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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 computationMon, 13 Oct 2014 17:09:46 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2014/Oct/13/t1413216701d5r6kwn4adff52x.htm/, Retrieved Fri, 10 May 2024 15:00:36 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=240790, Retrieved Fri, 10 May 2024 15:00:36 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact64
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2014-10-13 16:09:46] [23f6b347f5ddfa38e8c261c083a091fc] [Current]
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Dataseries X:
31566
30111
30019
31934
25826
26835
20205
17789
20520
22518
15572
11509
25447
24090
27786
26195
20516
22759
19028
16971
20036
22485
18730
14538
27561
25985
34670
32066
27186
29586
21359
21553
19573
24256
22380
16167
27297
28287
33474
28229
28785
25597
18130
20198
22849
23118
21925
20801
18785
20659
29367
23992
20645
22356
17902
15879
16963
21035
17988
10437
24470
22237
27053
26419
22311
20624
17336
15586
17733
19231
16102
11770




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ fisher.wessa.net

\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 & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=240790&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]'Sir Ronald Aylmer Fisher' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=240790&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=240790&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'Sir Ronald Aylmer Fisher' @ fisher.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean22512.4583333333630.24077978787535.7204088585168
Geometric Mean21854.4107485935
Harmonic Mean21154.0715667598
Quadratic Mean23130.3312662424
Winsorized Mean ( 1 / 24 )22510.7361111111622.05688139474336.1875847440811
Winsorized Mean ( 2 / 24 )22478.875611.0789090405136.7855520251802
Winsorized Mean ( 3 / 24 )22588.7083333333584.36078209043538.6554146438895
Winsorized Mean ( 4 / 24 )22625.7083333333569.20256502436939.749835513065
Winsorized Mean ( 5 / 24 )22525.6388888889547.97985749450841.10669138804
Winsorized Mean ( 6 / 24 )22542.3888888889542.1968992217241.576019562721
Winsorized Mean ( 7 / 24 )22521.9722222222530.43465913382442.4594657125151
Winsorized Mean ( 8 / 24 )22504.8611111111524.68120297165442.8924478019216
Winsorized Mean ( 9 / 24 )22531.6111111111495.14213730286245.5053396058055
Winsorized Mean ( 10 / 24 )22463.5555555556482.93648103447646.5145136839474
Winsorized Mean ( 11 / 24 )22510.4583333333472.66183272320947.6248699913865
Winsorized Mean ( 12 / 24 )22502.7916666667450.22341912360349.9813885969553
Winsorized Mean ( 13 / 24 )22472.2777777778442.06365152110750.8349367799239
Winsorized Mean ( 14 / 24 )22442.9166666667430.55427607210652.1256387729107
Winsorized Mean ( 15 / 24 )22437.7083333333424.24131049384952.8890227762453
Winsorized Mean ( 16 / 24 )22439.7083333333414.95857422703154.0769843715922
Winsorized Mean ( 17 / 24 )22529.9027777778386.70917543965658.2605849787846
Winsorized Mean ( 18 / 24 )22439.6527777778368.73481197852360.8558021884974
Winsorized Mean ( 19 / 24 )22444.6666666667350.91795729814663.9598692511403
Winsorized Mean ( 20 / 24 )22442.7222222222334.49588949184667.0941644643717
Winsorized Mean ( 21 / 24 )22496.0972222222314.29256338474271.5769313150548
Winsorized Mean ( 22 / 24 )22567.5972222222285.73365927953778.9812347594093
Winsorized Mean ( 23 / 24 )22571.4305555556272.18269118593282.9275015880297
Winsorized Mean ( 24 / 24 )22248.0972222222224.84863815050998.9469956554942
Trimmed Mean ( 1 / 24 )22511.2857142857599.66888349439237.539526118327
Trimmed Mean ( 2 / 24 )22511.8676470588572.95844383353539.2905766366528
Trimmed Mean ( 3 / 24 )22529.8636363636548.13934469782841.1024383750151
Trimmed Mean ( 4 / 24 )22507.796875530.94250913427342.3921544946552
Trimmed Mean ( 5 / 24 )22473.564516129515.8491772561243.5661536491525
Trimmed Mean ( 6 / 24 )22461.0666666667504.39124681954344.5310397599001
Trimmed Mean ( 7 / 24 )22444.2413793103491.96535943935245.6215888957873
Trimmed Mean ( 8 / 24 )22429.9642857143479.75600600876746.752857712644
Trimmed Mean ( 9 / 24 )22417.4814814815466.02049509155948.1040677772705
Trimmed Mean ( 10 / 24 )22399.9230769231455.91572020079549.1317190533761
Trimmed Mean ( 11 / 24 )22390.76445.89161816636650.2157006047281
Trimmed Mean ( 12 / 24 )22374.4375435.28896095216751.4013437213232
Trimmed Mean ( 13 / 24 )22357.6956521739426.54555218233952.415728021978
Trimmed Mean ( 14 / 24 )22343.2727272727416.786752430753.6084042906037
Trimmed Mean ( 15 / 24 )22331.0714285714406.38845521325154.9500635219898
