Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationFri, 19 Oct 2012 06:04:59 -0400
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/Oct/19/t1350641119hk1a5zc8e2dfdwt.htm/, Retrieved Mon, 29 Apr 2024 13:29:47 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=179987, Retrieved Mon, 29 Apr 2024 13:29:47 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact58
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2012-10-19 10:04:59] [72b460291cf9216c25149e3abf0bc35d] [Current]
Feedback Forum

Post a new message
Dataseries X:
0,98
0,99
0,99
0,99
1
1
1
1
1
1,01
1,02
1,02
1,01
1,03
1,03
1,03
1,03
1,03
1,03
1,03
1,04
1,06
1,07
1,08
1,08
1,09
1,09
1,09
1,1
1,1
1,1
1,1
1,1
1,11
1,12
1,13
1,13
1,13
1,13
1,13
1,14
1,14
1,14
1,14
1,14
1,14
1,15
1,15
1,15
1,15
1,15
1,15
1,16
1,15
1,16
1,16
1,16
1,17
1,17
1,17
1,18
1,19
1,2
1,21
1,21
1,21
1,21
1,22
1,22
1,22
1,23
1,22




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 seconds
R Server'Sir Maurice George Kendall' @ kendall.wessa.net

\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 & 4 seconds \tabularnewline
R Server & 'Sir Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=179987&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]4 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Maurice George Kendall' @ kendall.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=179987&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=179987&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 time4 seconds
R Server'Sir Maurice George Kendall' @ kendall.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean1.107777777777780.00856993284181577129.263297417284
Geometric Mean1.10539930995837
Harmonic Mean1.10299925533812
Quadratic Mean1.11012887139787
Winsorized Mean ( 1 / 24 )1.107777777777780.00851497397395213130.097611709272
Winsorized Mean ( 2 / 24 )1.107777777777780.00851497397395213130.097611709272
Winsorized Mean ( 3 / 24 )1.107777777777780.00851497397395213130.097611709272
Winsorized Mean ( 4 / 24 )1.108333333333330.00841044138298645131.780638240389
Winsorized Mean ( 5 / 24 )1.107638888888890.00828505511893371133.691191306334
Winsorized Mean ( 6 / 24 )1.107638888888890.00828505511893371133.691191306334
Winsorized Mean ( 7 / 24 )1.107638888888890.00828505511893371133.691191306334
Winsorized Mean ( 8 / 24 )1.107638888888890.00828505511893371133.691191306334
Winsorized Mean ( 9 / 24 )1.107638888888890.00784855940938482141.126394171705
Winsorized Mean ( 10 / 24 )1.106250.00762593153446764145.064244938468
Winsorized Mean ( 11 / 24 )1.106250.00713012712597404155.151511390321
Winsorized Mean ( 12 / 24 )1.104583333333330.00689723782911402160.148650909319
Winsorized Mean ( 13 / 24 )1.106388888888890.0065938083169233167.792091567068
Winsorized Mean ( 14 / 24 )1.106388888888890.0065938083169233167.792091567068
Winsorized Mean ( 15 / 24 )1.104305555555560.00632278089536075174.655040848533
Winsorized Mean ( 16 / 24 )1.104305555555560.00632278089536075174.655040848533
Winsorized Mean ( 17 / 24 )1.104305555555560.00632278089536075174.655040848533
Winsorized Mean ( 18 / 24 )1.104305555555560.00632278089536075174.655040848533
Winsorized Mean ( 19 / 24 )1.101666666666670.00600925212577331183.328414852438
Winsorized Mean ( 20 / 24 )1.104444444444440.00554850883296749199.05248016948
Winsorized Mean ( 21 / 24 )1.110277777777780.00462173296285052240.229755094504
Winsorized Mean ( 22 / 24 )1.113333333333330.00416314405084743267.426089449561
Winsorized Mean ( 23 / 24 )1.116527777777780.00370656758732788301.229574659584
Winsorized Mean ( 24 / 24 )1.116527777777780.00370656758732788301.229574659584
Trimmed Mean ( 1 / 24 )1.107857142857140.00844147519106468131.239755822515
Trimmed Mean ( 2 / 24 )1.107941176470590.00835073670350074132.675860323332
Trimmed Mean ( 3 / 24 )1.10803030303030.00823947996913381134.478183960776
Trimmed Mean ( 4 / 24 )1.1081250.00810360430782363136.744707405094
Trimmed Mean ( 5 / 24 )1.108064516129030.00797550026174128138.933543948892
Trimmed Mean ( 6 / 24 )1.108166666666670.0078563791298546141.053104534579
Trimmed Mean ( 7 / 24 )1.108275862068970.00770814392841771143.77986093164
Trimmed Mean ( 8 / 24 )1.108392857142860.00752388743863432147.31651239908
Trimmed Mean ( 9 / 24 )1.108518518518520.00729438584175147151.968725341289
Trimmed Mean ( 10 / 24 )1.108653846153850.00711375383863966155.846529315084
Trimmed Mean ( 11 / 24 )1.1090.00693556348225048159.900490109875
Trimmed Mean ( 12 / 24 )1.1093750.00681835139752578162.70428661136
Trimmed Mean ( 13 / 24 )1.110.0067100040677612165.42463891089
Trimmed Mean ( 14 / 24 )1.110454545454550.00663097467201491167.464754486405
