Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationWed, 16 Apr 2008 08:49:20 -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/2008/Apr/16/t1208357476zvfwyl5r33tv90l.htm/, Retrieved Fri, 10 May 2024 17:14:24 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=10147, Retrieved Fri, 10 May 2024 17:14:24 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact302
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Elke Van Buggenho...] [2008-04-16 14:49:20] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataseries X:
10.893
10.756
10.940
10.997
10.827
10.166
10.186
10.457
10.368
10.244
10.511
10.812
10.738
10.171
9.721
9.897
9.828
9.924
10.371
10.846
10.413
10.709
10.662
10.570
10.297
10.635
10.872
10.296
10.383
10.431
10.574
10.653
10.805
10.872
10.625
10.407
10.463
10.556
10.646
10.702
11.353
11.346
11.451
11.964
12.574
13.031
13.812
14.544
14.931
14.886
16.005
17.064
15.168
16.050
15.839
15.137
14.954
15.648
15.305
15.579
16.348
15.928
16.171
15.937
15.713
15.594
15.683
16.438
17.032
17.696
17.745
19.394




Summary of compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001

\begin{tabular}{lllllllll}
\hline
Summary of compuational 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 & 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=10147&T=0

[TABLE]
[ROW][C]Summary of compuational 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]'Herman Ole Andreas Wold' @ 193.190.124.10:1001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=10147&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=10147&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 compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean12.59088888888890.31536573307949239.9247209452373
Geometric Mean12.3311327981450
Harmonic Mean12.0957307709021
Quadratic Mean12.8682487833427
Winsorized Mean ( 1 / 24 )12.56947222222220.30898882169046940.6793752390620
Winsorized Mean ( 2 / 24 )12.57002777777780.30843222939566140.7545858693411
Winsorized Mean ( 3 / 24 )12.54481944444440.30243883441573841.4788645402598
Winsorized Mean ( 4 / 24 )12.55648611111110.30049142522316841.786503897027
Winsorized Mean ( 5 / 24 )12.51558333333330.29222056844456742.8292347795754
Winsorized Mean ( 6 / 24 )12.50933333333330.29067309170979643.0357459637939
Winsorized Mean ( 7 / 24 )12.49776388888890.28689137694384043.5627031457812
Winsorized Mean ( 8 / 24 )12.49009722222220.28385745099988944.0013012807161
Winsorized Mean ( 9 / 24 )12.48459722222220.28285402337012644.1379517019832
Winsorized Mean ( 10 / 24 )12.48501388888890.28014472386935544.566300290957
Winsorized Mean ( 11 / 24 )12.48409722222220.27985748536097344.6087665159988
Winsorized Mean ( 12 / 24 )12.47126388888890.27708983206968645.0080170597977
Winsorized Mean ( 13 / 24 )12.45284722222220.27276864452305745.6535143326181
Winsorized Mean ( 14 / 24 )12.44818055555560.27166532685402945.8217495022625
Winsorized Mean ( 15 / 24 )12.44463888888890.27005000573385146.0827203283002
Winsorized Mean ( 16 / 24 )12.43841666666670.26744559854436046.5082122658435
Winsorized Mean ( 17 / 24 )12.43629166666670.26670970048710346.6285689795075
Winsorized Mean ( 18 / 24 )12.37979166666670.25422517677765348.6961670106108
Winsorized Mean ( 19 / 24 )12.35551388888890.24717464189648849.9869800319692
Winsorized Mean ( 20 / 24 )12.35079166666670.24539798560104450.3296375331539
Winsorized Mean ( 21 / 24 )12.29858333333330.23679478922193551.9377279109236
Winsorized Mean ( 22 / 24 )12.30713888888890.23409719142585352.5727746408568
Winsorized Mean ( 23 / 24 )12.29595833333330.23150691154459953.1127051512006
Winsorized Mean ( 24 / 24 )12.1856250.21327169685951857.1366251567205
Trimmed Mean ( 1 / 24 )12.53470.30647841554104040.8991281747262
Trimmed Mean ( 2 / 24 )12.49788235294120.30330037639020941.2062869874652
Trimmed Mean ( 3 / 24 )12.45853030303030.29965960192441641.5756085338882
Trimmed Mean ( 4 / 24 )12.4261718750.29777744212254841.729728707543
Trimmed Mean ( 5 / 24 )12.38833870967740.295887702503241.8683798105582
Trimmed Mean ( 6 / 24 )12.35780.29579922741253641.7776615175712
Trimmed Mean ( 7 / 24 )12.32644827586210.29568616884989941.6876052194359
Trimmed Mean ( 8 / 24 )12.29498214285710.29600806795238541.5359697048355
Trimmed Mean ( 9 / 24 )12.26246296296300.29656712662744841.3480182460251
Trimmed Mean ( 10 / 24 )12.22828846153850.29690995244626441.1851753731683
Trimmed Mean ( 11 / 24 )12.191320.29726981551500741.0109582733082
Trimmed Mean ( 12 / 24 )12.15139583333330.29711380520654340.8981192404914
Trimmed Mean ( 13 / 24 )12.10967391304350.29679961042454640.8008416713272
