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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 computationThu, 18 Dec 2008 07:25:53 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/Dec/18/t12296104613jzv7k4bd7kjag1.htm/, Retrieved Sat, 11 May 2024 22:49:52 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=34794, Retrieved Sat, 11 May 2024 22:49:52 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact159
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Mean Plot] [Paper - Central T...] [2008-12-18 11:57:49] [85841a4a203c2f9589565c024425a91b]
- RMP     [Central Tendency] [Paper - Central T...] [2008-12-18 14:25:53] [07b7cf1321bc38017c2c7efcf91ca696] [Current]
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Dataseries X:
127.96
127.47
126.47
125.75
125.42
125.14
125.15
125.51
125.63
126.22
126.88
127.96
128.74
129.6
131.2
132.72
134.67
135.94
136.39
136.74
137.2
137.36
138.63
141.07
143.32
147.91
152.56
151.61
156.56
157.45
158.13
159.18
159.47
159.79
161.65
162.77
163.48
166.16
163.86
162.12
149.08
145.32
141.21
134.68
133.65
139.17
138.61
144.96
157.99
167.18
174.48
182.77
190.00
189.70
188.90
198.28
201.18
204.14
221.02
221.12
220.68




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=34794&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=34794&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=34794&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 Mean152.5567213114753.3612312725891445.3871539740738
Geometric Mean150.541388172624
Harmonic Mean148.720023735949
Quadratic Mean154.762481749864
Winsorized Mean ( 1 / 20 )152.5552459016393.3606520119931445.3945381304629
Winsorized Mean ( 2 / 20 )152.5529508196723.3556754334173345.4611758039771
Winsorized Mean ( 3 / 20 )151.7439344262303.1020385882846548.9174876803
Winsorized Mean ( 4 / 20 )151.5577049180333.0472571147080749.7357785093078
Winsorized Mean ( 5 / 20 )151.3298360655742.9824044421209450.7408834054564
Winsorized Mean ( 6 / 20 )150.5616393442622.7719405049278154.3163314929024
Winsorized Mean ( 7 / 20 )150.5559016393442.7596033449930254.5570804269789
Winsorized Mean ( 8 / 20 )150.5047540983612.7270983859985255.1886044416597
Winsorized Mean ( 9 / 20 )149.6873770491802.5086083693771859.6694880222948
Winsorized Mean ( 10 / 20 )148.408688524592.2127227432615767.0706210150102
Winsorized Mean ( 11 / 20 )147.0922950819671.9706390241685874.6419274549918
Winsorized Mean ( 12 / 20 )147.0450819672131.9122167295906376.8977070913363
Winsorized Mean ( 13 / 20 )146.7381967213111.803406211089681.3672459476857
Winsorized Mean ( 14 / 20 )147.0181967213111.7325582573760784.8561346179308
Winsorized Mean ( 15 / 20 )147.2173770491801.6491665373300489.267744473837
Winsorized Mean ( 16 / 20 )147.2908196721311.5871425727323192.8025132729984
Winsorized Mean ( 17 / 20 )147.4440983606561.5265942911898496.5836825223137
Winsorized Mean ( 18 / 20 )146.8981967213111.44270011933447101.821712463070
Winsorized Mean ( 19 / 20 )147.1909836065571.37333837414027107.177507290366
Winsorized Mean ( 20 / 20 )147.2434426229511.33915224560118109.952728008793
Trimmed Mean ( 1 / 20 )151.8593220338983.2375702864488546.9053359766488
Trimmed Mean ( 2 / 20 )151.1145614035093.0830569313574149.014521874877
Trimmed Mean ( 3 / 20 )150.3169090909092.8900253266599352.012315499198
Trimmed Mean ( 4 / 20 )149.7694339622642.7785970739221253.9010982800962
Trimmed Mean ( 5 / 20 )149.2347058823532.6596208686458656.111270460265
Trimmed Mean ( 6 / 20 )148.7130612244902.5310429171877758.7556458306617
Trimmed Mean ( 7 / 20 )148.3131914893622.437874430671360.8370921912175
Trimmed Mean ( 8 / 20 )147.8788888888892.3193070025207263.7599458494145
Trimmed Mean ( 9 / 20 )147.4132558139532.1717223166650567.8785011705938
Trimmed Mean ( 10 / 20 )147.0373170731712.0458391749606571.8713957933661
Trimmed Mean ( 11 / 20 )146.8228205128201.9689409851658574.569436879518
Trimmed Mean ( 12 / 20 )146.7824324324321.9326168836139475.9500932010662
Trimmed Mean ( 13 / 20 )146.7442857142861.8951420108520977.4318150692604
Trimmed Mean ( 14 / 20 )146.7451515151521.8685713085344378.5333430118051
Trimmed Mean ( 15 / 20 )146.7067741935481.8448805880928779.5210135227264
Trimmed Mean ( 16 / 20 )146.6351724137931.8273806000154280.2433671521716
Trimmed Mean ( 17 / 20 )146.5425925925931.8112114118778180.9086071518629
Trimmed Mean ( 18 / 20 )146.41321.7950352568496681.5656402520802
Trimmed Mean ( 19 / 20 )146.3417391304351.7873992027384881.8741212965877
Trimmed Mean ( 20 / 20 )146.2119047619051.7832990587335181.9895597689284
Median144.96
Midrange173.13
Midmean - Weighted Average at Xnp146.171333333333
Midmean - Weighted Average at X(n+1)p146.706774193548
Midmean - Empirical Distribution Function146.706774193548
Midmean - Empirical Distribution Function - Averaging146.706774193548
Midmean - Empirical Distribution Function - Interpolation146.706774193548
Midmean - Closest Observation146.2221875
Midmean - True Basic - Statistics Graphics Toolkit146.706774193548
