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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationTue, 12 Jan 2016 14:29:56 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Jan/12/t1452609020e499raddkg3efc4.htm/, Retrieved Fri, 03 May 2024 22:54:14 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=289732, Retrieved Fri, 03 May 2024 22:54:14 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact147
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2016-01-12 14:29:56] [d1a83db1c928d515dd26931964d56abe] [Current]
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Dataseries X:
90,65
90,93
91,42
91,52
91,76
91,47
91,37
91,35
91,74
91,78
91,88
91,99
92,55
92,94
92,81
93,35
93,72
93,94
94,03
93,66
93,78
94,1
94,85
94,83
95,06
95,87
95,97
95,96
96,3
96,17
96,18
96,55
96,76
97,63
97,86
97,82
98,62
99,24
99,63
100,27
100,84
101,05
100,38
100,02
99,97
99,95
100
100,04
100,51
100,29
100,22
101,29
100,29
100,26
100,39
99,3
98,9
98,76
99,12
99,28




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Herman Ole Andreas Wold' @ wold.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 & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=289732&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]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=289732&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=289732&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'Herman Ole Andreas Wold' @ wold.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean96.31950.446003814493075215.961157438701
Geometric Mean96.2583186313354
Harmonic Mean96.1969169669763
Quadratic Mean96.3804042583346
Winsorized Mean ( 1 / 20 )96.32016666666670.444282541779801216.799350883352
Winsorized Mean ( 2 / 20 )96.32716666666670.440261676917216218.795256814459
Winsorized Mean ( 3 / 20 )96.31166666666670.437294013924197220.244649137506
Winsorized Mean ( 4 / 20 )96.3070.435370956836233221.206762848507
Winsorized Mean ( 5 / 20 )96.31033333333330.434448801159153221.683966157503
Winsorized Mean ( 6 / 20 )96.30633333333330.4320896516272222.885072509038
Winsorized Mean ( 7 / 20 )96.3320.427342517330822225.421052418769
Winsorized Mean ( 8 / 20 )96.3320.426439390385452225.898456315039
Winsorized Mean ( 9 / 20 )96.33350.425660193443651226.315501152806
Winsorized Mean ( 10 / 20 )96.34350.421613247213591228.511558013717
Winsorized Mean ( 11 / 20 )96.33066666666670.412923083264949233.289613903364
Winsorized Mean ( 12 / 20 )96.43866666666670.392924171942147245.438365855654
Winsorized Mean ( 13 / 20 )96.49066666666670.382937860359121251.974737040044
Winsorized Mean ( 14 / 20 )96.5140.376941917328848256.044752687455
Winsorized Mean ( 15 / 20 )96.61150.360047456460888268.329905589806
Winsorized Mean ( 16 / 20 )96.60883333333330.334267146086658289.016837174563
Winsorized Mean ( 17 / 20 )96.53233333333330.317648703258383303.896513170436
Winsorized Mean ( 18 / 20 )96.54433333333330.314069549196639307.397942845095
Winsorized Mean ( 19 / 20 )96.58233333333330.30469456473291316.980821164288
Winsorized Mean ( 20 / 20 )96.57233333333330.294403578516489328.027036287959
Trimmed Mean ( 1 / 20 )96.33155172413790.442493744540986217.70149954112
Trimmed Mean ( 2 / 20 )96.343750.439845129363365219.040165658873
Trimmed Mean ( 3 / 20 )96.3529629629630.438658589071127219.653656313885
Trimmed Mean ( 4 / 20 )96.36884615384610.437920636301608220.06007062767
Trimmed Mean ( 5 / 20 )96.38740.437015836821337220.558139725736
Trimmed Mean ( 6 / 20 )96.40666666666670.435446531772957221.397254616172
Trimmed Mean ( 7 / 20 )96.42847826086960.433381710498181222.502417441712
Trimmed Mean ( 8 / 20 )96.44727272727270.431256383184841223.642539537634
Trimmed Mean ( 9 / 20 )96.46785714285710.427887137598204225.451640552567
Trimmed Mean ( 10 / 20 )96.490250.422826339981382228.203025393945
Trimmed Mean ( 11 / 20 )96.51342105263160.41633968178416231.814129844742
Trimmed Mean ( 12 / 20 )96.54111111111110.409014063828093236.033720228474
Trimmed Mean ( 13 / 20 )96.55617647058820.403581562373307239.248234985708
Trimmed Mean ( 14 / 20 )96.5656250.397639947341529242.846891127517
Trimmed Mean ( 15 / 20 )96.5730.389688985919703247.820706998117
Trimmed Mean ( 16 / 20 )96.56750.382008277494185252.789024974649
Trimmed Mean ( 17 / 20 )96.56153846153850.377216400780443255.984464784026
Trimmed Mean ( 18 / 20 )96.56583333333330.373283470725544258.693033328371
Trimmed Mean ( 19 / 20 )96.56909090909090.365705692170778264.062312882991
Trimmed Mean ( 20 / 20 )96.5670.354453693805879272.438972106992
Median96.24
Midrange95.97
Midmean - Weighted Average at Xnp96.4558064516129
Midmean - Weighted Average at X(n+1)p96.573
Midmean - Empirical Distribution Function96.4558064516129
Midmean - Empirical Distribution Function - Averaging96.573
Midmean - Empirical Distribution Function - Interpolation96.573
Midmean - Closest Observation96.4558064516129
