Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationTue, 16 Mar 2010 12:08:59 -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/16/t1268763186yo9ny7zyttmp6s2.htm/, Retrieved Fri, 21 Jan 2022 11:58:52 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=74476, Retrieved Fri, 21 Jan 2022 11:58:52 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP1W51
Estimated Impact155
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [opgave 5 oefening...] [2010-03-16 18:08:59] [bffa0fb6afa860209dcefcd4361c2008] [Current]
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Dataseries X:
41086
39690
43129
37863
35953
29133
24693
22205
21725
27192
21790
13253
37702
30364
32609
30212
29965
28352
25814
22414
20506
28806
22228
13971
36845
35338
35022
34777
26887
23970
22780
17351
21382
24561
17409
11514
31514
27071
29462
26105
22397
23843
21705
18089
20764
25316
17704
15548
28029
29383
36438
32034
22679
24319
18004
17537
20366
22782
19169
13807
29743
25591
29096
26482
22405
27044
17970
18730
19684
19785
18479
10698




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=74476&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=74476&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=74476&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'Gwilym Jenkins' @ 72.249.127.135







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean25253.6527777778858.00731972642129.4329106490956
Geometric Mean24195.2258777478
Harmonic Mean23101.5796548688
Quadratic Mean26268.1463836061
Winsorized Mean ( 1 / 24 )25236.6111111111847.45775109365529.7791967546971
Winsorized Mean ( 2 / 24 )25246.1388888889827.12969609191530.5225879425848
Winsorized Mean ( 3 / 24 )25193.0972222222804.65621168193731.3091440250765
Winsorized Mean ( 4 / 24 )25193.2638888889800.87354351647731.4572307861117
Winsorized Mean ( 5 / 24 )25243.2638888889767.41399430257432.8939321882317
Winsorized Mean ( 6 / 24 )25359.5972222222735.27211693281234.4900841990443
Winsorized Mean ( 7 / 24 )25318.0833333333724.52781848687234.9442529152413
Winsorized Mean ( 8 / 24 )25263.9722222222708.43299684726435.6617666521101
Winsorized Mean ( 9 / 24 )25245.3472222222697.38405601252936.200063658709
Winsorized Mean ( 10 / 24 )25248.2638888889685.11373837073636.8526603318912
Winsorized Mean ( 11 / 24 )24922.2361111111622.92065545633840.0086847222198
Winsorized Mean ( 12 / 24 )24840.5694444444604.3325492934541.1041395560881
Winsorized Mean ( 13 / 24 )24817.0972222222577.81262231805242.950078042016
Winsorized Mean ( 14 / 24 )24642.2916666667535.10247561036646.0515373967544
Winsorized Mean ( 15 / 24 )24702.0833333333516.3157371553547.8429797035238
Winsorized Mean ( 16 / 24 )24761.6388888889491.1174330663150.4189776654611
Winsorized Mean ( 17 / 24 )24733.0694444444479.88419448034151.5396625455179
Winsorized Mean ( 18 / 24 )24808.0694444444448.90639777331255.2633456941106
Winsorized Mean ( 19 / 24 )24824.1666666667440.74203018029656.323574714469
Winsorized Mean ( 20 / 24 )24826.3888888889420.85993108694258.9896710403638
Winsorized Mean ( 21 / 24 )24995.8472222222395.42051498333863.213329291414
Winsorized Mean ( 22 / 24 )25005.9305555556369.98052137873867.5871542165803
Winsorized Mean ( 23 / 24 )24867.2916666667348.46173950053071.3630474964349
Winsorized Mean ( 24 / 24 )24781.2916666667330.67292230891574.9420046057353
Trimmed Mean ( 1 / 24 )25206.2285714286817.98900992668630.8148743632726
Trimmed Mean ( 2 / 24 )25174.0588235294782.83655029555532.1574903650387
Trimmed Mean ( 3 / 24 )25134.7424242424754.03208748434133.3337835901637
Trimmed Mean ( 4 / 24 )25112.859375730.02233667011534.400124644882
Trimmed Mean ( 5 / 24 )25089.5161290323702.44022339756435.7176529665104
Trimmed Mean ( 6 / 24 )25052.6166666667679.98201001945236.8430580478886
Trimmed Mean ( 7 / 24 )24989.1034482759661.72554166529637.7635467801173
Trimmed Mean ( 8 / 24 )24928.6785714286642.07559842712238.8251455630704
Trimmed Mean ( 9 / 24 )24872.7962962963621.81532183209440.0002949798857
Trimmed Mean ( 10 / 24 )24815.4807692308599.15595200189341.4173984023985
Trimmed Mean ( 11 / 24 )24753.16573.47815456498943.1632134597637
Trimmed Mean ( 12 / 24 )24730.1041666667556.41735926790244.4452419658598
Trimmed Mean ( 13 / 24 )24715.6956521739538.82925411615145.8692535035341
Trimmed Mean ( 14 / 24 )24702.9318181818522.17073888459247.3081503397715
Trimmed Mean ( 15 / 24 )24710.3571428571510.14738575562348.4376825851151
Trimmed Mean ( 16 / 24 )24711.35498.18668567320349.6025901748204
Trimmed Mean ( 17 / 24 )24705.3947368421487.61322869241150.6659649146361
