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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, 15 Oct 2009 09:18:00 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Oct/15/t12556199656ob17jsujvr6ijj.htm/, Retrieved Sat, 04 May 2024 17:58:13 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=46782, Retrieved Sat, 04 May 2024 17:58:13 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsws03
Estimated Impact184
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Bivariate Data Series] [Bivariate dataset] [2008-01-05 23:51:08] [74be16979710d4c4e7c6647856088456]
F RMPD  [Univariate Explorative Data Analysis] [Colombia Coffee] [2008-01-07 14:21:11] [74be16979710d4c4e7c6647856088456]
F RMPD    [Univariate Data Series] [] [2009-10-14 08:30:28] [74be16979710d4c4e7c6647856088456]
- RMPD        [Central Tendency] [Central tendency ...] [2009-10-15 15:18:00] [a931a0a30926b49d162330b43e89b999] [Current]
-    D          [Central Tendency] [ws3] [2009-10-20 17:57:29] [757146c69eaf0537be37c7b0c18216d8]
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Post a new message
Dataseries X:
325412
326011
328282
317480
317539
313737
312276
309391
302950
300316
304035
333476
337698
335932
323931
313927
314485
313218
309664
302963
298989
298423
310631
239765
335083
327616
309119
295916
291413
291542
284678
276475
272566
264981
263290
296806
303598
286994
276427
266424
267153
268381
262522
255542
253158
243803
250741
280445
285257
270976
261076
255603
260376
263903
264291
263276
262572
256167
264221
293860
300713
287224




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'George Udny Yule' @ 72.249.76.132

\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 & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=46782&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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=46782&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=46782&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'George Udny Yule' @ 72.249.76.132







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean290398.6935483873371.8799968506786.1236739799812
Geometric Mean289198.640897153
Harmonic Mean287995.872331463
Quadratic Mean291590.372392699
Winsorized Mean ( 1 / 20 )290435.3387096773349.9841609090386.6975259461724
Winsorized Mean ( 2 / 20 )290631.7580645163296.1432688526388.1732783920172
Winsorized Mean ( 3 / 20 )290670.9516129033256.5213725267789.2581126797176
Winsorized Mean ( 4 / 20 )290489.6612903233159.0307297874991.9553135558969
Winsorized Mean ( 5 / 20 )290440.8709677423147.6720670713492.2716422737054
Winsorized Mean ( 6 / 20 )290340.1290322583108.1513991918493.4124795554523
Winsorized Mean ( 7 / 20 )290747.7096774193013.2708699147996.4890719185962
Winsorized Mean ( 8 / 20 )290646.9354838712962.7993952358398.0987561801281
Winsorized Mean ( 9 / 20 )289928.9677419352766.92196104877104.783933852634
Winsorized Mean ( 10 / 20 )289927.5161290322764.05712407727104.892013122131
Winsorized Mean ( 11 / 20 )289521.0483870972659.47155584223108.864126691292
Winsorized Mean ( 12 / 20 )289415.7580645162642.51152715964109.522987918846
Winsorized Mean ( 13 / 20 )289504.4516129032615.72919547292110.678296558357
Winsorized Mean ( 14 / 20 )289459.0645161292586.50183130778111.911409074771
Winsorized Mean ( 15 / 20 )289248.0967741942549.75583631194113.441488261312
Winsorized Mean ( 16 / 20 )289001.645161292459.16692567258117.520141534210
Winsorized Mean ( 17 / 20 )289132.1612903232358.20855787379122.606696649007
Winsorized Mean ( 18 / 20 )289264.5483870972313.6148413004125.027097520049
Winsorized Mean ( 19 / 20 )289557.5161290322243.10665006016129.087716859680
Winsorized Mean ( 20 / 20 )288754.6129032261886.85397289973153.034955036539
Trimmed Mean ( 1 / 20 )290454.2666666673284.8974284966588.421106895747
Trimmed Mean ( 2 / 20 )290474.53204.747418704890.6388123771062
Trimmed Mean ( 3 / 20 )290387.4464285713140.8943125191892.4537464604033
Trimmed Mean ( 4 / 20 )290278.9444444443079.5178817371794.2611654135604
Trimmed Mean ( 5 / 20 )290216.1346153853038.8686840013395.501373963041
Trimmed Mean ( 6 / 20 )290160.42989.3355167723797.065183339905
Trimmed Mean ( 7 / 20 )290121.7083333332936.4291556469298.800854015297
Trimmed Mean ( 8 / 20 )290001.1739130432892.74805011661100.251099953676
Trimmed Mean ( 9 / 20 )289887.4318181822846.79950193650101.829240738938
Trimmed Mean ( 10 / 20 )289880.6190476192832.91954666922102.325750615983
Trimmed Mean ( 11 / 20 )289873.352809.36018825849103.181269248245
Trimmed Mean ( 12 / 20 )289925.6052631582796.95159894761103.657712694151
Trimmed Mean ( 13 / 20 )289998.7777777782776.50802814166104.447303893400
Trimmed Mean ( 14 / 20 )290068.1176470592747.33377824094105.581680662327
Trimmed Mean ( 15 / 20 )290152.406252706.11274734246107.221107670013
Trimmed Mean ( 16 / 20 )2902772649.1660778528109.572971821863
Trimmed Mean ( 17 / 20 )290453.52584.72445774918112.373100014279
Trimmed Mean ( 18 / 20 )290638.8461538462512.53222907293115.675668869364
Trimmed Mean ( 19 / 20 )290836.0833333332407.40476350576120.808967292150