Trimmed Mean ( 14 / 24 )12.06647727272730.2965456150156840.6901220646586
Trimmed Mean ( 15 / 24 )12.01973809523810.29560876783874440.6609661246412
Trimmed Mean ( 16 / 24 )11.968750.29382951133398640.7336551922979
Trimmed Mean ( 17 / 24 )11.91313157894740.29109403233826140.9253720636359
Trimmed Mean ( 18 / 24 )11.85158333333330.28655119040447641.3593931213633
Trimmed Mean ( 19 / 24 )11.78944117647060.28260005308226241.7177599504513
Trimmed Mean ( 20 / 24 )11.722406250.27774693989260742.2053479852291
Trimmed Mean ( 21 / 24 )11.6470.26988320590134243.1557049320722
Trimmed Mean ( 22 / 24 )11.56721428571430.25999166326247144.4907122811732
Trimmed Mean ( 23 / 24 )11.47407692307690.2439229444727147.0397606419541
Trimmed Mean ( 24 / 24 )11.3668750.21724926670962552.3218106655014
Median10.872
Midrange14.5575
Midmean - Weighted Average at Xnp11.8140540540541
Midmean - Weighted Average at X(n+1)p11.8515833333333
Midmean - Empirical Distribution Function11.8140540540541
Midmean - Empirical Distribution Function - Averaging11.8515833333333
Midmean - Empirical Distribution Function - Interpolation11.8515833333333
Midmean - Closest Observation11.8140540540541
Midmean - True Basic - Statistics Graphics Toolkit11.8515833333333
Midmean - MS Excel (old versions)11.9131315789474
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 12.5908888888889 & 0.315365733079492 & 39.9247209452373 \tabularnewline
Geometric Mean & 12.3311327981450 &  &  \tabularnewline
Harmonic Mean & 12.0957307709021 &  &  \tabularnewline
Quadratic Mean & 12.8682487833427 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 12.5694722222222 & 0.308988821690469 & 40.6793752390620 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 12.5700277777778 & 0.308432229395661 & 40.7545858693411 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 12.5448194444444 & 0.302438834415738 & 41.4788645402598 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 12.5564861111111 & 0.300491425223168 & 41.786503897027 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 12.5155833333333 & 0.292220568444567 & 42.8292347795754 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 12.5093333333333 & 0.290673091709796 & 43.0357459637939 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 12.4977638888889 & 0.286891376943840 & 43.5627031457812 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 12.4900972222222 & 0.283857450999889 & 44.0013012807161 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 12.4845972222222 & 0.282854023370126 & 44.1379517019832 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 12.4850138888889 & 0.280144723869355 & 44.566300290957 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 12.4840972222222 & 0.279857485360973 & 44.6087665159988 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 12.4712638888889 & 0.277089832069686 & 45.0080170597977 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 12.4528472222222 & 0.272768644523057 & 45.6535143326181 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 12.4481805555556 & 0.271665326854029 & 45.8217495022625 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 12.4446388888889 & 0.270050005733851 & 46.0827203283002 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 12.4384166666667 & 0.267445598544360 & 46.5082122658435 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 12.4362916666667 & 0.266709700487103 & 46.6285689795075 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 12.3797916666667 & 0.254225176777653 & 48.6961670106108 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 12.3555138888889 & 0.247174641896488 & 49.9869800319692 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 12.3507916666667 & 0.245397985601044 & 50.3296375331539 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 12.2985833333333 & 0.236794789221935 & 51.9377279109236 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 12.3071388888889 & 0.234097191425853 & 52.5727746408568 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 12.2959583333333 & 0.231506911544599 & 53.1127051512006 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 12.185625 & 0.213271696859518 & 57.1366251567205 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 12.5347 & 0.306478415541040 & 40.8991281747262 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 12.4978823529412 & 0.303300376390209 & 41.2062869874652 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 12.4585303030303 & 0.299659601924416 & 41.5756085338882 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 12.426171875 & 0.297777442122548 & 41.729728707543 