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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationSun, 16 Dec 2007 11:32:31 -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/Dec/16/t1197828962oduk54bsl9bm9je.htm/, Retrieved Thu, 02 May 2024 04:31:53 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=4229, Retrieved Thu, 02 May 2024 04:31:53 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact195
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [pap 1] [2007-12-16 18:32:31] [6bae8369195607c4cbc8a8485fed7b2f] [Current]
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Dataseries X:
106,7
110,2
125,9
100,1
106,4
114,8
81,3
87
104,2
108
105
94,5
92
95,9
108,8
103,4
102,1
110,1
83,2
82,7
106,8
113,7
102,5
96,6
92,1
95,6
102,3
98,6
98,2
104,5
84
73,8
103,9
106
97,2
102,6
89
93,8
116,7
106,8
98,5
118,7
90
91,9
113,3
113,1
104,1
108,7
96,7
101
116,9
105,8
99
129,4
83
88,9
115,9
104,2
113,4
112,2
100,8
107,3
126,6
102,9
117,9
128,8
87,5
93,8
122,7
126,2
124,6
116,7
115,2
111,1
129,9
113,3
118,5
133,5
102,1
102,4




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=4229&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=4229&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=4229&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 Mean104.918751.4220673729232873.7790290373679
Geometric Mean104.147750384485
Harmonic Mean103.365339304624
Quadratic Mean105.677357437627
Winsorized Mean ( 1 / 26 )104.96751.3880842081759175.6204122067915
Winsorized Mean ( 2 / 26 )104.991.3779003932327276.1956383172813
Winsorized Mean ( 3 / 26 )104.978751.3706088614581576.5927851132646
Winsorized Mean ( 4 / 26 )104.878751.3452244339476977.9637563467559
Winsorized Mean ( 5 / 26 )104.903751.3300619141270878.8713283838733
Winsorized Mean ( 6 / 26 )105.106251.2829546394178581.9251490042488
Winsorized Mean ( 7 / 26 )105.036251.2522476548519883.8781766474267
Winsorized Mean ( 8 / 26 )104.986251.1911697045474488.1371055687543
Winsorized Mean ( 9 / 26 )104.54751.1103440209848194.1577547355754
Winsorized Mean ( 10 / 26 )104.64751.0845388902341896.490315785176
Winsorized Mean ( 11 / 26 )104.826251.02806618228508101.964495872243
Winsorized Mean ( 12 / 26 )104.691251.00202357559306104.479827171768
Winsorized Mean ( 13 / 26 )104.6750.994426716088665105.261653077578
Winsorized Mean ( 14 / 26 )104.97250.948396339664282110.684210397900
Winsorized Mean ( 15 / 26 )104.82250.925286433585414113.286541545650
Winsorized Mean ( 16 / 26 )104.82250.88334980778364118.664767996049
Winsorized Mean ( 17 / 26 )104.971250.836836254550662125.438219758254
Winsorized Mean ( 18 / 26 )104.791250.791194005857642132.446971569771
Winsorized Mean ( 19 / 26 )104.886250.757710875836397138.425161027577
Winsorized Mean ( 20 / 26 )104.886250.750703770543078139.717228173934
Winsorized Mean ( 21 / 26 )105.01750.732780760122059143.313669947485
Winsorized Mean ( 22 / 26 )105.23750.688488932005207152.852856608019
Winsorized Mean ( 23 / 26 )105.0650.640347265359324164.075035037503
Winsorized Mean ( 24 / 26 )104.7650.590714274781285177.353086716568
Winsorized Mean ( 25 / 26 )104.608750.536521242368518194.975970640409
Winsorized Mean ( 26 / 26 )104.933750.485977234679344215.923180165501
Trimmed Mean ( 1 / 26 )104.9512820512821.3530490519177777.5665020440517
Trimmed Mean ( 2 / 26 )104.9342105263161.3121290488410679.9724772643352
Trimmed Mean ( 3 / 26 )104.9040540540541.2705612737482382.5651278860256
Trimmed Mean ( 4 / 26 )104.8763888888891.2248830116530085.6215556025682
Trimmed Mean ( 5 / 26 )104.8757142857141.1802330466334188.8601743400342
Trimmed Mean ( 6 / 26 )104.8691176470591.1319280042551892.6464556516236
Trimmed Mean ( 7 / 26 )104.8212121212121.0877223592334196.367617371667
Trimmed Mean ( 8 / 26 )104.78281251.04277929789793100.484170246978
Trimmed Mean ( 9 / 26 )104.751.00382597024080104.350757108697
Trimmed Mean ( 10 / 26 )104.780.97544369159897107.417784237491