Trimmed Mean ( 18 / 24 )24702.1388888889475.35433092067751.9657385703108
Trimmed Mean ( 19 / 24 )24689.6764705882465.61646545904553.0257804483933
Trimmed Mean ( 20 / 24 )24673.75453.15825183888854.4484181847631
Trimmed Mean ( 21 / 24 )24655.4333333333440.12597643640656.0190369424737
Trimmed Mean ( 22 / 24 )24613.75427.31754243971757.6006074065455
Trimmed Mean ( 23 / 24 )24564.3846153846415.00077136878559.1911782100178
Trimmed Mean ( 24 / 24 )24524.875402.66563480273260.9063026002079
Median24440
Midrange26913.5
Midmean - Weighted Average at Xnp24569.2432432432
Midmean - Weighted Average at X(n+1)p24702.1388888889
Midmean - Empirical Distribution Function24569.2432432432
Midmean - Empirical Distribution Function - Averaging24702.1388888889
Midmean - Empirical Distribution Function - Interpolation24702.1388888889
Midmean - Closest Observation24569.2432432432
Midmean - True Basic - Statistics Graphics Toolkit24702.1388888889
Midmean - MS Excel (old versions)24705.3947368421
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 25253.6527777778 & 858.007319726421 & 29.4329106490956 \tabularnewline
Geometric Mean & 24195.2258777478 &  &  \tabularnewline
Harmonic Mean & 23101.5796548688 &  &  \tabularnewline
Quadratic Mean & 26268.1463836061 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 25236.6111111111 & 847.457751093655 & 29.7791967546971 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 25246.1388888889 & 827.129696091915 & 30.5225879425848 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 25193.0972222222 & 804.656211681937 & 31.3091440250765 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 25193.2638888889 & 800.873543516477 & 31.4572307861117 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 25243.2638888889 & 767.413994302574 & 32.8939321882317 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 25359.5972222222 & 735.272116932812 & 34.4900841990443 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 25318.0833333333 & 724.527818486872 & 34.9442529152413 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 25263.9722222222 & 708.432996847264 & 35.6617666521101 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 25245.3472222222 & 697.384056012529 & 36.200063658709 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 25248.2638888889 & 685.113738370736 & 36.8526603318912 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 24922.2361111111 & 622.920655456338 & 40.0086847222198 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 24840.5694444444 & 604.33254929345 & 41.1041395560881 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 24817.0972222222 & 577.812622318052 & 42.950078042016 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 24642.2916666667 & 535.102475610366 & 46.0515373967544 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 24702.0833333333 & 516.31573715535 & 47.8429797035238 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 24761.6388888889 & 491.11743306631 & 50.4189776654611 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 24733.0694444444 & 479.884194480341 & 51.5396625455179 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 24808.0694444444 & 448.906397773312 & 55.2633456941106 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 24824.1666666667 & 440.742030180296 & 56.323574714469 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 24826.3888888889 & 420.859931086942 & 58.9896710403638 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 24995.8472222222 & 395.420514983338 & 63.213329291414 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 25005.9305555556 & 369.980521378738 & 67.5871542165803 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 24867.2916666667 & 348.461739500530 & 71.3630474964349 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 24781.2916666667 & 330.672922308915 & 74.9420046057353 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 25206.2285714286 & 817.989009926686 & 30.8148743632726 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 25174.0588235294 & 782.836550295555 & 32.1574903650387 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 25134.7424242424 & 754.032087484341 & 33.3337835901637 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 25112.859375 & 730.022336670115 & 34.400124644882 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 25089.5161290323 & 702.440223397564 & 35.7176529665104 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 25052.6166666667 & 679.982010019452 & 36.8430580478886 