Midmean - True Basic - Statistics Graphics Toolkit96.573
Midmean - MS Excel (old versions)96.565625
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 96.3195 & 0.446003814493075 & 215.961157438701 \tabularnewline
Geometric Mean & 96.2583186313354 &  &  \tabularnewline
Harmonic Mean & 96.1969169669763 &  &  \tabularnewline
Quadratic Mean & 96.3804042583346 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 96.3201666666667 & 0.444282541779801 & 216.799350883352 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 96.3271666666667 & 0.440261676917216 & 218.795256814459 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 96.3116666666667 & 0.437294013924197 & 220.244649137506 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 96.307 & 0.435370956836233 & 221.206762848507 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 96.3103333333333 & 0.434448801159153 & 221.683966157503 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 96.3063333333333 & 0.4320896516272 & 222.885072509038 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 96.332 & 0.427342517330822 & 225.421052418769 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 96.332 & 0.426439390385452 & 225.898456315039 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 96.3335 & 0.425660193443651 & 226.315501152806 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 96.3435 & 0.421613247213591 & 228.511558013717 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 96.3306666666667 & 0.412923083264949 & 233.289613903364 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 96.4386666666667 & 0.392924171942147 & 245.438365855654 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 96.4906666666667 & 0.382937860359121 & 251.974737040044 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 96.514 & 0.376941917328848 & 256.044752687455 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 96.6115 & 0.360047456460888 & 268.329905589806 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 96.6088333333333 & 0.334267146086658 & 289.016837174563 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 96.5323333333333 & 0.317648703258383 & 303.896513170436 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 96.5443333333333 & 0.314069549196639 & 307.397942845095 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 96.5823333333333 & 0.30469456473291 & 316.980821164288 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 96.5723333333333 & 0.294403578516489 & 328.027036287959 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 96.3315517241379 & 0.442493744540986 & 217.70149954112 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 96.34375 & 0.439845129363365 & 219.040165658873 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 96.352962962963 & 0.438658589071127 & 219.653656313885 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 96.3688461538461 & 0.437920636301608 & 220.06007062767 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 96.3874 & 0.437015836821337 & 220.558139725736 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 96.4066666666667 & 0.435446531772957 & 221.397254616172 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 96.4284782608696 & 0.433381710498181 & 222.502417441712 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 96.4472727272727 & 0.431256383184841 & 223.642539537634 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 96.4678571428571 & 0.427887137598204 & 225.451640552567 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 96.49025 & 0.422826339981382 & 228.203025393945 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 96.5134210526316 & 0.41633968178416 & 231.814129844742 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 96.5411111111111 & 0.409014063828093 & 236.033720228474 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 96.5561764705882 & 0.403581562373307 & 239.248234985708 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 96.565625 & 0.397639947341529 & 242.846891127517 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 96.573 & 0.389688985919703 & 247.820706998117 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 96.5675 & 0.382008277494185 & 252.789024974649 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 96.5615384615385 & 0.377216400780443 & 255.984464784026 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 96.5658333333333 & 0.373283470725544 & 258.693033328371 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 96.5690909090909 & 0.365705692170778 & 264.062312882991 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 96.567 & 0.354453693805879 & 272.438972106992 \tabularnewline
Median & 96.24 &  &  \tabularnewline
