- quamean(x))
(win <- winmean(x))
(tri <- trimean(x))
(midr <- midrange(x))
midm <- array(NA,dim=8)
for (j in 1:8) midm[j] <- midmean(x,j)
midm
bitmap(file='test1.png')
lb <- win[,1] - 2*win[,2]
ub <- win[,1] + 2*win[,2]
if ((ylimmin == '') | (ylimmax == '')) plot(win[,1],type='b',main=main, xlab='j', pch=19, ylab='Winsorized Mean(j/n)', ylim=c(min(lb),max(ub))) else plot(win[,1],type='l',main=main, xlab='j', pch=19, ylab='Winsorized Mean(j/n)', ylim=c(ylimmin,ylimmax))
lines(ub,lty=3)
lines(lb,lty=3)
grid()
dev.off()
bitmap(file='test2.png')
lb <- tri[,1] - 2*tri[,2]
ub <- tri[,1] + 2*tri[,2]
if ((ylimmin == '') | (ylimmax == '')) plot(tri[,1],type='b',main=main, xlab='j', pch=19, ylab='Trimmed Mean(j/n)', ylim=c(min(lb),max(ub))) else plot(tri[,1],type='l',main=main, xlab='j', pch=19, ylab='Trimmed Mean(j/n)', ylim=c(ylimmin,ylimmax))
lines(ub,lty=3)
lines(lb,lty=3)
grid()
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Central Tendency - Ungrouped Data',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Measure',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.element(a,'S.E.',header=TRUE)
a<-table.element(a,'Value/S.E.',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('arithmetic_mean.htm', 'Arithmetic Mean', 'click to view the definition of the Arithmetic Mean'),header=TRUE)
a<-table.element(a,arm)
a<-table.element(a,hyperlink('arithmetic_mean_standard_error.htm', armse, 'click to view the definition of the Standard Error of the Arithmetic Mean'))
a<-table.element(a,armose)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('geometric_mean.htm', 'Geometric Mean', 'click to view the definition of the Geometric Mean'),header=TRUE)
a<-table.element(a,geo)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('harmonic_mean.htm', 'Harmonic Mean', 'click to view the definition of the Harmonic Mean'),header=TRUE)
a<-table.element(a,har)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('quadratic_mean.htm', 'Quadratic Mean', 'click to view the definition of the Quadratic Mean'),header=TRUE)
a<-table.element(a,qua)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
for (j in 1:length(win[,1])) {
a<-table.row.start(a)
mylabel <- paste('Winsorized Mean (',j)
mylabel <- paste(mylabel,'/')
mylabel <- paste(mylabel,length(win[,1]))
mylabel <- paste(mylabel,')')
a<-table.element(a,hyperlink('winsorized_mean.htm', mylabel, 'click to view the definition of the Winsorized Mean'),header=TRUE)
a<-table.element(a,win[j,1])
a<-table.element(a,win[j,2])
a<-table.element(a,win[j,1]/win[j,2])
a<-table.row.end(a)
}
for (j in 1:length(tri[,1])) {
a<-table.row.start(a)
mylabel <- paste('Trimmed Mean (',j)
mylabel <- paste(mylabel,'/')
mylabel <- paste(mylabel,length(tri[,1]))
mylabel <- paste(mylabel,')')
a<-table.element(a,hyperlink('arithmetic_mean.htm', mylabel, 'click to view the definition of the Trimmed Mean'),header=TRUE)
a<-table.element(a,tri[j,1])
a<-table.element(a,tri[j,2])
a<-table.element(a,tri[j,1]/tri[j,2])
a<-table.row.end(a)
}
a<-table.row.start(a)
a<-table.element(a,hyperlink('median_1.htm', 'Median', 'click to view the definition of the Median'),header=TRUE)
a<-table.element(a,median(x))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('midrange.htm', 'Midrange', 'click to view the definition of the Midrange'),header=TRUE)
a<-table.element(a,midr)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_1.htm','Weighted Average at Xnp',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[1])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_2.htm','Weighted Average at X(n+1)p',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[2])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_3.htm','Empirical Distribution Function',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[3])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_4.htm','Empirical Distribution Function - Averaging',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[4])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_5.htm','Empirical Distribution Function - Interpolation',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[5])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_6.htm','Closest Observation',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[6])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_7.htm','True Basic - Statistics Graphics Toolkit',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[7])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_8.htm','MS Excel (old versions)',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[8])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Number of observations',header=TRUE)
a<-table.element(a,length(x))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')