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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationFri, 05 Dec 2008 11:42:42 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/Dec/05/t122850267485vwqvaeriysncq.htm/, Retrieved Thu, 16 May 2024 18:33:13 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=29386, Retrieved Thu, 16 May 2024 18:33:13 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact211
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Data Series] [Run sequence plot...] [2008-12-02 22:19:27] [ed2ba3b6182103c15c0ab511ae4e6284]
- RMP     [Central Tendency] [central tendency ...] [2008-12-05 18:42:42] [577b699a0819d2125728ba9ae2c57238] [Current]
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Dataseries X:
92,66
94,2
94,37
94,45
94,62
94,37
93,43
94,79
94,88
94,79
94,62
94,71
93,77
95,73
95,99
95,82
95,47
95,82
94,71
96,33
96,5
96,16
96,33
96,33
95,05
96,84
96,92
97,44
97,78
97,69
96,67
98,29
98,2
98,71
98,54
98,2
96,92
99,06
99,65
99,82
99,99
100,33
99,31
101,1
101,1
100,93
100,85
100,93
99,6
101,88
101,81
102,38
102,74
102,82
101,72
103,47
102,98
102,68
102,9
103,03
101,29




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=29386&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]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=29386&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=29386&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'Sir Ronald Aylmer Fisher' @ 193.190.124.24







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean98.04049180327870.391328787610293250.532275946213
Geometric Mean97.9938118699185
Harmonic Mean97.9473279847603
Quadratic Mean98.08734029542
Winsorized Mean ( 1 / 20 )98.04590163934430.387018403499751253.336535815169
Winsorized Mean ( 2 / 20 )98.05540983606560.384524017296929255.004643208924
Winsorized Mean ( 3 / 20 )98.07262295081970.379926143357524258.136021080629
Winsorized Mean ( 4 / 20 )98.0785245901640.37695985755944260.182941560823
Winsorized Mean ( 5 / 20 )98.07196721311480.37559336077689261.112089442314
Winsorized Mean ( 6 / 20 )98.07393442622950.373091667392963262.868198347973
Winsorized Mean ( 7 / 20 )98.05901639344260.363013623682538270.124893381955
Winsorized Mean ( 8 / 20 )97.99344262295080.350441009063022279.628924950755
Winsorized Mean ( 9 / 20 )97.9963934426230.346423966597525282.879947380993
Winsorized Mean ( 10 / 20 )97.98163934426230.343733215612318285.051414567895
Winsorized Mean ( 11 / 20 )97.9185245901640.327757977154306298.752529046958
Winsorized Mean ( 12 / 20 )97.88114754098360.321434039019630304.513945814575
Winsorized Mean ( 13 / 20 )97.90032786885250.318380547571228307.494690287101
Winsorized Mean ( 14 / 20 )97.90032786885250.305774209280028320.171959889513
Winsorized Mean ( 15 / 20 )98.0036065573770.290224807606282337.681700491739
Winsorized Mean ( 16 / 20 )98.05081967213120.276966520148496354.016866802388
Winsorized Mean ( 17 / 20 )97.93098360655740.249604901446510392.343992602019
Winsorized Mean ( 18 / 20 )97.8306557377050.233838469871699418.368525039451
Winsorized Mean ( 19 / 20 )97.8306557377050.218220807216727448.310392512405
Winsorized Mean ( 20 / 20 )97.8306557377050.202040393739273484.213349257043
Trimmed Mean ( 1 / 20 )98.03966101694920.383033125950988255.956089368349
Trimmed Mean ( 2 / 20 )98.03298245614030.377923687523017259.398883141374
Trimmed Mean ( 3 / 20 )98.02054545454550.373015324351153262.778870077386
Trimmed Mean ( 4 / 20 )98.00056603773590.368783885318633265.739827414266
Trimmed Mean ( 5 / 20 )97.97725490196080.364279905139901268.961459360029
Trimmed Mean ( 6 / 20 )97.95367346938780.35872348960779273.061776847915
Trimmed Mean ( 7 / 20 )97.9276595744680.352088812902035278.133402669955
Trimmed Mean ( 8 / 20 )97.90222222222220.34613491981603282.844106784306
Trimmed Mean ( 9 / 20 )97.8860465116280.341496631033434286.638395861786
Trimmed Mean ( 10 / 20 )97.86780487804880.335970837910427291.298511164654
Trimmed Mean ( 11 / 20 )97.850.328877574242158297.527127611174
Trimmed Mean ( 12 / 20 )97.83972972972970.323146943231547302.771639277503
Trimmed Mean ( 13 / 20 )97.83371428571430.316441900813777309.168014836595
Trimmed Mean ( 14 / 20 )97.82424242424240.307367250941494318.265014000671
Trimmed Mean ( 15 / 20 )97.81354838709680.297696369956701328.568159569172
Trimmed Mean ( 16 / 20 )97.78689655172410.287666038346208339.932016702079
Trimmed Mean ( 17 / 20 )97.74962962962960.276175282650097353.94054345361
Trimmed Mean ( 18 / 20 )97.72360.268156596040448364.427358651508
Trimmed Mean ( 19 / 20 )97.70782608695650.260657390658764374.851546852433
Trimmed Mean ( 20 / 20 )97.68904761904760.253354546193862385.582374923314
Median97.69
Midrange98.065
Midmean - Weighted Average at Xnp97.7096666666667
Midmean - Weighted Average at X(n+1)p97.9109375
Midmean - Empirical Distribution Function97.9109375
Midmean - Empirical Distribution Function - Averaging97.9109375
Midmean - Empirical Distribution Function - Interpolation97.9109375
Midmean - Closest Observation97.8242424242424
