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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationMon, 20 Oct 2008 13:05:57 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/Oct/20/t1224529680pm2larq2r37hwti.htm/, Retrieved Sun, 19 May 2024 15:56:07 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=17920, Retrieved Sun, 19 May 2024 15:56:07 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact112
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
F       [Central Tendency] [Central tendandy ...] [2008-10-20 19:05:57] [2fdb1a8e4a6fa49ce74bdce2c154874d] [Current]
Feedback Forum
2008-10-22 17:16:52 [90714a39acc78a7b2ecd294ecc6b2864] [reply
De grafiek die voortkomt uit de central tendency kent een dalend verloop maar je datareeks kent een duidelijk stijgend verloop in de tijd. Je vaststelling dat de prijsindex daalt is juist omgekeerd. Je zegt dat de voorspelling in dit geval zinloos is maar soms ook handig kan zijn. Misschien kan je formuleren waarom ze volgens jou zinloos of handig is.
2008-10-27 09:44:59 [Joris Deboel] [reply
De observatie van mijn voorgaande collega is correct, het is opvallend dat de tijdreeks stijgend is en de central tendancy een dalend verloop kent. Voorspellen is inderdaad zinloos, maar kan handig zijn via deze eerste analyse kan je besluiten dat er andere technieken en analyses nodig zijn om de prijsindex grondig te evalueren.

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Dataseries X:
90,8
96,4
90
92,1
97,2
95,1
88,5
91
90,5
75
66,3
66
68,4
70,6
83,9
90,1
90,6
87,1
90,8
94,1
99,8
96,8
87
96,3
107,1
115,2
106,1
89,5
91,3
97,6
100,7
104,6
94,7
101,8
102,5
105,3
110,3
109,8
117,3
118,8
131,3
125,9
133,1
147
145,8
164,4
149,8
137,7
151,7
156,8
180
180,4
170,4
191,6
199,5
218,2
217,5
205
194
199,3




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=17920&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=17920&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=17920&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'Gwilym Jenkins' @ 72.249.127.135







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean119.445.3066365016318922.5076656302481
Geometric Mean113.376163932583
Harmonic Mean108.212337537993
Quadratic Mean126.203710986114
Winsorized Mean ( 1 / 20 )119.4333333333335.3021164448479422.5255960663381
Winsorized Mean ( 2 / 20 )119.0866666666675.1662335156504323.0509647513821
Winsorized Mean ( 3 / 20 )118.9216666666675.0724113052959523.4447996246882
Winsorized Mean ( 4 / 20 )119.2016666666675.0232501755138923.7299880558849
Winsorized Mean ( 5 / 20 )119.5016666666674.8033918640109624.8786003827886
Winsorized Mean ( 6 / 20 )119.5716666666674.7030132735538925.4244799475785
Winsorized Mean ( 7 / 20 )118.2766666666674.3743211687509127.0388620551245
Winsorized Mean ( 8 / 20 )118.414.3393070732210527.2877669180727
Winsorized Mean ( 9 / 20 )117.123.9849361832005329.3906839697328
Winsorized Mean ( 10 / 20 )116.2033333333333.7528324268618030.9641678913185
Winsorized Mean ( 11 / 20 )114.8283333333333.4552172061419833.2333183364609
Winsorized Mean ( 12 / 20 )113.8883333333333.2394409886615835.1567859182976
Winsorized Mean ( 13 / 20 )113.4983333333333.1559248303532135.9635730996263
Winsorized Mean ( 14 / 20 )112.8916666666673.0240031197360337.3318618389921
Winsorized Mean ( 15 / 20 )112.5916666666672.9668681690597637.9496695676735
Winsorized Mean ( 16 / 20 )110.4852.5598605463870843.1605542559479
Winsorized Mean ( 17 / 20 )109.2666666666672.3175962448297547.1465497540506
Winsorized Mean ( 18 / 20 )108.9666666666672.1924906079418849.6999468421691
Winsorized Mean ( 19 / 20 )107.891.8189720509215959.3137205958371
Winsorized Mean ( 20 / 20 )105.7233333333331.4062599486988575.1805051627576
Trimmed Mean ( 1 / 20 )118.6586206896555.1311593560187523.1251092504993
Trimmed Mean ( 2 / 20 )117.8285714285714.9179427083257923.9589150213350
Trimmed Mean ( 3 / 20 )117.1296296296304.7445195347748824.6873532232568
Trimmed Mean ( 4 / 20 )116.4403846153854.5726235160048525.4646778174119
Trimmed Mean ( 5 / 20 )115.6124.3721303264926526.4429445983017
Trimmed Mean ( 6 / 20 )114.6395833333334.1916263829085227.3496664208383
Trimmed Mean ( 7 / 20 )113.5673913043483.9865462808974728.4876640837043
Trimmed Mean ( 8 / 20 )112.653.8258488535640229.4444460070762
Trimmed Mean ( 9 / 20 )111.6214285714293.6171091949451330.8592919250041
Trimmed Mean ( 10 / 20 )110.7053.4485112915873032.1022582324340
Trimmed Mean ( 11 / 20 )109.8368421052633.2892112555347933.3930640424630
Trimmed Mean ( 12 / 20 )109.0805555555563.1617400760723534.5001653934375
Trimmed Mean ( 13 / 20 )108.3735294117653.0470268634033735.5669753730747
Trimmed Mean ( 14 / 20 )107.6343752.9043092613883837.0602319907717
Trimmed Mean ( 15 / 20 )106.8833333333332.7370513680913839.0505397813802
Trimmed Mean ( 16 / 20 )106.0678571428572.5002013335407342.4237263295297
Trimmed Mean ( 17 / 20 )105.4307692307692.3163550228140745.5158074614506
Trimmed Mean ( 18 / 20 )104.8666666666672.1343775750438949.1322003626796
Trimmed Mean ( 19 / 20 )104.2454545454551.8866554304125355.2541035660448