Midmean - MS Excel (old versions)146.706774193548
Number of observations61

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 152.556721311475 & 3.36123127258914 & 45.3871539740738 \tabularnewline
Geometric Mean & 150.541388172624 &  &  \tabularnewline
Harmonic Mean & 148.720023735949 &  &  \tabularnewline
Quadratic Mean & 154.762481749864 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 152.555245901639 & 3.36065201199314 & 45.3945381304629 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 152.552950819672 & 3.35567543341733 & 45.4611758039771 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 151.743934426230 & 3.10203858828465 & 48.9174876803 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 151.557704918033 & 3.04725711470807 & 49.7357785093078 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 151.329836065574 & 2.98240444212094 & 50.7408834054564 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 150.561639344262 & 2.77194050492781 & 54.3163314929024 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 150.555901639344 & 2.75960334499302 & 54.5570804269789 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 150.504754098361 & 2.72709838599852 & 55.1886044416597 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 149.687377049180 & 2.50860836937718 & 59.6694880222948 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 148.40868852459 & 2.21272274326157 & 67.0706210150102 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 147.092295081967 & 1.97063902416858 & 74.6419274549918 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 147.045081967213 & 1.91221672959063 & 76.8977070913363 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 146.738196721311 & 1.8034062110896 & 81.3672459476857 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 147.018196721311 & 1.73255825737607 & 84.8561346179308 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 147.217377049180 & 1.64916653733004 & 89.267744473837 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 147.290819672131 & 1.58714257273231 & 92.8025132729984 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 147.444098360656 & 1.52659429118984 & 96.5836825223137 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 146.898196721311 & 1.44270011933447 & 101.821712463070 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 147.190983606557 & 1.37333837414027 & 107.177507290366 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 147.243442622951 & 1.33915224560118 & 109.952728008793 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 151.859322033898 & 3.23757028644885 & 46.9053359766488 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 151.114561403509 & 3.08305693135741 & 49.014521874877 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 150.316909090909 & 2.89002532665993 & 52.012315499198 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 149.769433962264 & 2.77859707392212 & 53.9010982800962 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 149.234705882353 & 2.65962086864586 & 56.111270460265 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 148.713061224490 & 2.53104291718777 & 58.7556458306617 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 148.313191489362 & 2.4378744306713 & 60.8370921912175 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 147.878888888889 & 2.31930700252072 & 63.7599458494145 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 147.413255813953 & 2.17172231666505 & 67.8785011705938 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 147.037317073171 & 2.04583917496065 & 71.8713957933661 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 146.822820512820 & 1.96894098516585 & 74.569436879518 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 146.782432432432 & 1.93261688361394 & 75.9500932010662 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 146.744285714286 & 1.89514201085209 & 77.4318150692604 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 146.745151515152 & 1.86857130853443 & 78.5333430118051 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 146.706774193548 & 1.84488058809287 & 79.5210135227264 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 146.635172413793 & 1.82738060001542 & 80.2433671521716 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 146.542592592593 & 1.81121141187781 & 80.9086071518629 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 146.4132 & 1.79503525684966 & 81.5656402520802 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 146.341739130435 & 1.78739920273848 & 81.8741212965877 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 146.211904761905 & 1.78329905873351 & 81.9895597689284 \tabularnewline
Median & 144.96 &  &  \tabularnewline
Midrange & 173.13 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 146.171333333333 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 146.706774193548 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 146.706774193548 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 146.706774193548 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 146.706774193548 &  &  \tabularnewline