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 24989.1034482759 & 661.725541665296 & 37.7635467801173 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 24928.6785714286 & 642.075598427122 & 38.8251455630704 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 24872.7962962963 & 621.815321832094 & 40.0002949798857 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 24815.4807692308 & 599.155952001893 & 41.4173984023985 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 24753.16 & 573.478154564989 & 43.1632134597637 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 24730.1041666667 & 556.417359267902 & 44.4452419658598 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 24715.6956521739 & 538.829254116151 & 45.8692535035341 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 24702.9318181818 & 522.170738884592 & 47.3081503397715 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 24710.3571428571 & 510.147385755623 & 48.4376825851151 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 24711.35 & 498.186685673203 & 49.6025901748204 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 24705.3947368421 & 487.613228692411 & 50.6659649146361 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 24702.1388888889 & 475.354330920677 & 51.9657385703108 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 24689.6764705882 & 465.616465459045 & 53.0257804483933 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 24673.75 & 453.158251838888 & 54.4484181847631 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 24655.4333333333 & 440.125976436406 & 56.0190369424737 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 24613.75 & 427.317542439717 & 57.6006074065455 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 24564.3846153846 & 415.000771368785 & 59.1911782100178 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 24524.875 & 402.665634802732 & 60.9063026002079 \tabularnewline
Median & 24440 &  &  \tabularnewline
Midrange & 26913.5 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 24569.2432432432 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 24702.1388888889 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 24569.2432432432 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 24702.1388888889 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 24702.1388888889 &  &  \tabularnewline
Midmean - Closest Observation & 24569.2432432432 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 24702.1388888889 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 24705.3947368421 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=74476&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]25253.6527777778[/C][C]858.007319726421[/C][C]29.4329106490956[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]24195.2258777478[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]23101.5796548688[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]26268.1463836061[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]25236.6111111111[/C][C]847.457751093655[/C][C]29.7791967546971[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]25246.1388888889[/C][C]827.129696091915[/C][C]30.5225879425848[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]25193.0972222222[/C][C]804.656211681937[/C][C]31.3091440250765[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]25193.2638888889[/C][C]800.873543516477[/C][C]31.4572307861117[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]25243.2638888889[/C][C]767.413994302574[/C][C]32.8939321882317[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]25359.5972222222[/C][C]735.272116932812[/C][C]34.4900841990443[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]25318.0833333333[/C][C]724.527818486872[/C][C]34.9442529152413[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]25263.9722222222[/C][C]708.432996847264[/C][C]35.6617666521101[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]25245.3472222222[/C][C]697.384056012529[/C][C]36.200063658709[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]25248.2638888889[/C][C]685.113738370736[/C][C]36.8526603318912[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]24922.2361111111[/C][C]622.920655456338[/C][C]40.0086847222198[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]24840.5694444444[/C][C]604.33254929345[/C][C]41.1041395560881[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]24817.0972222222[/C][C]577.812622318052[/C][C]42.950078042016[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