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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationFri, 20 May 2011 02:26:04 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/May/20/t1305858124wpxxb3tcomm1qnu.htm/, Retrieved Mon, 13 May 2024 08:38:04 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=122361, Retrieved Mon, 13 May 2024 08:38:04 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP1W52
Estimated Impact68
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2011-05-20 02:26:04] [25018b84afebffe8bc31ee5ed84cfeb9] [Current]
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Dataseries X:
1,4442
1,3999
1,3649
1,336
1,322
1,3661
1,3898
1,3067
1,2894
1,277
1,2208
1,2565
1,3406
1,3569
1,3686
1,4272
1,4614
1,4914
1,4816
1,4562
1,4268
1,4088
1,4016
1,365
1,319
1,305
1,2785
1,3239
1,3449
1,2732
1,3322
1,4369
1,4975
1,577
1,5553
1,5557
1,575
1,5527
1,4748
1,4718
1,457
1,4684
1,4227
1,3896
1,3622
1,3716
1,3419
1,3511
1,3516
1,3242
1,3074
1,2999
1,3213
1,2881
1,2611
1,2727
1,2811
1,2684
1,265
1,277
1,2271
1,202
1,1938
1,2103
1,1856
1,1786
1,2015
1,2256
1,2292
1,2037
1,2165
1,2694
1,2938
1,3201
1,3014




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=122361&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=122361&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=122361&T=0

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean1.3463160.0116549772130982115.514254158041
Geometric Mean1.3426498485194
Harmonic Mean1.33905131786118
Quadratic Mean1.3500440068383
Winsorized Mean ( 1 / 25 )1.346382666666670.011630075545808115.767319082632
Winsorized Mean ( 2 / 25 )1.346086666666670.0114579961981525117.480111128306
Winsorized Mean ( 3 / 25 )1.346378666666670.011399926867686118.104149464598
Winsorized Mean ( 4 / 25 )1.346266666666670.0113611537184308118.497355113035
Winsorized Mean ( 5 / 25 )1.34270.0105203586415077127.62872880611
Winsorized Mean ( 6 / 25 )1.342740.0103315046914372129.965580048845
Winsorized Mean ( 7 / 25 )1.3424040.0100579213441827133.467339230727
Winsorized Mean ( 8 / 25 )1.342137333333330.00984706180595055136.298254218561
Winsorized Mean ( 9 / 25 )1.342353333333330.00968691145068713138.573924224126
Winsorized Mean ( 10 / 25 )1.34210.00957304323382887140.195752512361
Winsorized Mean ( 11 / 25 )1.341381333333330.00934238711963345143.580148858781
Winsorized Mean ( 12 / 25 )1.345045333333330.0085571617533662157.183581671133
Winsorized Mean ( 13 / 25 )1.3457040.00842273872987353159.770360111859
Winsorized Mean ( 14 / 25 )1.3441920.00793467808119852169.407250835432
Winsorized Mean ( 15 / 25 )1.3434120.00759766297875464176.819109212476
Winsorized Mean ( 16 / 25 )1.3415560.00723124981160503185.52201001921
Winsorized Mean ( 17 / 25 )1.342213333333330.0071169090196513188.594982685207
Winsorized Mean ( 18 / 25 )1.341349333333330.00694410823527277193.163655848553
Winsorized Mean ( 19 / 25 )1.338790666666670.00627117965922827213.483066889431
Winsorized Mean ( 20 / 25 )1.336870666666670.00598596459696816223.334208716133
Winsorized Mean ( 21 / 25 )1.336814666666670.00585993441322745228.127923010387
Winsorized Mean ( 22 / 25 )1.334614666666670.00533396618767792250.210559967512
Winsorized Mean ( 23 / 25 )1.33670.00503977834490424265.229918564087
Winsorized Mean ( 24 / 25 )1.3313560.00420001983693298316.988026649943
Winsorized Mean ( 25 / 25 )1.331822666666670.00387481290374633343.712767493627
Trimmed Mean ( 1 / 25 )1.345453424657530.0113115016158733118.945606900632
Trimmed Mean ( 2 / 25 )1.344471830985920.0109341582038194122.960707712852
Trimmed Mean ( 3 / 25 )1.343594202898550.0105962474425546126.799058834986
Trimmed Mean ( 4 / 25 )1.34255522388060.0102185246694688131.384448079077
Trimmed Mean ( 5 / 25 )1.341484615384620.00977814459324419137.192143416601
Trimmed Mean ( 6 / 25 )1.341195238095240.00952555659858838140.799671306766
Trimmed Mean ( 7 / 25 )1.340878688524590.00927294911700292144.601104956561
Trimmed Mean ( 8 / 25 )1.340601694915250.00903654328287997148.353375062682
