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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 computationTue, 02 Jun 2009 10:41:29 -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/Jun/02/t1243960969ets21hqe3cozcyr.htm/, Retrieved Fri, 10 May 2024 11:48:23 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=41316, Retrieved Fri, 10 May 2024 11:48:23 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact91
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Centrummaten 'aan...] [2009-06-02 16:41:29] [bddbb8640adbf7d76f1766fd0c9aa6ca] [Current]
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Dataseries X:
51772
48439
45716
43851
41622
45180
72550
77681
71177
63390
57386
56765
55772
53605
50338
47314
44596
47029
72490
78086
71058
63276
56918
55170
52980
50466
48553
46307
43796
45642
70765
75685
69220
62898
56011
54148
46626
46018
42408
42483
40113
41381
62348
63611
58389
46175
40555
37909
37866
34418
31736
29533
27604
30575
51345
52455
43367
37077
33016
33117
32279
30369
28983
27864
24591
29528
46549
47932
41584
37295
34666
36773
39591
39833




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=41316&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=41316&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41316&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 Mean48048.83783783781555.4979933817630.8896816596828
Geometric Mean46243.3264242868
Harmonic Mean44480.8224089489
Quadratic Mean49852.9810553803
Winsorized Mean ( 1 / 24 )48084.08108108111546.1553778113531.0991261105634
Winsorized Mean ( 2 / 24 )48037.16216216221531.1368639905031.3735259674738
Winsorized Mean ( 3 / 24 )47955.43243243241493.0165524193832.1198263707943
Winsorized Mean ( 4 / 24 )47981.64864864861487.2166715545332.2627156932657
Winsorized Mean ( 5 / 24 )47893.27027027031467.501886869832.6359173359751
Winsorized Mean ( 6 / 24 )47951.40540540541453.9793107044732.9794275973379
Winsorized Mean ( 7 / 24 )47943.17567567571444.7450834998433.1845224622845
Winsorized Mean ( 8 / 24 )47901.66216216221388.7537536421334.4925527916925
Winsorized Mean ( 9 / 24 )47285.5270270271244.4516856275137.9970774061698
Winsorized Mean ( 10 / 24 )47355.25675675681222.8591296492938.7250302251398
Winsorized Mean ( 11 / 24 )47353.32432432431217.4107733852338.8967514987976
Winsorized Mean ( 12 / 24 )475031173.3849084082640.4837318595136
Winsorized Mean ( 13 / 24 )47449.9459459461149.4771616867841.2795899975222
Winsorized Mean ( 14 / 24 )47099.5675675676962.50214481767848.9345066098418
Winsorized Mean ( 15 / 24 )46957.8783783784921.34006438256550.9669341361456
Winsorized Mean ( 16 / 24 )46903.8243243243898.8587839165652.1815274697014
Winsorized Mean ( 17 / 24 )46999.8513513514874.49664279561753.7450334870364
Winsorized Mean ( 18 / 24 )46826.9054054054845.31046704597855.3961026521376
Winsorized Mean ( 19 / 24 )47197.4054054054775.79923912661960.8371380442954
Winsorized Mean ( 20 / 24 )47100.1081081081742.59074830101563.4267370228746
Winsorized Mean ( 21 / 24 )46889.5405405405689.38783166439968.0161998614545
Winsorized Mean ( 22 / 24 )46859.5135135135648.64500760270272.2421555153866
Winsorized Mean ( 23 / 24 )46921.9864864865587.37618166140679.8840469727026
Winsorized Mean ( 24 / 24 )46817.5540540541554.99013140906984.3574532310846
Trimmed Mean ( 1 / 24 )47957.45833333331507.5083538695631.8123997192012
Trimmed Mean ( 2 / 24 )47823.61461.6158453077432.7196781244054
Trimmed Mean ( 3 / 24 )47707.39705882351416.6069770905333.6772286388186
Trimmed Mean ( 4 / 24 )47614.6969696971380.3941253296534.4935523094364
Trimmed Mean ( 5 / 24 )47508.6251338.8940849760035.483482624282
Trimmed Mean ( 6 / 24 )47416.80645161291295.1600206253636.6107706356763
Trimmed Mean ( 7 / 24 )47306.91666666671245.7631956807937.9742448891455
Trimmed Mean ( 8 / 24 )47190.94827586211187.6047532164639.7362406541842
Trimmed Mean ( 9 / 24 )47073.55357142861130.7239354190941.6313408577322
Trimmed Mean ( 10 / 24 )47041.27777777781097.2092450735942.8735703686335
Trimmed Mean ( 11 / 24 )46996.59615384621060.2828442679244.3245841502746
Trimmed Mean ( 12 / 24 )46948.61014.9093193633746.2589111206999
Trimmed Mean ( 13 / 24 )46877.375967.54915145596448.4496058204993
Trimmed Mean ( 14 / 24 )46806.5217391304912.41269146955451.2997267319273
Trimmed Mean ( 15 / 24 )46771.3181818182886.9469016314752.7329404903337
Trimmed Mean ( 16 / 24 )46749.4047619048862.73923279805254.1871784482157
Trimmed Mean ( 17 / 24 )46731.55835.47868971119755.9338623180848
Trimmed Mean ( 18 / 24 )46700.8157894737804.33323672305658.0615268116211
