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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 computationWed, 23 Dec 2009 14:30:38 -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/2009/Dec/23/t1261603870yfr8v1utqazmhy0.htm/, Retrieved Mon, 29 Apr 2024 08:25:23 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=70578, Retrieved Mon, 29 Apr 2024 08:25:23 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact98
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Central tendency ...] [2009-12-23 21:30:38] [b02b8a83db8a631da1ab9c106b4cdcf2] [Current]
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Dataseries X:
27071
29462
26105
22397
23843
21705
18089
20764
25316
17704
15548
28029
29383
36438
32034
22679
24319
18004
17537
20366
22782
19169
13807
29743
25591
29096
26482
22405
27044
17970
18730
19684
19785
18479
10698
31956
29506
34506
27165
26736
23691
18157
17328
18205
20995
17382
9367
31124
26551
30651
25859
25100
25778
20418
18688
20424
24776
19814
12738
31566
30111
30019
31934
25826
26835
20205
17789
20520
22518
15572
11509
25447
24090
27786
26195
20516
22759
19028
16971




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=70578&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=70578&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=70578&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 Mean23067.9620253165641.01159161026135.9868094855637
Geometric Mean22311.878982548
Harmonic Mean21472.8084376397
Quadratic Mean23752.4893248388
Winsorized Mean ( 1 / 26 )23060.3544303797630.46457140699636.5767649384586
Winsorized Mean ( 2 / 26 )23018.3037974684612.19689619645337.5995107790971
Winsorized Mean ( 3 / 26 )23062.0126582278600.8669371080438.3812309081688
Winsorized Mean ( 4 / 26 )23115.0253164557589.20696293570739.230740250057
Winsorized Mean ( 5 / 26 )23201.9240506329563.97865531605941.1397201506329
Winsorized Mean ( 6 / 26 )23170.1772151899557.39806567841341.5684564441201
Winsorized Mean ( 7 / 26 )23252.2278481013529.51423420805343.9123754300534
Winsorized Mean ( 8 / 26 )23233.6962025316514.51755363686545.1562751130731
Winsorized Mean ( 9 / 26 )23229.3670886076511.82505803087445.385365026826
Winsorized Mean ( 10 / 26 )23214.0506329114503.09098424506746.1428476356938
Winsorized Mean ( 11 / 26 )23204.3037974684494.30762029739546.943042843458
Winsorized Mean ( 12 / 26 )23210.5316455696491.38222233242947.235187987463
Winsorized Mean ( 13 / 26 )23227.3164556962485.08848861473947.8826379121594
Winsorized Mean ( 14 / 26 )23182.4810126582476.06180742189748.6963681001895
Winsorized Mean ( 15 / 26 )22996.0253164557442.84976420472251.9273739656436
Winsorized Mean ( 16 / 26 )22960.582278481433.79840893381252.9291528175805
Winsorized Mean ( 17 / 26 )22837.2784810127413.8236017492555.1860222193188
Winsorized Mean ( 18 / 26 )22878.2911392405402.09651533461356.897511584257
Winsorized Mean ( 19 / 26 )22922.0632911392394.24075295321558.1422978711169
Winsorized Mean ( 20 / 26 )22879.7848101266385.75088435569859.3123327464087
Winsorized Mean ( 21 / 26 )22932.6835443038371.49177439542561.7313359942492
Winsorized Mean ( 22 / 26 )22920.4303797468359.50230738856763.7560035323317
Winsorized Mean ( 23 / 26 )23050.2784810127337.25497215076368.3467417367193
Winsorized Mean ( 24 / 26 )22993.7721518987322.08693669636371.3899557297953
Winsorized Mean ( 25 / 26 )22974.4683544304317.29895271316872.4063794033346
Winsorized Mean ( 26 / 26 )23022.1898734177290.89998408165179.141255184654