Trimmed Mean ( 15 / 24 )1.110952380952380.00651817368065529170.439211254754
Trimmed Mean ( 16 / 24 )1.111750.00641400211076695173.331717202547
Trimmed Mean ( 17 / 24 )1.112631578947370.00626221946900589177.673680147144
Trimmed Mean ( 18 / 24 )1.113611111111110.00604418621063692184.245003761021
Trimmed Mean ( 19 / 24 )1.114705882352940.00573066452390109194.515989847913
Trimmed Mean ( 20 / 24 )1.116250.00534589833725427208.804943450033
Trimmed Mean ( 21 / 24 )1.117666666666670.00495226253489849225.688088785781
Trimmed Mean ( 22 / 24 )1.118571428571430.00473404548952593236.282357456485
Trimmed Mean ( 23 / 24 )1.119230769230770.00457158706403187244.823242684494
Trimmed Mean ( 24 / 24 )1.119583333333330.00448343030981803249.715788128036
Median1.13
Midrange1.105
Midmean - Weighted Average at Xnp1.10727272727273
Midmean - Weighted Average at X(n+1)p1.10727272727273
Midmean - Empirical Distribution Function1.10727272727273
Midmean - Empirical Distribution Function - Averaging1.10727272727273
Midmean - Empirical Distribution Function - Interpolation1.10727272727273
Midmean - Closest Observation1.10727272727273
Midmean - True Basic - Statistics Graphics Toolkit1.10727272727273
Midmean - MS Excel (old versions)1.10727272727273
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 1.10777777777778 & 0.00856993284181577 & 129.263297417284 \tabularnewline
Geometric Mean & 1.10539930995837 &  &  \tabularnewline
Harmonic Mean & 1.10299925533812 &  &  \tabularnewline
Quadratic Mean & 1.11012887139787 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 1.10777777777778 & 0.00851497397395213 & 130.097611709272 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 1.10777777777778 & 0.00851497397395213 & 130.097611709272 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 1.10777777777778 & 0.00851497397395213 & 130.097611709272 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 1.10833333333333 & 0.00841044138298645 & 131.780638240389 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 1.10763888888889 & 0.00828505511893371 & 133.691191306334 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 1.10763888888889 & 0.00828505511893371 & 133.691191306334 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 1.10763888888889 & 0.00828505511893371 & 133.691191306334 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 1.10763888888889 & 0.00828505511893371 & 133.691191306334 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 1.10763888888889 & 0.00784855940938482 & 141.126394171705 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 1.10625 & 0.00762593153446764 & 145.064244938468 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 1.10625 & 0.00713012712597404 & 155.151511390321 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 1.10458333333333 & 0.00689723782911402 & 160.148650909319 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 1.10638888888889 & 0.0065938083169233 & 167.792091567068 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 1.10638888888889 & 0.0065938083169233 & 167.792091567068 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 1.10430555555556 & 0.00632278089536075 & 174.655040848533 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 1.10430555555556 & 0.00632278089536075 & 174.655040848533 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 1.10430555555556 & 0.00632278089536075 & 174.655040848533 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 1.10430555555556 & 0.00632278089536075 & 174.655040848533 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 1.10166666666667 & 0.00600925212577331 & 183.328414852438 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 1.10444444444444 & 0.00554850883296749 & 199.05248016948 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 1.11027777777778 & 0.00462173296285052 & 240.229755094504 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 1.11333333333333 & 0.00416314405084743 & 267.426089449561 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 1.11652777777778 & 0.00370656758732788 & 301.229574659584 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 1.11652777777778 & 0.00370656758732788 & 301.229574659584 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 1.10785714285714 & 0.00844147519106468 & 131.239755822515 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 1.10794117647059 & 0.00835073670350074 & 132.675860323332 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 1.1080303030303 & 0.00823947996913381 & 134.478183960776 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 1.108125 & 0.00810360430782363 & 136.744707405094 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 1.10806451612903 & 