Free Statistics

of Irreproducible Research!

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationFri, 24 Dec 2010 11:08:42 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Dec/24/t1293188794liht8y7bh51xg9w.htm/, Retrieved Tue, 30 Apr 2024 07:06:37 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=114762, Retrieved Tue, 30 Apr 2024 07:06:37 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact130
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Central Tendency] [] [2009-12-13 10:46:37] [ebd107afac1bd6180acb277edd05815b]
-    D    [Central Tendency] [CT invoer] [2010-12-24 11:08:42] [817f44ab92560f82acbc5e6c80d9a294] [Current]
Feedback Forum

Post a new message
Dataseries X:
19437,5
18885,1
16579,0
17203,6
19165,7
17107,6
17690,5
18664,9
15878,6
16014,6
16842,6
15986,9
16773,3
16263,1
13597,3
14285,6
15496,8
13916,8
14345,5
15761,3
14531,6
15076,6
15816,8
17180,4
20432,3
21289,5
18203,6
20159,5
21053,2
19673,6
21473,3
20244,7
19049,6
20194,3
18021,9
19537,3
20286,6
17967,7
16409,9
17802,7
18509,9
18161,3
16721,3
19106,9
16772,1
17463,6
16162,3
17862,9
17664,9
17180,8
15672,7
15189,8
17699,4
17444,6
15930,7
19691,6
16698,0
16896,2
17972,4
17637,4
15214,0




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=114762&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=114762&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=114762&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 Mean17474.6590163934243.91328546677671.6429159770951
Geometric Mean17372.4109453813
Harmonic Mean17270.0968745963
Quadratic Mean17576.4993439778
Winsorized Mean ( 1 / 20 )17476.8836065574241.76883259900572.287579084043
Winsorized Mean ( 2 / 20 )17481.2278688525236.93279527352673.7813769034014
Winsorized Mean ( 3 / 20 )17453.6377049180229.11525821591276.178417102497
Winsorized Mean ( 4 / 20 )17456.2868852459224.36979634254477.8014116418571
Winsorized Mean ( 5 / 20 )17497.5245901639214.57527819977881.544923240752
Winsorized Mean ( 6 / 20 )17503.7016393443211.45828322312482.7761455949914
Winsorized Mean ( 7 / 20 )17502.4852459016210.10869773165583.302050009635
Winsorized Mean ( 8 / 20 )17478.2098360656191.11552243713891.4536381617799
Winsorized Mean ( 9 / 20 )17501.5065573770186.23360760178793.9760915484148
Winsorized Mean ( 10 / 20 )17493.6868852459179.58543313684397.4115025906127
Winsorized Mean ( 11 / 20 )17485.6983606557174.600046296162100.147157641619
Winsorized Mean ( 12 / 20 )17444.3868852459162.961552263898107.046027991908
Winsorized Mean ( 13 / 20 )17442.9590163934158.996359022426109.706656955164
Winsorized Mean ( 14 / 20 )17442.7065573770154.676716466214112.768792588036
Winsorized Mean ( 15 / 20 )17409.0672131148146.706721860023118.665777493994
Winsorized Mean ( 16 / 20 )17390.0508196721131.078901271697132.668573286455
Winsorized Mean ( 17 / 20 )17374.9459016393119.797162600246145.036372519257
Winsorized Mean ( 18 / 20 )17327.880327868999.2825583771978174.530961037851
Winsorized Mean ( 19 / 20 )17367.375409836189.4006655962233194.264497853691
Winsorized Mean ( 20 / 20 )17360.686885245977.0742686848748225.246209681556
Trimmed Mean ( 1 / 20 )17472.6033898305233.59289146277874.799379726051
Trimmed Mean ( 2 / 20 )17468.0228070175223.54372993184078.1414124759558
Trimmed Mean ( 3 / 20 )17460.7214.40209188197581.4390374960139
Trimmed Mean ( 4 / 20 )17463.4094339623206.91112132552784.4005354670503
Trimmed Mean ( 5 / 20 )17465.5392156863199.43480310821287.5751821822674
Trimmed Mean ( 6 / 20 )17457.5755102041193.41897980216290.2578202411184
Trimmed Mean ( 7 / 20 )17447.5978723404186.69095598878293.457113548601
Trimmed Mean ( 8 / 20 )17436.9688888889178.38336697788297.749970663189
Trimmed Mean ( 9 / 20 )17429.6558139535173.164991298885100.653461668067
Trimmed Mean ( 10 / 20 )17417.7780487805167.526770140069103.970117935286
Trimmed Mean ( 11 / 20 )17405.9051282051161.774005114394107.593955629009
Trimmed Mean ( 12 / 20 )17393.9459459459155.304707594844111.998832587373
Trimmed Mean ( 13 / 20 )17386.62149.761657522430116.095269561209
Trimmed Mean ( 14 / 20 )17378.6090909091143.048503267913121.487528313114
Trimmed Mean ( 15 / 20 )17369.6134.712814247868128.937993738594
Trimmed Mean ( 16 / 20 )17364.0655172414125.275857313027138.606638898138
Trimmed Mean ( 17 / 20 )17360.3962962963116.982397010399148.401783002900
Trimmed Mean ( 18 / 20 )17358.308108.637467895136159.781964144777
Trimmed Mean ( 19 / 20 )17362.7913043478103.942073582331167.042956773371
Trimmed Mean ( 20 / 20 )17362.0904761905100.176579789500173.314865736815
Median17444.6
Midrange17535.3