Trimmed Mean ( 20 / 20 )103.671.6748935551409361.8964707827518
Median102.15
Midrange142.1
Midmean - Weighted Average at Xnp106.364516129032
Midmean - Weighted Average at X(n+1)p106.364516129032
Midmean - Empirical Distribution Function106.364516129032
Midmean - Empirical Distribution Function - Averaging106.364516129032
Midmean - Empirical Distribution Function - Interpolation106.364516129032
Midmean - Closest Observation106.364516129032
Midmean - True Basic - Statistics Graphics Toolkit106.364516129032
Midmean - MS Excel (old versions)107.634375
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 119.44 & 5.30663650163189 & 22.5076656302481 \tabularnewline
Geometric Mean & 113.376163932583 &  &  \tabularnewline
Harmonic Mean & 108.212337537993 &  &  \tabularnewline
Quadratic Mean & 126.203710986114 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 119.433333333333 & 5.30211644484794 & 22.5255960663381 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 119.086666666667 & 5.16623351565043 & 23.0509647513821 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 118.921666666667 & 5.07241130529595 & 23.4447996246882 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 119.201666666667 & 5.02325017551389 & 23.7299880558849 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 119.501666666667 & 4.80339186401096 & 24.8786003827886 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 119.571666666667 & 4.70301327355389 & 25.4244799475785 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 118.276666666667 & 4.37432116875091 & 27.0388620551245 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 118.41 & 4.33930707322105 & 27.2877669180727 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 117.12 & 3.98493618320053 & 29.3906839697328 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 116.203333333333 & 3.75283242686180 & 30.9641678913185 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 114.828333333333 & 3.45521720614198 & 33.2333183364609 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 113.888333333333 & 3.23944098866158 & 35.1567859182976 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 113.498333333333 & 3.15592483035321 & 35.9635730996263 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 112.891666666667 & 3.02400311973603 & 37.3318618389921 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 112.591666666667 & 2.96686816905976 & 37.9496695676735 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 110.485 & 2.55986054638708 & 43.1605542559479 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 109.266666666667 & 2.31759624482975 & 47.1465497540506 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 108.966666666667 & 2.19249060794188 & 49.6999468421691 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 107.89 & 1.81897205092159 & 59.3137205958371 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 105.723333333333 & 1.40625994869885 & 75.1805051627576 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 118.658620689655 & 5.13115935601875 & 23.1251092504993 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 117.828571428571 & 4.91794270832579 & 23.9589150213350 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 117.129629629630 & 4.74451953477488 & 24.6873532232568 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 116.440384615385 & 4.57262351600485 & 25.4646778174119 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 115.612 & 4.37213032649265 & 26.4429445983017 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 114.639583333333 & 4.19162638290852 & 27.3496664208383 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 113.567391304348 & 3.98654628089747 & 28.4876640837043 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 112.65 & 3.82584885356402 & 29.4444460070762 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 111.621428571429 & 3.61710919494513 & 30.8592919250041 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 110.705 & 3.44851129158730 & 32.1022582324340 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 109.836842105263 & 3.28921125553479 & 33.3930640424630 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 109.080555555556 & 3.16174007607235 & 34.5001653934375 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 108.373529411765 & 3.04702686340337 & 35.5669753730747 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 107.634375 & 2.90430926138838 & 37.0602319907717 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 106.883333333333 & 2.73705136809138 & 39.0505397813802 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 106.067857142857 & 2.50020133354073 & 42.4237263295297 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 105.430769230769 & 2.31635502281407 & 45.5158074614506 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 104.866666666667 & 2.13437757504389 & 49.1322003626796 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 104.245454545455 & 1.88665543041253 & 55.2541035660448 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 103.67 & 1.67489355514093 & 61.8964707827518 \tabularnewline