0.00797550026174128 & 138.933543948892 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 1.10816666666667 & 0.0078563791298546 & 141.053104534579 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 1.10827586206897 & 0.00770814392841771 & 143.77986093164 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 1.10839285714286 & 0.00752388743863432 & 147.31651239908 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 1.10851851851852 & 0.00729438584175147 & 151.968725341289 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 1.10865384615385 & 0.00711375383863966 & 155.846529315084 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 1.109 & 0.00693556348225048 & 159.900490109875 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 1.109375 & 0.00681835139752578 & 162.70428661136 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 1.11 & 0.0067100040677612 & 165.42463891089 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 1.11045454545455 & 0.00663097467201491 & 167.464754486405 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 1.11095238095238 & 0.00651817368065529 & 170.439211254754 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 1.11175 & 0.00641400211076695 & 173.331717202547 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 1.11263157894737 & 0.00626221946900589 & 177.673680147144 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 1.11361111111111 & 0.00604418621063692 & 184.245003761021 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 1.11470588235294 & 0.00573066452390109 & 194.515989847913 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 1.11625 & 0.00534589833725427 & 208.804943450033 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 1.11766666666667 & 0.00495226253489849 & 225.688088785781 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 1.11857142857143 & 0.00473404548952593 & 236.282357456485 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 1.11923076923077 & 0.00457158706403187 & 244.823242684494 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 1.11958333333333 & 0.00448343030981803 & 249.715788128036 \tabularnewline
Median & 1.13 &  &  \tabularnewline
Midrange & 1.105 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 1.10727272727273 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 1.10727272727273 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 1.10727272727273 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 1.10727272727273 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 1.10727272727273 &  &  \tabularnewline
Midmean - Closest Observation & 1.10727272727273 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 1.10727272727273 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 1.10727272727273 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=179987&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]1.10777777777778[/C][C]0.00856993284181577[/C][C]129.263297417284[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]1.10539930995837[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]1.10299925533812[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]1.11012887139787[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]1.10777777777778[/C][C]0.00851497397395213[/C][C]130.097611709272[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]1.10777777777778[/C][C]0.00851497397395213[/C][C]130.097611709272[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]1.10777777777778[/C][C]0.00851497397395213[/C][C]130.097611709272[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]1.10833333333333[/C][C]0.00841044138298645[/C][C]131.780638240389[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]1.10763888888889[/C][C]0.00828505511893371[/C][C]133.691191306334[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]1.10763888888889[/C][C]0.00828505511893371[/C][C]133.691191306334[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]1.10763888888889[/C][C]0.00828505511893371[/C][C]133.691191306334[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]1.10763888888889[/C][C]0.00828505511893371[/C][C]133.691191306334[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]1.10763888888889[/C][C]0.00784855940938482[/C][C]141.126394171705[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]1.10625[/C][C]0.00762593153446764[/C][C]145.064244938468[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]1.10625[/C][C]0.00713012712597404[/C][C]155.151511390321[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]1.10458333333333[/C][C]0.00689723782911402[/C][C]160.148650909319[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]1.10638888888889[/C][C]0.0065938083169233