Trimmed Mean ( 1 / 26 )23072.2597402597608.30779968147237.9285942944362
Trimmed Mean ( 2 / 26 )23084.8582.26028667722339.6468736202803
Trimmed Mean ( 3 / 26 )23120.7808219178563.24143533425241.0495027025079
Trimmed Mean ( 4 / 26 )23142.5774647887545.97876583365142.3873214729377
Trimmed Mean ( 5 / 26 )23150.4637681159529.81741598356443.6951732232866
Trimmed Mean ( 6 / 26 )23138.3283582090518.41840565648344.6325363948227
Trimmed Mean ( 7 / 26 )23131.8769230769506.5492508269245.665602871419
Trimmed Mean ( 8 / 26 )23110.3174603175499.07759711218446.3060606086926
Trimmed Mean ( 9 / 26 )23090.3442622951493.24157277912146.8134592390395
Trimmed Mean ( 10 / 26 )23069.6610169492486.46635152804447.4229326334388
Trimmed Mean ( 11 / 26 )23049.6491228070479.742519503548.0458749969917
Trimmed Mean ( 12 / 26 )23029.4545454545472.96085345526548.6920944454715
Trimmed Mean ( 13 / 26 )23006.9622641509464.83697609082949.4946904990953
Trimmed Mean ( 14 / 26 )22980.7058823529455.65652896402550.4342732333971
Trimmed Mean ( 15 / 26 )22957.4693877551445.71249437029451.5073498672941
Trimmed Mean ( 16 / 26 )22953.1489361702439.61137805748252.212363195861
Trimmed Mean ( 17 / 26 )22952.3333333333433.13784984655552.9908280734748
Trimmed Mean ( 18 / 26 )22964.7674418605428.22242209815153.6281293476893
Trimmed Mean ( 19 / 26 )22974.0243902439423.53583873439254.2434011225468
Trimmed Mean ( 20 / 26 )22979.5641025641418.25062351256954.9420916807636
Trimmed Mean ( 21 / 26 )22979.5641025641412.20511551891655.7478867617537
Trimmed Mean ( 22 / 26 )22996.4406.45299106979156.5782526030208
Trimmed Mean ( 23 / 26 )23004.6666666667400.40979639677357.4528067836556
Trimmed Mean ( 24 / 26 )22999.6129032258396.47222218232758.0106540040248
Trimmed Mean ( 25 / 26 )23000.2758620690393.36031783427258.4712662138923
Trimmed Mean ( 26 / 26 )23003.2962962963388.30985151415959.2395382362776
Median22759
Midrange22902.5
Midmean - Weighted Average at Xnp22872.275
Midmean - Weighted Average at X(n+1)p22974.0243902439
Midmean - Empirical Distribution Function22974.0243902439
Midmean - Empirical Distribution Function - Averaging22974.0243902439
Midmean - Empirical Distribution Function - Interpolation22979.5641025641
Midmean - Closest Observation22872.275
Midmean - True Basic - Statistics Graphics Toolkit22974.0243902439
Midmean - MS Excel (old versions)22974.0243902439
Number of observations79

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 23067.9620253165 & 641.011591610261 & 35.9868094855637 \tabularnewline
Geometric Mean & 22311.878982548 &  &  \tabularnewline
Harmonic Mean & 21472.8084376397 &  &  \tabularnewline
Quadratic Mean & 23752.4893248388 &  &  \tabularnewline
Winsorized Mean ( 1 / 26 ) & 23060.3544303797 & 630.464571406996 & 36.5767649384586 \tabularnewline
Winsorized Mean ( 2 / 26 ) & 23018.3037974684 & 612.196896196453 & 37.5995107790971 \tabularnewline
Winsorized Mean ( 3 / 26 ) & 23062.0126582278 & 600.86693710804 & 38.3812309081688 \tabularnewline
Winsorized Mean ( 4 / 26 ) & 23115.0253164557 & 589.206962935707 & 39.230740250057 \tabularnewline
Winsorized Mean ( 5 / 26 ) & 23201.9240506329 & 563.978655316059 & 41.1397201506329 \tabularnewline
Winsorized Mean ( 6 / 26 ) & 23170.1772151899 & 557.398065678413 & 41.5684564441201 \tabularnewline
Winsorized Mean ( 7 / 26 ) & 23252.2278481013 & 529.514234208053 & 43.9123754300534 \tabularnewline
Winsorized Mean ( 8 / 26 ) & 23233.6962025316 & 514.517553636865 & 45.1562751130731 \tabularnewline