Trimmed Mean ( 16 / 24 )22318.275393.82400726964756.6706817970061
Trimmed Mean ( 17 / 24 )22303.8947368421379.0239182007458.8456128117736
Trimmed Mean ( 18 / 24 )22277.3055555556365.8602036328860.8902125302197
Trimmed Mean ( 19 / 24 )22258.2058823529352.34560791115563.1715150766557
Trimmed Mean ( 20 / 24 )22236.125338.02264415821365.782944972149
Trimmed Mean ( 21 / 24 )22211.3333333333322.06580798701668.9652014666169
Trimmed Mean ( 22 / 24 )22176.4642857143304.68409558246972.7851063027075
Trimmed Mean ( 23 / 24 )22127.2307692308287.79431387814476.8855731409611
Trimmed Mean ( 24 / 24 )22069.2916666667265.84992551349683.0140976117983
Median22274
Midrange22553.5
Midmean - Weighted Average at Xnp22181.4324324324
Midmean - Weighted Average at X(n+1)p22277.3055555556
Midmean - Empirical Distribution Function22181.4324324324
Midmean - Empirical Distribution Function - Averaging22277.3055555556
Midmean - Empirical Distribution Function - Interpolation22277.3055555556
Midmean - Closest Observation22181.4324324324
Midmean - True Basic - Statistics Graphics Toolkit22277.3055555556
Midmean - MS Excel (old versions)22303.8947368421
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 22512.4583333333 & 630.240779787875 & 35.7204088585168 \tabularnewline
Geometric Mean & 21854.4107485935 &  &  \tabularnewline
Harmonic Mean & 21154.0715667598 &  &  \tabularnewline
Quadratic Mean & 23130.3312662424 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 22510.7361111111 & 622.056881394743 & 36.1875847440811 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 22478.875 & 611.07890904051 & 36.7855520251802 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 22588.7083333333 & 584.360782090435 & 38.6554146438895 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 22625.7083333333 & 569.202565024369 & 39.749835513065 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 22525.6388888889 & 547.979857494508 & 41.10669138804 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 22542.3888888889 & 542.19689922172 & 41.576019562721 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 22521.9722222222 & 530.434659133824 & 42.4594657125151 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 22504.8611111111 & 524.681202971654 & 42.8924478019216 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 22531.6111111111 & 495.142137302862 & 45.5053396058055 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 22463.5555555556 & 482.936481034476 & 46.5145136839474 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 22510.4583333333 & 472.661832723209 & 47.6248699913865 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 22502.7916666667 & 450.223419123603 & 49.9813885969553 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 22472.2777777778 & 442.063651521107 & 50.8349367799239 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 22442.9166666667 & 430.554276072106 & 52.1256387729107 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 22437.7083333333 & 424.241310493849 & 52.8890227762453 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 22439.7083333333 & 414.958574227031 & 54.0769843715922 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 22529.9027777778 & 386.709175439656 & 58.2605849787846 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 22439.6527777778 & 368.734811978523 & 60.8558021884974 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 22444.6666666667 & 350.917957298146 & 63.9598692511403 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 22442.7222222222 & 334.495889491846 & 67.0941644643717 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 22496.0972222222 & 314.292563384742 & 71.5769313150548 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 22567.5972222222 & 285.733659279537 & 78.9812347594093 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 22571.4305555556 & 272.182691185932 & 82.9275015880297 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 22248.0972222222 & 224.848638150509 & 98.9469956554942 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 22511.2857142857 & 599.668883494392 & 37.539526118327 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 22511.8676470588 & 572.958443833535 & 39.2905766366528 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 22529.8636363636 & 548.139344697828 & 41.1024383750151 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 22507.796875 & 530.942509134273 & 42.3921544946552 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 22473.564516129 & 515.84917725612 & 43.5661536491525 