Trimmed Mean ( 19 / 24 )46686.4166666667769.26651869538360.6895211634106
Trimmed Mean ( 20 / 24 )46627.8823529412738.92426479260963.1023835250938
Trimmed Mean ( 21 / 24 )46573.28125705.24287630959766.0386411752348
Trimmed Mean ( 22 / 24 )46536.1333333333673.15996755281669.1308687034811
Trimmed Mean ( 23 / 24 )46497.2857142857638.75135481098272.7940306726161
Trimmed Mean ( 24 / 24 )46444.7307692308607.86728449730776.4060378864435
Median46241
Midrange51338.5
Midmean - Weighted Average at Xnp46449.1891891892
Midmean - Weighted Average at X(n+1)p46700.8157894737
Midmean - Empirical Distribution Function46700.8157894737
Midmean - Empirical Distribution Function - Averaging46700.8157894737
Midmean - Empirical Distribution Function - Interpolation46686.4166666667
Midmean - Closest Observation46700.8157894737
Midmean - True Basic - Statistics Graphics Toolkit46700.8157894737
Midmean - MS Excel (old versions)46700.8157894737
Number of observations74

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 48048.8378378378 & 1555.49799338176 & 30.8896816596828 \tabularnewline
Geometric Mean & 46243.3264242868 &  &  \tabularnewline
Harmonic Mean & 44480.8224089489 &  &  \tabularnewline
Quadratic Mean & 49852.9810553803 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 48084.0810810811 & 1546.15537781135 & 31.0991261105634 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 48037.1621621622 & 1531.13686399050 & 31.3735259674738 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 47955.4324324324 & 1493.01655241938 & 32.1198263707943 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 47981.6486486486 & 1487.21667155453 & 32.2627156932657 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 47893.2702702703 & 1467.5018868698 & 32.6359173359751 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 47951.4054054054 & 1453.97931070447 & 32.9794275973379 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 47943.1756756757 & 1444.74508349984 & 33.1845224622845 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 47901.6621621622 & 1388.75375364213 & 34.4925527916925 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 47285.527027027 & 1244.45168562751 & 37.9970774061698 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 47355.2567567568 & 1222.85912964929 & 38.7250302251398 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 47353.3243243243 & 1217.41077338523 & 38.8967514987976 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 47503 & 1173.38490840826 & 40.4837318595136 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 47449.945945946 & 1149.47716168678 & 41.2795899975222 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 47099.5675675676 & 962.502144817678 & 48.9345066098418 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 46957.8783783784 & 921.340064382565 & 50.9669341361456 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 46903.8243243243 & 898.85878391656 & 52.1815274697014 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 46999.8513513514 & 874.496642795617 & 53.7450334870364 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 46826.9054054054 & 845.310467045978 & 55.3961026521376 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 47197.4054054054 & 775.799239126619 & 60.8371380442954 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 47100.1081081081 & 742.590748301015 & 63.4267370228746 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 46889.5405405405 & 689.387831664399 & 68.0161998614545 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 46859.5135135135 & 648.645007602702 & 72.2421555153866 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 46921.9864864865 & 587.376181661406 & 79.8840469727026 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 46817.5540540541 & 554.990131409069 & 84.3574532310846 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 47957.4583333333 & 1507.50835386956 & 31.8123997192012 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 47823.6 & 1461.61584530774 & 32.7196781244054 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 47707.3970588235 & 1416.60697709053 & 33.6772286388186 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 47614.696969697 & 1380.39412532965 & 34.4935523094364 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 47508.625 & 1338.89408497600 & 35.483482624282 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 47416.8064516129 & 1295.16002062536 & 36.6107706356763 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 47306.9166666667 & 