Trimmed Mean ( 20 / 20 )291025.7272727272260.08221719758128.767761216045
Median292701
Midrange288731.5
Midmean - Weighted Average at Xnp289438.741935484
Midmean - Weighted Average at X(n+1)p290152.40625
Midmean - Empirical Distribution Function290152.40625
Midmean - Empirical Distribution Function - Averaging290152.40625
Midmean - Empirical Distribution Function - Interpolation290277
Midmean - Closest Observation290152.40625
Midmean - True Basic - Statistics Graphics Toolkit290152.40625
Midmean - MS Excel (old versions)290152.40625
Number of observations62

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 290398.693548387 & 3371.87999685067 & 86.1236739799812 \tabularnewline
Geometric Mean & 289198.640897153 &  &  \tabularnewline
Harmonic Mean & 287995.872331463 &  &  \tabularnewline
Quadratic Mean & 291590.372392699 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 290435.338709677 & 3349.98416090903 & 86.6975259461724 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 290631.758064516 & 3296.14326885263 & 88.1732783920172 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 290670.951612903 & 3256.52137252677 & 89.2581126797176 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 290489.661290323 & 3159.03072978749 & 91.9553135558969 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 290440.870967742 & 3147.67206707134 & 92.2716422737054 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 290340.129032258 & 3108.15139919184 & 93.4124795554523 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 290747.709677419 & 3013.27086991479 & 96.4890719185962 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 290646.935483871 & 2962.79939523583 & 98.0987561801281 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 289928.967741935 & 2766.92196104877 & 104.783933852634 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 289927.516129032 & 2764.05712407727 & 104.892013122131 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 289521.048387097 & 2659.47155584223 & 108.864126691292 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 289415.758064516 & 2642.51152715964 & 109.522987918846 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 289504.451612903 & 2615.72919547292 & 110.678296558357 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 289459.064516129 & 2586.50183130778 & 111.911409074771 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 289248.096774194 & 2549.75583631194 & 113.441488261312 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 289001.64516129 & 2459.16692567258 & 117.520141534210 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 289132.161290323 & 2358.20855787379 & 122.606696649007 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 289264.548387097 & 2313.6148413004 & 125.027097520049 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 289557.516129032 & 2243.10665006016 & 129.087716859680 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 288754.612903226 & 1886.85397289973 & 153.034955036539 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 290454.266666667 & 3284.89742849665 & 88.421106895747 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 290474.5 & 3204.7474187048 & 90.6388123771062 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 290387.446428571 & 3140.89431251918 & 92.4537464604033 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 290278.944444444 & 3079.51788173717 & 94.2611654135604 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 290216.134615385 & 3038.86868400133 & 95.501373963041 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 290160.4 & 2989.33551677237 & 97.065183339905 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 290121.708333333 & 2936.42915564692 & 98.800854015297 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 290001.173913043 & 2892.74805011661 & 100.251099953676 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 289887.431818182 & 2846.79950193650 & 101.829240738938 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 289880.619047619 & 2832.91954666922 & 102.325750615983 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 289873.35 & 2809.36018825849 & 103.181269248245 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 289925.605263158 & 2796.95159894761 & 103.657712694151 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 289998.777777778 & 2776.50802814166 & 104.447303893400 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 290068.117647059 & 2747.33377824094 & 105.581680662327 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 290152.40625 & 2706.11274734246 & 107.221107670013 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 290277 & 2649.1660778528 & 109.572971821863 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 290453.5 & 2584.72445774918 & 112.373100014279 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 290638.846153846 & 2512.53222907293 & 115.675668869364 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 290836.083333333 & 2407.40476350576 & 120.808967292150 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 291025.727272727 & 2260.08221719758 & 128.767761216045 \tabularnewline
