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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationSun, 19 Oct 2008 08:59:40 -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/19/t1224428458bpv7ozoskj4i3ub.htm/, Retrieved Sat, 18 May 2024 23:41:01 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=16894, Retrieved Sat, 18 May 2024 23:41:01 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact190
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Central Tendency] [Investigating Ass...] [2007-10-22 10:34:53] [b9964c45117f7aac638ab9056d451faa]
F    D    [Central Tendency] [Task 3 - Q9 - Inb...] [2008-10-19 14:59:40] [dafd615cb3e0decc017580d68ecea30a] [Current]
Feedback Forum
2008-10-24 15:57:39 [Bob Leysen] [reply
Goede grafiek. Er is duidelijk een dalend verloop die op het einde eerder constant blijft
2008-10-26 13:25:44 [Stijn Van de Velde] [reply
De 2 grafieken kennen een gelijkaardig verloop. Je kan zien dat ze in het begin stijl verkopen, waarna ze zich tegen het einde stabiliseren.
Hieruit vallen 2 dingen af te leiden.

1) Er zijn ouliers aanwezig, daardoor verlopen de grafiek in het begin stijl, want de outliers zijn de eerste waarde die wegvallen. (dit word tevens bevestigd doordat mediaan, gemiddelde en midrange sterk van elkaar verschillen)
2) De inbreng in natura bij kapitaalsverhoging zal in de toekomst gelijkaardig blijven. (want de 2 grafieken zijn om het einde constant).
2008-10-27 08:33:08 [Jeroen Michel] [reply
In dit geval is de correcte methode gebruikt en kan ik vaststellen dat beide grafieken een gelijkaardig verloop kennen. Er zijn inderdaad outliers aanwezig die de grafieken beïnvloeden. Anderzijds is vast te stellen dat in de toekomst het verloop constant blijft.
2008-10-27 18:24:59 [Jens Peeters] [reply
Zoals Jeroen zelf aanhaalt, zijn er enkele outliers die de grafieken beïnvloeden. En een zekerheid is het niet dat in de toekomst het verloop constant blijft. Er zijn altijd onverwachte omstandigheden.

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Dataseries X:
878
346
321
116
182
189
243
270
122
138
35
456
3929
262
236
222
2010
566
122
43
477
1048
307
687
186
248
78
135
7
90
280
20
223
29
175
93
83
28
57
40
51
42
78
83
25
587
241
79




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=16894&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]1 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=16894&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=16894&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 time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean336.72916666666790.86100531506713.70598108065208
Geometric Mean153.516944975718
Harmonic Mean74.4665900022331
Quadratic Mean708.09990761662
Winsorized Mean ( 1 / 16 )297.02083333333361.15121567645764.85715337050417
Winsorized Mean ( 2 / 16 )257.14583333333340.02315364441946.42492682155716
Winsorized Mean ( 3 / 16 )246.70833333333335.75693602225686.89959377894601
Winsorized Mean ( 4 / 16 )230.87530.15885284857247.65529780456914
Winsorized Mean ( 5 / 16 )221.08333333333326.87391484421978.2266887654772
Winsorized Mean ( 6 / 16 )219.08333333333326.02957662617788.4167075200525
Winsorized Mean ( 7 / 16 )206.39583333333322.46947771330329.1856088497836
Winsorized Mean ( 8 / 16 )203.062521.55782275307139.4194345285203
Winsorized Mean ( 9 / 16 )183.937516.531010142181911.1268155072175
Winsorized Mean ( 10 / 16 )179.97916666666715.260460009499611.7938231583209
Winsorized Mean ( 11 / 16 )181.58333333333313.838187006315113.1219019695620
Winsorized Mean ( 12 / 16 )174.83333333333312.584900799465513.8923092139716
Winsorized Mean ( 13 / 16 )172.39583333333312.066443548714014.2872116906150
Winsorized Mean ( 14 / 16 )171.22916666666711.47774749564914.9183597854524
Winsorized Mean ( 15 / 16 )166.85416666666710.758057741442115.509692425605
Winsorized Mean ( 16 / 16 )167.52083333333310.107927756534716.5732123703628
Trimmed Mean ( 1 / 16 )265.80434782608750.98253579512955.21363529060632
Trimmed Mean ( 2 / 16 )231.7534.30615679862376.75534719206138
Trimmed Mean ( 3 / 16 )217.23809523809529.60113884717487.33884248034021
Trimmed Mean ( 4 / 16 )205.4525.70652790485487.99213338963602
Trimmed Mean ( 5 / 16 )197.42105263157923.33218070786708.46132022991805
Trimmed Mean ( 6 / 16 )191.11111111111121.56252546454558.86311352653699
Trimmed Mean ( 7 / 16 )184.52941176470619.37017366920749.5264717248277