Midmean - Weighted Average at Xnp17319.0833333333
Midmean - Weighted Average at X(n+1)p17369.6
Midmean - Empirical Distribution Function17369.6
Midmean - Empirical Distribution Function - Averaging17369.6
Midmean - Empirical Distribution Function - Interpolation17369.6
Midmean - Closest Observation17326.390625
Midmean - True Basic - Statistics Graphics Toolkit17369.6
Midmean - MS Excel (old versions)17369.6
Number of observations61

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 17474.6590163934 & 243.913285466776 & 71.6429159770951 \tabularnewline
Geometric Mean & 17372.4109453813 &  &  \tabularnewline
Harmonic Mean & 17270.0968745963 &  &  \tabularnewline
Quadratic Mean & 17576.4993439778 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 17476.8836065574 & 241.768832599005 & 72.287579084043 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 17481.2278688525 & 236.932795273526 & 73.7813769034014 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 17453.6377049180 & 229.115258215912 & 76.178417102497 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 17456.2868852459 & 224.369796342544 & 77.8014116418571 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 17497.5245901639 & 214.575278199778 & 81.544923240752 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 17503.7016393443 & 211.458283223124 & 82.7761455949914 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 17502.4852459016 & 210.108697731655 & 83.302050009635 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 17478.2098360656 & 191.115522437138 & 91.4536381617799 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 17501.5065573770 & 186.233607601787 & 93.9760915484148 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 17493.6868852459 & 179.585433136843 & 97.4115025906127 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 17485.6983606557 & 174.600046296162 & 100.147157641619 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 17444.3868852459 & 162.961552263898 & 107.046027991908 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 17442.9590163934 & 158.996359022426 & 109.706656955164 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 17442.7065573770 & 154.676716466214 & 112.768792588036 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 17409.0672131148 & 146.706721860023 & 118.665777493994 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 17390.0508196721 & 131.078901271697 & 132.668573286455 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 17374.9459016393 & 119.797162600246 & 145.036372519257 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 17327.8803278689 & 99.2825583771978 & 174.530961037851 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 17367.3754098361 & 89.4006655962233 & 194.264497853691 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 17360.6868852459 & 77.0742686848748 & 225.246209681556 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 17472.6033898305 & 233.592891462778 & 74.799379726051 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 17468.0228070175 & 223.543729931840 & 78.1414124759558 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 17460.7 & 214.402091881975 & 81.4390374960139 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 17463.4094339623 & 206.911121325527 & 84.4005354670503 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 17465.5392156863 & 199.434803108212 & 87.5751821822674 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 17457.5755102041 & 193.418979802162 & 90.2578202411184 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 17447.5978723404 & 186.690955988782 & 93.457113548601 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 17436.9688888889 & 178.383366977882 & 97.749970663189 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 17429.6558139535 & 173.164991298885 & 100.653461668067 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 17417.7780487805 & 167.526770140069 & 103.970117935286 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 17405.9051282051 & 161.774005114394 & 107.593955629009 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 17393.9459459459 & 155.304707594844 & 111.998832587373 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 17386.62 & 149.761657522430 & 116.095269561209 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 17378.6090909091 & 143.048503267913 & 121.487528313114 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 17369.6 & 134.712814247868 & 128.937993738594 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 17364.0655172414 & 125.275857313027 & 138.606638898138 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 17360.3962962963 & 116.982397010399 & 148.401783002900 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 17358.308 & 108.637467895136 & 159.781964144777 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 17362.7913043478 & 103.942073582331 & 167.042956773371 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 17362.0904761905 & 100.176579789500 & 173.314865736815 \tabularnewline