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 22461.0666666667 & 504.391246819543 & 44.5310397599001 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 22444.2413793103 & 491.965359439352 & 45.6215888957873 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 22429.9642857143 & 479.756006008767 & 46.752857712644 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 22417.4814814815 & 466.020495091559 & 48.1040677772705 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 22399.9230769231 & 455.915720200795 & 49.1317190533761 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 22390.76 & 445.891618166366 & 50.2157006047281 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 22374.4375 & 435.288960952167 & 51.4013437213232 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 22357.6956521739 & 426.545552182339 & 52.415728021978 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 22343.2727272727 & 416.7867524307 & 53.6084042906037 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 22331.0714285714 & 406.388455213251 & 54.9500635219898 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 22318.275 & 393.824007269647 & 56.6706817970061 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 22303.8947368421 & 379.02391820074 & 58.8456128117736 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 22277.3055555556 & 365.86020363288 & 60.8902125302197 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 22258.2058823529 & 352.345607911155 & 63.1715150766557 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 22236.125 & 338.022644158213 & 65.782944972149 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 22211.3333333333 & 322.065807987016 & 68.9652014666169 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 22176.4642857143 & 304.684095582469 & 72.7851063027075 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 22127.2307692308 & 287.794313878144 & 76.8855731409611 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 22069.2916666667 & 265.849925513496 & 83.0140976117983 \tabularnewline
Median & 22274 &  &  \tabularnewline
Midrange & 22553.5 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 22181.4324324324 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 22277.3055555556 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 22181.4324324324 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 22277.3055555556 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 22277.3055555556 &  &  \tabularnewline
Midmean - Closest Observation & 22181.4324324324 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 22277.3055555556 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 22303.8947368421 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=240790&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]22512.4583333333[/C][C]630.240779787875[/C][C]35.7204088585168[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]21854.4107485935[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]21154.0715667598[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]23130.3312662424[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]22510.7361111111[/C][C]622.056881394743[/C][C]36.1875847440811[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]22478.875[/C][C]611.07890904051[/C][C]36.7855520251802[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]22588.7083333333[/C][C]584.360782090435[/C][C]38.6554146438895[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]22625.7083333333[/C][C]569.202565024369[/C][C]39.749835513065[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]22525.6388888889[/C][C]547.979857494508[/C][C]41.10669138804[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]22542.3888888889[/C][C]542.19689922172[/C][C]41.576019562721[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]22521.9722222222[/C][C]530.434659133824[/C][C]42.4594657125151[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]22504.8611111111[/C][C]524.681202971654[/C][C]42.8924478019216[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]22531.6111111111[/C][C]495.142137302862[/C][C]45.5053396058055[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]22463.5555555556[/C][C]482.936481034476[/C][C]46.5145136839474[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]22510.4583333333[/C][C]472.661832723209[/C][C]47.6248699913865[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]22502.7916666667[/C][C]450.223419123603[/C][C]49.9813885969553[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]22472.2777777778[/C][C]442.063651521107[/C][C]50.8349367799239[