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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, 24 Feb 2014 18:53:25 -0500
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/Feb/24/t1393286022h839zal8fw6cgk6.htm/, Retrieved Thu, 16 May 2024 11:28:57 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=234040, Retrieved Thu, 16 May 2024 11:28:57 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact81
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2014-02-24 23:53:25] [aa1782934d0b081042c527b5804d60cd] [Current]
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Dataseries X:
-2
0
1
-3
-3
-5
-7
-7
-5
-13
-16
-20
-18
-21
-20
-16
-14
-12
-10
-3
-4
-4
-1
-8
-10
-11
-7
-2
-6
-4
0
2
2
5
8
8
5
10
6
6
9
5
5
-4
-5
-1
-8
-8
-13
-18
-8
-8
-6
-5
-11
-14
-12
-13
-19
-21
-22
-13
-21
-17
-15
-14
-11
-8
-3
-2
-1
1




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=234040&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=234040&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=234040&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 Mean-6.666666666666670.975642318819915-6.83310526621099
Geometric MeanNaN
Harmonic Mean0
Quadratic Mean10.5843175395383
Winsorized Mean ( 1 / 24 )-6.666666666666670.969406833462449-6.87705763621987
Winsorized Mean ( 2 / 24 )-6.694444444444440.963260733023196-6.94977404864612
Winsorized Mean ( 3 / 24 )-6.694444444444440.963260733023196-6.94977404864612
Winsorized Mean ( 4 / 24 )-6.750.929172061501423-7.26453181243188
Winsorized Mean ( 5 / 24 )-6.750.929172061501423-7.26453181243188
Winsorized Mean ( 6 / 24 )-6.750.89703694119329-7.5247737189293
Winsorized Mean ( 7 / 24 )-6.652777777777780.87884182798493-7.56993757685809
Winsorized Mean ( 8 / 24 )-6.652777777777780.87884182798493-7.56993757685809
Winsorized Mean ( 9 / 24 )-6.527777777777780.856707910404073-7.61960721793604
Winsorized Mean ( 10 / 24 )-6.805555555555560.759045321462939-8.96594098286375
Winsorized Mean ( 11 / 24 )-6.805555555555560.759045321462939-8.96594098286375
Winsorized Mean ( 12 / 24 )-6.805555555555560.704512308949962-9.65995266384894
Winsorized Mean ( 13 / 24 )-6.6250.675828333112223-9.80278522726555
Winsorized Mean ( 14 / 24 )-6.819444444444440.645899061895001-10.5580652562599
Winsorized Mean ( 15 / 24 )-6.819444444444440.645899061895001-10.5580652562599
Winsorized Mean ( 16 / 24 )-6.819444444444440.579489815576732-11.7680143138624
Winsorized Mean ( 17 / 24 )-6.819444444444440.579489815576732-11.7680143138624
Winsorized Mean ( 18 / 24 )-6.819444444444440.579489815576732-11.7680143138624
Winsorized Mean ( 19 / 24 )-7.083333333333330.543401879370979-13.0351653209825
Winsorized Mean ( 20 / 24 )-6.805555555555560.501811619789953-13.5619728343561
Winsorized Mean ( 21 / 24 )-6.805555555555560.501811619789953-13.5619728343561
Winsorized Mean ( 22 / 24 )-6.805555555555560.417552527263124-16.2986812705051
Winsorized Mean ( 23 / 24 )-6.805555555555560.417552527263124-16.2986812705051
Winsorized Mean ( 24 / 24 )-6.805555555555560.417552527263124-16.2986812705051
Trimmed Mean ( 1 / 24 )-6.685714285714290.949347134747754-7.04243373262059
Trimmed Mean ( 2 / 24 )-6.705882352941180.925461426218107-7.24598796121058
Trimmed Mean ( 3 / 24 )-6.712121212121210.900858215915184-7.45080756720673
Trimmed Mean ( 4 / 24 )-6.718750.871298505857507-7.71119192197811
Trimmed Mean ( 5 / 24 )-6.709677419354840.848486722358777-7.90781663701474
Trimmed Mean ( 6 / 24 )-6.70.82074101835417-8.16335463948847
Trimmed Mean ( 7 / 24 )-6.689655172413790.796319002885627-8.40072276081876
Trimmed Mean ( 8 / 24 )-6.696428571428570.771202317710664-8.68310223873173