Median & 17444.6 &  &  \tabularnewline
Midrange & 17535.3 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 17319.0833333333 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 17369.6 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 17369.6 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 17369.6 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 17369.6 &  &  \tabularnewline
Midmean - Closest Observation & 17326.390625 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 17369.6 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 17369.6 &  &  \tabularnewline
Number of observations & 61 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=114762&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]17474.6590163934[/C][C]243.913285466776[/C][C]71.6429159770951[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]17372.4109453813[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]17270.0968745963[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]17576.4993439778[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]17476.8836065574[/C][C]241.768832599005[/C][C]72.287579084043[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]17481.2278688525[/C][C]236.932795273526[/C][C]73.7813769034014[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]17453.6377049180[/C][C]229.115258215912[/C][C]76.178417102497[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]17456.2868852459[/C][C]224.369796342544[/C][C]77.8014116418571[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]17497.5245901639[/C][C]214.575278199778[/C][C]81.544923240752[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]17503.7016393443[/C][C]211.458283223124[/C][C]82.7761455949914[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]17502.4852459016[/C][C]210.108697731655[/C][C]83.302050009635[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]17478.2098360656[/C][C]191.115522437138[/C][C]91.4536381617799[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]17501.5065573770[/C][C]186.233607601787[/C][C]93.9760915484148[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]17493.6868852459[/C][C]179.585433136843[/C][C]97.4115025906127[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]17485.6983606557[/C][C]174.600046296162[/C][C]100.147157641619[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]17444.3868852459[/C][C]162.961552263898[/C][C]107.046027991908[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]17442.9590163934[/C][C]158.996359022426[/C][C]109.706656955164[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]17442.7065573770[/C][C]154.676716466214[/C][C]112.768792588036[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]17409.0672131148[/C][C]146.706721860023[/C][C]118.665777493994[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]17390.0508196721[/C][C]131.078901271697[/C][C]132.668573286455[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]17374.9459016393[/C][C]119.797162600246[/C][C]145.036372519257[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]17327.8803278689[/C][C]99.2825583771978[/C][C]174.530961037851[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]17367.3754098361[/C][C]89.4006655962233[/C][C]194.264497853691[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]17360.6868852459[/C][C]77.0742686848748[/C][C]225.246209681556[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]17472.6033898305[/C][C]233.592891462778[/C][C]74.799379726051[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]17468.0228070175[/C][C]223.543729931840[/C][C]78.1414124759558[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]17460.7[/C][C]214.402091881975[/C][C]81.4390374960139[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]17463.4094339623[/C][C]206.911121325527[/C][C]84.4005354670503[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]17465.5392156863[/C][C]199.434803108212[/C][C]87.5751821822674[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]17457.5755102041[/C][C]193.418979802162[/C][C]90.2578202411184[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