Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationWed, 17 Mar 2010 00:44:42 -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/2010/Mar/17/t12688083788skuccmql4nhq8s.htm/, Retrieved Mon, 27 Jun 2022 05:10:27 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=74495, Retrieved Mon, 27 Jun 2022 05:10:27 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP1W52
Estimated Impact147
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [oefening 2 opgave 5] [2010-03-17 06:44:42] [1534a5b2c59cc18089304a939cd27237] [Current]
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Dataseries X:
66857.2
64722.8
68489.6
71342.9
63542.5
69425.0
58927.9
61009.0
66837.0
66147.6
65982.3
65527.5
65914.6
59189.9
66211.4
66400.8
60167.7
64547.9
57706.2
58642.6
60082.1
63414.8
66044.0
57628.5
62838.8
55758.6
61004.5
66173.4
57489.0
59552.2
57061.8
55895.3
56314.7
61232.8
60014.1
57685.4
60403.1
52349.7
55693.3
65676.1
54898.8
55518.2
53779.1
52340.9
55704.4
60330.3
52837.4
55388.1
60383.4
52070.3
54077.0
62887.8
49212.8
57722.0
53936.8
46991.0
54984.2
56485.1
51277.8
53596.4
54252.5
49413.0
53213.2
58695.3
48723.5
54510.0
49454.1
46136.6
54622.5
50583.0
53224.3
53056.4




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 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 & 3 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=74495&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]3 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=74495&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=74495&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 time3 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean58336.2611111111690.53448632052384.4798663452029
Geometric Mean58046.0398826769
Harmonic Mean57756.0896466578
Quadratic Mean58625.7183297262
Winsorized Mean ( 1 / 24 )58321.4902777778681.07238044625585.631853459634
Winsorized Mean ( 2 / 24 )58343.6319444444664.74234918896887.768790442835
Winsorized Mean ( 3 / 24 )58296.0027777778646.9858226623190.1039879635894
Winsorized Mean ( 4 / 24 )58306.0027777778644.59638963009190.4535050393896
Winsorized Mean ( 5 / 24 )58278.5652777778638.50394171402791.2736186425605
Winsorized Mean ( 6 / 24 )58356.8569444444618.17704700115794.4015265975012
Winsorized Mean ( 7 / 24 )58420.7125605.91980294869896.416575618913
Winsorized Mean ( 8 / 24 )58505.9013888889591.33486119236898.938698237607
Winsorized Mean ( 9 / 24 )58526.7763888889583.86559872691100.240152042702
Winsorized Mean ( 10 / 24 )58519.4291666667582.132544693143100.525953582468
Winsorized Mean ( 11 / 24 )58583.5958333333569.40162733677102.886245877700
Winsorized Mean ( 12 / 24 )58580.3458333333557.08837293726105.154493755573
Winsorized Mean ( 13 / 24 )58581.8263888889548.359258113239106.831106655249
Winsorized Mean ( 14 / 24 )58427.5152777778520.764960641406112.195557868976
Winsorized Mean ( 15 / 24 )58468.5986111111503.830017979076116.048263352064
Winsorized Mean ( 16 / 24 )58285.7763888889461.312740402984126.347640730609
Winsorized Mean ( 17 / 24 )58292.8597222222451.391243873446129.140430864373
Winsorized Mean ( 18 / 24 )58196.1597222222425.863534124979136.654479801371
Winsorized Mean ( 19 / 24 )58229.5416666667417.594066580772139.440538854983
Winsorized Mean ( 20 / 24 )57854.9583333333341.794367614479169.268319829629
Winsorized Mean ( 21 / 24 )57822.4958333333328.273689665251176.141121429184
Winsorized Mean ( 22 / 24 )57905.5458333333316.641042105917182.874416557673
Winsorized Mean ( 23 / 24 )57740.7125287.154847950776201.078661607335
Winsorized Mean ( 24 / 24 )57868.7791666667268.417771823300215.592204545837
Trimmed Mean ( 1 / 24 )58324.7328571429662.44755044295788.0443030065445
Trimmed Mean ( 2 / 24 )58328.1661764706640.30407751971191.0944787395564
Trimmed Mean ( 3 / 24 )58319.7303030303624.36956689538293.4057862445468
Trimmed Mean ( 4 / 24 )58328.628125613.2977114617995.1065478232002
Trimmed Mean ( 5 / 24 )58335.1967741936600.69788653112597.1123722626431
Trimmed Mean ( 6 / 24 )58348.7883333333587.23478473405299.3619415099167
Trimmed Mean ( 7 / 24 )58347.1189655172576.46468251776101.215426955006
Trimmed Mean ( 8 / 24 )58333.6017857143566.197656435047103.026921999290
Trimmed Mean ( 9 / 24 )58304.8851851852556.724250799643104.728481113298
Trimmed Mean ( 10 / 24 )58270.7480769231546.319813514658106.660506603354
Trimmed Mean ( 11 / 24 )58234.938533.352552773606109.186574053428
Trimmed Mean ( 12 / 24 )58187.39375519.444598130206112.018478889667
Trimmed Mean ( 13 / 24 )58136.1391304348504.181226528086115.308020353662
Trimmed Mean ( 14 / 24 )58080.0386363636486.164445912608119.465829154450