1245.76319568079 & 37.9742448891455 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 47190.9482758621 & 1187.60475321646 & 39.7362406541842 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 47073.5535714286 & 1130.72393541909 & 41.6313408577322 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 47041.2777777778 & 1097.20924507359 & 42.8735703686335 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 46996.5961538462 & 1060.28284426792 & 44.3245841502746 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 46948.6 & 1014.90931936337 & 46.2589111206999 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 46877.375 & 967.549151455964 & 48.4496058204993 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 46806.5217391304 & 912.412691469554 & 51.2997267319273 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 46771.3181818182 & 886.94690163147 & 52.7329404903337 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 46749.4047619048 & 862.739232798052 & 54.1871784482157 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 46731.55 & 835.478689711197 & 55.9338623180848 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 46700.8157894737 & 804.333236723056 & 58.0615268116211 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 46686.4166666667 & 769.266518695383 & 60.6895211634106 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 46627.8823529412 & 738.924264792609 & 63.1023835250938 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 46573.28125 & 705.242876309597 & 66.0386411752348 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 46536.1333333333 & 673.159967552816 & 69.1308687034811 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 46497.2857142857 & 638.751354810982 & 72.7940306726161 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 46444.7307692308 & 607.867284497307 & 76.4060378864435 \tabularnewline
Median & 46241 &  &  \tabularnewline
Midrange & 51338.5 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 46449.1891891892 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 46700.8157894737 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 46700.8157894737 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 46700.8157894737 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 46686.4166666667 &  &  \tabularnewline
Midmean - Closest Observation & 46700.8157894737 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 46700.8157894737 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 46700.8157894737 &  &  \tabularnewline
Number of observations & 74 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41316&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]48048.8378378378[/C][C]1555.49799338176[/C][C]30.8896816596828[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]46243.3264242868[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]44480.8224089489[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]49852.9810553803[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]48084.0810810811[/C][C]1546.15537781135[/C][C]31.0991261105634[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]48037.1621621622[/C][C]1531.13686399050[/C][C]31.3735259674738[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]47955.4324324324[/C][C]1493.01655241938[/C][C]32.1198263707943[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]47981.6486486486[/C][C]1487.21667155453[/C][C]32.2627156932657[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]47893.2702702703[/C][C]1467.5018868698[/C][C]32.6359173359751[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]47951.4054054054[/C][C]1453.97931070447[/C][C]32.9794275973379[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]47943.1756756757[/C][C]1444.74508349984[/C][C]33.1845224622845[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]47901.6621621622[/C][C]1388.75375364213[/C][C]34.4925527916925[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]47285.527027027[/C][C]1244.45168562751[/C][C]37.9970774061698[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]47355.2567567568[/C][C]1222.85912964929[/C][C]38.7250302251398[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]47353.3243243243[/C][C]1217.41077338523[/C][C]38.8967514987976[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]47503[/C][C]1173.38490840826[/C][C]40.4837318595136[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]47449.945945946[/C][C]1149.47716168678[/C][C]41.2795899975222[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]47099.5675675676[/C][C]962.502144817