]17447.5978723404[/C][C]186.690955988782[/C][C]93.457113548601[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]17436.9688888889[/C][C]178.383366977882[/C][C]97.749970663189[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]17429.6558139535[/C][C]173.164991298885[/C][C]100.653461668067[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]17417.7780487805[/C][C]167.526770140069[/C][C]103.970117935286[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]17405.9051282051[/C][C]161.774005114394[/C][C]107.593955629009[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]17393.9459459459[/C][C]155.304707594844[/C][C]111.998832587373[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]17386.62[/C][C]149.761657522430[/C][C]116.095269561209[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]17378.6090909091[/C][C]143.048503267913[/C][C]121.487528313114[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]17369.6[/C][C]134.712814247868[/C][C]128.937993738594[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]17364.0655172414[/C][C]125.275857313027[/C][C]138.606638898138[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]17360.3962962963[/C][C]116.982397010399[/C][C]148.401783002900[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]17358.308[/C][C]108.637467895136[/C][C]159.781964144777[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]17362.7913043478[/C][C]103.942073582331[/C][C]167.042956773371[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]17362.0904761905[/C][C]100.176579789500[/C][C]173.314865736815[/C][/ROW]
[ROW][C]Median[/C][C]17444.6[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]17535.3[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]17319.0833333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]17369.6[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]17369.6[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]17369.6[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]17369.6[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]17326.390625[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]17369.6[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]17369.6[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]61[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=114762&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=114762&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 Mean17474.6590163934243.91328546677671.6429159770951
Geometric Mean17372.4109453813
Harmonic Mean17270.0968745963
Quadratic Mean17576.4993439778
Winsorized Mean ( 1 / 20 )17476.8836065574241.76883259900572.287579084043
Winsorized Mean ( 2 / 20 )17481.2278688525236.93279527352673.7813769034014
Winsorized Mean ( 3 / 20 )17453.6377049180229.11525821591276.178417102497
Winsorized Mean ( 4 / 20 )17456.2868852459224.36979634254477.8014116418571
Winsorized Mean ( 5 / 20 )17497.5245901639214.57527819977881.544923240752
Winsorized Mean ( 6 / 20 )17503.7016393443211.45828322312482.7761455949914
Winsorized Mean ( 7 / 20 )17502.4852459016210.10869773165583.302050009635
Winsorized Mean ( 8 / 20 )17478.2098360656191.11552243713891.4536381617799
Winsorized Mean ( 9 / 20 )17501.5065573770186.23360760178793.9760915484148
Winsorized Mean ( 10 / 20 )17493.6868852459179.58543313684397.4115025906127
Winsorized Mean ( 11 / 20 )17485.6983606557174.600046296162100.147157641619
Winsorized Mean ( 12 / 20 )17444.3868852459162.961552263898107.046027991908
Winsorized Mean ( 13 / 20 )17442.9590163934158.996359022426109.706656955164
Winsorized Mean ( 14 / 20 )17442.7065573770154.676716466214112.768792588036
Winsorized Mean ( 15 / 20 )17409.0672131148146.706721860023118.665777493994
Winsorized Mean ( 16 / 20 )17390.0508196721131.078901271697132.668573286455
Winsorized Mean ( 17 / 20 )17374.9459016393119.797162600246145.036372519257
Winsorized Mean ( 18 / 20 )17327.880327868999.2825583771978174.530961037851
Winsorized Mean ( 19 / 20 )17367.375409836189.4006655962233194.264497853691
Winsorized Mean ( 20 / 20 )17360.686885245977.0742686848748225.246209681556
Trimmed Mean ( 1 / 20 )17472.6033898305233.59289146277874.799379726051
Trimmed Mean ( 2 / 20 )17468.0228070175223.54372993184078.1414124759558
Trimmed Mean ( 3 / 20 )17460.7214.40209188197581.4390374960139
Trimmed Mean ( 4 / 20 )17463.4094339623206.91112132552784.4005354670503
Trimmed Mean ( 5 / 20 )17465.5392156863199.43480310821287.5751821822674
Trimmed Mean ( 6 / 20 )17457.5755102041193.41897980216290.2578202411184
Trimmed Mean ( 7 / 20 )17447.5978723404186.69095598878293.457113548601