Trimmed Mean ( 9 / 25 )1.340349122807020.00879793035115095152.348230698561
Trimmed Mean ( 10 / 25 )1.340045454545450.00854026818043889156.909060258174
Trimmed Mean ( 11 / 25 )1.339754716981130.00824569226764483162.479349640318
Trimmed Mean ( 12 / 25 )1.339537254901960.0079301380749962168.917267547401
Trimmed Mean ( 13 / 25 )1.338834693877550.00770538538096708173.753112619724
Trimmed Mean ( 14 / 25 )1.33799148936170.00744372960005996179.747460110712
Trimmed Mean ( 15 / 25 )1.337253333333330.00721817193343343185.262050511624
Trimmed Mean ( 16 / 25 )1.336537209302330.00699903807918207190.960128260728
Trimmed Mean ( 17 / 25 )1.335963414634150.00679531021573107196.60079852446
Trimmed Mean ( 18 / 25 )1.335256410256410.00654353199708845204.057443419018
Trimmed Mean ( 19 / 25 )1.334570270270270.00624458908702877213.716267262874
Trimmed Mean ( 20 / 25 )1.334094285714290.00601879959954207221.654544839105
Trimmed Mean ( 21 / 25 )1.333778787878790.00578078183210973230.72636653925
Trimmed Mean ( 22 / 25 )1.333429032258060.0054730290674437243.636387789344
Trimmed Mean ( 23 / 25 )1.333289655172410.00519812950639088256.494120343326
Trimmed Mean ( 24 / 25 )1.332877777777780.00488079360850394273.086281594753
Trimmed Mean ( 25 / 25 )1.3330680.004713900437359282.795111546069
Median1.3322
Midrange1.3778
Midmean - Weighted Average at Xnp1.33295526315789
Midmean - Weighted Average at X(n+1)p1.33525641025641
Midmean - Empirical Distribution Function1.33525641025641
Midmean - Empirical Distribution Function - Averaging1.33525641025641
Midmean - Empirical Distribution Function - Interpolation1.33457027027027
Midmean - Closest Observation1.33295526315789
Midmean - True Basic - Statistics Graphics Toolkit1.33525641025641
Midmean - MS Excel (old versions)1.33525641025641
Number of observations75

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 1.346316 & 0.0116549772130982 & 115.514254158041 \tabularnewline
Geometric Mean & 1.3426498485194 &  &  \tabularnewline
Harmonic Mean & 1.33905131786118 &  &  \tabularnewline
Quadratic Mean & 1.3500440068383 &  &  \tabularnewline
Winsorized Mean ( 1 / 25 ) & 1.34638266666667 & 0.011630075545808 & 115.767319082632 \tabularnewline
Winsorized Mean ( 2 / 25 ) & 1.34608666666667 & 0.0114579961981525 & 117.480111128306 \tabularnewline
Winsorized Mean ( 3 / 25 ) & 1.34637866666667 & 0.011399926867686 & 118.104149464598 \tabularnewline
Winsorized Mean ( 4 / 25 ) & 1.34626666666667 & 0.0113611537184308 & 118.497355113035 \tabularnewline
Winsorized Mean ( 5 / 25 ) & 1.3427 & 0.0105203586415077 & 127.62872880611 \tabularnewline
Winsorized Mean ( 6 / 25 ) & 1.34274 & 0.0103315046914372 & 129.965580048845 \tabularnewline
Winsorized Mean ( 7 / 25 ) & 1.342404 & 0.0100579213441827 & 133.467339230727 \tabularnewline
Winsorized Mean ( 8 / 25 ) & 1.34213733333333 & 0.00984706180595055 & 136.298254218561 \tabularnewline
Winsorized Mean ( 9 / 25 ) & 1.34235333333333 & 0.00968691145068713 & 138.573924224126 \tabularnewline
Winsorized Mean ( 10 / 25 ) & 1.3421 & 0.00957304323382887 & 140.195752512361 \tabularnewline
Winsorized Mean ( 11 / 25 ) & 1.34138133333333 & 0.00934238711963345 & 143.580148858781 \tabularnewline
Winsorized Mean ( 12 / 25 ) & 1.34504533333333 & 0.0085571617533662 & 157.183581671133 \tabularnewline
Winsorized Mean ( 13 / 25 ) & 1.345704 & 0.00842273872987353 & 159.770360111859 \tabularnewline
Winsorized Mean ( 14 / 25 ) & 1.344192 & 0.00793467808119852 & 169.407250835432 \tabularnewline
Winsorized Mean ( 15 / 25 ) & 1.343412 & 0.00759766297875464 & 176.819109212476 \tabularnewline
Winsorized Mean ( 16 / 25 ) & 1.341556 & 0.00723124981160503 & 185.52201001921 \tabularnewline
Winsorized Mean ( 17 / 25 ) & 1.34221333333333 & 0.0071169090196513 & 188.594982685207 \tabularnewline
Winsorized Mean ( 18 / 25 ) & 1.34134933333333 & 0.00694410823527277 & 193.163655848553 \tabularnewline
Winsorized Mean ( 19 / 25 ) & 1.33879066666667 & 0.00627117965922827 & 213.483066889431 \tabularnewline