Trimmed Mean ( 11 / 26 )104.7982758620690.946475908178818110.724715712753
Trimmed Mean ( 12 / 26 )104.7946428571430.922930889206943113.545493040319
Trimmed Mean ( 13 / 26 )104.8074074074070.899043873876464116.57652140546
Trimmed Mean ( 14 / 26 )104.8230769230770.870665802447847120.394158847597
Trimmed Mean ( 15 / 26 )104.8060.844619996670402124.086571965095
Trimmed Mean ( 16 / 26 )104.8041666666670.816382341227784128.376327333401
Trimmed Mean ( 17 / 26 )104.8021739130430.789217732491841132.792472341119
Trimmed Mean ( 18 / 26 )104.7840909090910.764112767306547137.131710648480
Trimmed Mean ( 19 / 26 )104.7833333333330.741290244948043141.352640274765
Trimmed Mean ( 20 / 26 )104.77250.718366982673112145.848156342224
Trimmed Mean ( 21 / 26 )104.7605263157890.68884156031412152.082180215749
Trimmed Mean ( 22 / 26 )104.7333333333330.652856969191738160.423091543309
Trimmed Mean ( 23 / 26 )104.6794117647060.614918214230059170.233064076294
Trimmed Mean ( 24 / 26 )104.63750.576291501899247181.570437278969
Trimmed Mean ( 25 / 26 )104.6233333333330.537377269245654194.69251738206
Trimmed Mean ( 26 / 26 )104.6250.499354742372753209.520389258465
Median104.2
Midrange103.65
Midmean - Weighted Average at Xnp104.573170731707
Midmean - Weighted Average at X(n+1)p104.7725
Midmean - Empirical Distribution Function104.573170731707
Midmean - Empirical Distribution Function - Averaging104.7725
Midmean - Empirical Distribution Function - Interpolation104.7725
Midmean - Closest Observation104.573170731707
Midmean - True Basic - Statistics Graphics Toolkit104.7725
Midmean - MS Excel (old versions)104.783333333333
Number of observations80

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 104.91875 & 1.42206737292328 & 73.7790290373679 \tabularnewline
Geometric Mean & 104.147750384485 &  &  \tabularnewline
Harmonic Mean & 103.365339304624 &  &  \tabularnewline
Quadratic Mean & 105.677357437627 &  &  \tabularnewline
Winsorized Mean ( 1 / 26 ) & 104.9675 & 1.38808420817591 & 75.6204122067915 \tabularnewline
Winsorized Mean ( 2 / 26 ) & 104.99 & 1.37790039323272 & 76.1956383172813 \tabularnewline
Winsorized Mean ( 3 / 26 ) & 104.97875 & 1.37060886145815 & 76.5927851132646 \tabularnewline
Winsorized Mean ( 4 / 26 ) & 104.87875 & 1.34522443394769 & 77.9637563467559 \tabularnewline
Winsorized Mean ( 5 / 26 ) & 104.90375 & 1.33006191412708 & 78.8713283838733 \tabularnewline
Winsorized Mean ( 6 / 26 ) & 105.10625 & 1.28295463941785 & 81.9251490042488 \tabularnewline
Winsorized Mean ( 7 / 26 ) & 105.03625 & 1.25224765485198 & 83.8781766474267 \tabularnewline
Winsorized Mean ( 8 / 26 ) & 104.98625 & 1.19116970454744 & 88.1371055687543 \tabularnewline
Winsorized Mean ( 9 / 26 ) & 104.5475 & 1.11034402098481 & 94.1577547355754 \tabularnewline
Winsorized Mean ( 10 / 26 ) & 104.6475 & 1.08453889023418 & 96.490315785176 \tabularnewline
Winsorized Mean ( 11 / 26 ) & 104.82625 & 1.02806618228508 & 101.964495872243 \tabularnewline
Winsorized Mean ( 12 / 26 ) & 104.69125 & 1.00202357559306 & 104.479827171768 \tabularnewline
Winsorized Mean ( 13 / 26 ) & 104.675 & 0.994426716088665 & 105.261653077578 \tabularnewline
Winsorized Mean ( 14 / 26 ) & 104.9725 & 0.948396339664282 & 110.684210397900 \tabularnewline
Winsorized Mean ( 15 / 26 ) & 104.8225 & 0.925286433585414 & 113.286541545650 \tabularnewline
Winsorized Mean ( 16 / 26 ) & 104.8225 & 0.88334980778364 & 118.664767996049 \tabularnewline
Winsorized Mean ( 17 / 26 ) & 104.97125 & 0.836836254550662 & 125.438219758254 \tabularnewline
Winsorized Mean ( 18 / 26 ) & 104.79125 & 0.791194005857642 & 132.446971569771 \tabularnewline
Winsorized Mean ( 19 / 26 ) & 104.88625 & 0.757710875836397 & 138.425161027577 \tabularnewline
Winsorized Mean ( 20 / 26 ) & 104.88625 & 0.750703770543078 & 139.717228173934 \tabularnewline
Winsorized Mean ( 21 / 26 ) & 105.0175 & 0.732780760122059 & 143.313669947485 \tabularnewline