Trimmed Mean ( 9 / 24 )-6.70370370370370.740006624344549-9.05897796474649
Trimmed Mean ( 10 / 24 )-6.730769230769230.706634891045136-9.52510174075073
Trimmed Mean ( 11 / 24 )-6.720.688707751769166-9.75740433113688
Trimmed Mean ( 12 / 24 )-6.708333333333330.665751810221526-10.0763275898584
Trimmed Mean ( 13 / 24 )-6.695652173913040.648945309485163-10.3177449255701
Trimmed Mean ( 14 / 24 )-6.704545454545450.633440507705219-10.5843332925363
Trimmed Mean ( 15 / 24 )-6.690476190476190.619549961462413-10.7989292335419
Trimmed Mean ( 16 / 24 )-6.6750.600627342974165-11.113380165057
Trimmed Mean ( 17 / 24 )-6.657894736842110.590677114395073-11.2716314456513
Trimmed Mean ( 18 / 24 )-6.638888888888890.576184463653093-11.5221588010155
Trimmed Mean ( 19 / 24 )-6.617647058823530.555341435791734-11.9163574556416
Trimmed Mean ( 20 / 24 )-6.56250.534943281587991-12.2676557045806
Trimmed Mean ( 21 / 24 )-6.533333333333330.518027499676857-12.6119430675182
Trimmed Mean ( 22 / 24 )-6.50.491999483804091-13.2113959749361
Trimmed Mean ( 23 / 24 )-6.461538461538460.481122946803443-13.4301190672127
Trimmed Mean ( 24 / 24 )-6.416666666666670.462024007574151-13.8881671979715
Median-6.5
Midrange-6
Midmean - Weighted Average at Xnp-6.675
Midmean - Weighted Average at X(n+1)p-6.675
Midmean - Empirical Distribution Function-6.675
Midmean - Empirical Distribution Function - Averaging-6.675
Midmean - Empirical Distribution Function - Interpolation-6.675
Midmean - Closest Observation-6.675
Midmean - True Basic - Statistics Graphics Toolkit-6.675
Midmean - MS Excel (old versions)-6.675
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & -6.66666666666667 & 0.975642318819915 & -6.83310526621099 \tabularnewline
Geometric Mean & NaN &  &  \tabularnewline
Harmonic Mean & 0 &  &  \tabularnewline
Quadratic Mean & 10.5843175395383 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & -6.66666666666667 & 0.969406833462449 & -6.87705763621987 \tabularnewline
Winsorized Mean ( 2 / 24 ) & -6.69444444444444 & 0.963260733023196 & -6.94977404864612 \tabularnewline
Winsorized Mean ( 3 / 24 ) & -6.69444444444444 & 0.963260733023196 & -6.94977404864612 \tabularnewline
Winsorized Mean ( 4 / 24 ) & -6.75 & 0.929172061501423 & -7.26453181243188 \tabularnewline
Winsorized Mean ( 5 / 24 ) & -6.75 & 0.929172061501423 & -7.26453181243188 \tabularnewline
Winsorized Mean ( 6 / 24 ) & -6.75 & 0.89703694119329 & -7.5247737189293 \tabularnewline
Winsorized Mean ( 7 / 24 ) & -6.65277777777778 & 0.87884182798493 & -7.56993757685809 \tabularnewline
Winsorized Mean ( 8 / 24 ) & -6.65277777777778 & 0.87884182798493 & -7.56993757685809 \tabularnewline
Winsorized Mean ( 9 / 24 ) & -6.52777777777778 & 0.856707910404073 & -7.61960721793604 \tabularnewline
Winsorized Mean ( 10 / 24 ) & -6.80555555555556 & 0.759045321462939 & -8.96594098286375 \tabularnewline
Winsorized Mean ( 11 / 24 ) & -6.80555555555556 & 0.759045321462939 & -8.96594098286375 \tabularnewline
Winsorized Mean ( 12 / 24 ) & -6.80555555555556 & 0.704512308949962 & -9.65995266384894 \tabularnewline
Winsorized Mean ( 13 / 24 ) & -6.625 & 0.675828333112223 & -9.80278522726555 \tabularnewline
Winsorized Mean ( 14 / 24 ) & -6.81944444444444 & 0.645899061895001 & -10.5580652562599 \tabularnewline
Winsorized Mean ( 15 / 24 ) & -6.81944444444444 & 0.645899061895001 & -10.5580652562599 \tabularnewline
Winsorized Mean ( 16 / 24 ) & -6.81944444444444 & 0.579489815576732 & -11.7680143138624 \tabularnewline
Winsorized Mean ( 17 / 24 ) & -6.81944444444444 & 0.579489815576732 & -11.7680143138624 \tabularnewline
Winsorized Mean ( 18 / 24 ) & -6.81944444444444 & 0.579489815576732 & -11.7680143138624 \tabularnewline