Midmean - True Basic - Statistics Graphics Toolkit97.9109375
Midmean - MS Excel (old versions)97.9109375
Number of observations61

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 98.0404918032787 & 0.391328787610293 & 250.532275946213 \tabularnewline
Geometric Mean & 97.9938118699185 &  &  \tabularnewline
Harmonic Mean & 97.9473279847603 &  &  \tabularnewline
Quadratic Mean & 98.08734029542 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 98.0459016393443 & 0.387018403499751 & 253.336535815169 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 98.0554098360656 & 0.384524017296929 & 255.004643208924 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 98.0726229508197 & 0.379926143357524 & 258.136021080629 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 98.078524590164 & 0.37695985755944 & 260.182941560823 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 98.0719672131148 & 0.37559336077689 & 261.112089442314 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 98.0739344262295 & 0.373091667392963 & 262.868198347973 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 98.0590163934426 & 0.363013623682538 & 270.124893381955 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 97.9934426229508 & 0.350441009063022 & 279.628924950755 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 97.996393442623 & 0.346423966597525 & 282.879947380993 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 97.9816393442623 & 0.343733215612318 & 285.051414567895 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 97.918524590164 & 0.327757977154306 & 298.752529046958 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 97.8811475409836 & 0.321434039019630 & 304.513945814575 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 97.9003278688525 & 0.318380547571228 & 307.494690287101 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 97.9003278688525 & 0.305774209280028 & 320.171959889513 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 98.003606557377 & 0.290224807606282 & 337.681700491739 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 98.0508196721312 & 0.276966520148496 & 354.016866802388 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 97.9309836065574 & 0.249604901446510 & 392.343992602019 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 97.830655737705 & 0.233838469871699 & 418.368525039451 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 97.830655737705 & 0.218220807216727 & 448.310392512405 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 97.830655737705 & 0.202040393739273 & 484.213349257043 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 98.0396610169492 & 0.383033125950988 & 255.956089368349 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 98.0329824561403 & 0.377923687523017 & 259.398883141374 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 98.0205454545455 & 0.373015324351153 & 262.778870077386 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 98.0005660377359 & 0.368783885318633 & 265.739827414266 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 97.9772549019608 & 0.364279905139901 & 268.961459360029 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 97.9536734693878 & 0.35872348960779 & 273.061776847915 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 97.927659574468 & 0.352088812902035 & 278.133402669955 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 97.9022222222222 & 0.34613491981603 & 282.844106784306 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 97.886046511628 & 0.341496631033434 & 286.638395861786 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 97.8678048780488 & 0.335970837910427 & 291.298511164654 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 97.85 & 0.328877574242158 & 297.527127611174 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 97.8397297297297 & 0.323146943231547 & 302.771639277503 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 97.8337142857143 & 0.316441900813777 & 309.168014836595 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 97.8242424242424 & 0.307367250941494 & 318.265014000671 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 97.8135483870968 & 0.297696369956701 & 328.568159569172 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 97.7868965517241 & 0.287666038346208 & 339.932016702079 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 97.7496296296296 & 0.276175282650097 & 353.94054345361 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 97.7236 & 0.268156596040448 & 364.427358651508 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 97.7078260869565 & 0.260657390658764 & 374.851546852433 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 97.6890476190476 & 0.253354546193862 & 385.582374923314 \tabularnewline
Median & 97.69 &  &  \tabularnewline
Midrange & 98.065 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 97.7096666666667 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 97.9109375 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 97.9109375 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 97.9109375 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 97.9109375 &  &  \tabularnewline
