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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationSat, 15 Dec 2007 06:44:30 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2007/Dec/15/t1197725319aph7y4974u1k9pu.htm/, Retrieved Fri, 03 May 2024 03:31:46 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=4044, Retrieved Fri, 03 May 2024 03:31:46 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact187
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Voorspelling aant...] [2007-12-15 13:44:30] [d02236afd58a58d13a748bbf41a37c2e] [Current]
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Dataseries X:
58804
55526
63232
64929
58255
65877
58240
50356
58831
59065
45817
44520
54279
59232
68435
69861
60838
73166
59307
54174
60018
58757
50793
46916
60618
57322
69254
69687
65518
73280
59293
58216
61665
56979
54329
42812
68655
62938
77267
66985
62383
72098
62442
56514
61290
57161
55090
41015
66601
61698
76291
68017
72711
77167
67437
60659
45856
66097
54606
43816




Summary of compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001

\begin{tabular}{lllllllll}
\hline
Summary of compuational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 3 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=4044&T=0

[TABLE]
[ROW][C]Summary of compuational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ 193.190.124.10:1001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=4044&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=4044&T=0

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Summary of compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean60549.91666666671118.7578693449654.1224498399452
Geometric Mean59911.8186612978
Harmonic Mean59242.4087280149
Quadratic Mean61156.6671703367
Winsorized Mean ( 1 / 20 )60578.21109.8392981344754.5828572675575
Winsorized Mean ( 2 / 20 )60582.46666666671093.6959374769055.39242177897
Winsorized Mean ( 3 / 20 )60467.11666666671050.6548402173457.5518375322558
Winsorized Mean ( 4 / 20 )60545.98333333331027.4446650919058.9287047667117
Winsorized Mean ( 5 / 20 )60511.31666666671018.8588713422559.3912644515218
Winsorized Mean ( 6 / 20 )60556.0166666667981.1067866605861.722146345336
Winsorized Mean ( 7 / 20 )60696.3666666667841.34126236336472.1423866650352
Winsorized Mean ( 8 / 20 )60731.4333333333825.04735709539473.6096332059536
Winsorized Mean ( 9 / 20 )61173.6333333333718.57746672671485.131577548616
Winsorized Mean ( 10 / 20 )61091.3696.98324287421687.6510312472823
Winsorized Mean ( 11 / 20 )61060.1333333333688.09097844248588.7384593699293
Winsorized Mean ( 12 / 20 )61031.9333333333663.90333381286391.9289454126112
Winsorized Mean ( 13 / 20 )61011.1333333333624.70586365333897.6637756792206
Winsorized Mean ( 14 / 20 )61007.4590.274534519062103.354280817327
Winsorized Mean ( 15 / 20 )61158.4536.144518526267114.070736315853
Winsorized Mean ( 16 / 20 )61148495.233434086682123.473085198236
Winsorized Mean ( 17 / 20 )61137.2333333333477.389750260187128.065659767543
Winsorized Mean ( 18 / 20 )61077.8333333333452.56369166054134.959640949603
Winsorized Mean ( 19 / 20 )61174.4166666667383.002371466502159.723336522518
Winsorized Mean ( 20 / 20 )60616.75291.369485686586208.040831239284
Trimmed Mean ( 1 / 20 )60598.51067.8043008691456.7505674501179
Trimmed Mean ( 2 / 20 )60620.251015.8835723791759.6724385039803
Trimmed Mean ( 3 / 20 )60641.2407407407962.36678965471363.0126074513629
Trimmed Mean ( 4 / 20 )60708.2115384615917.15158694531266.1921239657425
Trimmed Mean ( 5 / 20 )60756.88869.83739209447369.8485493405889
Trimmed Mean ( 6 / 20 )60818.2708333333812.30391891460774.8713251495797
Trimmed Mean ( 7 / 20 )60875.2826086957751.14688906351881.0431135308183
Trimmed Mean ( 8 / 20 )60910.1363636364718.41047056590284.7845888377109
Trimmed Mean ( 9 / 20 )60942.0476190476680.34219113699989.5755818365465
Trimmed Mean ( 10 / 20 )60903.45661.24386182987992.1043710431733
Trimmed Mean ( 11 / 20 )60873.7894736842641.22065221998394.934230928046
Trimmed Mean ( 12 / 20 )60845.5555555556615.96588681625998.7807228579618
Trimmed Mean ( 13 / 20 )60818.1470588235587.810217915472103.465617311827
Trimmed Mean ( 14 / 20 )60790.3125559.943762364658108.565032036933
Trimmed Mean ( 15 / 20 )60759.3530.574107079726114.516142399821
Trimmed Mean ( 16 / 20 )60702.2857142857504.835978018045120.241599960049
Trimmed Mean ( 17 / 20 )60638479.744213898647126.396521819877
Trimmed Mean ( 18 / 20 )60564.5833333333446.269606059242135.712991678159
Trimmed Mean ( 19 / 20 )60486.8181818182402.241273013921150.374469851394
Trimmed Mean ( 20 / 20 )60378.25361.376606843448167.078468435995
Median60318
Midrange59141
Midmean - Weighted Average at Xnp60590.4838709677
Midmean - Weighted Average at X(n+1)p60759.3
Midmean - Empirical Distribution Function60590.4838709677
Midmean - Empirical Distribution Function - Averaging60759.3