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 12.3883387096774 & 0.2958877025032 & 41.8683798105582 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 12.3578 & 0.295799227412536 & 41.7776615175712 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 12.3264482758621 & 0.295686168849899 & 41.6876052194359 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 12.2949821428571 & 0.296008067952385 & 41.5359697048355 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 12.2624629629630 & 0.296567126627448 & 41.3480182460251 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 12.2282884615385 & 0.296909952446264 & 41.1851753731683 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 12.19132 & 0.297269815515007 & 41.0109582733082 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 12.1513958333333 & 0.297113805206543 & 40.8981192404914 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 12.1096739130435 & 0.296799610424546 & 40.8008416713272 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 12.0664772727273 & 0.29654561501568 & 40.6901220646586 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 12.0197380952381 & 0.295608767838744 & 40.6609661246412 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 11.96875 & 0.293829511333986 & 40.7336551922979 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 11.9131315789474 & 0.291094032338261 & 40.9253720636359 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 11.8515833333333 & 0.286551190404476 & 41.3593931213633 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 11.7894411764706 & 0.282600053082262 & 41.7177599504513 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 11.72240625 & 0.277746939892607 & 42.2053479852291 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 11.647 & 0.269883205901342 & 43.1557049320722 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 11.5672142857143 & 0.259991663262471 & 44.4907122811732 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 11.4740769230769 & 0.24392294447271 & 47.0397606419541 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 11.366875 & 0.217249266709625 & 52.3218106655014 \tabularnewline
Median & 10.872 &  &  \tabularnewline
Midrange & 14.5575 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 11.8140540540541 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 11.8515833333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 11.8140540540541 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 11.8515833333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 11.8515833333333 &  &  \tabularnewline
Midmean - Closest Observation & 11.8140540540541 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 11.8515833333333 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 11.9131315789474 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=10147&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]12.5908888888889[/C][C]0.315365733079492[/C][C]39.9247209452373[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]12.3311327981450[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]12.0957307709021[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]12.8682487833427[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]12.5694722222222[/C][C]0.308988821690469[/C][C]40.6793752390620[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]12.5700277777778[/C][C]0.308432229395661[/C][C]40.7545858693411[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]12.5448194444444[/C][C]0.302438834415738[/C][C]41.4788645402598[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]12.5564861111111[/C][C]0.300491425223168[/C][C]41.786503897027[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]12.5155833333333[/C][C]0.292220568444567[/C][C]42.8292347795754[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]12.5093333333333[/C][C]0.290673091709796[/C][C]43.0357459637939[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]12.4977638888889[/C][C]0.286891376943840[/C][C]43.5627031457812[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]12.4900972222222[/C][C]0.283857450999889[/C][C]44.0013012807161[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]12.4845972222222[/C][C]0.282854023370126[/C][C]44.1379517019832[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]12.4850138888889[/C][C]0.280144723869355[/C][C]44.566300290957[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]12.4840972222222[/C][C]0.279857485360973[/C][C]44.6087665159988[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]12.4712638888889[/C][C]0.277089832069686[/C][C]45.0080170597977[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