Trimmed Mean ( 8 / 16 )179.8437517.803310978703810.1017024426034
Trimmed Mean ( 9 / 16 )175.215.858091955206011.0479873931166
Trimmed Mean ( 10 / 16 )173.53571428571415.175819856417511.4350141163760
Trimmed Mean ( 11 / 16 )172.34615384615414.610211635143011.7962804475465
Trimmed Mean ( 12 / 16 )170.66666666666714.221802341326112.0003542849656
Trimmed Mean ( 13 / 16 )169.90909090909114.041822055107812.1002167839953
Trimmed Mean ( 14 / 16 )169.4513.841865367142712.2418471431050
Trimmed Mean ( 15 / 16 )169.11111111111113.620171720839512.4162245951982
Trimmed Mean ( 16 / 16 )169.562513.404591486377612.6495835529429
Median178.5
Midrange1968
Midmean - Weighted Average at Xnp166.96
Midmean - Weighted Average at X(n+1)p166.96
Midmean - Empirical Distribution Function166.96
Midmean - Empirical Distribution Function - Averaging166.96
Midmean - Empirical Distribution Function - Interpolation166.96
Midmean - Closest Observation166.96
Midmean - True Basic - Statistics Graphics Toolkit166.96
Midmean - MS Excel (old versions)172.346153846154
Number of observations48

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 336.729166666667 & 90.8610053150671 & 3.70598108065208 \tabularnewline
Geometric Mean & 153.516944975718 &  &  \tabularnewline
Harmonic Mean & 74.4665900022331 &  &  \tabularnewline
Quadratic Mean & 708.09990761662 &  &  \tabularnewline
Winsorized Mean ( 1 / 16 ) & 297.020833333333 & 61.1512156764576 & 4.85715337050417 \tabularnewline
Winsorized Mean ( 2 / 16 ) & 257.145833333333 & 40.0231536444194 & 6.42492682155716 \tabularnewline
Winsorized Mean ( 3 / 16 ) & 246.708333333333 & 35.7569360222568 & 6.89959377894601 \tabularnewline
Winsorized Mean ( 4 / 16 ) & 230.875 & 30.1588528485724 & 7.65529780456914 \tabularnewline
Winsorized Mean ( 5 / 16 ) & 221.083333333333 & 26.8739148442197 & 8.2266887654772 \tabularnewline
Winsorized Mean ( 6 / 16 ) & 219.083333333333 & 26.0295766261778 & 8.4167075200525 \tabularnewline
Winsorized Mean ( 7 / 16 ) & 206.395833333333 & 22.4694777133032 & 9.1856088497836 \tabularnewline
Winsorized Mean ( 8 / 16 ) & 203.0625 & 21.5578227530713 & 9.4194345285203 \tabularnewline
Winsorized Mean ( 9 / 16 ) & 183.9375 & 16.5310101421819 & 11.1268155072175 \tabularnewline
Winsorized Mean ( 10 / 16 ) & 179.979166666667 & 15.2604600094996 & 11.7938231583209 \tabularnewline
Winsorized Mean ( 11 / 16 ) & 181.583333333333 & 13.8381870063151 & 13.1219019695620 \tabularnewline
Winsorized Mean ( 12 / 16 ) & 174.833333333333 & 12.5849007994655 & 13.8923092139716 \tabularnewline
Winsorized Mean ( 13 / 16 ) & 172.395833333333 & 12.0664435487140 & 14.2872116906150 \tabularnewline
Winsorized Mean ( 14 / 16 ) & 171.229166666667 & 11.477747495649 & 14.9183597854524 \tabularnewline
Winsorized Mean ( 15 / 16 ) & 166.854166666667 & 10.7580577414421 & 15.509692425605 \tabularnewline
Winsorized Mean ( 16 / 16 ) & 167.520833333333 & 10.1079277565347 & 16.5732123703628 \tabularnewline
Trimmed Mean ( 1 / 16 ) & 265.804347826087 & 50.9825357951295 & 5.21363529060632 \tabularnewline
Trimmed Mean ( 2 / 16 ) & 231.75 & 34.3061567986237 & 6.75534719206138 \tabularnewline
Trimmed Mean ( 3 / 16 ) & 217.238095238095 & 29.6011388471748 & 7.33884248034021 \tabularnewline
Trimmed Mean ( 4 / 16 ) & 205.45 & 25.7065279048548 & 7.99213338963602 \tabularnewline
Trimmed Mean ( 5 / 16 ) & 197.421052631579 & 23.3321807078670 & 8.46132022991805 \tabularnewline
Trimmed Mean ( 6 / 16 ) & 191.111111111111 & 21.5625254645455 & 8.86311352653699 \tabularnewline
Trimmed Mean ( 7 / 16 ) & 184.529411764706 & 19.3701736692074 & 9.5264717248277 \tabularnewline
Trimmed Mean ( 8 / 16 ) & 179.84375 & 17.8033109787038 & 10.1017024426034 \tabularnewline
Trimmed Mean ( 9 / 16 ) & 175.2 & 15.8580919552060 & 11.0479873931166 \tabularnewline
Trimmed Mean ( 10 / 16 ) & 173.535714285714 & 15.1758198564175 & 11.4350141163760 \tabularnewline
Trimmed Mean ( 11 / 16 ) & 172.346153846154 & 14.6102116351430 & 11.7962804475465 \tabularnewline
Trimmed Mean ( 12 / 16 ) & 170.666666666667 & 14.2218023413261 & 12.0003542849656 \tabularnewline
Trimmed Mean ( 13 / 16 ) & 169.909090909091 & 14.0418220551078 & 12.1002167839953 \tabularnewline
Trimmed Mean ( 14 / 16 ) & 169.45 & 13.8418653671427 & 12.2418471431050 \tabularnewline
Trimmed Mean ( 15 / 16 ) & 169.111111111111 & 13.6201717208395 & 12.4162245951982 \tabularnewline
Trimmed Mean ( 16 / 16 ) & 169.5625 & 13.4045914863776 & 12.6495835529429 \tabularnewline