Trimmed Mean ( 8 / 20 )17436.9688888889178.38336697788297.749970663189
Trimmed Mean ( 9 / 20 )17429.6558139535173.164991298885100.653461668067
Trimmed Mean ( 10 / 20 )17417.7780487805167.526770140069103.970117935286
Trimmed Mean ( 11 / 20 )17405.9051282051161.774005114394107.593955629009
Trimmed Mean ( 12 / 20 )17393.9459459459155.304707594844111.998832587373
Trimmed Mean ( 13 / 20 )17386.62149.761657522430116.095269561209
Trimmed Mean ( 14 / 20 )17378.6090909091143.048503267913121.487528313114
Trimmed Mean ( 15 / 20 )17369.6134.712814247868128.937993738594
Trimmed Mean ( 16 / 20 )17364.0655172414125.275857313027138.606638898138
Trimmed Mean ( 17 / 20 )17360.3962962963116.982397010399148.401783002900
Trimmed Mean ( 18 / 20 )17358.308108.637467895136159.781964144777
Trimmed Mean ( 19 / 20 )17362.7913043478103.942073582331167.042956773371
Trimmed Mean ( 20 / 20 )17362.0904761905100.176579789500173.314865736815
Median17444.6
Midrange17535.3
Midmean - Weighted Average at Xnp17319.0833333333
Midmean - Weighted Average at X(n+1)p17369.6
Midmean - Empirical Distribution Function17369.6
Midmean - Empirical Distribution Function - Averaging17369.6
Midmean - Empirical Distribution Function - Interpolation17369.6
Midmean - Closest Observation17326.390625
Midmean - True Basic - Statistics Graphics Toolkit17369.6
Midmean - MS Excel (old versions)17369.6
Number of observations61



Parameters (Session):
Parameters (R input):
R code (references can be found in the software module):
geomean <- function(x) {
return(exp(mean(log(x))))
}
harmean <- function(x) {
return(1/mean(1/x))
}
quamean <- function(x) {
return(sqrt(mean(x*x)))
}
winmean <- function(x) {
x <-sort(x[!is.na(x)])
n<-length(x)
denom <- 3
nodenom <- n/denom
if (nodenom>40) denom <- n/40
sqrtn = sqrt(n)
roundnodenom = floor(nodenom)
win <- array(NA,dim=c(roundnodenom,2))
for (j in 1:roundnodenom) {
win[j,1] <- (j*x[j+1]+sum(x[(j+1):(n-j)])+j*x[n-j])/n
win[j,2] <- sd(c(rep(x[j+1],j),x[(j+1):(n-j)],rep(x[n-j],j)))/sqrtn
}
return(win)
}
trimean <- function(x) {
x <-sort(x[!is.na(x)])
n<-length(x)
denom <- 3
nodenom <- n/denom
if (nodenom>40) denom <- n/40
sqrtn = sqrt(n)
roundnodenom = floor(nodenom)
tri <- array(NA,dim=c(roundnodenom,2))
for (j in 1:roundnodenom) {
tri[j,1] <- mean(x,trim=j/n)
tri[j,2] <- sd(x[(j+1):(n-j)]) / sqrt(n-j*2)
}
return(tri)
}
midrange <- function(x) {
return((max(x)+min(x))/2)
}
q1 <- function(data,n,p,i,f) {
np <- n*p;
i <<- floor(np)
f <<- np - i
qvalue <- (1-f)*data[i] + f*data[i+1]
}
q2 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
qvalue <- (1-f)*data[i] + f*data[i+1]
}
q3 <- function(data,n,p,i,f) {
np <- n*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
qvalue <- data[i+1]
}
}
q4 <- function(data,n,p,i,f) {
np <- n*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- (data[i]+data[i+1])/2
} else {
qvalue <- data[i+1]
}
}
q5 <- function(data,n,p,i,f) {
np <- (n-1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i+1]
} else {
qvalue <- data[i+1] + f*(data[i+2]-data[i+1])
}
}
q6 <- function(data,n,p,i,f) {
np <- n*p+0.5
i <<- floor(np)
f <<- np - i
qvalue <- data[i]
}
q7 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
qvalue <- f*data[i] + (1-f)*data[i+1]
}
}
q8 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
if (f == 0.5) {
qvalue <- (data[i]+data[i+1])/2
} else {
if (f < 0.5) {
qvalue <- data[i]
} else {
qvalue <- data[i+1]
}
}
}
}
midmean <- function(x,def) {
x <-sort(x[!is.na(x)])
n<-length(x)
if (def==1) {
qvalue1 <- q1(x,n,0.25,i,f)
qvalue3 <- q1(x,n,0.75,i,f)
}
if (def==2) {
qvalue1 <- q2(x,n,0.25,i,f)
qvalue3 <- q2(x,n,0.75,i,f)
}
if (def==3) {
qvalue1 <- q3(x,n,0.25,i,f)
qvalue3 <- q3(x,n,0.75,i,f)
}
if (def==4) {
qvalue1 <- q4(x,n,0.25,i,f)
qvalue3 <- q4(x,n,0.75,i,f)
}
if (def==5) {
qvalue1 <- q5(x,n,0.25,i,f)
qvalue3 <- q5(x,n,0.75,i,f)
}
if (def==6) {
qvalue1 <- q6(x,n,0.25,i,f)
qvalue3 <- q6(x,n,0.75,i,f)
}
if (def==7) {
qvalue1 <- q7(x,n,0.25,i,f)
qvalue3 <- q7(x,n,0.75,i,f)
}
if (def==8) {
qvalue1 <- q8(x,n,0.25,i,f)
qvalue3 <- q8(x,n,0.75,i,f)
}
midm <- 0
myn <- 0
roundno4 <- round(n/4)
round3no4 <- round(3*n/4)
for (i in 1:n) {
if ((x[i]>=qvalue1) & (x[i]<=qvalue3)){
midm = midm + x[i]
myn = myn + 1
}
}
midm = midm / myn
return(midm)
}
(arm <- mean(x))
sqrtn <- sqrt(length(x))
(armse <- sd(x) / sqrtn)
(armose <- arm / armse)
(geo <- geomean(x))
(har <- harmean(x))
(qua <- quamean(x))
(win <- winmean(x))
(tri <- trimean(x))
(midr <- midrange(x))
midm <- array(NA,dim=8)
for (j in 1:8) midm[j] <- midmean(x,j)
midm
bitmap(file='test1.png')