Winsorized Mean ( 9 / 26 ) & 23229.3670886076 & 511.825058030874 & 45.385365026826 \tabularnewline
Winsorized Mean ( 10 / 26 ) & 23214.0506329114 & 503.090984245067 & 46.1428476356938 \tabularnewline
Winsorized Mean ( 11 / 26 ) & 23204.3037974684 & 494.307620297395 & 46.943042843458 \tabularnewline
Winsorized Mean ( 12 / 26 ) & 23210.5316455696 & 491.382222332429 & 47.235187987463 \tabularnewline
Winsorized Mean ( 13 / 26 ) & 23227.3164556962 & 485.088488614739 & 47.8826379121594 \tabularnewline
Winsorized Mean ( 14 / 26 ) & 23182.4810126582 & 476.061807421897 & 48.6963681001895 \tabularnewline
Winsorized Mean ( 15 / 26 ) & 22996.0253164557 & 442.849764204722 & 51.9273739656436 \tabularnewline
Winsorized Mean ( 16 / 26 ) & 22960.582278481 & 433.798408933812 & 52.9291528175805 \tabularnewline
Winsorized Mean ( 17 / 26 ) & 22837.2784810127 & 413.82360174925 & 55.1860222193188 \tabularnewline
Winsorized Mean ( 18 / 26 ) & 22878.2911392405 & 402.096515334613 & 56.897511584257 \tabularnewline
Winsorized Mean ( 19 / 26 ) & 22922.0632911392 & 394.240752953215 & 58.1422978711169 \tabularnewline
Winsorized Mean ( 20 / 26 ) & 22879.7848101266 & 385.750884355698 & 59.3123327464087 \tabularnewline
Winsorized Mean ( 21 / 26 ) & 22932.6835443038 & 371.491774395425 & 61.7313359942492 \tabularnewline
Winsorized Mean ( 22 / 26 ) & 22920.4303797468 & 359.502307388567 & 63.7560035323317 \tabularnewline
Winsorized Mean ( 23 / 26 ) & 23050.2784810127 & 337.254972150763 & 68.3467417367193 \tabularnewline
Winsorized Mean ( 24 / 26 ) & 22993.7721518987 & 322.086936696363 & 71.3899557297953 \tabularnewline
Winsorized Mean ( 25 / 26 ) & 22974.4683544304 & 317.298952713168 & 72.4063794033346 \tabularnewline
Winsorized Mean ( 26 / 26 ) & 23022.1898734177 & 290.899984081651 & 79.141255184654 \tabularnewline
Trimmed Mean ( 1 / 26 ) & 23072.2597402597 & 608.307799681472 & 37.9285942944362 \tabularnewline
Trimmed Mean ( 2 / 26 ) & 23084.8 & 582.260286677223 & 39.6468736202803 \tabularnewline
Trimmed Mean ( 3 / 26 ) & 23120.7808219178 & 563.241435334252 & 41.0495027025079 \tabularnewline
Trimmed Mean ( 4 / 26 ) & 23142.5774647887 & 545.978765833651 & 42.3873214729377 \tabularnewline
Trimmed Mean ( 5 / 26 ) & 23150.4637681159 & 529.817415983564 & 43.6951732232866 \tabularnewline
Trimmed Mean ( 6 / 26 ) & 23138.3283582090 & 518.418405656483 & 44.6325363948227 \tabularnewline
Trimmed Mean ( 7 / 26 ) & 23131.8769230769 & 506.54925082692 & 45.665602871419 \tabularnewline
Trimmed Mean ( 8 / 26 ) & 23110.3174603175 & 499.077597112184 & 46.3060606086926 \tabularnewline
Trimmed Mean ( 9 / 26 ) & 23090.3442622951 & 493.241572779121 & 46.8134592390395 \tabularnewline
Trimmed Mean ( 10 / 26 ) & 23069.6610169492 & 486.466351528044 & 47.4229326334388 \tabularnewline
Trimmed Mean ( 11 / 26 ) & 23049.6491228070 & 479.7425195035 & 48.0458749969917 \tabularnewline
Trimmed Mean ( 12 / 26 ) & 23029.4545454545 & 472.960853455265 & 48.6920944454715 \tabularnewline
Trimmed Mean ( 13 / 26 ) & 23006.9622641509 & 464.836976090829 & 49.4946904990953 \tabularnewline
Trimmed Mean ( 14 / 26 ) & 22980.7058823529 & 455.656528964025 & 50.4342732333971 \tabularnewline
Trimmed Mean ( 15 / 26 ) & 22957.4693877551 & 445.712494370294 & 51.5073498672941 \tabularnewline
Trimmed Mean ( 16 / 26 ) & 22953.1489361702 & 439.611378057482 & 52.212363195861 \tabularnewline
Trimmed Mean ( 17 / 26 ) & 22952.3333333333 & 433.137849846555 & 52.9908280734748 \tabularnewline