Midrange & 95.97 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 96.4558064516129 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 96.573 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 96.4558064516129 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 96.573 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 96.573 &  &  \tabularnewline
Midmean - Closest Observation & 96.4558064516129 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 96.573 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 96.565625 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=289732&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]96.3195[/C][C]0.446003814493075[/C][C]215.961157438701[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]96.2583186313354[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]96.1969169669763[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]96.3804042583346[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]96.3201666666667[/C][C]0.444282541779801[/C][C]216.799350883352[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]96.3271666666667[/C][C]0.440261676917216[/C][C]218.795256814459[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]96.3116666666667[/C][C]0.437294013924197[/C][C]220.244649137506[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]96.307[/C][C]0.435370956836233[/C][C]221.206762848507[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]96.3103333333333[/C][C]0.434448801159153[/C][C]221.683966157503[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]96.3063333333333[/C][C]0.4320896516272[/C][C]222.885072509038[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]96.332[/C][C]0.427342517330822[/C][C]225.421052418769[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]96.332[/C][C]0.426439390385452[/C][C]225.898456315039[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]96.3335[/C][C]0.425660193443651[/C][C]226.315501152806[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]96.3435[/C][C]0.421613247213591[/C][C]228.511558013717[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]96.3306666666667[/C][C]0.412923083264949[/C][C]233.289613903364[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]96.4386666666667[/C][C]0.392924171942147[/C][C]245.438365855654[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]96.4906666666667[/C][C]0.382937860359121[/C][C]251.974737040044[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]96.514[/C][C]0.376941917328848[/C][C]256.044752687455[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]96.6115[/C][C]0.360047456460888[/C][C]268.329905589806[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]96.6088333333333[/C][C]0.334267146086658[/C][C]289.016837174563[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]96.5323333333333[/C][C]0.317648703258383[/C][C]303.896513170436[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]96.5443333333333[/C][C]0.314069549196639[/C][C]307.397942845095[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]96.5823333333333[/C][C]0.30469456473291[/C][C]316.980821164288[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]96.5723333333333[/C][C]0.294403578516489[/C][C]328.027036287959[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]96.3315517241379[/C][C]0.442493744540986[/C][C]217.70149954112[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]96.34375[/C][C]0.439845129363365[/C][C]219.040165658873[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]96.352962962963[/C][C]0.438658589071127[/C][C]219.653656313885[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]96.3688461538461[/C][C]0.437920636301608[/C][C]220.06007062767[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]96.3874[/C][C]0.437015836821337[/C][C]220.558139725736[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]96.4066666666667[/C][C]0.435446531772957[/C][C]221.397254616172[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]96.4284782608696[/C][C]0.433381710498181[/C][C]222.502417441712[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]96.4472727272727[/C][C]0.431256383184841[/C][C]223.642539537634[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]96.4678571428571[/C][C]0.427887137598204[/C][C]225.451640552567[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]96.49025[/C][C]0.422826339981382[/C][C]228.203025393945[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]96.5134210526316[/C][C]0.41633968178416[/C][C]231.814129844742[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]96.5411111111111[/C][C]0.409014063828093[/C][C]236.033720228474[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]96.5561764705882[/C][C]0.403581562373307[/C][C]239.248234985708[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]96.565625[/C][C]0.397639947341529[/C][C]242.846891127517[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]96.573[/C][C]0.389688985919703[/C][C]247.820706998117[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]96.5675[/C][C]0.382008277494185[/C][C]252.789024974649[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]96.5615384615385[/C][C]0.377216400780443[/C][C]255.984464784026[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]96.5658333333333[/C][C]0.373283470725544[/C][C]258.693033328371[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]96.5690909090909[/C][C]0.365705692170778[/C][C]264.062312882991[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]96.567[/C][C]0.354453693805879[/C][C]272.438972106992[/C][/ROW]