Trimmed Mean ( 15 / 24 )58037.4904761905469.39108031702123.644212491198
Trimmed Mean ( 16 / 24 )57985.7575450.917173272879128.595141052455
Trimmed Mean ( 17 / 24 )57950.2289473684437.053126751476132.593100015324
Trimmed Mean ( 18 / 24 )57909.9194444444420.260745720986137.795214123784
Trimmed Mean ( 19 / 24 )57876.2441176471403.892530515998143.296148714874
Trimmed Mean ( 20 / 24 )57834.40625382.606247576048151.159074417635
Trimmed Mean ( 21 / 24 )57831.94375.416245449137154.047515793600
Trimmed Mean ( 22 / 24 )57833.0964285714367.713599318636157.277556597675
Trimmed Mean ( 23 / 24 )57823.9769230769358.525161966791161.282897428641
Trimmed Mean ( 24 / 24 )57834.8375353.123100164827163.780951948498
Median57695.8
Midrange58739.75
Midmean - Weighted Average at Xnp57802.5378378378
Midmean - Weighted Average at X(n+1)p57909.9194444445
Midmean - Empirical Distribution Function57802.5378378378
Midmean - Empirical Distribution Function - Averaging57909.9194444445
Midmean - Empirical Distribution Function - Interpolation57909.9194444445
Midmean - Closest Observation57802.5378378378
Midmean - True Basic - Statistics Graphics Toolkit57909.9194444445
Midmean - MS Excel (old versions)57950.2289473684
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 58336.2611111111 & 690.534486320523 & 84.4798663452029 \tabularnewline
Geometric Mean & 58046.0398826769 &  &  \tabularnewline
Harmonic Mean & 57756.0896466578 &  &  \tabularnewline
Quadratic Mean & 58625.7183297262 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 58321.4902777778 & 681.072380446255 & 85.631853459634 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 58343.6319444444 & 664.742349188968 & 87.768790442835 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 58296.0027777778 & 646.98582266231 & 90.1039879635894 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 58306.0027777778 & 644.596389630091 & 90.4535050393896 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 58278.5652777778 & 638.503941714027 & 91.2736186425605 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 58356.8569444444 & 618.177047001157 & 94.4015265975012 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 58420.7125 & 605.919802948698 & 96.416575618913 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 58505.9013888889 & 591.334861192368 & 98.938698237607 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 58526.7763888889 & 583.86559872691 & 100.240152042702 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 58519.4291666667 & 582.132544693143 & 100.525953582468 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 58583.5958333333 & 569.40162733677 & 102.886245877700 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 58580.3458333333 & 557.08837293726 & 105.154493755573 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 58581.8263888889 & 548.359258113239 & 106.831106655249 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 58427.5152777778 & 520.764960641406 & 112.195557868976 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 58468.5986111111 & 503.830017979076 & 116.048263352064 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 58285.7763888889 & 461.312740402984 & 126.347640730609 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 58292.8597222222 & 451.391243873446 & 129.140430864373 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 58196.1597222222 & 425.863534124979 & 136.654479801371 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 58229.5416666667 & 417.594066580772 & 139.440538854983 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 57854.9583333333 & 341.794367614479 & 169.268319829629 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 57822.4958333333 & 328.273689665251 & 176.141121429184 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 57905.5458333333 & 316.641042105917 & 182.874416557673 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 57740.7125 & 287.154847950776 & 201.078661607335 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 57868.7791666667 & 268.417771823300 & 215.592204545837 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 58324.7328571429 & 662.447550442957 & 88.0443030065445 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 58328.1661764706 & 640.304077519711 & 91.0944787395564 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 58319.7303030303 & 624.369566895382 & 93.4057862445468 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 58328.628125 & 613.29771146179 & 95.1065478232002 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 