678[/C][C]48.9345066098418[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]46957.8783783784[/C][C]921.340064382565[/C][C]50.9669341361456[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]46903.8243243243[/C][C]898.85878391656[/C][C]52.1815274697014[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]46999.8513513514[/C][C]874.496642795617[/C][C]53.7450334870364[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]46826.9054054054[/C][C]845.310467045978[/C][C]55.3961026521376[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]47197.4054054054[/C][C]775.799239126619[/C][C]60.8371380442954[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]47100.1081081081[/C][C]742.590748301015[/C][C]63.4267370228746[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]46889.5405405405[/C][C]689.387831664399[/C][C]68.0161998614545[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]46859.5135135135[/C][C]648.645007602702[/C][C]72.2421555153866[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]46921.9864864865[/C][C]587.376181661406[/C][C]79.8840469727026[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]46817.5540540541[/C][C]554.990131409069[/C][C]84.3574532310846[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]47957.4583333333[/C][C]1507.50835386956[/C][C]31.8123997192012[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]47823.6[/C][C]1461.61584530774[/C][C]32.7196781244054[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]47707.3970588235[/C][C]1416.60697709053[/C][C]33.6772286388186[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]47614.696969697[/C][C]1380.39412532965[/C][C]34.4935523094364[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]47508.625[/C][C]1338.89408497600[/C][C]35.483482624282[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]47416.8064516129[/C][C]1295.16002062536[/C][C]36.6107706356763[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]47306.9166666667[/C][C]1245.76319568079[/C][C]37.9742448891455[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]47190.9482758621[/C][C]1187.60475321646[/C][C]39.7362406541842[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]47073.5535714286[/C][C]1130.72393541909[/C][C]41.6313408577322[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]47041.2777777778[/C][C]1097.20924507359[/C][C]42.8735703686335[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]46996.5961538462[/C][C]1060.28284426792[/C][C]44.3245841502746[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]46948.6[/C][C]1014.90931936337[/C][C]46.2589111206999[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]46877.375[/C][C]967.549151455964[/C][C]48.4496058204993[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]46806.5217391304[/C][C]912.412691469554[/C][C]51.2997267319273[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]46771.3181818182[/C][C]886.94690163147[/C][C]52.7329404903337[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]46749.4047619048[/C][C]862.739232798052[/C][C]54.1871784482157[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]46731.55[/C][C]835.478689711197[/C][C]55.9338623180848[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]46700.8157894737[/C][C]804.333236723056[/C][C]58.0615268116211[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]46686.4166666667[/C][C]769.266518695383[/C][C]60.6895211634106[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]46627.8823529412[/C][C]738.924264792609[/C][C]63.1023835250938[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]46573.28125[/C][C]705.242876309597[/C][C]66.0386411752348[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]46536.1333333333[/C][C]673.159967552816[/C][C]69.1308687034811[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]46497.2857142857[/C][C]638.751354810982[/C][C]72.7940306726161[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]46444.7307692308[/C][C]607.867284497307[/C][C]76.4060378864435[/C][/ROW]
[ROW][C]Median[/C][C]46241[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]51338.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]46449.1891891892[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]46700.8157894737[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]46700.8157894737[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]46700.8157894737[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]46686.4166666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]46700.8157894737[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]46700.8157894737[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]46700.8157894737[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]74[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41316&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41316&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 Mean48048.83783783781555.4979933817630.8896816596828
