Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationFri, 10 Mar 2017 10:37:18 +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/2017/Mar/10/t1489142338qt6bbl5wm8jiv3s.htm/, Retrieved Wed, 15 May 2024 18:08:23 +0200
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Wed, 15 May 2024 18:08:23 +0200
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact0
Dataseries X:
101,03
100,65
100,66
100,54
100,51
100,53
100,53
101,02
101,07
101,37
101,45
101,44
101,45
100,99
101,11
101,31
101,53
101,6
101,61
102,04
102,36
102,74
102,96
103,01
103,02
102,34
102,38
102,54
102,71
102,78
102,78
103,27
103,4
103,74
103,89
103,92
99,68
99,06
99,12
99,37
99,63
99,69
99,76
100,16
100,46
100,83
101,09
101,14
101,25
101,09
101,18
101,14
101,23
101,17
100,84
101,04
101,18
101,1
101,21
101,26
101,85
101,82
101,93
101,95
101,97
102,04
101,37
101,2
101,14
101,27
101,39
101,4




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 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 & 1 seconds \tabularnewline
R Server & 'Sir Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]1 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=&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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 time1 seconds
R Server'Sir Maurice George Kendall' @ kendall.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean101.4345833333330.126638392183431800.978136128019
Geometric Mean101.42897775007
Harmonic Mean101.423379123337
Quadratic Mean101.440195894209
Winsorized Mean ( 1 / 24 )101.4350.126306164779657803.088275041483
Winsorized Mean ( 2 / 24 )101.4377777777780.123472232124153821.543241202449
Winsorized Mean ( 3 / 24 )101.4344444444440.117486204179434863.373237333683
Winsorized Mean ( 4 / 24 )101.430.115225165700213880.276451620779
Winsorized Mean ( 5 / 24 )101.4133333333330.111355638596621910.715744720361
Winsorized Mean ( 6 / 24 )101.4183333333330.109930444647545922.56820809283
Winsorized Mean ( 7 / 24 )101.4523611111110.1012734821888821001.76629576038
Winsorized Mean ( 8 / 24 )101.4656944444440.09155602080033971108.23617668701
Winsorized Mean ( 9 / 24 )101.4719444444440.09060517256825021119.93544704094
Winsorized Mean ( 10 / 24 )101.4691666666670.08906810840178581139.23118484722
Winsorized Mean ( 11 / 24 )101.4645833333330.08815153972222511151.02451588548
Winsorized Mean ( 12 / 24 )101.4379166666670.08240680644720011230.94099917172
Winsorized Mean ( 13 / 24 )101.4288888888890.07407028224514981369.36009711952
Winsorized Mean ( 14 / 24 )101.4269444444440.07308125659890831387.86535925491
Winsorized Mean ( 15 / 24 )101.4581944444440.06736788682183211506.03201660119
Winsorized Mean ( 16 / 24 )101.393750.05537729371885581830.96253339436
Winsorized Mean ( 17 / 24 )101.4291666666670.05070849752694112000.2400310279
Winsorized Mean ( 18 / 24 )101.4191666666670.04686650288139472164.00116141221
Winsorized Mean ( 19 / 24 )101.4165277777780.04568002945329362220.15022738707
Winsorized Mean ( 20 / 24 )101.413750.04443852354437972282.11339872083
Winsorized Mean ( 21 / 24 )101.3991666666670.03962744638558292558.81152875794
Winsorized Mean ( 22 / 24 )101.3961111111110.03745292065869852707.29516758159
Winsorized Mean ( 23 / 24 )101.3290277777780.02714301637834493733.15280679783
Winsorized Mean ( 24 / 24 )101.3290277777780.02624606664190743860.73193977129
Trimmed Mean ( 1 / 24 )101.4330.120528915458896841.565690803812
Trimmed Mean ( 2 / 24 )101.4308823529410.113584879343025892.996347221722
Trimmed Mean ( 3 / 24 )101.4271212121210.107090307870029947.117654524056
Trimmed Mean ( 4 / 24 )101.4243750.102155313544218992.84483088683
Trimmed Mean ( 5 / 24 )101.4227419354840.09705803825436211044.97003813
Trimmed Mean ( 6 / 24 )101.4250.09217016319314421100.41033330344
Trimmed Mean ( 7 / 24 )101.4263793103450.08659195612089751171.31410184031
Trimmed Mean ( 8 / 24 )101.4216071428570.08224124189968331233.22076369627
Trimmed Mean ( 9 / 24 )101.4142592592590.07943528931657921276.69024852526
Trimmed Mean ( 10 / 24 )101.4053846153850.07613419006806251331.92964323558
Trimmed Mean ( 11 / 24 )101.39620.0723381458632911401.69752472817
Trimmed Mean ( 12 / 24 )101.3868750.06769976759783911497.5956136552
Trimmed Mean ( 13 / 24 )101.3802173913040.06328716023241651601.90814406895
Trimmed Mean ( 14 / 24 )101.3740909090910.05975842681367261696.39825400987
Trimmed Mean ( 15 / 24 )101.3676190476190.05533533033472511831.8788093329
Trimmed Mean ( 16 / 24 )101.356750.05084842672099111993.31142645084
Trimmed Mean ( 17 / 24 )101.3523684210530.04843854050581792092.39104569799
Trimmed Mean ( 18 / 24 )101.3433333333330.04622065778793292192.59824899748
Trimmed Mean ( 19 / 24 )101.3344117647060.0441985295415032292.7100248788
Trimmed Mean ( 20 / 24 )101.32468750.04160583176545272435.34820001207
Trimmed Mean ( 21 / 24 )101.3140.03815154295549582655.56756428394
Trimmed Mean ( 22 / 24 )101.3035714285710.03481703608166122909.59779548638
Trimmed Mean ( 23 / 24 )101.2919230769230.03039746563711783332.2489541114