Trimmed Mean ( 18 / 26 ) & 22964.7674418605 & 428.222422098151 & 53.6281293476893 \tabularnewline
Trimmed Mean ( 19 / 26 ) & 22974.0243902439 & 423.535838734392 & 54.2434011225468 \tabularnewline
Trimmed Mean ( 20 / 26 ) & 22979.5641025641 & 418.250623512569 & 54.9420916807636 \tabularnewline
Trimmed Mean ( 21 / 26 ) & 22979.5641025641 & 412.205115518916 & 55.7478867617537 \tabularnewline
Trimmed Mean ( 22 / 26 ) & 22996.4 & 406.452991069791 & 56.5782526030208 \tabularnewline
Trimmed Mean ( 23 / 26 ) & 23004.6666666667 & 400.409796396773 & 57.4528067836556 \tabularnewline
Trimmed Mean ( 24 / 26 ) & 22999.6129032258 & 396.472222182327 & 58.0106540040248 \tabularnewline
Trimmed Mean ( 25 / 26 ) & 23000.2758620690 & 393.360317834272 & 58.4712662138923 \tabularnewline
Trimmed Mean ( 26 / 26 ) & 23003.2962962963 & 388.309851514159 & 59.2395382362776 \tabularnewline
Median & 22759 &  &  \tabularnewline
Midrange & 22902.5 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 22872.275 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 22974.0243902439 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 22974.0243902439 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 22974.0243902439 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 22979.5641025641 &  &  \tabularnewline
Midmean - Closest Observation & 22872.275 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 22974.0243902439 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 22974.0243902439 &  &  \tabularnewline
Number of observations & 79 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=70578&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]23067.9620253165[/C][C]641.011591610261[/C][C]35.9868094855637[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]22311.878982548[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]21472.8084376397[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]23752.4893248388[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 26 )[/C][C]23060.3544303797[/C][C]630.464571406996[/C][C]36.5767649384586[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 26 )[/C][C]23018.3037974684[/C][C]612.196896196453[/C][C]37.5995107790971[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 26 )[/C][C]23062.0126582278[/C][C]600.86693710804[/C][C]38.3812309081688[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 26 )[/C][C]23115.0253164557[/C][C]589.206962935707[/C][C]39.230740250057[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 26 )[/C][C]23201.9240506329[/C][C]563.978655316059[/C][C]41.1397201506329[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 26 )[/C][C]23170.1772151899[/C][C]557.398065678413[/C][C]41.5684564441201[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 26 )[/C][C]23252.2278481013[/C][C]529.514234208053[/C][C]43.9123754300534[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 26 )[/C][C]23233.6962025316[/C][C]514.517553636865[/C][C]45.1562751130731[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 26 )[/C][C]23229.3670886076[/C][C]511.825058030874[/C][C]45.385365026826[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 26 )[/C][C]23214.0506329114[/C][C]503.090984245067[/C][C]46.1428476356938[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 26 )[/C][C]23204.3037974684[/C][C]494.307620297395[/C][C]46.943042843458[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 26 )[/C][C]23210.5316455696[/C][C]491.382222332429[/C][C]47.235187987463[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 