Winsorized Mean ( 19 / 24 ) & -7.08333333333333 & 0.543401879370979 & -13.0351653209825 \tabularnewline
Winsorized Mean ( 20 / 24 ) & -6.80555555555556 & 0.501811619789953 & -13.5619728343561 \tabularnewline
Winsorized Mean ( 21 / 24 ) & -6.80555555555556 & 0.501811619789953 & -13.5619728343561 \tabularnewline
Winsorized Mean ( 22 / 24 ) & -6.80555555555556 & 0.417552527263124 & -16.2986812705051 \tabularnewline
Winsorized Mean ( 23 / 24 ) & -6.80555555555556 & 0.417552527263124 & -16.2986812705051 \tabularnewline
Winsorized Mean ( 24 / 24 ) & -6.80555555555556 & 0.417552527263124 & -16.2986812705051 \tabularnewline
Trimmed Mean ( 1 / 24 ) & -6.68571428571429 & 0.949347134747754 & -7.04243373262059 \tabularnewline
Trimmed Mean ( 2 / 24 ) & -6.70588235294118 & 0.925461426218107 & -7.24598796121058 \tabularnewline
Trimmed Mean ( 3 / 24 ) & -6.71212121212121 & 0.900858215915184 & -7.45080756720673 \tabularnewline
Trimmed Mean ( 4 / 24 ) & -6.71875 & 0.871298505857507 & -7.71119192197811 \tabularnewline
Trimmed Mean ( 5 / 24 ) & -6.70967741935484 & 0.848486722358777 & -7.90781663701474 \tabularnewline
Trimmed Mean ( 6 / 24 ) & -6.7 & 0.82074101835417 & -8.16335463948847 \tabularnewline
Trimmed Mean ( 7 / 24 ) & -6.68965517241379 & 0.796319002885627 & -8.40072276081876 \tabularnewline
Trimmed Mean ( 8 / 24 ) & -6.69642857142857 & 0.771202317710664 & -8.68310223873173 \tabularnewline
Trimmed Mean ( 9 / 24 ) & -6.7037037037037 & 0.740006624344549 & -9.05897796474649 \tabularnewline
Trimmed Mean ( 10 / 24 ) & -6.73076923076923 & 0.706634891045136 & -9.52510174075073 \tabularnewline
Trimmed Mean ( 11 / 24 ) & -6.72 & 0.688707751769166 & -9.75740433113688 \tabularnewline
Trimmed Mean ( 12 / 24 ) & -6.70833333333333 & 0.665751810221526 & -10.0763275898584 \tabularnewline
Trimmed Mean ( 13 / 24 ) & -6.69565217391304 & 0.648945309485163 & -10.3177449255701 \tabularnewline
Trimmed Mean ( 14 / 24 ) & -6.70454545454545 & 0.633440507705219 & -10.5843332925363 \tabularnewline
Trimmed Mean ( 15 / 24 ) & -6.69047619047619 & 0.619549961462413 & -10.7989292335419 \tabularnewline
Trimmed Mean ( 16 / 24 ) & -6.675 & 0.600627342974165 & -11.113380165057 \tabularnewline
Trimmed Mean ( 17 / 24 ) & -6.65789473684211 & 0.590677114395073 & -11.2716314456513 \tabularnewline
Trimmed Mean ( 18 / 24 ) & -6.63888888888889 & 0.576184463653093 & -11.5221588010155 \tabularnewline
Trimmed Mean ( 19 / 24 ) & -6.61764705882353 & 0.555341435791734 & -11.9163574556416 \tabularnewline
Trimmed Mean ( 20 / 24 ) & -6.5625 & 0.534943281587991 & -12.2676557045806 \tabularnewline
Trimmed Mean ( 21 / 24 ) & -6.53333333333333 & 0.518027499676857 & -12.6119430675182 \tabularnewline
Trimmed Mean ( 22 / 24 ) & -6.5 & 0.491999483804091 & -13.2113959749361 \tabularnewline
Trimmed Mean ( 23 / 24 ) & -6.46153846153846 & 0.481122946803443 & -13.4301190672127 \tabularnewline
Trimmed Mean ( 24 / 24 ) & -6.41666666666667 & 0.462024007574151 & -13.8881671979715 \tabularnewline
Median & -6.5 &  &  \tabularnewline
Midrange & -6 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & -6.675 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & -6.675 &  &  \tabularnewline
Midmean - Empirical Distribution Function & -6.675 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & -6.675 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & -6.675 &  &  \tabularnewline
Midmean - Closest Observation & -6.675 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & -6.675 &  &  \tabularnewline
