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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationSun, 20 Apr 2008 12:45:18 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/Apr/20/t12087171798q2ti1keiyn9fgd.htm/, Retrieved Mon, 13 May 2024 10:46:39 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=10424, Retrieved Mon, 13 May 2024 10:46:39 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact179
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Opgave 5, oef 2, ...] [2008-04-20 18:45:18] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataseries X:
1
1,04
1,09
1,08
1,06
1,06
1,03
0,97
0,98
0,93
0,88
0,86
0,9
0,91
0,93
0,89
0,88
0,83
0,81
0,83
0,8
0,76
0,73
0,74
0,74
0,75
0,74
0,74
0,73
0,71
0,71
0,7
0,75
0,81
0,78
0,75
0,74
0,74
0,78
0,74
0,72
0,72
0,72
0,75
0,75
0,73
0,71
0,72
0,73
0,74
0,76
0,78
0,76
0,78
0,79
0,78
0,77
0,76
0,77
0,76




Summary of compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'George Udny Yule' @ 72.249.76.132

\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 & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=10424&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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=10424&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=10424&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'George Udny Yule' @ 72.249.76.132







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean0.8150.014173062697056357.5034498485124
Geometric Mean0.808365129769921
Harmonic Mean0.802340981887462
Quadratic Mean0.822238813646417
Winsorized Mean ( 1 / 20 )0.8150.014097120754229357.8132240057241
Winsorized Mean ( 2 / 20 )0.8143333333333330.013890952765675658.6232886303914
Winsorized Mean ( 3 / 20 )0.8143333333333330.013890952765675658.6232886303914
Winsorized Mean ( 4 / 20 )0.8136666666666670.013418443051858560.6379341867066
Winsorized Mean ( 5 / 20 )0.8128333333333330.013182962096668061.657867736628
Winsorized Mean ( 6 / 20 )0.8098333333333330.012372494705410365.4543285421014
Winsorized Mean ( 7 / 20 )0.80750.011778619431249868.5564216344088
Winsorized Mean ( 8 / 20 )0.80750.011288774985708971.531233550342
Winsorized Mean ( 9 / 20 )0.80150.0098915731983837281.0285668341377
Winsorized Mean ( 10 / 20 )0.80150.0098915731983837281.0285668341377
Winsorized Mean ( 11 / 20 )0.7978333333333330.0091042042397962987.6335056111599
Winsorized Mean ( 12 / 20 )0.7978333333333330.0084475505983161394.4455228823806
Winsorized Mean ( 13 / 20 )0.7956666666666670.008009057960596699.3458494845749
Winsorized Mean ( 14 / 20 )0.7933333333333330.0075489613408601105.091720239614
Winsorized Mean ( 15 / 20 )0.7933333333333330.0075489613408601105.091720239614
Winsorized Mean ( 16 / 20 )0.7880.00653024255266297120.669330985058
Winsorized Mean ( 17 / 20 )0.77950.0049995762532303155.913213544118
Winsorized Mean ( 18 / 20 )0.77950.0049995762532303155.913213544118
Winsorized Mean ( 19 / 20 )0.7731666666666670.00395234084015547195.622467275938
Winsorized Mean ( 20 / 20 )0.77650.0035221.857142857143
Trimmed Mean ( 1 / 20 )0.8122413793103450.013714404188344359.2254222754103
Trimmed Mean ( 2 / 20 )0.8092857142857140.013230860086445161.1665234911537
Trimmed Mean ( 3 / 20 )0.8064814814814810.012760650468447063.2006560696614
Trimmed Mean ( 4 / 20 )0.8034615384615380.012157477930757266.0878467588134
Trimmed Mean ( 5 / 20 )0.80040.011580983709230869.1132998798736
Trimmed Mean ( 6 / 20 )0.7972916666666670.010918539374319273.0218245621688
Trimmed Mean ( 7 / 20 )0.7945652173913040.010345278377554476.8046241380251
Trimmed Mean ( 8 / 20 )0.7920454545454540.0097894296526055880.9082329259745
Trimmed Mean ( 9 / 20 )0.7892857142857140.0091914269576150685.8719454471424
Trimmed Mean ( 10 / 20 )0.787250.0088432757302385289.0224419112132
Trimmed Mean ( 11 / 20 )0.7850.0083551161488394393.954409013098
Trimmed Mean ( 12 / 20 )0.7830555555555560.007936448412475298.665739995825
Trimmed Mean ( 13 / 20 )0.7808823529411760.00753326132652346103.657940312227
Trimmed Mean ( 14 / 20 )0.778750.0070959722787399109.745355450894
Trimmed Mean ( 15 / 20 )0.7766666666666670.00661474030268994117.414536493720
Trimmed Mean ( 16 / 20 )0.7742857142857140.00585152653687834132.322003396191
Trimmed Mean ( 17 / 20 )0.7723076923076920.00515327206905976149.867439940660
Trimmed Mean ( 18 / 20 )0.771250.00482717623821449159.772496784844
Trimmed Mean ( 19 / 20 )0.770.00426401432711221180.581006753202
Trimmed Mean ( 20 / 20 )0.76950.00393867463682098195.370288473761
Median0.765
Midrange0.895
Midmean - Weighted Average at Xnp0.776470588235294
Midmean - Weighted Average at X(n+1)p0.776470588235294
Midmean - Empirical Distribution Function0.776470588235294
Midmean - Empirical Distribution Function - Averaging0.776470588235294
Midmean - Empirical Distribution Function - Interpolation0.776470588235294
Midmean - Closest Observation0.776470588235294
Midmean - True Basic - Statistics Graphics Toolkit0.776470588235294