Median & 102.15 &  &  \tabularnewline
Midrange & 142.1 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 106.364516129032 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 106.364516129032 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 106.364516129032 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 106.364516129032 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 106.364516129032 &  &  \tabularnewline
Midmean - Closest Observation & 106.364516129032 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 106.364516129032 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 107.634375 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=17920&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]119.44[/C][C]5.30663650163189[/C][C]22.5076656302481[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]113.376163932583[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]108.212337537993[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]126.203710986114[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]119.433333333333[/C][C]5.30211644484794[/C][C]22.5255960663381[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]119.086666666667[/C][C]5.16623351565043[/C][C]23.0509647513821[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]118.921666666667[/C][C]5.07241130529595[/C][C]23.4447996246882[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]119.201666666667[/C][C]5.02325017551389[/C][C]23.7299880558849[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]119.501666666667[/C][C]4.80339186401096[/C][C]24.8786003827886[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]119.571666666667[/C][C]4.70301327355389[/C][C]25.4244799475785[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]118.276666666667[/C][C]4.37432116875091[/C][C]27.0388620551245[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]118.41[/C][C]4.33930707322105[/C][C]27.2877669180727[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]117.12[/C][C]3.98493618320053[/C][C]29.3906839697328[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]116.203333333333[/C][C]3.75283242686180[/C][C]30.9641678913185[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]114.828333333333[/C][C]3.45521720614198[/C][C]33.2333183364609[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]113.888333333333[/C][C]3.23944098866158[/C][C]35.1567859182976[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]113.498333333333[/C][C]3.15592483035321[/C][C]35.9635730996263[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]112.891666666667[/C][C]3.02400311973603[/C][C]37.3318618389921[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]112.591666666667[/C][C]2.96686816905976[/C][C]37.9496695676735[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]110.485[/C][C]2.55986054638708[/C][C]43.1605542559479[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]109.266666666667[/C][C]2.31759624482975[/C][C]47.1465497540506[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]108.966666666667[/C][C]2.19249060794188[/C][C]49.6999468421691[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]107.89[/C][C]1.81897205092159[/C][C]59.3137205958371[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]105.723333333333[/C][C]1.40625994869885[/C][C]75.1805051627576[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]118.658620689655[/C][C]5.13115935601875[/C][C]23.1251092504993[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]117.828571428571[/C][C]4.91794270832579[/C][C]23.9589150213350[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]117.129629629630[/C][C]4.74451953477488[/C][C]24.6873532232568[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]116.440384615385[/C][C]4.57262351600485[/C][C]25.4646778174119[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]115.612[/C][C]4.37213032649265[/C][C]26.4429445983017[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]114.639583333333[/C][C]4.19162638290852[/C][C]27.3496664208383[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]113.567391304348[/C][C]3.98654628089747[/C][C]28.4876640837043[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]112.65[/C][C]3.82584885356402[/C][C]29.4444460070762[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]111.621428571429[/C][C]3.61710919494513[/C][C]30.8592919250041[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]110.705[/C][C]3.44851129158730[/C][C]32.1022582324340[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]109.836842105263[/C][C]3.28921125553479[/C][C]33.3930640424630[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]109.080555555556[/C][C]3.16174007607235[/C][C]34.5001653934375[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]108.373529411765[/C][C]3.04702686340337[/C][C]35.5669753730747[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]107.634375[/C][C]2.90430926138838[/C][C]37.0602319907717[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]106.883333333333[/C][C]2.73705136809138[/C][C]39.0505397813802[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]106.067857142857[/C][C]2.50020133354073[/C][C]42.4237263295297[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]105.430769230769[/C][C]2.31635502281407[/C][C]45.5158074614506[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]104.866666666667[/C][C]2.13437757504389[/C][C]49.1322003626796[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]104.245454545455[/C][C]1.88665543041253[/C][C]55.2541035660448[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]103.67[/C][C]1.67489355514093[/C][C]61.8964707827518[/C][/ROW]