Median & 178.5 &  &  \tabularnewline
Midrange & 1968 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 166.96 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 166.96 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 166.96 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 166.96 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 166.96 &  &  \tabularnewline
Midmean - Closest Observation & 166.96 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 166.96 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 172.346153846154 &  &  \tabularnewline
Number of observations & 48 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=16894&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]336.729166666667[/C][C]90.8610053150671[/C][C]3.70598108065208[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]153.516944975718[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]74.4665900022331[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]708.09990761662[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 16 )[/C][C]297.020833333333[/C][C]61.1512156764576[/C][C]4.85715337050417[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 16 )[/C][C]257.145833333333[/C][C]40.0231536444194[/C][C]6.42492682155716[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 16 )[/C][C]246.708333333333[/C][C]35.7569360222568[/C][C]6.89959377894601[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 16 )[/C][C]230.875[/C][C]30.1588528485724[/C][C]7.65529780456914[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 16 )[/C][C]221.083333333333[/C][C]26.8739148442197[/C][C]8.2266887654772[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 16 )[/C][C]219.083333333333[/C][C]26.0295766261778[/C][C]8.4167075200525[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 16 )[/C][C]206.395833333333[/C][C]22.4694777133032[/C][C]9.1856088497836[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 16 )[/C][C]203.0625[/C][C]21.5578227530713[/C][C]9.4194345285203[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 16 )[/C][C]183.9375[/C][C]16.5310101421819[/C][C]11.1268155072175[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 16 )[/C][C]179.979166666667[/C][C]15.2604600094996[/C][C]11.7938231583209[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 16 )[/C][C]181.583333333333[/C][C]13.8381870063151[/C][C]13.1219019695620[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 16 )[/C][C]174.833333333333[/C][C]12.5849007994655[/C][C]13.8923092139716[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 16 )[/C][C]172.395833333333[/C][C]12.0664435487140[/C][C]14.2872116906150[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 16 )[/C][C]171.229166666667[/C][C]11.477747495649[/C][C]14.9183597854524[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 16 )[/C][C]166.854166666667[/C][C]10.7580577414421[/C][C]15.509692425605[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 16 )[/C][C]167.520833333333[/C][C]10.1079277565347[/C][C]16.5732123703628[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 16 )[/C][C]265.804347826087[/C][C]50.9825357951295[/C][C]5.21363529060632[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 16 )[/C][C]231.75[/C][C]34.3061567986237[/C][C]6.75534719206138[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 16 )[/C][C]217.238095238095[/C][C]29.6011388471748[/C][C]7.33884248034021[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 16 )[/C][C]205.45[/C][C]25.7065279048548[/C][C]7.99213338963602[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 16 )[/C][C]197.421052631579[/C][C]23.3321807078670[/C][C]8.46132022991805[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 16 )[/C][C]191.111111111111[/C][C]21.5625254645455[/C][C]8.86311352653699[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 16 )[/C][C]184.529411764706[/C][C]19.3701736692074[/C][C]9.5264717248277[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 16 )[/C][C]179.84375[/C][C]17.8033109787038[/C][C]10.1017024426034[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 16 )[/C][C]175.2[/C][C]15.8580919552060[/C][C]11.0479873931166[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 16 )[/C][C]173.535714285714[/C][C]15.1758198564175[/C][C]11.4350141163760[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 16 )[/C][C]172.346153846154[/C][C]14.6102116351430[/C][C]11.7962804475465[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 16 )[/C][C]170.666666666667[/C][C]14.2218023413261[/C][C]12.0003542849656[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 16 )[/C][C]169.909090909091[/C][C]14.0418220551078[/C][C]12.1002167839953[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 16 )[/C][C]169.45[/C][C]13.8418653671427[/C][C]12.2418471431050[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 16 )[/C][C]169.111111111111[/C][C]13.6201717208395[/C][C]12.4162245951982[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 16 )[/C][C]169.5625[/C][C]13.4045914863776[/C][C]12.6495835529429[/C][/ROW]