Winsorized Mean ( 22 / 26 ) & 105.2375 & 0.688488932005207 & 152.852856608019 \tabularnewline
Winsorized Mean ( 23 / 26 ) & 105.065 & 0.640347265359324 & 164.075035037503 \tabularnewline
Winsorized Mean ( 24 / 26 ) & 104.765 & 0.590714274781285 & 177.353086716568 \tabularnewline
Winsorized Mean ( 25 / 26 ) & 104.60875 & 0.536521242368518 & 194.975970640409 \tabularnewline
Winsorized Mean ( 26 / 26 ) & 104.93375 & 0.485977234679344 & 215.923180165501 \tabularnewline
Trimmed Mean ( 1 / 26 ) & 104.951282051282 & 1.35304905191777 & 77.5665020440517 \tabularnewline
Trimmed Mean ( 2 / 26 ) & 104.934210526316 & 1.31212904884106 & 79.9724772643352 \tabularnewline
Trimmed Mean ( 3 / 26 ) & 104.904054054054 & 1.27056127374823 & 82.5651278860256 \tabularnewline
Trimmed Mean ( 4 / 26 ) & 104.876388888889 & 1.22488301165300 & 85.6215556025682 \tabularnewline
Trimmed Mean ( 5 / 26 ) & 104.875714285714 & 1.18023304663341 & 88.8601743400342 \tabularnewline
Trimmed Mean ( 6 / 26 ) & 104.869117647059 & 1.13192800425518 & 92.6464556516236 \tabularnewline
Trimmed Mean ( 7 / 26 ) & 104.821212121212 & 1.08772235923341 & 96.367617371667 \tabularnewline
Trimmed Mean ( 8 / 26 ) & 104.7828125 & 1.04277929789793 & 100.484170246978 \tabularnewline
Trimmed Mean ( 9 / 26 ) & 104.75 & 1.00382597024080 & 104.350757108697 \tabularnewline
Trimmed Mean ( 10 / 26 ) & 104.78 & 0.97544369159897 & 107.417784237491 \tabularnewline
Trimmed Mean ( 11 / 26 ) & 104.798275862069 & 0.946475908178818 & 110.724715712753 \tabularnewline
Trimmed Mean ( 12 / 26 ) & 104.794642857143 & 0.922930889206943 & 113.545493040319 \tabularnewline
Trimmed Mean ( 13 / 26 ) & 104.807407407407 & 0.899043873876464 & 116.57652140546 \tabularnewline
Trimmed Mean ( 14 / 26 ) & 104.823076923077 & 0.870665802447847 & 120.394158847597 \tabularnewline
Trimmed Mean ( 15 / 26 ) & 104.806 & 0.844619996670402 & 124.086571965095 \tabularnewline
Trimmed Mean ( 16 / 26 ) & 104.804166666667 & 0.816382341227784 & 128.376327333401 \tabularnewline
Trimmed Mean ( 17 / 26 ) & 104.802173913043 & 0.789217732491841 & 132.792472341119 \tabularnewline
Trimmed Mean ( 18 / 26 ) & 104.784090909091 & 0.764112767306547 & 137.131710648480 \tabularnewline
Trimmed Mean ( 19 / 26 ) & 104.783333333333 & 0.741290244948043 & 141.352640274765 \tabularnewline
Trimmed Mean ( 20 / 26 ) & 104.7725 & 0.718366982673112 & 145.848156342224 \tabularnewline
Trimmed Mean ( 21 / 26 ) & 104.760526315789 & 0.68884156031412 & 152.082180215749 \tabularnewline
Trimmed Mean ( 22 / 26 ) & 104.733333333333 & 0.652856969191738 & 160.423091543309 \tabularnewline
Trimmed Mean ( 23 / 26 ) & 104.679411764706 & 0.614918214230059 & 170.233064076294 \tabularnewline
Trimmed Mean ( 24 / 26 ) & 104.6375 & 0.576291501899247 & 181.570437278969 \tabularnewline
Trimmed Mean ( 25 / 26 ) & 104.623333333333 & 0.537377269245654 & 194.69251738206 \tabularnewline
Trimmed Mean ( 26 / 26 ) & 104.625 & 0.499354742372753 & 209.520389258465 \tabularnewline
Median & 104.2 &  &  \tabularnewline
Midrange & 103.65 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 104.573170731707 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 104.7725 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 104.573170731707 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 104.7725 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 104.7725 &  &  \tabularnewline
Midmean - Closest Observation & 104.573170731707 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 104.7725 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 104.783333333333 &  &  \tabularnewline