Midmean - Closest Observation & 146.2221875 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 146.706774193548 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 146.706774193548 &  &  \tabularnewline
Number of observations & 61 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=34794&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]152.556721311475[/C][C]3.36123127258914[/C][C]45.3871539740738[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]150.541388172624[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]148.720023735949[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]154.762481749864[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]152.555245901639[/C][C]3.36065201199314[/C][C]45.3945381304629[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]152.552950819672[/C][C]3.35567543341733[/C][C]45.4611758039771[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]151.743934426230[/C][C]3.10203858828465[/C][C]48.9174876803[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]151.557704918033[/C][C]3.04725711470807[/C][C]49.7357785093078[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]151.329836065574[/C][C]2.98240444212094[/C][C]50.7408834054564[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]150.561639344262[/C][C]2.77194050492781[/C][C]54.3163314929024[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]150.555901639344[/C][C]2.75960334499302[/C][C]54.5570804269789[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]150.504754098361[/C][C]2.72709838599852[/C][C]55.1886044416597[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]149.687377049180[/C][C]2.50860836937718[/C][C]59.6694880222948[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]148.40868852459[/C][C]2.21272274326157[/C][C]67.0706210150102[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]147.092295081967[/C][C]1.97063902416858[/C][C]74.6419274549918[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]147.045081967213[/C][C]1.91221672959063[/C][C]76.8977070913363[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]146.738196721311[/C][C]1.8034062110896[/C][C]81.3672459476857[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]147.018196721311[/C][C]1.73255825737607[/C][C]84.8561346179308[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]147.217377049180[/C][C]1.64916653733004[/C][C]89.267744473837[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]147.290819672131[/C][C]1.58714257273231[/C][C]92.8025132729984[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]147.444098360656[/C][C]1.52659429118984[/C][C]96.5836825223137[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]146.898196721311[/C][C]1.44270011933447[/C][C]101.821712463070[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]147.190983606557[/C][C]1.37333837414027[/C][C]107.177507290366[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]147.243442622951[/C][C]1.33915224560118[/C][C]109.952728008793[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]151.859322033898[/C][C]3.23757028644885[/C][C]46.9053359766488[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]151.114561403509[/C][C]3.08305693135741[/C][C]49.014521874877[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]150.316909090909[/C][C]2.89002532665993[/C][C]52.012315499198[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]149.769433962264[/C][C]2.77859707392212[/C][C]53.9010982800962[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]149.234705882353[/C][C]2.65962086864586[/C][C]56.111270460265[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]148.713061224490[/C][C]2.53104291718777[/C][C]58.7556458306617[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]148.313191489362[/C][C]2.4378744306713[/C][C]60.8370921912175[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]147.878888888889[/C][C]2.31930700252072[/C][C]63.7599458494145[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]147.413255813953[/C][C]2.17172231666505[/C][C]67.8785011705938[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]147.037317073171[/C][C]2.04583917496065[/C][C]71.8713957933661[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]146.822820512820[/C][C]1.96894098516585[/C][C]74.569436879518[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]146.782432432432[/C][C]1.93261688361394[/C][C]75.9500932010662[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]146.744285714286[/C][C]1.89514201085209[/C][C]77.4318150692604[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]146.745151515152[/C][C]1.86857130853443[/C][C]78.5333430118051[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]146.706774193548[/C][C]1.84488058809287[/C][C]79.5210135227264[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]146.635172413793[/C][C]1.82738060001542[/C][C]80.2433671521716[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]146.542592592593[/C][C]1.81121141187781[/C][C]80.9086071518629[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]146.4132[/C][C]1.79503525684966[/C][C]81.5656402520802[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]146.341739130435[/C][C]1.78739920273848[/C][C]81.8741212965877[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]146.211904761905[/C][C]1.78329905873351[/C][C]81.9895597689284[/C][/ROW]
