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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationFri, 09 Nov 2007 02:03:30 -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/2007/Nov/09/t1194598794sc1k2yextc3doif.htm/, Retrieved Tue, 07 May 2024 02:10:57 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=722, Retrieved Tue, 07 May 2024 02:10:57 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact212
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [paper central ten...] [2007-11-09 09:03:30] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataseries X:
120,3
133,4
109,4
93,2
91,2
99,2
108,2
101,5
106,9
104,4
77,9
60
99,5
95
105,6
102,5
93,3
97,3
127
111,7
96,4
133
72,2
95,8
124,1
127,6
110,7
104,6
112,7
115,3
139,4
119
97,4
154
81,5
88,8
127,7
105,1
114,9
106,4
104,5
121,6
141,4
99
126,7
134,1
81,3
88,6
132,7
132,9
134,4
103,7
119,7
115
132,9
108,5
113,9
142,9
95,2
93




Summary of compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001

\begin{tabular}{lllllllll}
\hline
Summary of compuational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 3 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=722&T=0

[TABLE]
[ROW][C]Summary of compuational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ 193.190.124.10:1001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=722&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=722&T=0

As an alternative you can also use a QR Code:  

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

Summary of compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean109.7683333333332.4429253229908644.933151374003
Geometric Mean108.095552365755
Harmonic Mean106.329396437006
Quadratic Mean111.3606401143
Winsorized Mean ( 1 / 20 )109.7866666666672.3290143239749747.1386824617255
Winsorized Mean ( 2 / 20 )109.9266666666672.2683462537563248.4611493878552
Winsorized Mean ( 3 / 20 )109.9966666666672.2061841263246149.8583347392292
Winsorized Mean ( 4 / 20 )109.6766666666672.1327436066958651.4251531793747
Winsorized Mean ( 5 / 20 )110.2433333333332.0070882395915254.9269988028876
Winsorized Mean ( 6 / 20 )110.1933333333331.9894664228969255.3883855817368
Winsorized Mean ( 7 / 20 )110.4266666666671.931060226141857.184475746412
Winsorized Mean ( 8 / 20 )110.6533333333331.8891385455927958.5734347496528
Winsorized Mean ( 9 / 20 )110.6833333333331.8844039754653358.7365208174121
Winsorized Mean ( 10 / 20 )110.6666666666671.8751356510879959.0179524358443
Winsorized Mean ( 11 / 20 )110.0616666666671.6518062219058766.6311006745554
Winsorized Mean ( 12 / 20 )110.0816666666671.6420248827684967.040193983581
Winsorized Mean ( 13 / 20 )110.0816666666671.5987839511361668.8533723324145
Winsorized Mean ( 14 / 20 )110.1516666666671.5652105716835670.3749825483137
Winsorized Mean ( 15 / 20 )109.7266666666671.4175292156470077.4069877752637
Winsorized Mean ( 16 / 20 )109.0866666666671.3018011569952083.796719706763
Winsorized Mean ( 17 / 20 )109.1716666666671.1743686647848892.962005833717
Winsorized Mean ( 18 / 20 )109.0516666666671.1368121044520295.9276086519446
Winsorized Mean ( 19 / 20 )108.9251.08786221969492100.127569491794
Winsorized Mean ( 20 / 20 )108.3583333333330.80233167151192135.054288869268
Trimmed Mean ( 1 / 20 )109.8637931034482.2470289563166548.8929138160899
Trimmed Mean ( 2 / 20 )109.9464285714292.1458294861599551.2372624575042
Trimmed Mean ( 3 / 20 )109.9574074074072.0617487333900853.332108625384
Trimmed Mean ( 4 / 20 )109.9423076923081.9876776245202555.311941099525
Trimmed Mean ( 5 / 20 )110.0221.9240927679277457.1812346233671
Trimmed Mean ( 6 / 20 )109.9666666666671.8868040573486858.2819748761782
Trimmed Mean ( 7 / 20 )109.9173913043481.8434065932655659.6273180891858
Trimmed Mean ( 8 / 20 )109.8181818181821.8030080360579660.9083152276377
Trimmed Mean ( 9 / 20 )109.6690476190481.7599938235533362.312177549369
Trimmed Mean ( 10 / 20 )109.51.7025584066942164.314974199688
Trimmed Mean ( 11 / 20 )109.3157894736841.6265949665317367.2052918660939
Trimmed Mean ( 12 / 20 )109.2027777777781.5878081433776568.7758015558967
Trimmed Mean ( 13 / 20 )109.0735294117651.5343732939066771.0866969888746
Trimmed Mean ( 14 / 20 )108.9281251.4698943508707674.1060913224623
Trimmed Mean ( 15 / 20 )108.7533333333331.3853065832161278.5048845150597
Trimmed Mean ( 16 / 20 )108.6142857142861.3125131824554882.7529103449363
Trimmed Mean ( 17 / 20 )108.5461538461541.2452028660081087.1714616222603
Trimmed Mean ( 18 / 20 )108.4541666666671.1874644032295091.3325623670974
Trimmed Mean ( 19 / 20 )108.3636363636361.1069154023632497.8969450892833
Trimmed Mean ( 20 / 20 )108.2750.992362279984907109.108338944167
Median107.55
Midrange107
Midmean - Weighted Average at Xnp108.354838709677
Midmean - Weighted Average at X(n+1)p108.753333333333
Midmean - Empirical Distribution Function108.354838709677
Midmean - Empirical Distribution Function - Averaging108.753333333333
Midmean - Empirical Distribution Function - Interpolation108.753333333333