Trimmed Mean ( 24 / 24 )101.2870833333330.02880770306773253515.97220698879
Median101.255
Midrange101.49
Midmean - Weighted Average at Xnp101.333783783784
Midmean - Weighted Average at X(n+1)p101.343333333333
Midmean - Empirical Distribution Function101.333783783784
Midmean - Empirical Distribution Function - Averaging101.343333333333
Midmean - Empirical Distribution Function - Interpolation101.343333333333
Midmean - Closest Observation101.333783783784
Midmean - True Basic - Statistics Graphics Toolkit101.343333333333
Midmean - MS Excel (old versions)101.37
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 101.434583333333 & 0.126638392183431 & 800.978136128019 \tabularnewline
Geometric Mean & 101.42897775007 &  &  \tabularnewline
Harmonic Mean & 101.423379123337 &  &  \tabularnewline
Quadratic Mean & 101.440195894209 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 101.435 & 0.126306164779657 & 803.088275041483 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 101.437777777778 & 0.123472232124153 & 821.543241202449 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 101.434444444444 & 0.117486204179434 & 863.373237333683 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 101.43 & 0.115225165700213 & 880.276451620779 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 101.413333333333 & 0.111355638596621 & 910.715744720361 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 101.418333333333 & 0.109930444647545 & 922.56820809283 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 101.452361111111 & 0.101273482188882 & 1001.76629576038 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 101.465694444444 & 0.0915560208003397 & 1108.23617668701 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 101.471944444444 & 0.0906051725682502 & 1119.93544704094 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 101.469166666667 & 0.0890681084017858 & 1139.23118484722 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 101.464583333333 & 0.0881515397222251 & 1151.02451588548 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 101.437916666667 & 0.0824068064472001 & 1230.94099917172 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 101.428888888889 & 0.0740702822451498 & 1369.36009711952 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 101.426944444444 & 0.0730812565989083 & 1387.86535925491 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 101.458194444444 & 0.0673678868218321 & 1506.03201660119 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 101.39375 & 0.0553772937188558 & 1830.96253339436 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 101.429166666667 & 0.0507084975269411 & 2000.2400310279 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 101.419166666667 & 0.0468665028813947 & 2164.00116141221 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 101.416527777778 & 0.0456800294532936 & 2220.15022738707 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 101.41375 & 0.0444385235443797 & 2282.11339872083 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 101.399166666667 & 0.0396274463855829 & 2558.81152875794 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 101.396111111111 & 0.0374529206586985 & 2707.29516758159 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 101.329027777778 & 0.0271430163783449 & 3733.15280679783 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 101.329027777778 & 0.0262460666419074 & 3860.73193977129 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 101.433 & 0.120528915458896 & 841.565690803812 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 101.430882352941 & 0.113584879343025 & 892.996347221722 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 101.427121212121 & 0.107090307870029 & 947.117654524056 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 101.424375 & 0.102155313544218 & 992.84483088683 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 101.422741935484 & 0.0970580382543621 & 1044.97003813 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 101.425 & 0.0921701631931442 & 1100.41033330344 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 101.426379310345 & 0.0865919561208975 & 1171.31410184031 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 101.421607142857 & 0.0822412418996833 & 1233.22076369627 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 101.414259259259 & 0.0794352893165792 & 1276.69024852526 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 101.405384615385 & 0.0761341900680625 & 1331.92964323558 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 101.3962 & 0.072338145863291 & 1401.69752472817 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 101.386875 & 0.0676997675978391 & 1497.5956136552 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 101.380217391304 & 0.0632871602324165 & 1601.90814406895 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 101.374090909091 & 0.0597584268136726 & 1696.39825400987 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 