Winsorized Mean ( 20 / 25 ) & 1.33687066666667 & 0.00598596459696816 & 223.334208716133 \tabularnewline
Winsorized Mean ( 21 / 25 ) & 1.33681466666667 & 0.00585993441322745 & 228.127923010387 \tabularnewline
Winsorized Mean ( 22 / 25 ) & 1.33461466666667 & 0.00533396618767792 & 250.210559967512 \tabularnewline
Winsorized Mean ( 23 / 25 ) & 1.3367 & 0.00503977834490424 & 265.229918564087 \tabularnewline
Winsorized Mean ( 24 / 25 ) & 1.331356 & 0.00420001983693298 & 316.988026649943 \tabularnewline
Winsorized Mean ( 25 / 25 ) & 1.33182266666667 & 0.00387481290374633 & 343.712767493627 \tabularnewline
Trimmed Mean ( 1 / 25 ) & 1.34545342465753 & 0.0113115016158733 & 118.945606900632 \tabularnewline
Trimmed Mean ( 2 / 25 ) & 1.34447183098592 & 0.0109341582038194 & 122.960707712852 \tabularnewline
Trimmed Mean ( 3 / 25 ) & 1.34359420289855 & 0.0105962474425546 & 126.799058834986 \tabularnewline
Trimmed Mean ( 4 / 25 ) & 1.3425552238806 & 0.0102185246694688 & 131.384448079077 \tabularnewline
Trimmed Mean ( 5 / 25 ) & 1.34148461538462 & 0.00977814459324419 & 137.192143416601 \tabularnewline
Trimmed Mean ( 6 / 25 ) & 1.34119523809524 & 0.00952555659858838 & 140.799671306766 \tabularnewline
Trimmed Mean ( 7 / 25 ) & 1.34087868852459 & 0.00927294911700292 & 144.601104956561 \tabularnewline
Trimmed Mean ( 8 / 25 ) & 1.34060169491525 & 0.00903654328287997 & 148.353375062682 \tabularnewline
Trimmed Mean ( 9 / 25 ) & 1.34034912280702 & 0.00879793035115095 & 152.348230698561 \tabularnewline
Trimmed Mean ( 10 / 25 ) & 1.34004545454545 & 0.00854026818043889 & 156.909060258174 \tabularnewline
Trimmed Mean ( 11 / 25 ) & 1.33975471698113 & 0.00824569226764483 & 162.479349640318 \tabularnewline
Trimmed Mean ( 12 / 25 ) & 1.33953725490196 & 0.0079301380749962 & 168.917267547401 \tabularnewline
Trimmed Mean ( 13 / 25 ) & 1.33883469387755 & 0.00770538538096708 & 173.753112619724 \tabularnewline
Trimmed Mean ( 14 / 25 ) & 1.3379914893617 & 0.00744372960005996 & 179.747460110712 \tabularnewline
Trimmed Mean ( 15 / 25 ) & 1.33725333333333 & 0.00721817193343343 & 185.262050511624 \tabularnewline
Trimmed Mean ( 16 / 25 ) & 1.33653720930233 & 0.00699903807918207 & 190.960128260728 \tabularnewline
Trimmed Mean ( 17 / 25 ) & 1.33596341463415 & 0.00679531021573107 & 196.60079852446 \tabularnewline
Trimmed Mean ( 18 / 25 ) & 1.33525641025641 & 0.00654353199708845 & 204.057443419018 \tabularnewline
Trimmed Mean ( 19 / 25 ) & 1.33457027027027 & 0.00624458908702877 & 213.716267262874 \tabularnewline
Trimmed Mean ( 20 / 25 ) & 1.33409428571429 & 0.00601879959954207 & 221.654544839105 \tabularnewline
Trimmed Mean ( 21 / 25 ) & 1.33377878787879 & 0.00578078183210973 & 230.72636653925 \tabularnewline
Trimmed Mean ( 22 / 25 ) & 1.33342903225806 & 0.0054730290674437 & 243.636387789344 \tabularnewline
Trimmed Mean ( 23 / 25 ) & 1.33328965517241 & 0.00519812950639088 & 256.494120343326 \tabularnewline
Trimmed Mean ( 24 / 25 ) & 1.33287777777778 & 0.00488079360850394 & 273.086281594753 \tabularnewline
Trimmed Mean ( 25 / 25 ) & 1.333068 & 0.004713900437359 & 282.795111546069 \tabularnewline
Median & 1.3322 &  &  \tabularnewline
Midrange & 1.3778 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 1.33295526315789 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 1.33525641025641 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 1.33525641025641 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 1.33525641025641 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 1.33457027027027 &  &  \tabularnewline
Midmean - Closest Observation & 1.33295526315789 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 1.33525641025641 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 1.33525641025641 &  &  \tabularnewline