[/C][C]167.792091567068[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]1.10638888888889[/C][C]0.0065938083169233[/C][C]167.792091567068[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]1.10430555555556[/C][C]0.00632278089536075[/C][C]174.655040848533[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]1.10430555555556[/C][C]0.00632278089536075[/C][C]174.655040848533[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]1.10430555555556[/C][C]0.00632278089536075[/C][C]174.655040848533[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]1.10430555555556[/C][C]0.00632278089536075[/C][C]174.655040848533[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]1.10166666666667[/C][C]0.00600925212577331[/C][C]183.328414852438[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]1.10444444444444[/C][C]0.00554850883296749[/C][C]199.05248016948[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]1.11027777777778[/C][C]0.00462173296285052[/C][C]240.229755094504[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]1.11333333333333[/C][C]0.00416314405084743[/C][C]267.426089449561[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]1.11652777777778[/C][C]0.00370656758732788[/C][C]301.229574659584[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]1.11652777777778[/C][C]0.00370656758732788[/C][C]301.229574659584[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]1.10785714285714[/C][C]0.00844147519106468[/C][C]131.239755822515[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]1.10794117647059[/C][C]0.00835073670350074[/C][C]132.675860323332[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]1.1080303030303[/C][C]0.00823947996913381[/C][C]134.478183960776[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]1.108125[/C][C]0.00810360430782363[/C][C]136.744707405094[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]1.10806451612903[/C][C]0.00797550026174128[/C][C]138.933543948892[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]1.10816666666667[/C][C]0.0078563791298546[/C][C]141.053104534579[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]1.10827586206897[/C][C]0.00770814392841771[/C][C]143.77986093164[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]1.10839285714286[/C][C]0.00752388743863432[/C][C]147.31651239908[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]1.10851851851852[/C][C]0.00729438584175147[/C][C]151.968725341289[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]1.10865384615385[/C][C]0.00711375383863966[/C][C]155.846529315084[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]1.109[/C][C]0.00693556348225048[/C][C]159.900490109875[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]1.109375[/C][C]0.00681835139752578[/C][C]162.70428661136[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]1.11[/C][C]0.0067100040677612[/C][C]165.42463891089[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]1.11045454545455[/C][C]0.00663097467201491[/C][C]167.464754486405[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]1.11095238095238[/C][C]0.00651817368065529[/C][C]170.439211254754[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]1.11175[/C][C]0.00641400211076695[/C][C]173.331717202547[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]1.11263157894737[/C][C]0.00626221946900589[/C][C]177.673680147144[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]1.11361111111111[/C][C]0.00604418621063692[/C][C]184.245003761021[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]1.11470588235294[/C][C]0.00573066452390109[/C][C]194.515989847913[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]1.11625[/C][C]0.00534589833725427[/C][C]208.804943450033[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]1.11766666666667[/C][C]0.00495226253489849[/C][C]225.688088785781[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]1.11857142857143[/C][C]0.00473404548952593[/C][C]236.282357456485[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]1.11923076923077[/C][C]0.00457158706403187[/C][C]244.823242684494[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]1.11958333333333[/C][C]0.00448343030981803[/C][C]249.715788128036[/C][/ROW]
[ROW][C]Median[/C][C]1.13[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]1.105[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]1.10727272727273[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]1.10727272727273[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]1.10727272727273[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]1.10727272727273[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]1.10727272727273[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]1.10727272727273[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]1.10727272727273[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]1.10727272727273[/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=179987&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=179987&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 Mean1.107777777777780.00856993284181577129.263297417284