Midmean - MS Excel (old versions) & -6.675 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=234040&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]-6.66666666666667[/C][C]0.975642318819915[/C][C]-6.83310526621099[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]NaN[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]0[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]10.5843175395383[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]-6.66666666666667[/C][C]0.969406833462449[/C][C]-6.87705763621987[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]-6.69444444444444[/C][C]0.963260733023196[/C][C]-6.94977404864612[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]-6.69444444444444[/C][C]0.963260733023196[/C][C]-6.94977404864612[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]-6.75[/C][C]0.929172061501423[/C][C]-7.26453181243188[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]-6.75[/C][C]0.929172061501423[/C][C]-7.26453181243188[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]-6.75[/C][C]0.89703694119329[/C][C]-7.5247737189293[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]-6.65277777777778[/C][C]0.87884182798493[/C][C]-7.56993757685809[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]-6.65277777777778[/C][C]0.87884182798493[/C][C]-7.56993757685809[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]-6.52777777777778[/C][C]0.856707910404073[/C][C]-7.61960721793604[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]-6.80555555555556[/C][C]0.759045321462939[/C][C]-8.96594098286375[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]-6.80555555555556[/C][C]0.759045321462939[/C][C]-8.96594098286375[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]-6.80555555555556[/C][C]0.704512308949962[/C][C]-9.65995266384894[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]-6.625[/C][C]0.675828333112223[/C][C]-9.80278522726555[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]-6.81944444444444[/C][C]0.645899061895001[/C][C]-10.5580652562599[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]-6.81944444444444[/C][C]0.645899061895001[/C][C]-10.5580652562599[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]-6.81944444444444[/C][C]0.579489815576732[/C][C]-11.7680143138624[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]-6.81944444444444[/C][C]0.579489815576732[/C][C]-11.7680143138624[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]-6.81944444444444[/C][C]0.579489815576732[/C][C]-11.7680143138624[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]-7.08333333333333[/C][C]0.543401879370979[/C][C]-13.0351653209825[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]-6.80555555555556[/C][C]0.501811619789953[/C][C]-13.5619728343561[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]-6.80555555555556[/C][C]0.501811619789953[/C][C]-13.5619728343561[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]-6.80555555555556[/C][C]0.417552527263124[/C][C]-16.2986812705051[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]-6.80555555555556[/C][C]0.417552527263124[/C][C]-16.2986812705051[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]-6.80555555555556[/C][C]0.417552527263124[/C][C]-16.2986812705051[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]-6.68571428571429[/C][C]0.949347134747754[/C][C]-7.04243373262059[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]-6.70588235294118[/C][C]0.925461426218107[/C][C]-7.24598796121058[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]-6.71212121212121[/C][C]0.900858215915184[/C][C]-7.45080756720673[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]-6.71875[/C][C]0.871298505857507[/C][C]-7.71119192197811[