lb <- win[,1] - 2*win[,2]
ub <- win[,1] + 2*win[,2]
if ((ylimmin == '') | (ylimmax == '')) plot(win[,1],type='b',main=main, xlab='j', pch=19, ylab='Winsorized Mean(j/n)', ylim=c(min(lb),max(ub))) else plot(win[,1],type='l',main=main, xlab='j', pch=19, ylab='Winsorized Mean(j/n)', ylim=c(ylimmin,ylimmax))
lines(ub,lty=3)
lines(lb,lty=3)
grid()
dev.off()
bitmap(file='test2.png')
lb <- tri[,1] - 2*tri[,2]
ub <- tri[,1] + 2*tri[,2]
if ((ylimmin == '') | (ylimmax == '')) plot(tri[,1],type='b',main=main, xlab='j', pch=19, ylab='Trimmed Mean(j/n)', ylim=c(min(lb),max(ub))) else plot(tri[,1],type='l',main=main, xlab='j', pch=19, ylab='Trimmed Mean(j/n)', ylim=c(ylimmin,ylimmax))
lines(ub,lty=3)
lines(lb,lty=3)
grid()
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Central Tendency - Ungrouped Data',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Measure',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.element(a,'S.E.',header=TRUE)
a<-table.element(a,'Value/S.E.',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('arithmetic_mean.htm', 'Arithmetic Mean', 'click to view the definition of the Arithmetic Mean'),header=TRUE)
a<-table.element(a,arm)
a<-table.element(a,hyperlink('arithmetic_mean_standard_error.htm', armse, 'click to view the definition of the Standard Error of the Arithmetic Mean'))
a<-table.element(a,armose)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('geometric_mean.htm', 'Geometric Mean', 'click to view the definition of the Geometric Mean'),header=TRUE)
a<-table.element(a,geo)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('harmonic_mean.htm', 'Harmonic Mean', 'click to view the definition of the Harmonic Mean'),header=TRUE)
a<-table.element(a,har)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('quadratic_mean.htm', 'Quadratic Mean', 'click to view the definition of the Quadratic Mean'),header=TRUE)
a<-table.element(a,qua)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
for (j in 1:length(win[,1])) {
a<-table.row.start(a)
mylabel <- paste('Winsorized Mean (',j)
mylabel <- paste(mylabel,'/')
mylabel <- paste(mylabel,length(win[,1]))
mylabel <- paste(mylabel,')')
a<-table.element(a,hyperlink('winsorized_mean.htm', mylabel, 'click to view the definition of the Winsorized Mean'),header=TRUE)
a<-table.element(a,win[j,1])
a<-table.element(a,win[j,2])
a<-table.element(a,win[j,1]/win[j,2])
a<-table.row.end(a)
}
for (j in 1:length(tri[,1])) {
a<-table.row.start(a)
mylabel <- paste('Trimmed Mean (',j)
mylabel <- paste(mylabel,'/')
mylabel <- paste(mylabel,length(tri[,1]))
mylabel <- paste(mylabel,')')
a<-table.element(a,hyperlink('arithmetic_mean.htm', mylabel, 'click to view the definition of the Trimmed Mean'),header=TRUE)
a<-table.element(a,tri[j,1])
a<-table.element(a,tri[j,2])
a<-table.element(a,tri[j,1]/tri[j,2])
a<-table.row.end(a)
}
a<-table.row.start(a)
a<-table.element(a,hyperlink('median_1.htm', 'Median', 'click to view the definition of the Median'),header=TRUE)
a<-table.element(a,median(x))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('midrange.htm', 'Midrange', 'click to view the definition of the Midrange'),header=TRUE)
a<-table.element(a,midr)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_1.htm','Weighted Average at Xnp',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[1])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_2.htm','Weighted Average at X(n+1)p',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[2])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_3.htm','Empirical Distribution Function',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[3])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_4.htm','Empirical Distribution Function - Averaging',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[4])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_5.htm','Empirical Distribution Function - Interpolation',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[5])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_6.htm','Closest Observation',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[6])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_7.htm','True Basic - Statistics Graphics Toolkit',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[7])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_8.htm','MS Excel (old versions)',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[8])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Number of observations',header=TRUE)
a<-table.element(a,length(x))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')