26 )[/C][C]23227.3164556962[/C][C]485.088488614739[/C][C]47.8826379121594[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 26 )[/C][C]23182.4810126582[/C][C]476.061807421897[/C][C]48.6963681001895[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 26 )[/C][C]22996.0253164557[/C][C]442.849764204722[/C][C]51.9273739656436[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 26 )[/C][C]22960.582278481[/C][C]433.798408933812[/C][C]52.9291528175805[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 26 )[/C][C]22837.2784810127[/C][C]413.82360174925[/C][C]55.1860222193188[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 26 )[/C][C]22878.2911392405[/C][C]402.096515334613[/C][C]56.897511584257[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 26 )[/C][C]22922.0632911392[/C][C]394.240752953215[/C][C]58.1422978711169[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 26 )[/C][C]22879.7848101266[/C][C]385.750884355698[/C][C]59.3123327464087[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 26 )[/C][C]22932.6835443038[/C][C]371.491774395425[/C][C]61.7313359942492[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 26 )[/C][C]22920.4303797468[/C][C]359.502307388567[/C][C]63.7560035323317[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 26 )[/C][C]23050.2784810127[/C][C]337.254972150763[/C][C]68.3467417367193[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 26 )[/C][C]22993.7721518987[/C][C]322.086936696363[/C][C]71.3899557297953[/C][/ROW]
[ROW][C]Winsorized Mean ( 25 / 26 )[/C][C]22974.4683544304[/C][C]317.298952713168[/C][C]72.4063794033346[/C][/ROW]
[ROW][C]Winsorized Mean ( 26 / 26 )[/C][C]23022.1898734177[/C][C]290.899984081651[/C][C]79.141255184654[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 26 )[/C][C]23072.2597402597[/C][C]608.307799681472[/C][C]37.9285942944362[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 26 )[/C][C]23084.8[/C][C]582.260286677223[/C][C]39.6468736202803[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 26 )[/C][C]23120.7808219178[/C][C]563.241435334252[/C][C]41.0495027025079[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 26 )[/C][C]23142.5774647887[/C][C]545.978765833651[/C][C]42.3873214729377[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 26 )[/C][C]23150.4637681159[/C][C]529.817415983564[/C][C]43.6951732232866[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 26 )[/C][C]23138.3283582090[/C][C]518.418405656483[/C][C]44.6325363948227[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 26 )[/C][C]23131.8769230769[/C][C]506.54925082692[/C][C]45.665602871419[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 26 )[/C][C]23110.3174603175[/C][C]499.077597112184[/C][C]46.3060606086926[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 26 )[/C][C]23090.3442622951[/C][C]493.241572779121[/C][C]46.8134592390395[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 26 )[/C][C]23069.6610169492[/C][C]486.466351528044[/C][C]47.4229326334388[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 26 )[/C][C]23049.6491228070[/C][C]479.7425195035[/C][C]48.0458749969917[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 26 )[/C][C]23029.4545454545[/C][C]472.960853455265[/C][C]48.6920944454715[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 26 )[/C][C]23006.9622641509[/C][C]464.836976090829[/C][C]49.4946904990953[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 26 )[/C][C]22980.7058823529[/C][C]455.656528964025[/C][C]50.4342732333971[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 26 )[/C][C]22957.4693877551[/C][C]445.712494370294[/C][C]51.5073498672941[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 26 )[/C][C]22953.1489361702[/C][C]439.611378057482[/C][C]52.212363195861[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 26 )[/C][C]22952.3333333333[/C][C]433.137849846555[/C][C]52.9908280734748[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 26 )[/C][C]22964.7674418605[/C][C]428.222422098151[/C][C]53.6281293476893[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 26 )[/C][C]22974.0243902439[/C][C]423.535838734392[/C][C]54.2434011225468[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 26 )[/C][C]22979.5641025641[/C][C]418.250623512569[/C][C]54.9420916807636[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 26 )[/C][C]22979.5641025641[/C][C]412.205115518916[/C][C]55.7478867617537[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 26 )[/C][C]22996.4[/C][C]406.452991069791[/C][C]56.5782526030208[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 26 )[/C][C]23004.6666666667[/C][C]400.409796396773[/C][C]57.4528067836556[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 26 )[/C][C]22999.6129032258[/C][C]396.472222182327[/C][C]58.0106540040248[/C][/ROW]
[ROW][C]Trimmed Mean ( 25 / 26 )[/C][C]23000.2758620690[/C][C]393.360317834272[/C][C]58.4712662138923[/C][/ROW]
[ROW][C]Trimmed Mean ( 26 / 26 )[/C][C]23003.2962962963[/C][C]388.309851514159[/C][C]59.2395382362776[/C][/ROW]
[ROW][C]Median[/C][C]22759[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]22902.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]22872.275[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]22974.0243902439[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]22974.0243902439[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]22974.0243902439[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]22979.5641025641[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]22872.275[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]22974.0243902439[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]22974.0243902439[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]79[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=70578&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=70578&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 Mean23067.9620253165641.01159161026135.9868094855637
Geometric Mean22311.878982548
Harmonic Mean21472.8084376397
Quadratic Mean23752.4893248388
Winsorized Mean ( 1 / 26 )23060.3544303797630.46457140699636.5767649384586
Winsorized Mean ( 2 / 26 )23018.3037974684612.19689619645337.5995107790971
Winsorized Mean ( 3 / 26 )23062.0126582278600.8669371080438.3812309081688
Winsorized Mean ( 4 / 26 )23115.0253164557589.20696293570739.230740250057
Winsorized Mean ( 5 / 26 )23201.9240506329563.97865531605941.1397201506329
Winsorized Mean ( 6 / 26 )23170.1772151899557.39806567841341.5684564441201
Winsorized Mean ( 7 / 26 )23252.2278481013529.51423420805343.9123754300534
Winsorized Mean ( 8 / 26 )23233.6962025316514.51755363686545.1562751130731
Winsorized Mean ( 9 / 26 )23229.3670886076511.82505803087445.385365026826
Winsorized Mean ( 10 / 26 )23214.0506329114503.09098424506746.1428476356938
Winsorized Mean ( 11 / 26 )23204.3037974684494.30762029739546.943042843458
Winsorized Mean ( 12 / 26 )23210.5316455696491.38222233242947.235187987463