Midmean - Closest Observation & 97.8242424242424 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 97.9109375 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 97.9109375 &  &  \tabularnewline
Number of observations & 61 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=29386&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]98.0404918032787[/C][C]0.391328787610293[/C][C]250.532275946213[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]97.9938118699185[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]97.9473279847603[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]98.08734029542[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]98.0459016393443[/C][C]0.387018403499751[/C][C]253.336535815169[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]98.0554098360656[/C][C]0.384524017296929[/C][C]255.004643208924[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]98.0726229508197[/C][C]0.379926143357524[/C][C]258.136021080629[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]98.078524590164[/C][C]0.37695985755944[/C][C]260.182941560823[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]98.0719672131148[/C][C]0.37559336077689[/C][C]261.112089442314[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]98.0739344262295[/C][C]0.373091667392963[/C][C]262.868198347973[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]98.0590163934426[/C][C]0.363013623682538[/C][C]270.124893381955[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]97.9934426229508[/C][C]0.350441009063022[/C][C]279.628924950755[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]97.996393442623[/C][C]0.346423966597525[/C][C]282.879947380993[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]97.9816393442623[/C][C]0.343733215612318[/C][C]285.051414567895[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]97.918524590164[/C][C]0.327757977154306[/C][C]298.752529046958[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]97.8811475409836[/C][C]0.321434039019630[/C][C]304.513945814575[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]97.9003278688525[/C][C]0.318380547571228[/C][C]307.494690287101[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]97.9003278688525[/C][C]0.305774209280028[/C][C]320.171959889513[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]98.003606557377[/C][C]0.290224807606282[/C][C]337.681700491739[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]98.0508196721312[/C][C]0.276966520148496[/C][C]354.016866802388[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]97.9309836065574[/C][C]0.249604901446510[/C][C]392.343992602019[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]97.830655737705[/C][C]0.233838469871699[/C][C]418.368525039451[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]97.830655737705[/C][C]0.218220807216727[/C][C]448.310392512405[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]97.830655737705[/C][C]0.202040393739273[/C][C]484.213349257043[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]98.0396610169492[/C][C]0.383033125950988[/C][C]255.956089368349[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]98.0329824561403[/C][C]0.377923687523017[/C][C]259.398883141374[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]98.0205454545455[/C][C]0.373015324351153[/C][C]262.778870077386[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]98.0005660377359[/C][C]0.368783885318633[/C][C]265.739827414266[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]97.9772549019608[/C][C]0.364279905139901[/C][C]268.961459360029[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]97.9536734693878[/C][C]0.35872348960779[/C][C]273.061776847915[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]97.927659574468[/C][C]0.352088812902035[/C][C]278.133402669955[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]97.9022222222222[/C][C]0.34613491981603[/C][C]282.844106784306[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]97.886046511628[/C][C]0.341496631033434[/C][C]286.638395861786[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]97.8678048780488[/C][C]0.335970837910427[/C][C]291.298511164654[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]97.85[/C][C]0.328877574242158[/C][C]297.527127611174[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]97.8397297297297[/C][C]0.323146943231547[/C][C]302.771639277503[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]97.8337142857143[/C][C]0.316441900813777[/C][C]309.168014836595[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]97.8242424242424[/C][C]0.307367250941494[/C][C]318.265014000671[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]97.8135483870968[/C][C]0.297696369956701[/C][C]328.568159569172[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]97.7868965517241[/C][C]0.287666038346208[/C][C]339.932016702079[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]97.7496296296296[/C][C]0.276175282650097[/C][C]353.94054345361[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]97.7236[/C][C]0.268156596040448[/C][C]364.427358651508[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]97.7078260869565[/C][C]0.260657390658764[/C][C]374.851546852433[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]97.6890476190476[/C][C]0.253354546193862[/C][C]385.582374923314[/C][/ROW]