58335.1967741936 & 600.697886531125 & 97.1123722626431 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 58348.7883333333 & 587.234784734052 & 99.3619415099167 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 58347.1189655172 & 576.46468251776 & 101.215426955006 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 58333.6017857143 & 566.197656435047 & 103.026921999290 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 58304.8851851852 & 556.724250799643 & 104.728481113298 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 58270.7480769231 & 546.319813514658 & 106.660506603354 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 58234.938 & 533.352552773606 & 109.186574053428 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 58187.39375 & 519.444598130206 & 112.018478889667 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 58136.1391304348 & 504.181226528086 & 115.308020353662 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 58080.0386363636 & 486.164445912608 & 119.465829154450 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 58037.4904761905 & 469.39108031702 & 123.644212491198 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 57985.7575 & 450.917173272879 & 128.595141052455 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 57950.2289473684 & 437.053126751476 & 132.593100015324 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 57909.9194444444 & 420.260745720986 & 137.795214123784 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 57876.2441176471 & 403.892530515998 & 143.296148714874 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 57834.40625 & 382.606247576048 & 151.159074417635 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 57831.94 & 375.416245449137 & 154.047515793600 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 57833.0964285714 & 367.713599318636 & 157.277556597675 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 57823.9769230769 & 358.525161966791 & 161.282897428641 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 57834.8375 & 353.123100164827 & 163.780951948498 \tabularnewline
Median & 57695.8 &  &  \tabularnewline
Midrange & 58739.75 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 57802.5378378378 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 57909.9194444445 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 57802.5378378378 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 57909.9194444445 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 57909.9194444445 &  &  \tabularnewline
Midmean - Closest Observation & 57802.5378378378 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 57909.9194444445 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 57950.2289473684 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=74495&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]58336.2611111111[/C][C]690.534486320523[/C][C]84.4798663452029[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]58046.0398826769[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]57756.0896466578[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]58625.7183297262[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]58321.4902777778[/C][C]681.072380446255[/C][C]85.631853459634[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]58343.6319444444[/C][C]664.742349188968[/C][C]87.768790442835[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]58296.0027777778[/C][C]646.98582266231[/C][C]90.1039879635894[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]58306.0027777778[/C][C]644.596389630091[/C][C]90.4535050393896[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]58278.5652777778[/C][C]638.503941714027[/C][C]91.2736186425605[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]58356.8569444444[/C][C]618.177047001157[/C][C]94.4015265975012[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]58420.7125[/C][C]605.919802948698[/C][C]96.416575618913[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]58505.9013888889[/C][C]591.334861192368[/C][C]98.938698237607[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]58526.7763888889[/C][C]583.86559872691[/C][C]100.240152042702[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]58519.4291666667[/C][C]582.132544693143[/C][C]100.525953582468[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]58583.5958333333[/C][C]569.40162733677[/C][C]102.886245877700[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]58580.3458333333[/C][C]557.08837293726[/C][C]105.154493755573[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]58581.8263