Median & 292701 &  &  \tabularnewline
Midrange & 288731.5 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 289438.741935484 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 290152.40625 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 290152.40625 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 290152.40625 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 290277 &  &  \tabularnewline
Midmean - Closest Observation & 290152.40625 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 290152.40625 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 290152.40625 &  &  \tabularnewline
Number of observations & 62 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=46782&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]290398.693548387[/C][C]3371.87999685067[/C][C]86.1236739799812[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]289198.640897153[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]287995.872331463[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]291590.372392699[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]290435.338709677[/C][C]3349.98416090903[/C][C]86.6975259461724[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]290631.758064516[/C][C]3296.14326885263[/C][C]88.1732783920172[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]290670.951612903[/C][C]3256.52137252677[/C][C]89.2581126797176[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]290489.661290323[/C][C]3159.03072978749[/C][C]91.9553135558969[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]290440.870967742[/C][C]3147.67206707134[/C][C]92.2716422737054[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]290340.129032258[/C][C]3108.15139919184[/C][C]93.4124795554523[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]290747.709677419[/C][C]3013.27086991479[/C][C]96.4890719185962[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]290646.935483871[/C][C]2962.79939523583[/C][C]98.0987561801281[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]289928.967741935[/C][C]2766.92196104877[/C][C]104.783933852634[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]289927.516129032[/C][C]2764.05712407727[/C][C]104.892013122131[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]289521.048387097[/C][C]2659.47155584223[/C][C]108.864126691292[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]289415.758064516[/C][C]2642.51152715964[/C][C]109.522987918846[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]289504.451612903[/C][C]2615.72919547292[/C][C]110.678296558357[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]289459.064516129[/C][C]2586.50183130778[/C][C]111.911409074771[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]289248.096774194[/C][C]2549.75583631194[/C][C]113.441488261312[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]289001.64516129[/C][C]2459.16692567258[/C][C]117.520141534210[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]289132.161290323[/C][C]2358.20855787379[/C][C]122.606696649007[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]289264.548387097[/C][C]2313.6148413004[/C][C]125.027097520049[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]289557.516129032[/C][C]2243.10665006016[/C][C]129.087716859680[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]288754.612903226[/C][C]1886.85397289973[/C][C]153.034955036539[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]290454.266666667[/C][C]3284.89742849665[/C][C]88.421106895747[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]290474.5[/C][C]3204.7474187048[/C][C]90.6388123771062[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]290387.446428571[/C][C]3140.89431251918[/C][C]92.4537464604033[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]290278.944444444[/C][C]3079.51788173717[/C][C]94.2611654135604[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]290216.134615385[/C][C]3038.86868400133[/C][C]95.501373963041[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]290160.4[/C][C]2989.33551677237[/C][C]97.065183339905[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]290121.708333333[/C][C]2936.42915564692[/C][C]98.800854015297[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]290001.173913043[/C][C]2892.74805011661[/C][C]100.251099953676[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]289887.431818182[/C][C]2846.79950193650[/C][C]101.829240738938[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]289880.619047619[/C][C]2832.91954666922[/C][C]102.325750615983[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]289873.35[/C][C]2809.36018825849[/C][C]103.181269248245[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]289925.605263158[/C][C]2796.95159894761[/C][C]103.657712694151[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]289998.777777778[/C][C]2776.50802814166[/C][C]104.447303893400[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]290068.117647059[/C][C]2747.33377824094[/C][C]105.581680662327[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]290152.40625[/C][C]2706.11274734246[/C][C]107.221107670013[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]290277[/C][C]2649.1660778528[/C][C]109.572971821863[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]290453.5[/C][C]2584.72445774918[/C][C]112.373100014279[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]290638.846153846[/C][C]2512.53222907293[/C][C]115.675668869364[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]290836.083333333[/C][C]2407.40476350576[/C][C]120.808967292150[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]291025.727272727[/C][C]2260.08221719758[/C][C]128.767761216045[/C][/ROW]