Midmean - Empirical Distribution Function - Interpolation60759.3
Midmean - Closest Observation60590.4838709677
Midmean - True Basic - Statistics Graphics Toolkit60759.3
Midmean - MS Excel (old versions)60790.3125
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 60549.9166666667 & 1118.75786934496 & 54.1224498399452 \tabularnewline
Geometric Mean & 59911.8186612978 &  &  \tabularnewline
Harmonic Mean & 59242.4087280149 &  &  \tabularnewline
Quadratic Mean & 61156.6671703367 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 60578.2 & 1109.83929813447 & 54.5828572675575 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 60582.4666666667 & 1093.69593747690 & 55.39242177897 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 60467.1166666667 & 1050.65484021734 & 57.5518375322558 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 60545.9833333333 & 1027.44466509190 & 58.9287047667117 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 60511.3166666667 & 1018.85887134225 & 59.3912644515218 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 60556.0166666667 & 981.10678666058 & 61.722146345336 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 60696.3666666667 & 841.341262363364 & 72.1423866650352 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 60731.4333333333 & 825.047357095394 & 73.6096332059536 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 61173.6333333333 & 718.577466726714 & 85.131577548616 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 61091.3 & 696.983242874216 & 87.6510312472823 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 61060.1333333333 & 688.090978442485 & 88.7384593699293 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 61031.9333333333 & 663.903333812863 & 91.9289454126112 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 61011.1333333333 & 624.705863653338 & 97.6637756792206 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 61007.4 & 590.274534519062 & 103.354280817327 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 61158.4 & 536.144518526267 & 114.070736315853 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 61148 & 495.233434086682 & 123.473085198236 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 61137.2333333333 & 477.389750260187 & 128.065659767543 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 61077.8333333333 & 452.56369166054 & 134.959640949603 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 61174.4166666667 & 383.002371466502 & 159.723336522518 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 60616.75 & 291.369485686586 & 208.040831239284 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 60598.5 & 1067.80430086914 & 56.7505674501179 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 60620.25 & 1015.88357237917 & 59.6724385039803 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 60641.2407407407 & 962.366789654713 & 63.0126074513629 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 60708.2115384615 & 917.151586945312 & 66.1921239657425 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 60756.88 & 869.837392094473 & 69.8485493405889 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 60818.2708333333 & 812.303918914607 & 74.8713251495797 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 60875.2826086957 & 751.146889063518 & 81.0431135308183 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 60910.1363636364 & 718.410470565902 & 84.7845888377109 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 60942.0476190476 & 680.342191136999 & 89.5755818365465 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 60903.45 & 661.243861829879 & 92.1043710431733 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 60873.7894736842 & 641.220652219983 & 94.934230928046 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 60845.5555555556 & 615.965886816259 & 98.7807228579618 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 60818.1470588235 & 587.810217915472 & 103.465617311827 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 60790.3125 & 559.943762364658 & 108.565032036933 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 60759.3 & 530.574107079726 & 114.516142399821 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 60702.2857142857 & 504.835978018045 & 120.241599960049 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 60638 & 479.744213898647 & 126.396521819877 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 60564.5833333333 & 446.269606059242 & 135.712991678159 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 60486.8181818182 & 402.241273013921 & 150.374469851394 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 60378.25 & 361.376606843448 & 167.078468435995 \tabularnewline
Median & 60318 &  &  \tabularnewline