[ROW][C]Median[/C][C]97.69[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]98.065[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]97.7096666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]97.9109375[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]97.9109375[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]97.9109375[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]97.9109375[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]97.8242424242424[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]97.9109375[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]97.9109375[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]61[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=29386&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=29386&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 Mean98.04049180327870.391328787610293250.532275946213
Geometric Mean97.9938118699185
Harmonic Mean97.9473279847603
Quadratic Mean98.08734029542
Winsorized Mean ( 1 / 20 )98.04590163934430.387018403499751253.336535815169
Winsorized Mean ( 2 / 20 )98.05540983606560.384524017296929255.004643208924
Winsorized Mean ( 3 / 20 )98.07262295081970.379926143357524258.136021080629
Winsorized Mean ( 4 / 20 )98.0785245901640.37695985755944260.182941560823
Winsorized Mean ( 5 / 20 )98.07196721311480.37559336077689261.112089442314
Winsorized Mean ( 6 / 20 )98.07393442622950.373091667392963262.868198347973
Winsorized Mean ( 7 / 20 )98.05901639344260.363013623682538270.124893381955
Winsorized Mean ( 8 / 20 )97.99344262295080.350441009063022279.628924950755
Winsorized Mean ( 9 / 20 )97.9963934426230.346423966597525282.879947380993
Winsorized Mean ( 10 / 20 )97.98163934426230.343733215612318285.051414567895
Winsorized Mean ( 11 / 20 )97.9185245901640.327757977154306298.752529046958
Winsorized Mean ( 12 / 20 )97.88114754098360.321434039019630304.513945814575
Winsorized Mean ( 13 / 20 )97.90032786885250.318380547571228307.494690287101
Winsorized Mean ( 14 / 20 )97.90032786885250.305774209280028320.171959889513
Winsorized Mean ( 15 / 20 )98.0036065573770.290224807606282337.681700491739
Winsorized Mean ( 16 / 20 )98.05081967213120.276966520148496354.016866802388
Winsorized Mean ( 17 / 20 )97.93098360655740.249604901446510392.343992602019
Winsorized Mean ( 18 / 20 )97.8306557377050.233838469871699418.368525039451
Winsorized Mean ( 19 / 20 )97.8306557377050.218220807216727448.310392512405
Winsorized Mean ( 20 / 20 )97.8306557377050.202040393739273484.213349257043
Trimmed Mean ( 1 / 20 )98.03966101694920.383033125950988255.956089368349
Trimmed Mean ( 2 / 20 )98.03298245614030.377923687523017259.398883141374
Trimmed Mean ( 3 / 20 )98.02054545454550.373015324351153262.778870077386
Trimmed Mean ( 4 / 20 )98.00056603773590.368783885318633265.739827414266
Trimmed Mean ( 5 / 20 )97.97725490196080.364279905139901268.961459360029
Trimmed Mean ( 6 / 20 )97.95367346938780.35872348960779273.061776847915
Trimmed Mean ( 7 / 20 )97.9276595744680.352088812902035278.133402669955
Trimmed Mean ( 8 / 20 )97.90222222222220.34613491981603282.844106784306
Trimmed Mean ( 9 / 20 )97.8860465116280.341496631033434286.638395861786
Trimmed Mean ( 10 / 20 )97.86780487804880.335970837910427291.298511164654
Trimmed Mean ( 11 / 20 )97.850.328877574242158297.527127611174
Trimmed Mean ( 12 / 20 )97.83972972972970.323146943231547302.771639277503
Trimmed Mean ( 13 / 20 )97.83371428571430.316441900813777309.168014836595
Trimmed Mean ( 14 / 20 )97.82424242424240.307367250941494318.265014000671
Trimmed Mean ( 15 / 20 )97.81354838709680.297696369956701328.568159569172
Trimmed Mean ( 16 / 20 )97.78689655172410.287666038346208339.932016702079
Trimmed Mean ( 17 / 20 )97.74962962962960.276175282650097353.94054345361
Trimmed Mean ( 18 / 20 )97.72360.268156596040448364.427358651508
Trimmed Mean ( 19 / 20 )97.70782608695650.260657390658764374.851546852433
Trimmed Mean ( 20 / 20 )97.68904761904760.253354546193862385.582374923314
Median97.69
Midrange98.065
Midmean - Weighted Average at Xnp97.7096666666667
Midmean - Weighted Average at X(n+1)p97.9109375
Midmean - Empirical Distribution Function97.9109375
Midmean - Empirical Distribution Function - Averaging97.9109375
Midmean - Empirical Distribution Function - Interpolation97.9109375
Midmean - Closest Observation97.8242424242424
Midmean - True Basic - Statistics Graphics Toolkit97.9109375
Midmean - MS Excel (old versions)97.9109375
Number of observations61



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')