Number of observations & 80 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=4229&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]104.91875[/C][C]1.42206737292328[/C][C]73.7790290373679[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]104.147750384485[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]103.365339304624[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]105.677357437627[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 26 )[/C][C]104.9675[/C][C]1.38808420817591[/C][C]75.6204122067915[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 26 )[/C][C]104.99[/C][C]1.37790039323272[/C][C]76.1956383172813[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 26 )[/C][C]104.97875[/C][C]1.37060886145815[/C][C]76.5927851132646[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 26 )[/C][C]104.87875[/C][C]1.34522443394769[/C][C]77.9637563467559[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 26 )[/C][C]104.90375[/C][C]1.33006191412708[/C][C]78.8713283838733[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 26 )[/C][C]105.10625[/C][C]1.28295463941785[/C][C]81.9251490042488[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 26 )[/C][C]105.03625[/C][C]1.25224765485198[/C][C]83.8781766474267[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 26 )[/C][C]104.98625[/C][C]1.19116970454744[/C][C]88.1371055687543[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 26 )[/C][C]104.5475[/C][C]1.11034402098481[/C][C]94.1577547355754[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 26 )[/C][C]104.6475[/C][C]1.08453889023418[/C][C]96.490315785176[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 26 )[/C][C]104.82625[/C][C]1.02806618228508[/C][C]101.964495872243[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 26 )[/C][C]104.69125[/C][C]1.00202357559306[/C][C]104.479827171768[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 26 )[/C][C]104.675[/C][C]0.994426716088665[/C][C]105.261653077578[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 26 )[/C][C]104.9725[/C][C]0.948396339664282[/C][C]110.684210397900[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 26 )[/C][C]104.8225[/C][C]0.925286433585414[/C][C]113.286541545650[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 26 )[/C][C]104.8225[/C][C]0.88334980778364[/C][C]118.664767996049[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 26 )[/C][C]104.97125[/C][C]0.836836254550662[/C][C]125.438219758254[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 26 )[/C][C]104.79125[/C][C]0.791194005857642[/C][C]132.446971569771[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 26 )[/C][C]104.88625[/C][C]0.757710875836397[/C][C]138.425161027577[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 26 )[/C][C]104.88625[/C][C]0.750703770543078[/C][C]139.717228173934[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 26 )[/C][C]105.0175[/C][C]0.732780760122059[/C][C]143.313669947485[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 26 )[/C][C]105.2375[/C][C]0.688488932005207[/C][C]152.852856608019[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 26 )[/C][C]105.065[/C][C]0.640347265359324[/C][C]164.075035037503[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 26 )[/C][C]104.765[/C][C]0.590714274781285[/C][C]177.353086716568[/C][/ROW]
[ROW][C]Winsorized Mean ( 25 / 26 )[/C][C]104.60875[/C][C]0.536521242368518[/C][C]194.975970640409[/C][/ROW]
[ROW][C]Winsorized Mean ( 26 / 26 )[/C][C]104.93375[/C][C]0.485977234679344[/C][C]215.923180165501[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 26 )[/C][C]104.951282051282[/C][C]1.35304905191777[/C][C]77.5665020440517[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 26 )[/C][C]104.934210526316[/C][C]1.31212904884106[/C][C]79.9724772643352[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 26 )[/C][C]104.904054054054[/C][C]1.27056127374823[/C][C]82.5651278860256[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 26 )[/C][C]104.876388888889[/C][C]1.22488301165300[/C][C]85.6215556025682[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 26 )[/C][C]104.875714285714[/C][C]1.18023304663341[/C][C]88.8601743400342[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 