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]22442.9166666667[/C][C]430.554276072106[/C][C]52.1256387729107[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]22437.7083333333[/C][C]424.241310493849[/C][C]52.8890227762453[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]22439.7083333333[/C][C]414.958574227031[/C][C]54.0769843715922[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]22529.9027777778[/C][C]386.709175439656[/C][C]58.2605849787846[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]22439.6527777778[/C][C]368.734811978523[/C][C]60.8558021884974[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]22444.6666666667[/C][C]350.917957298146[/C][C]63.9598692511403[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]22442.7222222222[/C][C]334.495889491846[/C][C]67.0941644643717[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]22496.0972222222[/C][C]314.292563384742[/C][C]71.5769313150548[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]22567.5972222222[/C][C]285.733659279537[/C][C]78.9812347594093[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]22571.4305555556[/C][C]272.182691185932[/C][C]82.9275015880297[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]22248.0972222222[/C][C]224.848638150509[/C][C]98.9469956554942[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]22511.2857142857[/C][C]599.668883494392[/C][C]37.539526118327[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]22511.8676470588[/C][C]572.958443833535[/C][C]39.2905766366528[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]22529.8636363636[/C][C]548.139344697828[/C][C]41.1024383750151[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]22507.796875[/C][C]530.942509134273[/C][C]42.3921544946552[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]22473.564516129[/C][C]515.84917725612[/C][C]43.5661536491525[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]22461.0666666667[/C][C]504.391246819543[/C][C]44.5310397599001[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]22444.2413793103[/C][C]491.965359439352[/C][C]45.6215888957873[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]22429.9642857143[/C][C]479.756006008767[/C][C]46.752857712644[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]22417.4814814815[/C][C]466.020495091559[/C][C]48.1040677772705[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]22399.9230769231[/C][C]455.915720200795[/C][C]49.1317190533761[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]22390.76[/C][C]445.891618166366[/C][C]50.2157006047281[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]22374.4375[/C][C]435.288960952167[/C][C]51.4013437213232[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]22357.6956521739[/C][C]426.545552182339[/C][C]52.415728021978[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]22343.2727272727[/C][C]416.7867524307[/C][C]53.6084042906037[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]22331.0714285714[/C][C]406.388455213251[/C][C]54.9500635219898[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]22318.275[/C][C]393.824007269647[/C][C]56.6706817970061[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]22303.8947368421[/C][C]379.02391820074[/C][C]58.8456128117736[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]22277.3055555556[/C][C]365.86020363288[/C][C]60.8902125302197[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]22258.2058823529[/C][C]352.345607911155[/C][C]63.1715150766557[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]22236.125[/C][C]338.022644158213[/C][C]65.782944972149[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]22211.3333333333[/C][C]322.065807987016[/C][C]68.9652014666169[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]22176.4642857143[/C][C]304.684095582469[/C][C]72.7851063027075[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]22127.2307692308[/C][C]287.794313878144[/C][C]76.8855731409611[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]22069.2916666667[/C][C]265.849925513496[/C][C]83.0140976117983[/C][/ROW]
[ROW][C]Median[/C][C]22274[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]22553.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]22181.4324324324[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]22277.3055555556[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]22181.4324324324[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]22277.3055555556[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]22277.3055555556[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]22181.4324324324[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]22277.3055555556[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]22303.8947368421[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]72[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=240790&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=240790&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 Mean22512.4583333333630.24077978787535.7204088585168