[ROW][C]Median[/C][C]292701[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]288731.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]289438.741935484[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]290152.40625[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]290152.40625[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]290152.40625[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]290277[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]290152.40625[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]290152.40625[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]290152.40625[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]62[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=46782&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=46782&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 Mean290398.6935483873371.8799968506786.1236739799812
Geometric Mean289198.640897153
Harmonic Mean287995.872331463
Quadratic Mean291590.372392699
Winsorized Mean ( 1 / 20 )290435.3387096773349.9841609090386.6975259461724
Winsorized Mean ( 2 / 20 )290631.7580645163296.1432688526388.1732783920172
Winsorized Mean ( 3 / 20 )290670.9516129033256.5213725267789.2581126797176
Winsorized Mean ( 4 / 20 )290489.6612903233159.0307297874991.9553135558969
Winsorized Mean ( 5 / 20 )290440.8709677423147.6720670713492.2716422737054
Winsorized Mean ( 6 / 20 )290340.1290322583108.1513991918493.4124795554523
Winsorized Mean ( 7 / 20 )290747.7096774193013.2708699147996.4890719185962
Winsorized Mean ( 8 / 20 )290646.9354838712962.7993952358398.0987561801281
Winsorized Mean ( 9 / 20 )289928.9677419352766.92196104877104.783933852634
Winsorized Mean ( 10 / 20 )289927.5161290322764.05712407727104.892013122131
Winsorized Mean ( 11 / 20 )289521.0483870972659.47155584223108.864126691292
Winsorized Mean ( 12 / 20 )289415.7580645162642.51152715964109.522987918846
Winsorized Mean ( 13 / 20 )289504.4516129032615.72919547292110.678296558357
Winsorized Mean ( 14 / 20 )289459.0645161292586.50183130778111.911409074771
Winsorized Mean ( 15 / 20 )289248.0967741942549.75583631194113.441488261312
Winsorized Mean ( 16 / 20 )289001.645161292459.16692567258117.520141534210
Winsorized Mean ( 17 / 20 )289132.1612903232358.20855787379122.606696649007
Winsorized Mean ( 18 / 20 )289264.5483870972313.6148413004125.027097520049
Winsorized Mean ( 19 / 20 )289557.5161290322243.10665006016129.087716859680
Winsorized Mean ( 20 / 20 )288754.6129032261886.85397289973153.034955036539
Trimmed Mean ( 1 / 20 )290454.2666666673284.8974284966588.421106895747
Trimmed Mean ( 2 / 20 )290474.53204.747418704890.6388123771062
Trimmed Mean ( 3 / 20 )290387.4464285713140.8943125191892.4537464604033
Trimmed Mean ( 4 / 20 )290278.9444444443079.5178817371794.2611654135604
Trimmed Mean ( 5 / 20 )290216.1346153853038.8686840013395.501373963041
Trimmed Mean ( 6 / 20 )290160.42989.3355167723797.065183339905
Trimmed Mean ( 7 / 20 )290121.7083333332936.4291556469298.800854015297
Trimmed Mean ( 8 / 20 )290001.1739130432892.74805011661100.251099953676
Trimmed Mean ( 9 / 20 )289887.4318181822846.79950193650101.829240738938
Trimmed Mean ( 10 / 20 )289880.6190476192832.91954666922102.325750615983
Trimmed Mean ( 11 / 20 )289873.352809.36018825849103.181269248245
Trimmed Mean ( 12 / 20 )289925.6052631582796.95159894761103.657712694151
Trimmed Mean ( 13 / 20 )289998.7777777782776.50802814166104.447303893400
Trimmed Mean ( 14 / 20 )290068.1176470592747.33377824094105.581680662327
Trimmed Mean ( 15 / 20 )290152.406252706.11274734246107.221107670013
Trimmed Mean ( 16 / 20 )2902772649.1660778528109.572971821863
Trimmed Mean ( 17 / 20 )290453.52584.72445774918112.373100014279
Trimmed Mean ( 18 / 20 )290638.8461538462512.53222907293115.675668869364
Trimmed Mean ( 19 / 20 )290836.0833333332407.40476350576120.808967292150
Trimmed Mean ( 20 / 20 )291025.7272727272260.08221719758128.767761216045
Median292701
Midrange288731.5
Midmean - Weighted Average at Xnp289438.741935484
Midmean - Weighted Average at X(n+1)p290152.40625
Midmean - Empirical Distribution Function290152.40625
Midmean - Empirical Distribution Function - Averaging290152.40625
Midmean - Empirical Distribution Function - Interpolation290277
Midmean - Closest Observation290152.40625
Midmean - True Basic - Statistics Graphics Toolkit290152.40625
Midmean - MS Excel (old versions)290152.40625
Number of observations62



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')