Geometric Mean46243.3264242868
Harmonic Mean44480.8224089489
Quadratic Mean49852.9810553803
Winsorized Mean ( 1 / 24 )48084.08108108111546.1553778113531.0991261105634
Winsorized Mean ( 2 / 24 )48037.16216216221531.1368639905031.3735259674738
Winsorized Mean ( 3 / 24 )47955.43243243241493.0165524193832.1198263707943
Winsorized Mean ( 4 / 24 )47981.64864864861487.2166715545332.2627156932657
Winsorized Mean ( 5 / 24 )47893.27027027031467.501886869832.6359173359751
Winsorized Mean ( 6 / 24 )47951.40540540541453.9793107044732.9794275973379
Winsorized Mean ( 7 / 24 )47943.17567567571444.7450834998433.1845224622845
Winsorized Mean ( 8 / 24 )47901.66216216221388.7537536421334.4925527916925
Winsorized Mean ( 9 / 24 )47285.5270270271244.4516856275137.9970774061698
Winsorized Mean ( 10 / 24 )47355.25675675681222.8591296492938.7250302251398
Winsorized Mean ( 11 / 24 )47353.32432432431217.4107733852338.8967514987976
Winsorized Mean ( 12 / 24 )475031173.3849084082640.4837318595136
Winsorized Mean ( 13 / 24 )47449.9459459461149.4771616867841.2795899975222
Winsorized Mean ( 14 / 24 )47099.5675675676962.50214481767848.9345066098418
Winsorized Mean ( 15 / 24 )46957.8783783784921.34006438256550.9669341361456
Winsorized Mean ( 16 / 24 )46903.8243243243898.8587839165652.1815274697014
Winsorized Mean ( 17 / 24 )46999.8513513514874.49664279561753.7450334870364
Winsorized Mean ( 18 / 24 )46826.9054054054845.31046704597855.3961026521376
Winsorized Mean ( 19 / 24 )47197.4054054054775.79923912661960.8371380442954
Winsorized Mean ( 20 / 24 )47100.1081081081742.59074830101563.4267370228746
Winsorized Mean ( 21 / 24 )46889.5405405405689.38783166439968.0161998614545
Winsorized Mean ( 22 / 24 )46859.5135135135648.64500760270272.2421555153866
Winsorized Mean ( 23 / 24 )46921.9864864865587.37618166140679.8840469727026
Winsorized Mean ( 24 / 24 )46817.5540540541554.99013140906984.3574532310846
Trimmed Mean ( 1 / 24 )47957.45833333331507.5083538695631.8123997192012
Trimmed Mean ( 2 / 24 )47823.61461.6158453077432.7196781244054
Trimmed Mean ( 3 / 24 )47707.39705882351416.6069770905333.6772286388186
Trimmed Mean ( 4 / 24 )47614.6969696971380.3941253296534.4935523094364
Trimmed Mean ( 5 / 24 )47508.6251338.8940849760035.483482624282
Trimmed Mean ( 6 / 24 )47416.80645161291295.1600206253636.6107706356763
Trimmed Mean ( 7 / 24 )47306.91666666671245.7631956807937.9742448891455
Trimmed Mean ( 8 / 24 )47190.94827586211187.6047532164639.7362406541842
Trimmed Mean ( 9 / 24 )47073.55357142861130.7239354190941.6313408577322
Trimmed Mean ( 10 / 24 )47041.27777777781097.2092450735942.8735703686335
Trimmed Mean ( 11 / 24 )46996.59615384621060.2828442679244.3245841502746
Trimmed Mean ( 12 / 24 )46948.61014.9093193633746.2589111206999
Trimmed Mean ( 13 / 24 )46877.375967.54915145596448.4496058204993
Trimmed Mean ( 14 / 24 )46806.5217391304912.41269146955451.2997267319273
Trimmed Mean ( 15 / 24 )46771.3181818182886.9469016314752.7329404903337
Trimmed Mean ( 16 / 24 )46749.4047619048862.73923279805254.1871784482157
Trimmed Mean ( 17 / 24 )46731.55835.47868971119755.9338623180848
Trimmed Mean ( 18 / 24 )46700.8157894737804.33323672305658.0615268116211
Trimmed Mean ( 19 / 24 )46686.4166666667769.26651869538360.6895211634106
Trimmed Mean ( 20 / 24 )46627.8823529412738.92426479260963.1023835250938
Trimmed Mean ( 21 / 24 )46573.28125705.24287630959766.0386411752348
Trimmed Mean ( 22 / 24 )46536.1333333333673.15996755281669.1308687034811
Trimmed Mean ( 23 / 24 )46497.2857142857638.75135481098272.7940306726161
Trimmed Mean ( 24 / 24 )46444.7307692308607.86728449730776.4060378864435
Median46241
Midrange51338.5
Midmean - Weighted Average at Xnp46449.1891891892
Midmean - Weighted Average at X(n+1)p46700.8157894737
Midmean - Empirical Distribution Function46700.8157894737
Midmean - Empirical Distribution Function - Averaging46700.8157894737
Midmean - Empirical Distribution Function - Interpolation46686.4166666667
Midmean - Closest Observation46700.8157894737
Midmean - True Basic - Statistics Graphics Toolkit46700.8157894737
Midmean - MS Excel (old versions)46700.8157894737
Number of observations74



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')