Winsorized Mean ( 13 / 26 )23227.3164556962485.08848861473947.8826379121594
Winsorized Mean ( 14 / 26 )23182.4810126582476.06180742189748.6963681001895
Winsorized Mean ( 15 / 26 )22996.0253164557442.84976420472251.9273739656436
Winsorized Mean ( 16 / 26 )22960.582278481433.79840893381252.9291528175805
Winsorized Mean ( 17 / 26 )22837.2784810127413.8236017492555.1860222193188
Winsorized Mean ( 18 / 26 )22878.2911392405402.09651533461356.897511584257
Winsorized Mean ( 19 / 26 )22922.0632911392394.24075295321558.1422978711169
Winsorized Mean ( 20 / 26 )22879.7848101266385.75088435569859.3123327464087
Winsorized Mean ( 21 / 26 )22932.6835443038371.49177439542561.7313359942492
Winsorized Mean ( 22 / 26 )22920.4303797468359.50230738856763.7560035323317
Winsorized Mean ( 23 / 26 )23050.2784810127337.25497215076368.3467417367193
Winsorized Mean ( 24 / 26 )22993.7721518987322.08693669636371.3899557297953
Winsorized Mean ( 25 / 26 )22974.4683544304317.29895271316872.4063794033346
Winsorized Mean ( 26 / 26 )23022.1898734177290.89998408165179.141255184654
Trimmed Mean ( 1 / 26 )23072.2597402597608.30779968147237.9285942944362
Trimmed Mean ( 2 / 26 )23084.8582.26028667722339.6468736202803
Trimmed Mean ( 3 / 26 )23120.7808219178563.24143533425241.0495027025079
Trimmed Mean ( 4 / 26 )23142.5774647887545.97876583365142.3873214729377
Trimmed Mean ( 5 / 26 )23150.4637681159529.81741598356443.6951732232866
Trimmed Mean ( 6 / 26 )23138.3283582090518.41840565648344.6325363948227
Trimmed Mean ( 7 / 26 )23131.8769230769506.5492508269245.665602871419
Trimmed Mean ( 8 / 26 )23110.3174603175499.07759711218446.3060606086926
Trimmed Mean ( 9 / 26 )23090.3442622951493.24157277912146.8134592390395
Trimmed Mean ( 10 / 26 )23069.6610169492486.46635152804447.4229326334388
Trimmed Mean ( 11 / 26 )23049.6491228070479.742519503548.0458749969917
Trimmed Mean ( 12 / 26 )23029.4545454545472.96085345526548.6920944454715
Trimmed Mean ( 13 / 26 )23006.9622641509464.83697609082949.4946904990953
Trimmed Mean ( 14 / 26 )22980.7058823529455.65652896402550.4342732333971
Trimmed Mean ( 15 / 26 )22957.4693877551445.71249437029451.5073498672941
Trimmed Mean ( 16 / 26 )22953.1489361702439.61137805748252.212363195861
Trimmed Mean ( 17 / 26 )22952.3333333333433.13784984655552.9908280734748
Trimmed Mean ( 18 / 26 )22964.7674418605428.22242209815153.6281293476893
Trimmed Mean ( 19 / 26 )22974.0243902439423.53583873439254.2434011225468
Trimmed Mean ( 20 / 26 )22979.5641025641418.25062351256954.9420916807636
Trimmed Mean ( 21 / 26 )22979.5641025641412.20511551891655.7478867617537
Trimmed Mean ( 22 / 26 )22996.4406.45299106979156.5782526030208
Trimmed Mean ( 23 / 26 )23004.6666666667400.40979639677357.4528067836556
Trimmed Mean ( 24 / 26 )22999.6129032258396.47222218232758.0106540040248
Trimmed Mean ( 25 / 26 )23000.2758620690393.36031783427258.4712662138923
Trimmed Mean ( 26 / 26 )23003.2962962963388.30985151415959.2395382362776
Median22759
Midrange22902.5
Midmean - Weighted Average at Xnp22872.275
Midmean - Weighted Average at X(n+1)p22974.0243902439
Midmean - Empirical Distribution Function22974.0243902439
Midmean - Empirical Distribution Function - Averaging22974.0243902439
Midmean - Empirical Distribution Function - Interpolation22979.5641025641
Midmean - Closest Observation22872.275
Midmean - True Basic - Statistics Graphics Toolkit22974.0243902439
Midmean - MS Excel (old versions)22974.0243902439
Number of observations79



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')