]24642.2916666667[/C][C]535.102475610366[/C][C]46.0515373967544[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]24702.0833333333[/C][C]516.31573715535[/C][C]47.8429797035238[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]24761.6388888889[/C][C]491.11743306631[/C][C]50.4189776654611[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]24733.0694444444[/C][C]479.884194480341[/C][C]51.5396625455179[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]24808.0694444444[/C][C]448.906397773312[/C][C]55.2633456941106[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]24824.1666666667[/C][C]440.742030180296[/C][C]56.323574714469[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]24826.3888888889[/C][C]420.859931086942[/C][C]58.9896710403638[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]24995.8472222222[/C][C]395.420514983338[/C][C]63.213329291414[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]25005.9305555556[/C][C]369.980521378738[/C][C]67.5871542165803[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]24867.2916666667[/C][C]348.461739500530[/C][C]71.3630474964349[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]24781.2916666667[/C][C]330.672922308915[/C][C]74.9420046057353[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]25206.2285714286[/C][C]817.989009926686[/C][C]30.8148743632726[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]25174.0588235294[/C][C]782.836550295555[/C][C]32.1574903650387[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]25134.7424242424[/C][C]754.032087484341[/C][C]33.3337835901637[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]25112.859375[/C][C]730.022336670115[/C][C]34.400124644882[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]25089.5161290323[/C][C]702.440223397564[/C][C]35.7176529665104[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]25052.6166666667[/C][C]679.982010019452[/C][C]36.8430580478886[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]24989.1034482759[/C][C]661.725541665296[/C][C]37.7635467801173[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]24928.6785714286[/C][C]642.075598427122[/C][C]38.8251455630704[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]24872.7962962963[/C][C]621.815321832094[/C][C]40.0002949798857[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]24815.4807692308[/C][C]599.155952001893[/C][C]41.4173984023985[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]24753.16[/C][C]573.478154564989[/C][C]43.1632134597637[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]24730.1041666667[/C][C]556.417359267902[/C][C]44.4452419658598[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]24715.6956521739[/C][C]538.829254116151[/C][C]45.8692535035341[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]24702.9318181818[/C][C]522.170738884592[/C][C]47.3081503397715[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]24710.3571428571[/C][C]510.147385755623[/C][C]48.4376825851151[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]24711.35[/C][C]498.186685673203[/C][C]49.6025901748204[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]24705.3947368421[/C][C]487.613228692411[/C][C]50.6659649146361[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]24702.1388888889[/C][C]475.354330920677[/C][C]51.9657385703108[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]24689.6764705882[/C][C]465.616465459045[/C][C]53.0257804483933[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]24673.75[/C][C]453.158251838888[/C][C]54.4484181847631[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]24655.4333333333[/C][C]440.125976436406[/C][C]56.0190369424737[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]24613.75[/C][C]427.317542439717[/C][C]57.6006074065455[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]24564.3846153846[/C][C]415.000771368785[/C][C]59.1911782100178[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]24524.875[/C][C]402.665634802732[/C][C]60.9063026002079[/C][/ROW]
[ROW][C]Median[/C][C]24440[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]26913.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]24569.2432432432[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]24702.1388888889[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]24569.2432432432[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]24702.1388888889[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]24702.1388888889[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]24569.2432432432[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]24702.1388888889[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]24705.3947368421[/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=74476&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=74476&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 Mean25253.6527777778858.00731972642129.4329106490956