[ROW][C]Median[/C][C]96.24[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]95.97[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]96.4558064516129[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]96.573[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]96.4558064516129[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]96.573[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]96.573[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]96.4558064516129[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]96.573[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]96.565625[/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=289732&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=289732&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 Mean96.31950.446003814493075215.961157438701
Geometric Mean96.2583186313354
Harmonic Mean96.1969169669763
Quadratic Mean96.3804042583346
Winsorized Mean ( 1 / 20 )96.32016666666670.444282541779801216.799350883352
Winsorized Mean ( 2 / 20 )96.32716666666670.440261676917216218.795256814459
Winsorized Mean ( 3 / 20 )96.31166666666670.437294013924197220.244649137506
Winsorized Mean ( 4 / 20 )96.3070.435370956836233221.206762848507
Winsorized Mean ( 5 / 20 )96.31033333333330.434448801159153221.683966157503
Winsorized Mean ( 6 / 20 )96.30633333333330.4320896516272222.885072509038
Winsorized Mean ( 7 / 20 )96.3320.427342517330822225.421052418769
Winsorized Mean ( 8 / 20 )96.3320.426439390385452225.898456315039
Winsorized Mean ( 9 / 20 )96.33350.425660193443651226.315501152806
Winsorized Mean ( 10 / 20 )96.34350.421613247213591228.511558013717
Winsorized Mean ( 11 / 20 )96.33066666666670.412923083264949233.289613903364
Winsorized Mean ( 12 / 20 )96.43866666666670.392924171942147245.438365855654
Winsorized Mean ( 13 / 20 )96.49066666666670.382937860359121251.974737040044
Winsorized Mean ( 14 / 20 )96.5140.376941917328848256.044752687455
Winsorized Mean ( 15 / 20 )96.61150.360047456460888268.329905589806
Winsorized Mean ( 16 / 20 )96.60883333333330.334267146086658289.016837174563
Winsorized Mean ( 17 / 20 )96.53233333333330.317648703258383303.896513170436
Winsorized Mean ( 18 / 20 )96.54433333333330.314069549196639307.397942845095
Winsorized Mean ( 19 / 20 )96.58233333333330.30469456473291316.980821164288
Winsorized Mean ( 20 / 20 )96.57233333333330.294403578516489328.027036287959
Trimmed Mean ( 1 / 20 )96.33155172413790.442493744540986217.70149954112
Trimmed Mean ( 2 / 20 )96.343750.439845129363365219.040165658873
Trimmed Mean ( 3 / 20 )96.3529629629630.438658589071127219.653656313885
Trimmed Mean ( 4 / 20 )96.36884615384610.437920636301608220.06007062767
Trimmed Mean ( 5 / 20 )96.38740.437015836821337220.558139725736
Trimmed Mean ( 6 / 20 )96.40666666666670.435446531772957221.397254616172
Trimmed Mean ( 7 / 20 )96.42847826086960.433381710498181222.502417441712
Trimmed Mean ( 8 / 20 )96.44727272727270.431256383184841223.642539537634
Trimmed Mean ( 9 / 20 )96.46785714285710.427887137598204225.451640552567
Trimmed Mean ( 10 / 20 )96.490250.422826339981382228.203025393945
Trimmed Mean ( 11 / 20 )96.51342105263160.41633968178416231.814129844742
Trimmed Mean ( 12 / 20 )96.54111111111110.409014063828093236.033720228474
Trimmed Mean ( 13 / 20 )96.55617647058820.403581562373307239.248234985708
Trimmed Mean ( 14 / 20 )96.5656250.397639947341529242.846891127517
Trimmed Mean ( 15 / 20 )96.5730.389688985919703247.820706998117
Trimmed Mean ( 16 / 20 )96.56750.382008277494185252.789024974649
Trimmed Mean ( 17 / 20 )96.56153846153850.377216400780443255.984464784026
Trimmed Mean ( 18 / 20 )96.56583333333330.373283470725544258.693033328371
Trimmed Mean ( 19 / 20 )96.56909090909090.365705692170778264.062312882991
Trimmed Mean ( 20 / 20 )96.5670.354453693805879272.438972106992
Median96.24
Midrange95.97
Midmean - Weighted Average at Xnp96.4558064516129
Midmean - Weighted Average at X(n+1)p96.573
Midmean - Empirical Distribution Function96.4558064516129
Midmean - Empirical Distribution Function - Averaging96.573
Midmean - Empirical Distribution Function - Interpolation96.573
Midmean - Closest Observation96.4558064516129
Midmean - True Basic - Statistics Graphics Toolkit96.573
Midmean - MS Excel (old versions)96.565625
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')