Midmean - MS Excel (old versions)0.776470588235294
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 0.815 & 0.0141730626970563 & 57.5034498485124 \tabularnewline
Geometric Mean & 0.808365129769921 &  &  \tabularnewline
Harmonic Mean & 0.802340981887462 &  &  \tabularnewline
Quadratic Mean & 0.822238813646417 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 0.815 & 0.0140971207542293 & 57.8132240057241 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 0.814333333333333 & 0.0138909527656756 & 58.6232886303914 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 0.814333333333333 & 0.0138909527656756 & 58.6232886303914 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 0.813666666666667 & 0.0134184430518585 & 60.6379341867066 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 0.812833333333333 & 0.0131829620966680 & 61.657867736628 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 0.809833333333333 & 0.0123724947054103 & 65.4543285421014 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 0.8075 & 0.0117786194312498 & 68.5564216344088 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 0.8075 & 0.0112887749857089 & 71.531233550342 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 0.8015 & 0.00989157319838372 & 81.0285668341377 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 0.8015 & 0.00989157319838372 & 81.0285668341377 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 0.797833333333333 & 0.00910420423979629 & 87.6335056111599 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 0.797833333333333 & 0.00844755059831613 & 94.4455228823806 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 0.795666666666667 & 0.0080090579605966 & 99.3458494845749 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 0.793333333333333 & 0.0075489613408601 & 105.091720239614 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 0.793333333333333 & 0.0075489613408601 & 105.091720239614 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 0.788 & 0.00653024255266297 & 120.669330985058 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 0.7795 & 0.0049995762532303 & 155.913213544118 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 0.7795 & 0.0049995762532303 & 155.913213544118 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 0.773166666666667 & 0.00395234084015547 & 195.622467275938 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 0.7765 & 0.0035 & 221.857142857143 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 0.812241379310345 & 0.0137144041883443 & 59.2254222754103 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 0.809285714285714 & 0.0132308600864451 & 61.1665234911537 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 0.806481481481481 & 0.0127606504684470 & 63.2006560696614 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 0.803461538461538 & 0.0121574779307572 & 66.0878467588134 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 0.8004 & 0.0115809837092308 & 69.1132998798736 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 0.797291666666667 & 0.0109185393743192 & 73.0218245621688 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 0.794565217391304 & 0.0103452783775544 & 76.8046241380251 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 0.792045454545454 & 0.00978942965260558 & 80.9082329259745 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 0.789285714285714 & 0.00919142695761506 & 85.8719454471424 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 0.78725 & 0.00884327573023852 & 89.0224419112132 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 0.785 & 0.00835511614883943 & 93.954409013098 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 0.783055555555556 & 0.0079364484124752 & 98.665739995825 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 0.780882352941176 & 0.00753326132652346 & 103.657940312227 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 0.77875 & 0.0070959722787399 & 109.745355450894 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 0.776666666666667 & 0.00661474030268994 & 117.414536493720 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 0.774285714285714 & 0.00585152653687834 & 132.322003396191 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 0.772307692307692 & 0.00515327206905976 & 149.867439940660 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 0.77125 & 0.00482717623821449 & 159.772496784844 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 0.77 & 0.00426401432711221 & 180.581006753202 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 0.7695 & 0.00393867463682098 & 195.370288473761 \tabularnewline
Median & 0.765 &  &  \tabularnewline
Midrange & 0.895 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 0.776470588235294 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 0.776470588235294 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 0.776470588235294 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 0.776470588235294 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 0.776470588235294 &  &  \tabularnewline