[ROW][C]Median[/C][C]102.15[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]142.1[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]106.364516129032[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]106.364516129032[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]106.364516129032[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]106.364516129032[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]106.364516129032[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]106.364516129032[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]106.364516129032[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]107.634375[/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=17920&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=17920&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 Mean119.445.3066365016318922.5076656302481
Geometric Mean113.376163932583
Harmonic Mean108.212337537993
Quadratic Mean126.203710986114
Winsorized Mean ( 1 / 20 )119.4333333333335.3021164448479422.5255960663381
Winsorized Mean ( 2 / 20 )119.0866666666675.1662335156504323.0509647513821
Winsorized Mean ( 3 / 20 )118.9216666666675.0724113052959523.4447996246882
Winsorized Mean ( 4 / 20 )119.2016666666675.0232501755138923.7299880558849
Winsorized Mean ( 5 / 20 )119.5016666666674.8033918640109624.8786003827886
Winsorized Mean ( 6 / 20 )119.5716666666674.7030132735538925.4244799475785
Winsorized Mean ( 7 / 20 )118.2766666666674.3743211687509127.0388620551245
Winsorized Mean ( 8 / 20 )118.414.3393070732210527.2877669180727
Winsorized Mean ( 9 / 20 )117.123.9849361832005329.3906839697328
Winsorized Mean ( 10 / 20 )116.2033333333333.7528324268618030.9641678913185
Winsorized Mean ( 11 / 20 )114.8283333333333.4552172061419833.2333183364609
Winsorized Mean ( 12 / 20 )113.8883333333333.2394409886615835.1567859182976
Winsorized Mean ( 13 / 20 )113.4983333333333.1559248303532135.9635730996263
Winsorized Mean ( 14 / 20 )112.8916666666673.0240031197360337.3318618389921
Winsorized Mean ( 15 / 20 )112.5916666666672.9668681690597637.9496695676735
Winsorized Mean ( 16 / 20 )110.4852.5598605463870843.1605542559479
Winsorized Mean ( 17 / 20 )109.2666666666672.3175962448297547.1465497540506
Winsorized Mean ( 18 / 20 )108.9666666666672.1924906079418849.6999468421691
Winsorized Mean ( 19 / 20 )107.891.8189720509215959.3137205958371
Winsorized Mean ( 20 / 20 )105.7233333333331.4062599486988575.1805051627576
Trimmed Mean ( 1 / 20 )118.6586206896555.1311593560187523.1251092504993
Trimmed Mean ( 2 / 20 )117.8285714285714.9179427083257923.9589150213350
Trimmed Mean ( 3 / 20 )117.1296296296304.7445195347748824.6873532232568
Trimmed Mean ( 4 / 20 )116.4403846153854.5726235160048525.4646778174119
Trimmed Mean ( 5 / 20 )115.6124.3721303264926526.4429445983017
Trimmed Mean ( 6 / 20 )114.6395833333334.1916263829085227.3496664208383
Trimmed Mean ( 7 / 20 )113.5673913043483.9865462808974728.4876640837043
Trimmed Mean ( 8 / 20 )112.653.8258488535640229.4444460070762
Trimmed Mean ( 9 / 20 )111.6214285714293.6171091949451330.8592919250041
Trimmed Mean ( 10 / 20 )110.7053.4485112915873032.1022582324340
Trimmed Mean ( 11 / 20 )109.8368421052633.2892112555347933.3930640424630
Trimmed Mean ( 12 / 20 )109.0805555555563.1617400760723534.5001653934375
Trimmed Mean ( 13 / 20 )108.3735294117653.0470268634033735.5669753730747
Trimmed Mean ( 14 / 20 )107.6343752.9043092613883837.0602319907717
Trimmed Mean ( 15 / 20 )106.8833333333332.7370513680913839.0505397813802
Trimmed Mean ( 16 / 20 )106.0678571428572.5002013335407342.4237263295297
Trimmed Mean ( 17 / 20 )105.4307692307692.3163550228140745.5158074614506
Trimmed Mean ( 18 / 20 )104.8666666666672.1343775750438949.1322003626796
Trimmed Mean ( 19 / 20 )104.2454545454551.8866554304125355.2541035660448
Trimmed Mean ( 20 / 20 )103.671.6748935551409361.8964707827518
Median102.15
Midrange142.1
Midmean - Weighted Average at Xnp106.364516129032
Midmean - Weighted Average at X(n+1)p106.364516129032
Midmean - Empirical Distribution Function106.364516129032
Midmean - Empirical Distribution Function - Averaging106.364516129032
Midmean - Empirical Distribution Function - Interpolation106.364516129032
Midmean - Closest Observation106.364516129032
Midmean - True Basic - Statistics Graphics Toolkit106.364516129032
Midmean - MS Excel (old versions)107.634375
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')