[ROW][C]Median[/C][C]144.96[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]173.13[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]146.171333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]146.706774193548[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]146.706774193548[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]146.706774193548[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]146.706774193548[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]146.2221875[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]146.706774193548[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]146.706774193548[/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=34794&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=34794&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 Mean152.5567213114753.3612312725891445.3871539740738
Geometric Mean150.541388172624
Harmonic Mean148.720023735949
Quadratic Mean154.762481749864
Winsorized Mean ( 1 / 20 )152.5552459016393.3606520119931445.3945381304629
Winsorized Mean ( 2 / 20 )152.5529508196723.3556754334173345.4611758039771
Winsorized Mean ( 3 / 20 )151.7439344262303.1020385882846548.9174876803
Winsorized Mean ( 4 / 20 )151.5577049180333.0472571147080749.7357785093078
Winsorized Mean ( 5 / 20 )151.3298360655742.9824044421209450.7408834054564
Winsorized Mean ( 6 / 20 )150.5616393442622.7719405049278154.3163314929024
Winsorized Mean ( 7 / 20 )150.5559016393442.7596033449930254.5570804269789
Winsorized Mean ( 8 / 20 )150.5047540983612.7270983859985255.1886044416597
Winsorized Mean ( 9 / 20 )149.6873770491802.5086083693771859.6694880222948
Winsorized Mean ( 10 / 20 )148.408688524592.2127227432615767.0706210150102
Winsorized Mean ( 11 / 20 )147.0922950819671.9706390241685874.6419274549918
Winsorized Mean ( 12 / 20 )147.0450819672131.9122167295906376.8977070913363
Winsorized Mean ( 13 / 20 )146.7381967213111.803406211089681.3672459476857
Winsorized Mean ( 14 / 20 )147.0181967213111.7325582573760784.8561346179308
Winsorized Mean ( 15 / 20 )147.2173770491801.6491665373300489.267744473837
Winsorized Mean ( 16 / 20 )147.2908196721311.5871425727323192.8025132729984
Winsorized Mean ( 17 / 20 )147.4440983606561.5265942911898496.5836825223137
Winsorized Mean ( 18 / 20 )146.8981967213111.44270011933447101.821712463070
Winsorized Mean ( 19 / 20 )147.1909836065571.37333837414027107.177507290366
Winsorized Mean ( 20 / 20 )147.2434426229511.33915224560118109.952728008793
Trimmed Mean ( 1 / 20 )151.8593220338983.2375702864488546.9053359766488
Trimmed Mean ( 2 / 20 )151.1145614035093.0830569313574149.014521874877
Trimmed Mean ( 3 / 20 )150.3169090909092.8900253266599352.012315499198
Trimmed Mean ( 4 / 20 )149.7694339622642.7785970739221253.9010982800962
Trimmed Mean ( 5 / 20 )149.2347058823532.6596208686458656.111270460265
Trimmed Mean ( 6 / 20 )148.7130612244902.5310429171877758.7556458306617
Trimmed Mean ( 7 / 20 )148.3131914893622.437874430671360.8370921912175
Trimmed Mean ( 8 / 20 )147.8788888888892.3193070025207263.7599458494145
Trimmed Mean ( 9 / 20 )147.4132558139532.1717223166650567.8785011705938
Trimmed Mean ( 10 / 20 )147.0373170731712.0458391749606571.8713957933661
Trimmed Mean ( 11 / 20 )146.8228205128201.9689409851658574.569436879518
Trimmed Mean ( 12 / 20 )146.7824324324321.9326168836139475.9500932010662
Trimmed Mean ( 13 / 20 )146.7442857142861.8951420108520977.4318150692604
Trimmed Mean ( 14 / 20 )146.7451515151521.8685713085344378.5333430118051
Trimmed Mean ( 15 / 20 )146.7067741935481.8448805880928779.5210135227264
Trimmed Mean ( 16 / 20 )146.6351724137931.8273806000154280.2433671521716
Trimmed Mean ( 17 / 20 )146.5425925925931.8112114118778180.9086071518629
Trimmed Mean ( 18 / 20 )146.41321.7950352568496681.5656402520802
Trimmed Mean ( 19 / 20 )146.3417391304351.7873992027384881.8741212965877
Trimmed Mean ( 20 / 20 )146.2119047619051.7832990587335181.9895597689284
Median144.96
Midrange173.13
Midmean - Weighted Average at Xnp146.171333333333
Midmean - Weighted Average at X(n+1)p146.706774193548
Midmean - Empirical Distribution Function146.706774193548
Midmean - Empirical Distribution Function - Averaging146.706774193548
Midmean - Empirical Distribution Function - Interpolation146.706774193548
Midmean - Closest Observation146.2221875
Midmean - True Basic - Statistics Graphics Toolkit146.706774193548
Midmean - MS Excel (old versions)146.706774193548
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')