Midmean - Closest Observation108.354838709677
Midmean - True Basic - Statistics Graphics Toolkit108.753333333333
Midmean - MS Excel (old versions)108.928125
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 109.768333333333 & 2.44292532299086 & 44.933151374003 \tabularnewline
Geometric Mean & 108.095552365755 &  &  \tabularnewline
Harmonic Mean & 106.329396437006 &  &  \tabularnewline
Quadratic Mean & 111.3606401143 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 109.786666666667 & 2.32901432397497 & 47.1386824617255 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 109.926666666667 & 2.26834625375632 & 48.4611493878552 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 109.996666666667 & 2.20618412632461 & 49.8583347392292 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 109.676666666667 & 2.13274360669586 & 51.4251531793747 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 110.243333333333 & 2.00708823959152 & 54.9269988028876 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 110.193333333333 & 1.98946642289692 & 55.3883855817368 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 110.426666666667 & 1.9310602261418 & 57.184475746412 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 110.653333333333 & 1.88913854559279 & 58.5734347496528 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 110.683333333333 & 1.88440397546533 & 58.7365208174121 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 110.666666666667 & 1.87513565108799 & 59.0179524358443 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 110.061666666667 & 1.65180622190587 & 66.6311006745554 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 110.081666666667 & 1.64202488276849 & 67.040193983581 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 110.081666666667 & 1.59878395113616 & 68.8533723324145 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 110.151666666667 & 1.56521057168356 & 70.3749825483137 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 109.726666666667 & 1.41752921564700 & 77.4069877752637 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 109.086666666667 & 1.30180115699520 & 83.796719706763 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 109.171666666667 & 1.17436866478488 & 92.962005833717 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 109.051666666667 & 1.13681210445202 & 95.9276086519446 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 108.925 & 1.08786221969492 & 100.127569491794 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 108.358333333333 & 0.80233167151192 & 135.054288869268 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 109.863793103448 & 2.24702895631665 & 48.8929138160899 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 109.946428571429 & 2.14582948615995 & 51.2372624575042 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 109.957407407407 & 2.06174873339008 & 53.332108625384 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 109.942307692308 & 1.98767762452025 & 55.311941099525 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 110.022 & 1.92409276792774 & 57.1812346233671 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 109.966666666667 & 1.88680405734868 & 58.2819748761782 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 109.917391304348 & 1.84340659326556 & 59.6273180891858 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 109.818181818182 & 1.80300803605796 & 60.9083152276377 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 109.669047619048 & 1.75999382355333 & 62.312177549369 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 109.5 & 1.70255840669421 & 64.314974199688 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 109.315789473684 & 1.62659496653173 & 67.2052918660939 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 109.202777777778 & 1.58780814337765 & 68.7758015558967 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 109.073529411765 & 1.53437329390667 & 71.0866969888746 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 108.928125 & 1.46989435087076 & 74.1060913224623 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 108.753333333333 & 1.38530658321612 & 78.5048845150597 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 108.614285714286 & 1.31251318245548 & 82.7529103449363 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 108.546153846154 & 1.24520286600810 & 87.1714616222603 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 108.454166666667 & 1.18746440322950 & 91.3325623670974 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 108.363636363636 & 1.10691540236324 & 97.8969450892833 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 108.275 & 0.992362279984907 & 109.108338944167 \tabularnewline
Median & 107.55 &  &  \tabularnewline