Number of observations & 75 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=122361&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]1.346316[/C][C]0.0116549772130982[/C][C]115.514254158041[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]1.3426498485194[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]1.33905131786118[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]1.3500440068383[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 25 )[/C][C]1.34638266666667[/C][C]0.011630075545808[/C][C]115.767319082632[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 25 )[/C][C]1.34608666666667[/C][C]0.0114579961981525[/C][C]117.480111128306[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 25 )[/C][C]1.34637866666667[/C][C]0.011399926867686[/C][C]118.104149464598[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 25 )[/C][C]1.34626666666667[/C][C]0.0113611537184308[/C][C]118.497355113035[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 25 )[/C][C]1.3427[/C][C]0.0105203586415077[/C][C]127.62872880611[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 25 )[/C][C]1.34274[/C][C]0.0103315046914372[/C][C]129.965580048845[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 25 )[/C][C]1.342404[/C][C]0.0100579213441827[/C][C]133.467339230727[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 25 )[/C][C]1.34213733333333[/C][C]0.00984706180595055[/C][C]136.298254218561[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 25 )[/C][C]1.34235333333333[/C][C]0.00968691145068713[/C][C]138.573924224126[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 25 )[/C][C]1.3421[/C][C]0.00957304323382887[/C][C]140.195752512361[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 25 )[/C][C]1.34138133333333[/C][C]0.00934238711963345[/C][C]143.580148858781[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 25 )[/C][C]1.34504533333333[/C][C]0.0085571617533662[/C][C]157.183581671133[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 25 )[/C][C]1.345704[/C][C]0.00842273872987353[/C][C]159.770360111859[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 25 )[/C][C]1.344192[/C][C]0.00793467808119852[/C][C]169.407250835432[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 25 )[/C][C]1.343412[/C][C]0.00759766297875464[/C][C]176.819109212476[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 25 )[/C][C]1.341556[/C][C]0.00723124981160503[/C][C]185.52201001921[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 25 )[/C][C]1.34221333333333[/C][C]0.0071169090196513[/C][C]188.594982685207[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 25 )[/C][C]1.34134933333333[/C][C]0.00694410823527277[/C][C]193.163655848553[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 25 )[/C][C]1.33879066666667[/C][C]0.00627117965922827[/C][C]213.483066889431[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 25 )[/C][C]1.33687066666667[/C][C]0.00598596459696816[/C][C]223.334208716133[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 25 )[/C][C]1.33681466666667[/C][C]0.00585993441322745[/C][C]228.127923010387[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 25 )[/C][C]1.33461466666667[/C][C]0.00533396618767792[/C][C]250.210559967512[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 25 )[/C][C]1.3367[/C][C]0.00503977834490424[/C][C]265.229918564087[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 25 )[/C][C]1.331356[/C][C]0.00420001983693298[/C][C]316.988026649943[/C][/ROW]
[ROW][C]Winsorized Mean ( 25 / 25 )[/C][C]1.33182266666667[/C][C]0.00387481290374633[/C][C]343.712767493627[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 25 )[/C][C]1.34545342465753[/C][C]0.0113115016158733[/C][C]118.945606900632[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 25 )[/C][C]1.34447183098592[/C][C]0.0109341582038194[/C][C]122.960707712852[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 25 )[/C][C]1.34359420289855[/C][C]0.0105962474425546[/C][C]126.799058834986[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 25 )[/C][C]1.3425552238806[/C][C]0.0102185246694688[/C][C]131.384448079077[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 25 )[/C][C]1.34148461538462[/C][C]0.00977814459324419[/C][C]137.192143416601[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 25 )[/C][C]1.34119523809524[/C][C]0.00952555659858838[/C][C]140.799671306766[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 25 )[/C][C]1.34087868852459[/C][C]0.00927294911700292[/C][C]144.601104956561[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 25 )[/C][C]1.34060169491525[/C][C]0.00903654328287997[/C][C]148.353375062682[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 25 )[/C][C]1.34034912280702[/C][C]0.00879793035115095[/C][C]152.348230698561[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 25 )[/C][C]1.34004545454545[/C][C]0.00854026818043889[/C][C]156.909060258174[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 25 )[/C][C]1.33975471698113[/C][C]0.00824569226764483[/C][C]162.479349640318[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 25 )[/C][C]1.33953725490196[/C][C]0.0079301380749962[/C][C]168.917267547401[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 25 )[/C][C]1.33883469387755[/C][C]0.00770538538096708[/C][C]173.753112619724[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 25 )[/C][C]1.3379914893617[/C][C]0.00744372960005996[/C][C]179.747460110712[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 25 )[/C][C]1.33725333333333[/C][C]0.00721817193343343[/C][C]185.262050511624[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 25 )[/C][C]1.33653720930233[/C][C]0.00699903807918207[/C][C]190.960128260728[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 25 )[/C][C]1.33596341463415[/C][C]0.00679531021573107[/C][C]196.60079852446[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 25 )[/C][C]1.33525641025641[/C][C]0.00654353199708845[/C][C]204.057443419018[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 25 )[/C][C]1.33457027027027[/C][C]0.00624458908702877[/C][C]213.716267262874[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 25 )[/C][C]1.33409428571429[/C][C]0.00601879959954207[/C][C]221.654544839105[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 25 )[/C][C]1.33377878787879[/C][C]0.00578078183210973[/C][C]230.72636653925[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 25 )[/C][C]1.33342903225806[/C][C]0.0054730290674437[/C][C]243.636387789344[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 25 )[/C][C]1.33328965517241[/C][C]0.00519812950639088[/C][C]256.494120343326[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 25 )[/C][C]1.33287777777778[/C][C]0.00488079360850394[/C][C]273.086281594753[/C][/ROW]
[ROW][C]Trimmed Mean ( 25 / 25 )[/C][C]1.333068[/C][C]0.004713900437359[/C][C]282.795111546069[/C][/ROW]
[ROW][C]Median[/C][C]1.3322[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]1.3778[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]1.33295526315789[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]1.33525641025641[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]1.33525641025641[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]1.33525641025641[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]1.33457027027027[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]1.33295526315789[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]1.33525641025641[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]1.33525641025641[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]75[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=122361&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=122361&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 Mean1.3463160.0116549772130982115.514254158041
Geometric Mean1.3426498485194
Harmonic Mean1.33905131786118
Quadratic Mean1.3500440068383
Winsorized Mean ( 1 / 25 )1.346382666666670.011630075545808115.767319082632
Winsorized Mean ( 2 / 25 )1.346086666666670.0114579961981525117.480111128306
Winsorized Mean ( 3 / 25 )1.346378666666670.011399926867686118.104149464598
Winsorized Mean ( 4 / 25 )1.346266666666670.0113611537184308118.497355113035
Winsorized Mean ( 5 / 25 )1.34270.0105203586415077127.62872880611