[ROW][C]Median[/C][C]178.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]1968[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]166.96[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]166.96[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]166.96[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]166.96[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]166.96[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]166.96[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]166.96[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]172.346153846154[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]48[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=16894&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=16894&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 Mean336.72916666666790.86100531506713.70598108065208
Geometric Mean153.516944975718
Harmonic Mean74.4665900022331
Quadratic Mean708.09990761662
Winsorized Mean ( 1 / 16 )297.02083333333361.15121567645764.85715337050417
Winsorized Mean ( 2 / 16 )257.14583333333340.02315364441946.42492682155716
Winsorized Mean ( 3 / 16 )246.70833333333335.75693602225686.89959377894601
Winsorized Mean ( 4 / 16 )230.87530.15885284857247.65529780456914
Winsorized Mean ( 5 / 16 )221.08333333333326.87391484421978.2266887654772
Winsorized Mean ( 6 / 16 )219.08333333333326.02957662617788.4167075200525
Winsorized Mean ( 7 / 16 )206.39583333333322.46947771330329.1856088497836
Winsorized Mean ( 8 / 16 )203.062521.55782275307139.4194345285203
Winsorized Mean ( 9 / 16 )183.937516.531010142181911.1268155072175
Winsorized Mean ( 10 / 16 )179.97916666666715.260460009499611.7938231583209
Winsorized Mean ( 11 / 16 )181.58333333333313.838187006315113.1219019695620
Winsorized Mean ( 12 / 16 )174.83333333333312.584900799465513.8923092139716
Winsorized Mean ( 13 / 16 )172.39583333333312.066443548714014.2872116906150
Winsorized Mean ( 14 / 16 )171.22916666666711.47774749564914.9183597854524
Winsorized Mean ( 15 / 16 )166.85416666666710.758057741442115.509692425605
Winsorized Mean ( 16 / 16 )167.52083333333310.107927756534716.5732123703628
Trimmed Mean ( 1 / 16 )265.80434782608750.98253579512955.21363529060632
Trimmed Mean ( 2 / 16 )231.7534.30615679862376.75534719206138
Trimmed Mean ( 3 / 16 )217.23809523809529.60113884717487.33884248034021
Trimmed Mean ( 4 / 16 )205.4525.70652790485487.99213338963602
Trimmed Mean ( 5 / 16 )197.42105263157923.33218070786708.46132022991805
Trimmed Mean ( 6 / 16 )191.11111111111121.56252546454558.86311352653699
Trimmed Mean ( 7 / 16 )184.52941176470619.37017366920749.5264717248277
Trimmed Mean ( 8 / 16 )179.8437517.803310978703810.1017024426034
Trimmed Mean ( 9 / 16 )175.215.858091955206011.0479873931166
Trimmed Mean ( 10 / 16 )173.53571428571415.175819856417511.4350141163760
Trimmed Mean ( 11 / 16 )172.34615384615414.610211635143011.7962804475465
Trimmed Mean ( 12 / 16 )170.66666666666714.221802341326112.0003542849656
Trimmed Mean ( 13 / 16 )169.90909090909114.041822055107812.1002167839953
Trimmed Mean ( 14 / 16 )169.4513.841865367142712.2418471431050
Trimmed Mean ( 15 / 16 )169.11111111111113.620171720839512.4162245951982
Trimmed Mean ( 16 / 16 )169.562513.404591486377612.6495835529429
Median178.5
Midrange1968
Midmean - Weighted Average at Xnp166.96
Midmean - Weighted Average at X(n+1)p166.96
Midmean - Empirical Distribution Function166.96
Midmean - Empirical Distribution Function - Averaging166.96
Midmean - Empirical Distribution Function - Interpolation166.96
Midmean - Closest Observation166.96
Midmean - True Basic - Statistics Graphics Toolkit166.96
Midmean - MS Excel (old versions)172.346153846154
Number of observations48



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')