Geometric Mean24195.2258777478
Harmonic Mean23101.5796548688
Quadratic Mean26268.1463836061
Winsorized Mean ( 1 / 24 )25236.6111111111847.45775109365529.7791967546971
Winsorized Mean ( 2 / 24 )25246.1388888889827.12969609191530.5225879425848
Winsorized Mean ( 3 / 24 )25193.0972222222804.65621168193731.3091440250765
Winsorized Mean ( 4 / 24 )25193.2638888889800.87354351647731.4572307861117
Winsorized Mean ( 5 / 24 )25243.2638888889767.41399430257432.8939321882317
Winsorized Mean ( 6 / 24 )25359.5972222222735.27211693281234.4900841990443
Winsorized Mean ( 7 / 24 )25318.0833333333724.52781848687234.9442529152413
Winsorized Mean ( 8 / 24 )25263.9722222222708.43299684726435.6617666521101
Winsorized Mean ( 9 / 24 )25245.3472222222697.38405601252936.200063658709
Winsorized Mean ( 10 / 24 )25248.2638888889685.11373837073636.8526603318912
Winsorized Mean ( 11 / 24 )24922.2361111111622.92065545633840.0086847222198
Winsorized Mean ( 12 / 24 )24840.5694444444604.3325492934541.1041395560881
Winsorized Mean ( 13 / 24 )24817.0972222222577.81262231805242.950078042016
Winsorized Mean ( 14 / 24 )24642.2916666667535.10247561036646.0515373967544
Winsorized Mean ( 15 / 24 )24702.0833333333516.3157371553547.8429797035238
Winsorized Mean ( 16 / 24 )24761.6388888889491.1174330663150.4189776654611
Winsorized Mean ( 17 / 24 )24733.0694444444479.88419448034151.5396625455179
Winsorized Mean ( 18 / 24 )24808.0694444444448.90639777331255.2633456941106
Winsorized Mean ( 19 / 24 )24824.1666666667440.74203018029656.323574714469
Winsorized Mean ( 20 / 24 )24826.3888888889420.85993108694258.9896710403638
Winsorized Mean ( 21 / 24 )24995.8472222222395.42051498333863.213329291414
Winsorized Mean ( 22 / 24 )25005.9305555556369.98052137873867.5871542165803
Winsorized Mean ( 23 / 24 )24867.2916666667348.46173950053071.3630474964349
Winsorized Mean ( 24 / 24 )24781.2916666667330.67292230891574.9420046057353
Trimmed Mean ( 1 / 24 )25206.2285714286817.98900992668630.8148743632726
Trimmed Mean ( 2 / 24 )25174.0588235294782.83655029555532.1574903650387
Trimmed Mean ( 3 / 24 )25134.7424242424754.03208748434133.3337835901637
Trimmed Mean ( 4 / 24 )25112.859375730.02233667011534.400124644882
Trimmed Mean ( 5 / 24 )25089.5161290323702.44022339756435.7176529665104
Trimmed Mean ( 6 / 24 )25052.6166666667679.98201001945236.8430580478886
Trimmed Mean ( 7 / 24 )24989.1034482759661.72554166529637.7635467801173
Trimmed Mean ( 8 / 24 )24928.6785714286642.07559842712238.8251455630704
Trimmed Mean ( 9 / 24 )24872.7962962963621.81532183209440.0002949798857
Trimmed Mean ( 10 / 24 )24815.4807692308599.15595200189341.4173984023985
Trimmed Mean ( 11 / 24 )24753.16573.47815456498943.1632134597637
Trimmed Mean ( 12 / 24 )24730.1041666667556.41735926790244.4452419658598
Trimmed Mean ( 13 / 24 )24715.6956521739538.82925411615145.8692535035341
Trimmed Mean ( 14 / 24 )24702.9318181818522.17073888459247.3081503397715
Trimmed Mean ( 15 / 24 )24710.3571428571510.14738575562348.4376825851151
Trimmed Mean ( 16 / 24 )24711.35498.18668567320349.6025901748204
Trimmed Mean ( 17 / 24 )24705.3947368421487.61322869241150.6659649146361
Trimmed Mean ( 18 / 24 )24702.1388888889475.35433092067751.9657385703108
Trimmed Mean ( 19 / 24 )24689.6764705882465.61646545904553.0257804483933
Trimmed Mean ( 20 / 24 )24673.75453.15825183888854.4484181847631
Trimmed Mean ( 21 / 24 )24655.4333333333440.12597643640656.0190369424737
Trimmed Mean ( 22 / 24 )24613.75427.31754243971757.6006074065455
Trimmed Mean ( 23 / 24 )24564.3846153846415.00077136878559.1911782100178
Trimmed Mean ( 24 / 24 )24524.875402.66563480273260.9063026002079
Median24440
Midrange26913.5
Midmean - Weighted Average at Xnp24569.2432432432
Midmean - Weighted Average at X(n+1)p24702.1388888889
Midmean - Empirical Distribution Function24569.2432432432
Midmean - Empirical Distribution Function - Averaging24702.1388888889
Midmean - Empirical Distribution Function - Interpolation24702.1388888889
Midmean - Closest Observation24569.2432432432
Midmean - True Basic - Statistics Graphics Toolkit24702.1388888889
Midmean - MS Excel (old versions)24705.3947368421
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')