Winsorized Mean ( 6 / 25 )1.342740.0103315046914372129.965580048845
Winsorized Mean ( 7 / 25 )1.3424040.0100579213441827133.467339230727
Winsorized Mean ( 8 / 25 )1.342137333333330.00984706180595055136.298254218561
Winsorized Mean ( 9 / 25 )1.342353333333330.00968691145068713138.573924224126
Winsorized Mean ( 10 / 25 )1.34210.00957304323382887140.195752512361
Winsorized Mean ( 11 / 25 )1.341381333333330.00934238711963345143.580148858781
Winsorized Mean ( 12 / 25 )1.345045333333330.0085571617533662157.183581671133
Winsorized Mean ( 13 / 25 )1.3457040.00842273872987353159.770360111859
Winsorized Mean ( 14 / 25 )1.3441920.00793467808119852169.407250835432
Winsorized Mean ( 15 / 25 )1.3434120.00759766297875464176.819109212476
Winsorized Mean ( 16 / 25 )1.3415560.00723124981160503185.52201001921
Winsorized Mean ( 17 / 25 )1.342213333333330.0071169090196513188.594982685207
Winsorized Mean ( 18 / 25 )1.341349333333330.00694410823527277193.163655848553
Winsorized Mean ( 19 / 25 )1.338790666666670.00627117965922827213.483066889431
Winsorized Mean ( 20 / 25 )1.336870666666670.00598596459696816223.334208716133
Winsorized Mean ( 21 / 25 )1.336814666666670.00585993441322745228.127923010387
Winsorized Mean ( 22 / 25 )1.334614666666670.00533396618767792250.210559967512
Winsorized Mean ( 23 / 25 )1.33670.00503977834490424265.229918564087
Winsorized Mean ( 24 / 25 )1.3313560.00420001983693298316.988026649943
Winsorized Mean ( 25 / 25 )1.331822666666670.00387481290374633343.712767493627
Trimmed Mean ( 1 / 25 )1.345453424657530.0113115016158733118.945606900632
Trimmed Mean ( 2 / 25 )1.344471830985920.0109341582038194122.960707712852
Trimmed Mean ( 3 / 25 )1.343594202898550.0105962474425546126.799058834986
Trimmed Mean ( 4 / 25 )1.34255522388060.0102185246694688131.384448079077
Trimmed Mean ( 5 / 25 )1.341484615384620.00977814459324419137.192143416601
Trimmed Mean ( 6 / 25 )1.341195238095240.00952555659858838140.799671306766
Trimmed Mean ( 7 / 25 )1.340878688524590.00927294911700292144.601104956561
Trimmed Mean ( 8 / 25 )1.340601694915250.00903654328287997148.353375062682
Trimmed Mean ( 9 / 25 )1.340349122807020.00879793035115095152.348230698561
Trimmed Mean ( 10 / 25 )1.340045454545450.00854026818043889156.909060258174
Trimmed Mean ( 11 / 25 )1.339754716981130.00824569226764483162.479349640318
Trimmed Mean ( 12 / 25 )1.339537254901960.0079301380749962168.917267547401
Trimmed Mean ( 13 / 25 )1.338834693877550.00770538538096708173.753112619724
Trimmed Mean ( 14 / 25 )1.33799148936170.00744372960005996179.747460110712
Trimmed Mean ( 15 / 25 )1.337253333333330.00721817193343343185.262050511624
Trimmed Mean ( 16 / 25 )1.336537209302330.00699903807918207190.960128260728
Trimmed Mean ( 17 / 25 )1.335963414634150.00679531021573107196.60079852446
Trimmed Mean ( 18 / 25 )1.335256410256410.00654353199708845204.057443419018
Trimmed Mean ( 19 / 25 )1.334570270270270.00624458908702877213.716267262874
Trimmed Mean ( 20 / 25 )1.334094285714290.00601879959954207221.654544839105
Trimmed Mean ( 21 / 25 )1.333778787878790.00578078183210973230.72636653925
Trimmed Mean ( 22 / 25 )1.333429032258060.0054730290674437243.636387789344
Trimmed Mean ( 23 / 25 )1.333289655172410.00519812950639088256.494120343326
Trimmed Mean ( 24 / 25 )1.332877777777780.00488079360850394273.086281594753
Trimmed Mean ( 25 / 25 )1.3330680.004713900437359282.795111546069
Median1.3322
Midrange1.3778
Midmean - Weighted Average at Xnp1.33295526315789
Midmean - Weighted Average at X(n+1)p1.33525641025641
Midmean - Empirical Distribution Function1.33525641025641
Midmean - Empirical Distribution Function - Averaging1.33525641025641
Midmean - Empirical Distribution Function - Interpolation1.33457027027027
Midmean - Closest Observation1.33295526315789
Midmean - True Basic - Statistics Graphics Toolkit1.33525641025641
Midmean - MS Excel (old versions)1.33525641025641
Number of observations75



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')