Geometric Mean1.10539930995837
Harmonic Mean1.10299925533812
Quadratic Mean1.11012887139787
Winsorized Mean ( 1 / 24 )1.107777777777780.00851497397395213130.097611709272
Winsorized Mean ( 2 / 24 )1.107777777777780.00851497397395213130.097611709272
Winsorized Mean ( 3 / 24 )1.107777777777780.00851497397395213130.097611709272
Winsorized Mean ( 4 / 24 )1.108333333333330.00841044138298645131.780638240389
Winsorized Mean ( 5 / 24 )1.107638888888890.00828505511893371133.691191306334
Winsorized Mean ( 6 / 24 )1.107638888888890.00828505511893371133.691191306334
Winsorized Mean ( 7 / 24 )1.107638888888890.00828505511893371133.691191306334
Winsorized Mean ( 8 / 24 )1.107638888888890.00828505511893371133.691191306334
Winsorized Mean ( 9 / 24 )1.107638888888890.00784855940938482141.126394171705
Winsorized Mean ( 10 / 24 )1.106250.00762593153446764145.064244938468
Winsorized Mean ( 11 / 24 )1.106250.00713012712597404155.151511390321
Winsorized Mean ( 12 / 24 )1.104583333333330.00689723782911402160.148650909319
Winsorized Mean ( 13 / 24 )1.106388888888890.0065938083169233167.792091567068
Winsorized Mean ( 14 / 24 )1.106388888888890.0065938083169233167.792091567068
Winsorized Mean ( 15 / 24 )1.104305555555560.00632278089536075174.655040848533
Winsorized Mean ( 16 / 24 )1.104305555555560.00632278089536075174.655040848533
Winsorized Mean ( 17 / 24 )1.104305555555560.00632278089536075174.655040848533
Winsorized Mean ( 18 / 24 )1.104305555555560.00632278089536075174.655040848533
Winsorized Mean ( 19 / 24 )1.101666666666670.00600925212577331183.328414852438
Winsorized Mean ( 20 / 24 )1.104444444444440.00554850883296749199.05248016948
Winsorized Mean ( 21 / 24 )1.110277777777780.00462173296285052240.229755094504
Winsorized Mean ( 22 / 24 )1.113333333333330.00416314405084743267.426089449561
Winsorized Mean ( 23 / 24 )1.116527777777780.00370656758732788301.229574659584
Winsorized Mean ( 24 / 24 )1.116527777777780.00370656758732788301.229574659584
Trimmed Mean ( 1 / 24 )1.107857142857140.00844147519106468131.239755822515
Trimmed Mean ( 2 / 24 )1.107941176470590.00835073670350074132.675860323332
Trimmed Mean ( 3 / 24 )1.10803030303030.00823947996913381134.478183960776
Trimmed Mean ( 4 / 24 )1.1081250.00810360430782363136.744707405094
Trimmed Mean ( 5 / 24 )1.108064516129030.00797550026174128138.933543948892
Trimmed Mean ( 6 / 24 )1.108166666666670.0078563791298546141.053104534579
Trimmed Mean ( 7 / 24 )1.108275862068970.00770814392841771143.77986093164
Trimmed Mean ( 8 / 24 )1.108392857142860.00752388743863432147.31651239908
Trimmed Mean ( 9 / 24 )1.108518518518520.00729438584175147151.968725341289
Trimmed Mean ( 10 / 24 )1.108653846153850.00711375383863966155.846529315084
Trimmed Mean ( 11 / 24 )1.1090.00693556348225048159.900490109875
Trimmed Mean ( 12 / 24 )1.1093750.00681835139752578162.70428661136
Trimmed Mean ( 13 / 24 )1.110.0067100040677612165.42463891089
Trimmed Mean ( 14 / 24 )1.110454545454550.00663097467201491167.464754486405
Trimmed Mean ( 15 / 24 )1.110952380952380.00651817368065529170.439211254754
Trimmed Mean ( 16 / 24 )1.111750.00641400211076695173.331717202547
Trimmed Mean ( 17 / 24 )1.112631578947370.00626221946900589177.673680147144
Trimmed Mean ( 18 / 24 )1.113611111111110.00604418621063692184.245003761021
Trimmed Mean ( 19 / 24 )1.114705882352940.00573066452390109194.515989847913
Trimmed Mean ( 20 / 24 )1.116250.00534589833725427208.804943450033
Trimmed Mean ( 21 / 24 )1.117666666666670.00495226253489849225.688088785781
Trimmed Mean ( 22 / 24 )1.118571428571430.00473404548952593236.282357456485
Trimmed Mean ( 23 / 24 )1.119230769230770.00457158706403187244.823242684494
Trimmed Mean ( 24 / 24 )1.119583333333330.00448343030981803249.715788128036
Median1.13
Midrange1.105
Midmean - Weighted Average at Xnp1.10727272727273
Midmean - Weighted Average at X(n+1)p1.10727272727273
Midmean - Empirical Distribution Function1.10727272727273
Midmean - Empirical Distribution Function - Averaging1.10727272727273
Midmean - Empirical Distribution Function - Interpolation1.10727272727273
Midmean - Closest Observation1.10727272727273
Midmean - True Basic - Statistics Graphics Toolkit1.10727272727273
Midmean - MS Excel (old versions)1.10727272727273
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')