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]-6.70967741935484[/C][C]0.848486722358777[/C][C]-7.90781663701474[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]-6.7[/C][C]0.82074101835417[/C][C]-8.16335463948847[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]-6.68965517241379[/C][C]0.796319002885627[/C][C]-8.40072276081876[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]-6.69642857142857[/C][C]0.771202317710664[/C][C]-8.68310223873173[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]-6.7037037037037[/C][C]0.740006624344549[/C][C]-9.05897796474649[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]-6.73076923076923[/C][C]0.706634891045136[/C][C]-9.52510174075073[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]-6.72[/C][C]0.688707751769166[/C][C]-9.75740433113688[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]-6.70833333333333[/C][C]0.665751810221526[/C][C]-10.0763275898584[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]-6.69565217391304[/C][C]0.648945309485163[/C][C]-10.3177449255701[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]-6.70454545454545[/C][C]0.633440507705219[/C][C]-10.5843332925363[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]-6.69047619047619[/C][C]0.619549961462413[/C][C]-10.7989292335419[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]-6.675[/C][C]0.600627342974165[/C][C]-11.113380165057[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]-6.65789473684211[/C][C]0.590677114395073[/C][C]-11.2716314456513[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]-6.63888888888889[/C][C]0.576184463653093[/C][C]-11.5221588010155[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]-6.61764705882353[/C][C]0.555341435791734[/C][C]-11.9163574556416[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]-6.5625[/C][C]0.534943281587991[/C][C]-12.2676557045806[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]-6.53333333333333[/C][C]0.518027499676857[/C][C]-12.6119430675182[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]-6.5[/C][C]0.491999483804091[/C][C]-13.2113959749361[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]-6.46153846153846[/C][C]0.481122946803443[/C][C]-13.4301190672127[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]-6.41666666666667[/C][C]0.462024007574151[/C][C]-13.8881671979715[/C][/ROW]
[ROW][C]Median[/C][C]-6.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]-6[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]-6.675[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]-6.675[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]-6.675[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]-6.675[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]-6.675[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]-6.675[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]-6.675[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]-6.675[/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=234040&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=234040&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 Mean-6.666666666666670.975642318819915-6.83310526621099
Geometric MeanNaN
Harmonic Mean0
Quadratic Mean10.5843175395383
Winsorized Mean ( 1 / 24 )-6.666666666666670.969406833462449-6.87705763621987
Winsorized Mean ( 2 / 24 )-6.694444444444440.963260733023196-6.94977404864612
Winsorized Mean ( 3 / 24 )-6.694444444444440.963260733023196-6.94977404864612
Winsorized Mean ( 4 / 24 )-6.750.929172061501423-7.26453181243188
Winsorized Mean ( 5 / 24 )-6.750.929172061501423-7.26453181243188
Winsorized Mean ( 6 / 24 )-6.750.89703694119329-7.5247737189293