Midmean - Closest Observation & 0.776470588235294 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 0.776470588235294 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 0.776470588235294 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=10424&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]0.815[/C][C]0.0141730626970563[/C][C]57.5034498485124[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]0.808365129769921[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]0.802340981887462[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]0.822238813646417[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]0.815[/C][C]0.0140971207542293[/C][C]57.8132240057241[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]0.814333333333333[/C][C]0.0138909527656756[/C][C]58.6232886303914[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]0.814333333333333[/C][C]0.0138909527656756[/C][C]58.6232886303914[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]0.813666666666667[/C][C]0.0134184430518585[/C][C]60.6379341867066[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]0.812833333333333[/C][C]0.0131829620966680[/C][C]61.657867736628[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]0.809833333333333[/C][C]0.0123724947054103[/C][C]65.4543285421014[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]0.8075[/C][C]0.0117786194312498[/C][C]68.5564216344088[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]0.8075[/C][C]0.0112887749857089[/C][C]71.531233550342[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]0.8015[/C][C]0.00989157319838372[/C][C]81.0285668341377[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]0.8015[/C][C]0.00989157319838372[/C][C]81.0285668341377[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]0.797833333333333[/C][C]0.00910420423979629[/C][C]87.6335056111599[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]0.797833333333333[/C][C]0.00844755059831613[/C][C]94.4455228823806[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]0.795666666666667[/C][C]0.0080090579605966[/C][C]99.3458494845749[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]0.793333333333333[/C][C]0.0075489613408601[/C][C]105.091720239614[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]0.793333333333333[/C][C]0.0075489613408601[/C][C]105.091720239614[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]0.788[/C][C]0.00653024255266297[/C][C]120.669330985058[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]0.7795[/C][C]0.0049995762532303[/C][C]155.913213544118[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]0.7795[/C][C]0.0049995762532303[/C][C]155.913213544118[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]0.773166666666667[/C][C]0.00395234084015547[/C][C]195.622467275938[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]0.7765[/C][C]0.0035[/C][C]221.857142857143[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]0.812241379310345[/C][C]0.0137144041883443[/C][C]59.2254222754103[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]0.809285714285714[/C][C]0.0132308600864451[/C][C]61.1665234911537[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]0.806481481481481[/C][C]0.0127606504684470[/C][C]63.2006560696614[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]0.803461538461538[/C][C]0.0121574779307572[/C][C]66.0878467588134[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]0.8004[/C][C]0.0115809837092308[/C][C]69.1132998798736[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]0.797291666666667[/C][C]0.0109185393743192[/C][C]73.0218245621688[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]0.794565217391304[/C][C]0.0103452783775544[/C][C]76.8046241380251[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]0.792045454545454[/C][C]0.00978942965260558[/C][C]80.9082329259745[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]0.789285714285714[/C][C]0.00919142695761506[/C][C]85.8719454471424[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]0.78725[/C][C]0.00884327573023852[/C][C]89.0224419112132[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]0.785[/C][C]0.00835511614883943[/C][C]93.954409013098[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]0.783055555555556[/C][C]0.0079364484124752[/C][C]98.665739995825[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]0.780882352941176[/C][C]0.00753326132652346[/C][C]103.657940312227[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]0.77875[/C][C]0.0070959722787399[/C][C]109.745355450894[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]0.776666666666667[/C][C]0.00661474030268994[/C][C]117.414536493720[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]0.774285714285714[/C][C]0.00585152653687834[/C][C]132.322003396191[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]0.772307692307692[/C][C]0.00515327206905976[/C][C]149.867439940660[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]0.77125[/C][C]0.00482717623821449[/C][C]159.772496784844[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]0.77[/C][C]0.00426401432711221[/C][C]180.581006753202[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]0.7695[/C][C]0.00393867463682098[/C][C]195.370288473761[/C][/ROW]
