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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, 20 Oct 2008 15:44:08 -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/Oct/20/t12245390825380vx8zy02p8gb.htm/, Retrieved Sun, 19 May 2024 15:37:28 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=18197, Retrieved Sun, 19 May 2024 15:37:28 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact102
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
F       [Central Tendency] [Central Tendency ...] [2008-10-20 21:44:08] [d67aed6fd81b78d9d6977a60b85d8b5e] [Current]
Feedback Forum
2008-10-27 19:12:02 [Jeroen Aerts] [reply
Ik zou toch even je werkje nalezen vooraleer je het indiend, vooral in je laatste vraag staan er een hoop spellingsfouten. dat terzijde is je oplossing wel correct, net als je conclusie. Ik denk alleen dat, wanneer je het over 'extremen' hebt, je outliers bedoelt.

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Dataseries X:
0,76
0,77
0,76
0,77
0,78
0,79
0,78
0,76
0,78
0,76
0,74
0,73
0,72
0,71
0,73
0,75
0,75
0,72
0,72
0,72
0,74
0,78
0,74
0,74
0,75
0,78
0,81
0,75
0,7
0,71
0,71
0,73
0,74
0,74
0,75
0,74
0,74
0,73
0,76
0,8
0,83
0,81
0,83
0,88
0,89
0,93
0,91
0,9
0,86
0,88
0,93
0,98
0,97
1,03
1,06
1,06
1,08
1,09
1,04
1




Summary of computational 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 computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=18197&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=18197&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=18197&T=0

As an alternative you can also use a QR Code:  

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

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







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=18197&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=18197&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=18197&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')