26 )[/C][C]104.869117647059[/C][C]1.13192800425518[/C][C]92.6464556516236[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 26 )[/C][C]104.821212121212[/C][C]1.08772235923341[/C][C]96.367617371667[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 26 )[/C][C]104.7828125[/C][C]1.04277929789793[/C][C]100.484170246978[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 26 )[/C][C]104.75[/C][C]1.00382597024080[/C][C]104.350757108697[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 26 )[/C][C]104.78[/C][C]0.97544369159897[/C][C]107.417784237491[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 26 )[/C][C]104.798275862069[/C][C]0.946475908178818[/C][C]110.724715712753[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 26 )[/C][C]104.794642857143[/C][C]0.922930889206943[/C][C]113.545493040319[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 26 )[/C][C]104.807407407407[/C][C]0.899043873876464[/C][C]116.57652140546[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 26 )[/C][C]104.823076923077[/C][C]0.870665802447847[/C][C]120.394158847597[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 26 )[/C][C]104.806[/C][C]0.844619996670402[/C][C]124.086571965095[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 26 )[/C][C]104.804166666667[/C][C]0.816382341227784[/C][C]128.376327333401[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 26 )[/C][C]104.802173913043[/C][C]0.789217732491841[/C][C]132.792472341119[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 26 )[/C][C]104.784090909091[/C][C]0.764112767306547[/C][C]137.131710648480[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 26 )[/C][C]104.783333333333[/C][C]0.741290244948043[/C][C]141.352640274765[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 26 )[/C][C]104.7725[/C][C]0.718366982673112[/C][C]145.848156342224[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 26 )[/C][C]104.760526315789[/C][C]0.68884156031412[/C][C]152.082180215749[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 26 )[/C][C]104.733333333333[/C][C]0.652856969191738[/C][C]160.423091543309[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 26 )[/C][C]104.679411764706[/C][C]0.614918214230059[/C][C]170.233064076294[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 26 )[/C][C]104.6375[/C][C]0.576291501899247[/C][C]181.570437278969[/C][/ROW]
[ROW][C]Trimmed Mean ( 25 / 26 )[/C][C]104.623333333333[/C][C]0.537377269245654[/C][C]194.69251738206[/C][/ROW]
[ROW][C]Trimmed Mean ( 26 / 26 )[/C][C]104.625[/C][C]0.499354742372753[/C][C]209.520389258465[/C][/ROW]
[ROW][C]Median[/C][C]104.2[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]103.65[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]104.573170731707[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]104.7725[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]104.573170731707[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]104.7725[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]104.7725[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]104.573170731707[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]104.7725[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]104.783333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]80[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=4229&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=4229&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 Mean104.918751.4220673729232873.7790290373679
Geometric Mean104.147750384485
Harmonic Mean103.365339304624
Quadratic Mean105.677357437627
Winsorized Mean ( 1 / 26 )104.96751.3880842081759175.6204122067915
Winsorized Mean ( 2 / 26 )104.991.3779003932327276.1956383172813
Winsorized Mean ( 3 / 26 )104.978751.3706088614581576.5927851132646
Winsorized Mean ( 4 / 26 )104.878751.3452244339476977.9637563467559