Midrange & 107 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 108.354838709677 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 108.753333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 108.354838709677 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 108.753333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 108.753333333333 &  &  \tabularnewline
Midmean - Closest Observation & 108.354838709677 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 108.753333333333 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 108.928125 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=722&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]109.768333333333[/C][C]2.44292532299086[/C][C]44.933151374003[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]108.095552365755[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]106.329396437006[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]111.3606401143[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]109.786666666667[/C][C]2.32901432397497[/C][C]47.1386824617255[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]109.926666666667[/C][C]2.26834625375632[/C][C]48.4611493878552[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]109.996666666667[/C][C]2.20618412632461[/C][C]49.8583347392292[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]109.676666666667[/C][C]2.13274360669586[/C][C]51.4251531793747[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]110.243333333333[/C][C]2.00708823959152[/C][C]54.9269988028876[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]110.193333333333[/C][C]1.98946642289692[/C][C]55.3883855817368[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]110.426666666667[/C][C]1.9310602261418[/C][C]57.184475746412[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]110.653333333333[/C][C]1.88913854559279[/C][C]58.5734347496528[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]110.683333333333[/C][C]1.88440397546533[/C][C]58.7365208174121[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]110.666666666667[/C][C]1.87513565108799[/C][C]59.0179524358443[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]110.061666666667[/C][C]1.65180622190587[/C][C]66.6311006745554[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]110.081666666667[/C][C]1.64202488276849[/C][C]67.040193983581[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]110.081666666667[/C][C]1.59878395113616[/C][C]68.8533723324145[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]110.151666666667[/C][C]1.56521057168356[/C][C]70.3749825483137[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]109.726666666667[/C][C]1.41752921564700[/C][C]77.4069877752637[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]109.086666666667[/C][C]1.30180115699520[/C][C]83.796719706763[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]109.171666666667[/C][C]1.17436866478488[/C][C]92.962005833717[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]109.051666666667[/C][C]1.13681210445202[/C][C]95.9276086519446[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]108.925[/C][C]1.08786221969492[/C][C]100.127569491794[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]108.358333333333[/C][C]0.80233167151192[/C][C]135.054288869268[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]109.863793103448[/C][C]2.24702895631665[/C][C]48.8929138160899[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]109.946428571429[/C][C]2.14582948615995[/C][C]51.2372624575042[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]109.957407407407[/C][C]2.06174873339008[/C][C]53.332108625384[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]109.942307692308[/C][C]1.98767762452025[/C][C]55.311941099525[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]110.022[/C][C]1.92409276792774[/C][C]57.1812346233671[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]109.966666666667[/C][C]1.88680405734868[/C][C]58.2819748761782[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]109.917391304348[/C][C]1.84340659326556[/C][C]59.6273180891858[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]109.818181818182[/C][C]1.80300803605796[/C][C]60.9083152276377[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]109.669047619048[/C][C]1.75999382355333[/C][C]62.312177549369[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]109.5[/C][C]1.70255840669421[/C][C]64.314974199688[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]109.315789473684[/C][C]1.62659496653173[/C][C]67.2052918660939[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]109.202777777778[/C][C]1.58780814337765[/C][C]68.7758015558967[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]109.073529411765[/C][C]1.53437329390667[/C][C]71.0866969888746[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]108.928125[/C][C]1.46989435087076[/C][C]74.1060913224623[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]108.753333333333[/C][C]1.38530658321612[/C][C]78.5048845150597[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]108.614285714286[/C][C]1.31251318245548[/C][C]82.7529103449363[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]108.546153846154[/C][C]1.24520286600810[/C][C]87.1714616222603[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]108.454166666667[/C][C]1.18746440322950[/C][C]91.3325623670974[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]108.363636363636[/C][C]1.10691540236324[/C][C]97.8969450892833[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]108.275[/C][C]0.992362279984907[/C][C]109.108338944167[/C][/ROW]