Midrange & 59141 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 60590.4838709677 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 60759.3 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 60590.4838709677 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 60759.3 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 60759.3 &  &  \tabularnewline
Midmean - Closest Observation & 60590.4838709677 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 60759.3 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 60790.3125 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=4044&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]60549.9166666667[/C][C]1118.75786934496[/C][C]54.1224498399452[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]59911.8186612978[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]59242.4087280149[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]61156.6671703367[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]60578.2[/C][C]1109.83929813447[/C][C]54.5828572675575[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]60582.4666666667[/C][C]1093.69593747690[/C][C]55.39242177897[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]60467.1166666667[/C][C]1050.65484021734[/C][C]57.5518375322558[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]60545.9833333333[/C][C]1027.44466509190[/C][C]58.9287047667117[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]60511.3166666667[/C][C]1018.85887134225[/C][C]59.3912644515218[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]60556.0166666667[/C][C]981.10678666058[/C][C]61.722146345336[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]60696.3666666667[/C][C]841.341262363364[/C][C]72.1423866650352[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]60731.4333333333[/C][C]825.047357095394[/C][C]73.6096332059536[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]61173.6333333333[/C][C]718.577466726714[/C][C]85.131577548616[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]61091.3[/C][C]696.983242874216[/C][C]87.6510312472823[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]61060.1333333333[/C][C]688.090978442485[/C][C]88.7384593699293[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]61031.9333333333[/C][C]663.903333812863[/C][C]91.9289454126112[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]61011.1333333333[/C][C]624.705863653338[/C][C]97.6637756792206[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]61007.4[/C][C]590.274534519062[/C][C]103.354280817327[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]61158.4[/C][C]536.144518526267[/C][C]114.070736315853[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]61148[/C][C]495.233434086682[/C][C]123.473085198236[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]61137.2333333333[/C][C]477.389750260187[/C][C]128.065659767543[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]61077.8333333333[/C][C]452.56369166054[/C][C]134.959640949603[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]61174.4166666667[/C][C]383.002371466502[/C][C]159.723336522518[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]60616.75[/C][C]291.369485686586[/C][C]208.040831239284[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]60598.5[/C][C]1067.80430086914[/C][C]56.7505674501179[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]60620.25[/C][C]1015.88357237917[/C][C]59.6724385039803[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]60641.2407407407[/C][C]962.366789654713[/C][C]63.0126074513629[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]60708.2115384615[/C][C]917.151586945312[/C][C]66.1921239657425[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]60756.88[/C][C]869.837392094473[/C][C]69.8485493405889[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]60818.2708333333[/C][C]812.303918914607[/C][C]74.8713251495797[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]60875.2826086957[/C][C]751.146889063518[/C][C]81.0431135308183[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]60910.1363636364[/C][C]718.410470565902[/C][C]84.7845888377109[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]60942.0476190476[/C][C]680.342191136999[/C][C]89.5755818365465[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]60903.45[/C][C]661.243861829879[/C][C]92.1043710431733[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]60873.7894736842[/C][C]641.220652219983[/C][C]94.934230928046[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]60845.5555555556[/C][C]615.965886816259[/C][C]98.7807228579618[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]60818.1470588235[/C][C]587.810217915472[/C][C]103.465617311827[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]60790.3125[/C][C]559.943762364658[/C][C]108.565032036933[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]60759.3[/C][C]530.574107079726[/C][C]114.516142399821[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]60702.2857142857[/C][C]504.835978018045[/C][C]120.241599960049[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]60638[/C][C]479.744213898647[/C][C]126.396521819877[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]60564.5833333333[/C][C]446.269606059242[/C][C]135.712991678159[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]60486.8181818182[/C][C]402.241273013921[/C][C]150.374469851394[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]60378.25[/C][C]361.376606843448[/C][C]167.078468435995[/C][/ROW]