Winsorized Mean ( 5 / 26 )104.903751.3300619141270878.8713283838733
Winsorized Mean ( 6 / 26 )105.106251.2829546394178581.9251490042488
Winsorized Mean ( 7 / 26 )105.036251.2522476548519883.8781766474267
Winsorized Mean ( 8 / 26 )104.986251.1911697045474488.1371055687543
Winsorized Mean ( 9 / 26 )104.54751.1103440209848194.1577547355754
Winsorized Mean ( 10 / 26 )104.64751.0845388902341896.490315785176
Winsorized Mean ( 11 / 26 )104.826251.02806618228508101.964495872243
Winsorized Mean ( 12 / 26 )104.691251.00202357559306104.479827171768
Winsorized Mean ( 13 / 26 )104.6750.994426716088665105.261653077578
Winsorized Mean ( 14 / 26 )104.97250.948396339664282110.684210397900
Winsorized Mean ( 15 / 26 )104.82250.925286433585414113.286541545650
Winsorized Mean ( 16 / 26 )104.82250.88334980778364118.664767996049
Winsorized Mean ( 17 / 26 )104.971250.836836254550662125.438219758254
Winsorized Mean ( 18 / 26 )104.791250.791194005857642132.446971569771
Winsorized Mean ( 19 / 26 )104.886250.757710875836397138.425161027577
Winsorized Mean ( 20 / 26 )104.886250.750703770543078139.717228173934
Winsorized Mean ( 21 / 26 )105.01750.732780760122059143.313669947485
Winsorized Mean ( 22 / 26 )105.23750.688488932005207152.852856608019
Winsorized Mean ( 23 / 26 )105.0650.640347265359324164.075035037503
Winsorized Mean ( 24 / 26 )104.7650.590714274781285177.353086716568
Winsorized Mean ( 25 / 26 )104.608750.536521242368518194.975970640409
Winsorized Mean ( 26 / 26 )104.933750.485977234679344215.923180165501
Trimmed Mean ( 1 / 26 )104.9512820512821.3530490519177777.5665020440517
Trimmed Mean ( 2 / 26 )104.9342105263161.3121290488410679.9724772643352
Trimmed Mean ( 3 / 26 )104.9040540540541.2705612737482382.5651278860256
Trimmed Mean ( 4 / 26 )104.8763888888891.2248830116530085.6215556025682
Trimmed Mean ( 5 / 26 )104.8757142857141.1802330466334188.8601743400342
Trimmed Mean ( 6 / 26 )104.8691176470591.1319280042551892.6464556516236
Trimmed Mean ( 7 / 26 )104.8212121212121.0877223592334196.367617371667
Trimmed Mean ( 8 / 26 )104.78281251.04277929789793100.484170246978
Trimmed Mean ( 9 / 26 )104.751.00382597024080104.350757108697
Trimmed Mean ( 10 / 26 )104.780.97544369159897107.417784237491
Trimmed Mean ( 11 / 26 )104.7982758620690.946475908178818110.724715712753
Trimmed Mean ( 12 / 26 )104.7946428571430.922930889206943113.545493040319
Trimmed Mean ( 13 / 26 )104.8074074074070.899043873876464116.57652140546
Trimmed Mean ( 14 / 26 )104.8230769230770.870665802447847120.394158847597
Trimmed Mean ( 15 / 26 )104.8060.844619996670402124.086571965095
Trimmed Mean ( 16 / 26 )104.8041666666670.816382341227784128.376327333401
Trimmed Mean ( 17 / 26 )104.8021739130430.789217732491841132.792472341119
Trimmed Mean ( 18 / 26 )104.7840909090910.764112767306547137.131710648480
Trimmed Mean ( 19 / 26 )104.7833333333330.741290244948043141.352640274765
Trimmed Mean ( 20 / 26 )104.77250.718366982673112145.848156342224
Trimmed Mean ( 21 / 26 )104.7605263157890.68884156031412152.082180215749
Trimmed Mean ( 22 / 26 )104.7333333333330.652856969191738160.423091543309
Trimmed Mean ( 23 / 26 )104.6794117647060.614918214230059170.233064076294
Trimmed Mean ( 24 / 26 )104.63750.576291501899247181.570437278969
Trimmed Mean ( 25 / 26 )104.6233333333330.537377269245654194.69251738206
Trimmed Mean ( 26 / 26 )104.6250.499354742372753209.520389258465
Median104.2
Midrange103.65
Midmean - Weighted Average at Xnp104.573170731707
Midmean - Weighted Average at X(n+1)p104.7725
Midmean - Empirical Distribution Function104.573170731707
Midmean - Empirical Distribution Function - Averaging104.7725
Midmean - Empirical Distribution Function - Interpolation104.7725
Midmean - Closest Observation104.573170731707
Midmean - True Basic - Statistics Graphics Toolkit104.7725
Midmean - MS Excel (old versions)104.783333333333
Number of observations80



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')