[ROW][C]Median[/C][C]107.55[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]107[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]108.354838709677[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]108.753333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]108.354838709677[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]108.753333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]108.753333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]108.354838709677[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]108.753333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]108.928125[/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=722&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=722&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 Mean109.7683333333332.4429253229908644.933151374003
Geometric Mean108.095552365755
Harmonic Mean106.329396437006
Quadratic Mean111.3606401143
Winsorized Mean ( 1 / 20 )109.7866666666672.3290143239749747.1386824617255
Winsorized Mean ( 2 / 20 )109.9266666666672.2683462537563248.4611493878552
Winsorized Mean ( 3 / 20 )109.9966666666672.2061841263246149.8583347392292
Winsorized Mean ( 4 / 20 )109.6766666666672.1327436066958651.4251531793747
Winsorized Mean ( 5 / 20 )110.2433333333332.0070882395915254.9269988028876
Winsorized Mean ( 6 / 20 )110.1933333333331.9894664228969255.3883855817368
Winsorized Mean ( 7 / 20 )110.4266666666671.931060226141857.184475746412
Winsorized Mean ( 8 / 20 )110.6533333333331.8891385455927958.5734347496528
Winsorized Mean ( 9 / 20 )110.6833333333331.8844039754653358.7365208174121
Winsorized Mean ( 10 / 20 )110.6666666666671.8751356510879959.0179524358443
Winsorized Mean ( 11 / 20 )110.0616666666671.6518062219058766.6311006745554
Winsorized Mean ( 12 / 20 )110.0816666666671.6420248827684967.040193983581
Winsorized Mean ( 13 / 20 )110.0816666666671.5987839511361668.8533723324145
Winsorized Mean ( 14 / 20 )110.1516666666671.5652105716835670.3749825483137
Winsorized Mean ( 15 / 20 )109.7266666666671.4175292156470077.4069877752637
Winsorized Mean ( 16 / 20 )109.0866666666671.3018011569952083.796719706763
Winsorized Mean ( 17 / 20 )109.1716666666671.1743686647848892.962005833717
Winsorized Mean ( 18 / 20 )109.0516666666671.1368121044520295.9276086519446
Winsorized Mean ( 19 / 20 )108.9251.08786221969492100.127569491794
Winsorized Mean ( 20 / 20 )108.3583333333330.80233167151192135.054288869268
Trimmed Mean ( 1 / 20 )109.8637931034482.2470289563166548.8929138160899
Trimmed Mean ( 2 / 20 )109.9464285714292.1458294861599551.2372624575042
Trimmed Mean ( 3 / 20 )109.9574074074072.0617487333900853.332108625384
Trimmed Mean ( 4 / 20 )109.9423076923081.9876776245202555.311941099525
Trimmed Mean ( 5 / 20 )110.0221.9240927679277457.1812346233671
Trimmed Mean ( 6 / 20 )109.9666666666671.8868040573486858.2819748761782
Trimmed Mean ( 7 / 20 )109.9173913043481.8434065932655659.6273180891858
Trimmed Mean ( 8 / 20 )109.8181818181821.8030080360579660.9083152276377
Trimmed Mean ( 9 / 20 )109.6690476190481.7599938235533362.312177549369
Trimmed Mean ( 10 / 20 )109.51.7025584066942164.314974199688
Trimmed Mean ( 11 / 20 )109.3157894736841.6265949665317367.2052918660939
Trimmed Mean ( 12 / 20 )109.2027777777781.5878081433776568.7758015558967
Trimmed Mean ( 13 / 20 )109.0735294117651.5343732939066771.0866969888746
Trimmed Mean ( 14 / 20 )108.9281251.4698943508707674.1060913224623
Trimmed Mean ( 15 / 20 )108.7533333333331.3853065832161278.5048845150597
Trimmed Mean ( 16 / 20 )108.6142857142861.3125131824554882.7529103449363
Trimmed Mean ( 17 / 20 )108.5461538461541.2452028660081087.1714616222603
Trimmed Mean ( 18 / 20 )108.4541666666671.1874644032295091.3325623670974
Trimmed Mean ( 19 / 20 )108.3636363636361.1069154023632497.8969450892833
Trimmed Mean ( 20 / 20 )108.2750.992362279984907109.108338944167
Median107.55
Midrange107
Midmean - Weighted Average at Xnp108.354838709677
Midmean - Weighted Average at X(n+1)p108.753333333333
Midmean - Empirical Distribution Function108.354838709677
Midmean - Empirical Distribution Function - Averaging108.753333333333
Midmean - Empirical Distribution Function - Interpolation108.753333333333
Midmean - Closest Observation108.354838709677
Midmean - True Basic - Statistics Graphics Toolkit108.753333333333
Midmean - MS Excel (old versions)108.928125
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')