888889[/C][C]548.359258113239[/C][C]106.831106655249[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]58427.5152777778[/C][C]520.764960641406[/C][C]112.195557868976[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]58468.5986111111[/C][C]503.830017979076[/C][C]116.048263352064[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]58285.7763888889[/C][C]461.312740402984[/C][C]126.347640730609[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]58292.8597222222[/C][C]451.391243873446[/C][C]129.140430864373[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]58196.1597222222[/C][C]425.863534124979[/C][C]136.654479801371[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]58229.5416666667[/C][C]417.594066580772[/C][C]139.440538854983[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]57854.9583333333[/C][C]341.794367614479[/C][C]169.268319829629[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]57822.4958333333[/C][C]328.273689665251[/C][C]176.141121429184[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]57905.5458333333[/C][C]316.641042105917[/C][C]182.874416557673[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]57740.7125[/C][C]287.154847950776[/C][C]201.078661607335[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]57868.7791666667[/C][C]268.417771823300[/C][C]215.592204545837[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]58324.7328571429[/C][C]662.447550442957[/C][C]88.0443030065445[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]58328.1661764706[/C][C]640.304077519711[/C][C]91.0944787395564[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]58319.7303030303[/C][C]624.369566895382[/C][C]93.4057862445468[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]58328.628125[/C][C]613.29771146179[/C][C]95.1065478232002[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]58335.1967741936[/C][C]600.697886531125[/C][C]97.1123722626431[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]58348.7883333333[/C][C]587.234784734052[/C][C]99.3619415099167[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]58347.1189655172[/C][C]576.46468251776[/C][C]101.215426955006[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]58333.6017857143[/C][C]566.197656435047[/C][C]103.026921999290[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]58304.8851851852[/C][C]556.724250799643[/C][C]104.728481113298[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]58270.7480769231[/C][C]546.319813514658[/C][C]106.660506603354[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]58234.938[/C][C]533.352552773606[/C][C]109.186574053428[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]58187.39375[/C][C]519.444598130206[/C][C]112.018478889667[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]58136.1391304348[/C][C]504.181226528086[/C][C]115.308020353662[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]58080.0386363636[/C][C]486.164445912608[/C][C]119.465829154450[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]58037.4904761905[/C][C]469.39108031702[/C][C]123.644212491198[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]57985.7575[/C][C]450.917173272879[/C][C]128.595141052455[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]57950.2289473684[/C][C]437.053126751476[/C][C]132.593100015324[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]57909.9194444444[/C][C]420.260745720986[/C][C]137.795214123784[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]57876.2441176471[/C][C]403.892530515998[/C][C]143.296148714874[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]57834.40625[/C][C]382.606247576048[/C][C]151.159074417635[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]57831.94[/C][C]375.416245449137[/C][C]154.047515793600[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]57833.0964285714[/C][C]367.713599318636[/C][C]157.277556597675[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]57823.9769230769[/C][C]358.525161966791[/C][C]161.282897428641[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]57834.8375[/C][C]353.123100164827[/C][C]163.780951948498[/C][/ROW]
[ROW][C]Median[/C][C]57695.8[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]58739.75[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]57802.5378378378[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]57909.9194444445[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]57802.5378378378[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]57909.9194444445[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]57909.9194444445[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]57802.5378378378[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]57909.9194444445[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]57950.2289473684[/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=74495&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=74495&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 Mean58336.2611111111690.53448632052384.4798663452029