]12.4528472222222[/C][C]0.272768644523057[/C][C]45.6535143326181[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]12.4481805555556[/C][C]0.271665326854029[/C][C]45.8217495022625[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]12.4446388888889[/C][C]0.270050005733851[/C][C]46.0827203283002[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]12.4384166666667[/C][C]0.267445598544360[/C][C]46.5082122658435[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]12.4362916666667[/C][C]0.266709700487103[/C][C]46.6285689795075[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]12.3797916666667[/C][C]0.254225176777653[/C][C]48.6961670106108[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]12.3555138888889[/C][C]0.247174641896488[/C][C]49.9869800319692[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]12.3507916666667[/C][C]0.245397985601044[/C][C]50.3296375331539[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]12.2985833333333[/C][C]0.236794789221935[/C][C]51.9377279109236[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]12.3071388888889[/C][C]0.234097191425853[/C][C]52.5727746408568[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]12.2959583333333[/C][C]0.231506911544599[/C][C]53.1127051512006[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]12.185625[/C][C]0.213271696859518[/C][C]57.1366251567205[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]12.5347[/C][C]0.306478415541040[/C][C]40.8991281747262[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]12.4978823529412[/C][C]0.303300376390209[/C][C]41.2062869874652[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]12.4585303030303[/C][C]0.299659601924416[/C][C]41.5756085338882[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]12.426171875[/C][C]0.297777442122548[/C][C]41.729728707543[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]12.3883387096774[/C][C]0.2958877025032[/C][C]41.8683798105582[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]12.3578[/C][C]0.295799227412536[/C][C]41.7776615175712[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]12.3264482758621[/C][C]0.295686168849899[/C][C]41.6876052194359[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]12.2949821428571[/C][C]0.296008067952385[/C][C]41.5359697048355[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]12.2624629629630[/C][C]0.296567126627448[/C][C]41.3480182460251[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]12.2282884615385[/C][C]0.296909952446264[/C][C]41.1851753731683[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]12.19132[/C][C]0.297269815515007[/C][C]41.0109582733082[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]12.1513958333333[/C][C]0.297113805206543[/C][C]40.8981192404914[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]12.1096739130435[/C][C]0.296799610424546[/C][C]40.8008416713272[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]12.0664772727273[/C][C]0.29654561501568[/C][C]40.6901220646586[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]12.0197380952381[/C][C]0.295608767838744[/C][C]40.6609661246412[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]11.96875[/C][C]0.293829511333986[/C][C]40.7336551922979[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]11.9131315789474[/C][C]0.291094032338261[/C][C]40.9253720636359[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]11.8515833333333[/C][C]0.286551190404476[/C][C]41.3593931213633[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]11.7894411764706[/C][C]0.282600053082262[/C][C]41.7177599504513[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]11.72240625[/C][C]0.277746939892607[/C][C]42.2053479852291[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]11.647[/C][C]0.269883205901342[/C][C]43.1557049320722[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]11.5672142857143[/C][C]0.259991663262471[/C][C]44.4907122811732[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]11.4740769230769[/C][C]0.24392294447271[/C][C]47.0397606419541[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]11.366875[/C][C]0.217249266709625[/C][C]52.3218106655014[/C][/ROW]
[ROW][C]Median[/C][C]10.872[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]14.5575[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]11.8140540540541[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]11.8515833333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]11.8140540540541[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]11.8515833333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]11.8515833333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]11.8140540540541[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]11.8515833333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]11.9131315789474[/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=10147&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=10147&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 Mean12.59088888888890.31536573307949239.9247209452373