Winsorized Mean ( 7 / 24 )-6.652777777777780.87884182798493-7.56993757685809
Winsorized Mean ( 8 / 24 )-6.652777777777780.87884182798493-7.56993757685809
Winsorized Mean ( 9 / 24 )-6.527777777777780.856707910404073-7.61960721793604
Winsorized Mean ( 10 / 24 )-6.805555555555560.759045321462939-8.96594098286375
Winsorized Mean ( 11 / 24 )-6.805555555555560.759045321462939-8.96594098286375
Winsorized Mean ( 12 / 24 )-6.805555555555560.704512308949962-9.65995266384894
Winsorized Mean ( 13 / 24 )-6.6250.675828333112223-9.80278522726555
Winsorized Mean ( 14 / 24 )-6.819444444444440.645899061895001-10.5580652562599
Winsorized Mean ( 15 / 24 )-6.819444444444440.645899061895001-10.5580652562599
Winsorized Mean ( 16 / 24 )-6.819444444444440.579489815576732-11.7680143138624
Winsorized Mean ( 17 / 24 )-6.819444444444440.579489815576732-11.7680143138624
Winsorized Mean ( 18 / 24 )-6.819444444444440.579489815576732-11.7680143138624
Winsorized Mean ( 19 / 24 )-7.083333333333330.543401879370979-13.0351653209825
Winsorized Mean ( 20 / 24 )-6.805555555555560.501811619789953-13.5619728343561
Winsorized Mean ( 21 / 24 )-6.805555555555560.501811619789953-13.5619728343561
Winsorized Mean ( 22 / 24 )-6.805555555555560.417552527263124-16.2986812705051
Winsorized Mean ( 23 / 24 )-6.805555555555560.417552527263124-16.2986812705051
Winsorized Mean ( 24 / 24 )-6.805555555555560.417552527263124-16.2986812705051
Trimmed Mean ( 1 / 24 )-6.685714285714290.949347134747754-7.04243373262059
Trimmed Mean ( 2 / 24 )-6.705882352941180.925461426218107-7.24598796121058
Trimmed Mean ( 3 / 24 )-6.712121212121210.900858215915184-7.45080756720673
Trimmed Mean ( 4 / 24 )-6.718750.871298505857507-7.71119192197811
Trimmed Mean ( 5 / 24 )-6.709677419354840.848486722358777-7.90781663701474
Trimmed Mean ( 6 / 24 )-6.70.82074101835417-8.16335463948847
Trimmed Mean ( 7 / 24 )-6.689655172413790.796319002885627-8.40072276081876
Trimmed Mean ( 8 / 24 )-6.696428571428570.771202317710664-8.68310223873173
Trimmed Mean ( 9 / 24 )-6.70370370370370.740006624344549-9.05897796474649
Trimmed Mean ( 10 / 24 )-6.730769230769230.706634891045136-9.52510174075073
Trimmed Mean ( 11 / 24 )-6.720.688707751769166-9.75740433113688
Trimmed Mean ( 12 / 24 )-6.708333333333330.665751810221526-10.0763275898584
Trimmed Mean ( 13 / 24 )-6.695652173913040.648945309485163-10.3177449255701
Trimmed Mean ( 14 / 24 )-6.704545454545450.633440507705219-10.5843332925363
Trimmed Mean ( 15 / 24 )-6.690476190476190.619549961462413-10.7989292335419
Trimmed Mean ( 16 / 24 )-6.6750.600627342974165-11.113380165057
Trimmed Mean ( 17 / 24 )-6.657894736842110.590677114395073-11.2716314456513
Trimmed Mean ( 18 / 24 )-6.638888888888890.576184463653093-11.5221588010155
Trimmed Mean ( 19 / 24 )-6.617647058823530.555341435791734-11.9163574556416
Trimmed Mean ( 20 / 24 )-6.56250.534943281587991-12.2676557045806
Trimmed Mean ( 21 / 24 )-6.533333333333330.518027499676857-12.6119430675182
Trimmed Mean ( 22 / 24 )-6.50.491999483804091-13.2113959749361
Trimmed Mean ( 23 / 24 )-6.461538461538460.481122946803443-13.4301190672127
Trimmed Mean ( 24 / 24 )-6.416666666666670.462024007574151-13.8881671979715
Median-6.5
Midrange-6
Midmean - Weighted Average at Xnp-6.675
Midmean - Weighted Average at X(n+1)p-6.675
Midmean - Empirical Distribution Function-6.675
Midmean - Empirical Distribution Function - Averaging-6.675
Midmean - Empirical Distribution Function - Interpolation-6.675
Midmean - Closest Observation-6.675
Midmean - True Basic - Statistics Graphics Toolkit-6.675
Midmean - MS Excel (old versions)-6.675
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')