Geometric Mean58046.0398826769
Harmonic Mean57756.0896466578
Quadratic Mean58625.7183297262
Winsorized Mean ( 1 / 24 )58321.4902777778681.07238044625585.631853459634
Winsorized Mean ( 2 / 24 )58343.6319444444664.74234918896887.768790442835
Winsorized Mean ( 3 / 24 )58296.0027777778646.9858226623190.1039879635894
Winsorized Mean ( 4 / 24 )58306.0027777778644.59638963009190.4535050393896
Winsorized Mean ( 5 / 24 )58278.5652777778638.50394171402791.2736186425605
Winsorized Mean ( 6 / 24 )58356.8569444444618.17704700115794.4015265975012
Winsorized Mean ( 7 / 24 )58420.7125605.91980294869896.416575618913
Winsorized Mean ( 8 / 24 )58505.9013888889591.33486119236898.938698237607
Winsorized Mean ( 9 / 24 )58526.7763888889583.86559872691100.240152042702
Winsorized Mean ( 10 / 24 )58519.4291666667582.132544693143100.525953582468
Winsorized Mean ( 11 / 24 )58583.5958333333569.40162733677102.886245877700
Winsorized Mean ( 12 / 24 )58580.3458333333557.08837293726105.154493755573
Winsorized Mean ( 13 / 24 )58581.8263888889548.359258113239106.831106655249
Winsorized Mean ( 14 / 24 )58427.5152777778520.764960641406112.195557868976
Winsorized Mean ( 15 / 24 )58468.5986111111503.830017979076116.048263352064
Winsorized Mean ( 16 / 24 )58285.7763888889461.312740402984126.347640730609
Winsorized Mean ( 17 / 24 )58292.8597222222451.391243873446129.140430864373
Winsorized Mean ( 18 / 24 )58196.1597222222425.863534124979136.654479801371
Winsorized Mean ( 19 / 24 )58229.5416666667417.594066580772139.440538854983
Winsorized Mean ( 20 / 24 )57854.9583333333341.794367614479169.268319829629
Winsorized Mean ( 21 / 24 )57822.4958333333328.273689665251176.141121429184
Winsorized Mean ( 22 / 24 )57905.5458333333316.641042105917182.874416557673
Winsorized Mean ( 23 / 24 )57740.7125287.154847950776201.078661607335
Winsorized Mean ( 24 / 24 )57868.7791666667268.417771823300215.592204545837
Trimmed Mean ( 1 / 24 )58324.7328571429662.44755044295788.0443030065445
Trimmed Mean ( 2 / 24 )58328.1661764706640.30407751971191.0944787395564
Trimmed Mean ( 3 / 24 )58319.7303030303624.36956689538293.4057862445468
Trimmed Mean ( 4 / 24 )58328.628125613.2977114617995.1065478232002
Trimmed Mean ( 5 / 24 )58335.1967741936600.69788653112597.1123722626431
Trimmed Mean ( 6 / 24 )58348.7883333333587.23478473405299.3619415099167
Trimmed Mean ( 7 / 24 )58347.1189655172576.46468251776101.215426955006
Trimmed Mean ( 8 / 24 )58333.6017857143566.197656435047103.026921999290
Trimmed Mean ( 9 / 24 )58304.8851851852556.724250799643104.728481113298
Trimmed Mean ( 10 / 24 )58270.7480769231546.319813514658106.660506603354
Trimmed Mean ( 11 / 24 )58234.938533.352552773606109.186574053428
Trimmed Mean ( 12 / 24 )58187.39375519.444598130206112.018478889667
Trimmed Mean ( 13 / 24 )58136.1391304348504.181226528086115.308020353662
Trimmed Mean ( 14 / 24 )58080.0386363636486.164445912608119.465829154450
Trimmed Mean ( 15 / 24 )58037.4904761905469.39108031702123.644212491198
Trimmed Mean ( 16 / 24 )57985.7575450.917173272879128.595141052455
Trimmed Mean ( 17 / 24 )57950.2289473684437.053126751476132.593100015324
Trimmed Mean ( 18 / 24 )57909.9194444444420.260745720986137.795214123784
Trimmed Mean ( 19 / 24 )57876.2441176471403.892530515998143.296148714874
Trimmed Mean ( 20 / 24 )57834.40625382.606247576048151.159074417635
Trimmed Mean ( 21 / 24 )57831.94375.416245449137154.047515793600
Trimmed Mean ( 22 / 24 )57833.0964285714367.713599318636157.277556597675
Trimmed Mean ( 23 / 24 )57823.9769230769358.525161966791161.282897428641
Trimmed Mean ( 24 / 24 )57834.8375353.123100164827163.780951948498
Median57695.8
Midrange58739.75
Midmean - Weighted Average at Xnp57802.5378378378
Midmean - Weighted Average at X(n+1)p57909.9194444445
Midmean - Empirical Distribution Function57802.5378378378
Midmean - Empirical Distribution Function - Averaging57909.9194444445
Midmean - Empirical Distribution Function - Interpolation57909.9194444445
Midmean - Closest Observation57802.5378378378
Midmean - True Basic - Statistics Graphics Toolkit57909.9194444445
Midmean - MS Excel (old versions)57950.2289473684
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')