Geometric Mean12.3311327981450
Harmonic Mean12.0957307709021
Quadratic Mean12.8682487833427
Winsorized Mean ( 1 / 24 )12.56947222222220.30898882169046940.6793752390620
Winsorized Mean ( 2 / 24 )12.57002777777780.30843222939566140.7545858693411
Winsorized Mean ( 3 / 24 )12.54481944444440.30243883441573841.4788645402598
Winsorized Mean ( 4 / 24 )12.55648611111110.30049142522316841.786503897027
Winsorized Mean ( 5 / 24 )12.51558333333330.29222056844456742.8292347795754
Winsorized Mean ( 6 / 24 )12.50933333333330.29067309170979643.0357459637939
Winsorized Mean ( 7 / 24 )12.49776388888890.28689137694384043.5627031457812
Winsorized Mean ( 8 / 24 )12.49009722222220.28385745099988944.0013012807161
Winsorized Mean ( 9 / 24 )12.48459722222220.28285402337012644.1379517019832
Winsorized Mean ( 10 / 24 )12.48501388888890.28014472386935544.566300290957
Winsorized Mean ( 11 / 24 )12.48409722222220.27985748536097344.6087665159988
Winsorized Mean ( 12 / 24 )12.47126388888890.27708983206968645.0080170597977
Winsorized Mean ( 13 / 24 )12.45284722222220.27276864452305745.6535143326181
Winsorized Mean ( 14 / 24 )12.44818055555560.27166532685402945.8217495022625
Winsorized Mean ( 15 / 24 )12.44463888888890.27005000573385146.0827203283002
Winsorized Mean ( 16 / 24 )12.43841666666670.26744559854436046.5082122658435
Winsorized Mean ( 17 / 24 )12.43629166666670.26670970048710346.6285689795075
Winsorized Mean ( 18 / 24 )12.37979166666670.25422517677765348.6961670106108
Winsorized Mean ( 19 / 24 )12.35551388888890.24717464189648849.9869800319692
Winsorized Mean ( 20 / 24 )12.35079166666670.24539798560104450.3296375331539
Winsorized Mean ( 21 / 24 )12.29858333333330.23679478922193551.9377279109236
Winsorized Mean ( 22 / 24 )12.30713888888890.23409719142585352.5727746408568
Winsorized Mean ( 23 / 24 )12.29595833333330.23150691154459953.1127051512006
Winsorized Mean ( 24 / 24 )12.1856250.21327169685951857.1366251567205
Trimmed Mean ( 1 / 24 )12.53470.30647841554104040.8991281747262
Trimmed Mean ( 2 / 24 )12.49788235294120.30330037639020941.2062869874652
Trimmed Mean ( 3 / 24 )12.45853030303030.29965960192441641.5756085338882
Trimmed Mean ( 4 / 24 )12.4261718750.29777744212254841.729728707543
Trimmed Mean ( 5 / 24 )12.38833870967740.295887702503241.8683798105582
Trimmed Mean ( 6 / 24 )12.35780.29579922741253641.7776615175712
Trimmed Mean ( 7 / 24 )12.32644827586210.29568616884989941.6876052194359
Trimmed Mean ( 8 / 24 )12.29498214285710.29600806795238541.5359697048355
Trimmed Mean ( 9 / 24 )12.26246296296300.29656712662744841.3480182460251
Trimmed Mean ( 10 / 24 )12.22828846153850.29690995244626441.1851753731683
Trimmed Mean ( 11 / 24 )12.191320.29726981551500741.0109582733082
Trimmed Mean ( 12 / 24 )12.15139583333330.29711380520654340.8981192404914
Trimmed Mean ( 13 / 24 )12.10967391304350.29679961042454640.8008416713272
Trimmed Mean ( 14 / 24 )12.06647727272730.2965456150156840.6901220646586
Trimmed Mean ( 15 / 24 )12.01973809523810.29560876783874440.6609661246412
Trimmed Mean ( 16 / 24 )11.968750.29382951133398640.7336551922979
Trimmed Mean ( 17 / 24 )11.91313157894740.29109403233826140.9253720636359
Trimmed Mean ( 18 / 24 )11.85158333333330.28655119040447641.3593931213633
Trimmed Mean ( 19 / 24 )11.78944117647060.28260005308226241.7177599504513
Trimmed Mean ( 20 / 24 )11.722406250.27774693989260742.2053479852291
Trimmed Mean ( 21 / 24 )11.6470.26988320590134243.1557049320722
Trimmed Mean ( 22 / 24 )11.56721428571430.25999166326247144.4907122811732
Trimmed Mean ( 23 / 24 )11.47407692307690.2439229444727147.0397606419541
Trimmed Mean ( 24 / 24 )11.3668750.21724926670962552.3218106655014
Median10.872
Midrange14.5575
Midmean - Weighted Average at Xnp11.8140540540541
Midmean - Weighted Average at X(n+1)p11.8515833333333
Midmean - Empirical Distribution Function11.8140540540541
Midmean - Empirical Distribution Function - Averaging11.8515833333333
Midmean - Empirical Distribution Function - Interpolation11.8515833333333
Midmean - Closest Observation11.8140540540541
Midmean - True Basic - Statistics Graphics Toolkit11.8515833333333
Midmean - MS Excel (old versions)11.9131315789474
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')