Geometric Mean21854.4107485935
Harmonic Mean21154.0715667598
Quadratic Mean23130.3312662424
Winsorized Mean ( 1 / 24 )22510.7361111111622.05688139474336.1875847440811
Winsorized Mean ( 2 / 24 )22478.875611.0789090405136.7855520251802
Winsorized Mean ( 3 / 24 )22588.7083333333584.36078209043538.6554146438895
Winsorized Mean ( 4 / 24 )22625.7083333333569.20256502436939.749835513065
Winsorized Mean ( 5 / 24 )22525.6388888889547.97985749450841.10669138804
Winsorized Mean ( 6 / 24 )22542.3888888889542.1968992217241.576019562721
Winsorized Mean ( 7 / 24 )22521.9722222222530.43465913382442.4594657125151
Winsorized Mean ( 8 / 24 )22504.8611111111524.68120297165442.8924478019216
Winsorized Mean ( 9 / 24 )22531.6111111111495.14213730286245.5053396058055
Winsorized Mean ( 10 / 24 )22463.5555555556482.93648103447646.5145136839474
Winsorized Mean ( 11 / 24 )22510.4583333333472.66183272320947.6248699913865
Winsorized Mean ( 12 / 24 )22502.7916666667450.22341912360349.9813885969553
Winsorized Mean ( 13 / 24 )22472.2777777778442.06365152110750.8349367799239
Winsorized Mean ( 14 / 24 )22442.9166666667430.55427607210652.1256387729107
Winsorized Mean ( 15 / 24 )22437.7083333333424.24131049384952.8890227762453
Winsorized Mean ( 16 / 24 )22439.7083333333414.95857422703154.0769843715922
Winsorized Mean ( 17 / 24 )22529.9027777778386.70917543965658.2605849787846
Winsorized Mean ( 18 / 24 )22439.6527777778368.73481197852360.8558021884974
Winsorized Mean ( 19 / 24 )22444.6666666667350.91795729814663.9598692511403
Winsorized Mean ( 20 / 24 )22442.7222222222334.49588949184667.0941644643717
Winsorized Mean ( 21 / 24 )22496.0972222222314.29256338474271.5769313150548
Winsorized Mean ( 22 / 24 )22567.5972222222285.73365927953778.9812347594093
Winsorized Mean ( 23 / 24 )22571.4305555556272.18269118593282.9275015880297
Winsorized Mean ( 24 / 24 )22248.0972222222224.84863815050998.9469956554942
Trimmed Mean ( 1 / 24 )22511.2857142857599.66888349439237.539526118327
Trimmed Mean ( 2 / 24 )22511.8676470588572.95844383353539.2905766366528
Trimmed Mean ( 3 / 24 )22529.8636363636548.13934469782841.1024383750151
Trimmed Mean ( 4 / 24 )22507.796875530.94250913427342.3921544946552
Trimmed Mean ( 5 / 24 )22473.564516129515.8491772561243.5661536491525
Trimmed Mean ( 6 / 24 )22461.0666666667504.39124681954344.5310397599001
Trimmed Mean ( 7 / 24 )22444.2413793103491.96535943935245.6215888957873
Trimmed Mean ( 8 / 24 )22429.9642857143479.75600600876746.752857712644
Trimmed Mean ( 9 / 24 )22417.4814814815466.02049509155948.1040677772705
Trimmed Mean ( 10 / 24 )22399.9230769231455.91572020079549.1317190533761
Trimmed Mean ( 11 / 24 )22390.76445.89161816636650.2157006047281
Trimmed Mean ( 12 / 24 )22374.4375435.28896095216751.4013437213232
Trimmed Mean ( 13 / 24 )22357.6956521739426.54555218233952.415728021978
Trimmed Mean ( 14 / 24 )22343.2727272727416.786752430753.6084042906037
Trimmed Mean ( 15 / 24 )22331.0714285714406.38845521325154.9500635219898
Trimmed Mean ( 16 / 24 )22318.275393.82400726964756.6706817970061
Trimmed Mean ( 17 / 24 )22303.8947368421379.0239182007458.8456128117736
Trimmed Mean ( 18 / 24 )22277.3055555556365.8602036328860.8902125302197
Trimmed Mean ( 19 / 24 )22258.2058823529352.34560791115563.1715150766557
Trimmed Mean ( 20 / 24 )22236.125338.02264415821365.782944972149
Trimmed Mean ( 21 / 24 )22211.3333333333322.06580798701668.9652014666169
Trimmed Mean ( 22 / 24 )22176.4642857143304.68409558246972.7851063027075
Trimmed Mean ( 23 / 24 )22127.2307692308287.79431387814476.8855731409611
Trimmed Mean ( 24 / 24 )22069.2916666667265.84992551349683.0140976117983
Median22274
Midrange22553.5
Midmean - Weighted Average at Xnp22181.4324324324
Midmean - Weighted Average at X(n+1)p22277.3055555556
Midmean - Empirical Distribution Function22181.4324324324
Midmean - Empirical Distribution Function - Averaging22277.3055555556
Midmean - Empirical Distribution Function - Interpolation22277.3055555556
Midmean - Closest Observation22181.4324324324
Midmean - True Basic - Statistics Graphics Toolkit22277.3055555556
Midmean - MS Excel (old versions)22303.8947368421
Number of observations72



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')