[ROW][C]Median[/C][C]60318[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]59141[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]60590.4838709677[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]60759.3[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]60590.4838709677[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]60759.3[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]60759.3[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]60590.4838709677[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]60759.3[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]60790.3125[/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=4044&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=4044&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 Mean60549.91666666671118.7578693449654.1224498399452
Geometric Mean59911.8186612978
Harmonic Mean59242.4087280149
Quadratic Mean61156.6671703367
Winsorized Mean ( 1 / 20 )60578.21109.8392981344754.5828572675575
Winsorized Mean ( 2 / 20 )60582.46666666671093.6959374769055.39242177897
Winsorized Mean ( 3 / 20 )60467.11666666671050.6548402173457.5518375322558
Winsorized Mean ( 4 / 20 )60545.98333333331027.4446650919058.9287047667117
Winsorized Mean ( 5 / 20 )60511.31666666671018.8588713422559.3912644515218
Winsorized Mean ( 6 / 20 )60556.0166666667981.1067866605861.722146345336
Winsorized Mean ( 7 / 20 )60696.3666666667841.34126236336472.1423866650352
Winsorized Mean ( 8 / 20 )60731.4333333333825.04735709539473.6096332059536
Winsorized Mean ( 9 / 20 )61173.6333333333718.57746672671485.131577548616
Winsorized Mean ( 10 / 20 )61091.3696.98324287421687.6510312472823
Winsorized Mean ( 11 / 20 )61060.1333333333688.09097844248588.7384593699293
Winsorized Mean ( 12 / 20 )61031.9333333333663.90333381286391.9289454126112
Winsorized Mean ( 13 / 20 )61011.1333333333624.70586365333897.6637756792206
Winsorized Mean ( 14 / 20 )61007.4590.274534519062103.354280817327
Winsorized Mean ( 15 / 20 )61158.4536.144518526267114.070736315853
Winsorized Mean ( 16 / 20 )61148495.233434086682123.473085198236
Winsorized Mean ( 17 / 20 )61137.2333333333477.389750260187128.065659767543
Winsorized Mean ( 18 / 20 )61077.8333333333452.56369166054134.959640949603
Winsorized Mean ( 19 / 20 )61174.4166666667383.002371466502159.723336522518
Winsorized Mean ( 20 / 20 )60616.75291.369485686586208.040831239284
Trimmed Mean ( 1 / 20 )60598.51067.8043008691456.7505674501179
Trimmed Mean ( 2 / 20 )60620.251015.8835723791759.6724385039803
Trimmed Mean ( 3 / 20 )60641.2407407407962.36678965471363.0126074513629
Trimmed Mean ( 4 / 20 )60708.2115384615917.15158694531266.1921239657425
Trimmed Mean ( 5 / 20 )60756.88869.83739209447369.8485493405889
Trimmed Mean ( 6 / 20 )60818.2708333333812.30391891460774.8713251495797
Trimmed Mean ( 7 / 20 )60875.2826086957751.14688906351881.0431135308183
Trimmed Mean ( 8 / 20 )60910.1363636364718.41047056590284.7845888377109
Trimmed Mean ( 9 / 20 )60942.0476190476680.34219113699989.5755818365465
Trimmed Mean ( 10 / 20 )60903.45661.24386182987992.1043710431733
Trimmed Mean ( 11 / 20 )60873.7894736842641.22065221998394.934230928046
Trimmed Mean ( 12 / 20 )60845.5555555556615.96588681625998.7807228579618
Trimmed Mean ( 13 / 20 )60818.1470588235587.810217915472103.465617311827
Trimmed Mean ( 14 / 20 )60790.3125559.943762364658108.565032036933
Trimmed Mean ( 15 / 20 )60759.3530.574107079726114.516142399821
Trimmed Mean ( 16 / 20 )60702.2857142857504.835978018045120.241599960049
Trimmed Mean ( 17 / 20 )60638479.744213898647126.396521819877
Trimmed Mean ( 18 / 20 )60564.5833333333446.269606059242135.712991678159
Trimmed Mean ( 19 / 20 )60486.8181818182402.241273013921150.374469851394
Trimmed Mean ( 20 / 20 )60378.25361.376606843448167.078468435995
Median60318
Midrange59141
Midmean - Weighted Average at Xnp60590.4838709677
Midmean - Weighted Average at X(n+1)p60759.3
Midmean - Empirical Distribution Function60590.4838709677
Midmean - Empirical Distribution Function - Averaging60759.3
Midmean - Empirical Distribution Function - Interpolation60759.3
Midmean - Closest Observation60590.4838709677
Midmean - True Basic - Statistics Graphics Toolkit60759.3
Midmean - MS Excel (old versions)60790.3125
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')