[ROW][C]Median[/C][C]0.765[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]0.895[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]0.776470588235294[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]0.776470588235294[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]0.776470588235294[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]0.776470588235294[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]0.776470588235294[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]0.776470588235294[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]0.776470588235294[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]0.776470588235294[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]60[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=10424&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=10424&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 Mean0.8150.014173062697056357.5034498485124
Geometric Mean0.808365129769921
Harmonic Mean0.802340981887462
Quadratic Mean0.822238813646417
Winsorized Mean ( 1 / 20 )0.8150.014097120754229357.8132240057241
Winsorized Mean ( 2 / 20 )0.8143333333333330.013890952765675658.6232886303914
Winsorized Mean ( 3 / 20 )0.8143333333333330.013890952765675658.6232886303914
Winsorized Mean ( 4 / 20 )0.8136666666666670.013418443051858560.6379341867066
Winsorized Mean ( 5 / 20 )0.8128333333333330.013182962096668061.657867736628
Winsorized Mean ( 6 / 20 )0.8098333333333330.012372494705410365.4543285421014
Winsorized Mean ( 7 / 20 )0.80750.011778619431249868.5564216344088
Winsorized Mean ( 8 / 20 )0.80750.011288774985708971.531233550342
Winsorized Mean ( 9 / 20 )0.80150.0098915731983837281.0285668341377
Winsorized Mean ( 10 / 20 )0.80150.0098915731983837281.0285668341377
Winsorized Mean ( 11 / 20 )0.7978333333333330.0091042042397962987.6335056111599
Winsorized Mean ( 12 / 20 )0.7978333333333330.0084475505983161394.4455228823806
Winsorized Mean ( 13 / 20 )0.7956666666666670.008009057960596699.3458494845749
Winsorized Mean ( 14 / 20 )0.7933333333333330.0075489613408601105.091720239614
Winsorized Mean ( 15 / 20 )0.7933333333333330.0075489613408601105.091720239614
Winsorized Mean ( 16 / 20 )0.7880.00653024255266297120.669330985058
Winsorized Mean ( 17 / 20 )0.77950.0049995762532303155.913213544118
Winsorized Mean ( 18 / 20 )0.77950.0049995762532303155.913213544118
Winsorized Mean ( 19 / 20 )0.7731666666666670.00395234084015547195.622467275938
Winsorized Mean ( 20 / 20 )0.77650.0035221.857142857143
Trimmed Mean ( 1 / 20 )0.8122413793103450.013714404188344359.2254222754103
Trimmed Mean ( 2 / 20 )0.8092857142857140.013230860086445161.1665234911537
Trimmed Mean ( 3 / 20 )0.8064814814814810.012760650468447063.2006560696614
Trimmed Mean ( 4 / 20 )0.8034615384615380.012157477930757266.0878467588134
Trimmed Mean ( 5 / 20 )0.80040.011580983709230869.1132998798736
Trimmed Mean ( 6 / 20 )0.7972916666666670.010918539374319273.0218245621688
Trimmed Mean ( 7 / 20 )0.7945652173913040.010345278377554476.8046241380251
Trimmed Mean ( 8 / 20 )0.7920454545454540.0097894296526055880.9082329259745
Trimmed Mean ( 9 / 20 )0.7892857142857140.0091914269576150685.8719454471424
Trimmed Mean ( 10 / 20 )0.787250.0088432757302385289.0224419112132
Trimmed Mean ( 11 / 20 )0.7850.0083551161488394393.954409013098
Trimmed Mean ( 12 / 20 )0.7830555555555560.007936448412475298.665739995825
Trimmed Mean ( 13 / 20 )0.7808823529411760.00753326132652346103.657940312227
Trimmed Mean ( 14 / 20 )0.778750.0070959722787399109.745355450894
Trimmed Mean ( 15 / 20 )0.7766666666666670.00661474030268994117.414536493720
Trimmed Mean ( 16 / 20 )0.7742857142857140.00585152653687834132.322003396191
Trimmed Mean ( 17 / 20 )0.7723076923076920.00515327206905976149.867439940660
Trimmed Mean ( 18 / 20 )0.771250.00482717623821449159.772496784844
Trimmed Mean ( 19 / 20 )0.770.00426401432711221180.581006753202
Trimmed Mean ( 20 / 20 )0.76950.00393867463682098195.370288473761
Median0.765
Midrange0.895
Midmean - Weighted Average at Xnp0.776470588235294
Midmean - Weighted Average at X(n+1)p0.776470588235294
Midmean - Empirical Distribution Function0.776470588235294
Midmean - Empirical Distribution Function - Averaging0.776470588235294
Midmean - Empirical Distribution Function - Interpolation0.776470588235294
Midmean - Closest Observation0.776470588235294
Midmean - True Basic - Statistics Graphics Toolkit0.776470588235294
Midmean - MS Excel (old versions)0.776470588235294
Number of observations60



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')