101.367619047619 & 0.0553353303347251 & 1831.8788093329 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 101.35675 & 0.0508484267209911 & 1993.31142645084 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 101.352368421053 & 0.0484385405058179 & 2092.39104569799 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 101.343333333333 & 0.0462206577879329 & 2192.59824899748 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 101.334411764706 & 0.044198529541503 & 2292.7100248788 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 101.3246875 & 0.0416058317654527 & 2435.34820001207 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 101.314 & 0.0381515429554958 & 2655.56756428394 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 101.303571428571 & 0.0348170360816612 & 2909.59779548638 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 101.291923076923 & 0.0303974656371178 & 3332.2489541114 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 101.287083333333 & 0.0288077030677325 & 3515.97220698879 \tabularnewline
Median & 101.255 &  &  \tabularnewline
Midrange & 101.49 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 101.333783783784 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 101.343333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 101.333783783784 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 101.343333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 101.343333333333 &  &  \tabularnewline
Midmean - Closest Observation & 101.333783783784 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 101.343333333333 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 101.37 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]101.434583333333[/C][C]0.126638392183431[/C][C]800.978136128019[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]101.42897775007[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]101.423379123337[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]101.440195894209[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]101.435[/C][C]0.126306164779657[/C][C]803.088275041483[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]101.437777777778[/C][C]0.123472232124153[/C][C]821.543241202449[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]101.434444444444[/C][C]0.117486204179434[/C][C]863.373237333683[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]101.43[/C][C]0.115225165700213[/C][C]880.276451620779[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]101.413333333333[/C][C]0.111355638596621[/C][C]910.715744720361[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]101.418333333333[/C][C]0.109930444647545[/C][C]922.56820809283[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]101.452361111111[/C][C]0.101273482188882[/C][C]1001.76629576038[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]101.465694444444[/C][C]0.0915560208003397[/C][C]1108.23617668701[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]101.471944444444[/C][C]0.0906051725682502[/C][C]1119.93544704094[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]101.469166666667[/C][C]0.0890681084017858[/C][C]1139.23118484722[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]101.464583333333[/C][C]0.0881515397222251[/C][C]1151.02451588548[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]101.437916666667[/C][C]0.0824068064472001[/C][C]1230.94099917172[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]101.428888888889[/C][C]0.0740702822451498[/C][C]1369.36009711952[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]101.426944444444[/C][C]0.0730812565989083[/C][C]1387.86535925491[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]101.458194444444[/C][C]0.0673678868218321[/C][C]1506.03201660119[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]101.39375[/C][C]0.0553772937188558[/C][C]1830.96253339436[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]101.429166666667[/C][C]0.0507084975269411[/C][C]2000.2400310279[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]101.419166666667[/C][C]0.0468665028813947[/C][C]2164.00116141221[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]101.416527777778[/C][C]0.0456800294532936[/C][C]2220.15022738707[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]101.41375[/C][C]0.0444385235443797[/C][C]2282.11339872083[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]101.399166666667[/C][C]0.0396274463855829[/C][C]2558.81152875794[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]101.396111111111[/C][C]0.0374529206586985[/C][C]2707.29516758159[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]101.329027777778[/C][C]0.0271430163783449[/C][C]3733.15280679783[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]101.329027777778[/C][C]0.0262460666419074[/C][C]3860.73193977129[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]101.433[/C][C]0.120528915458896[/C][C]841.565690803812[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]101.430882352941[/C][C]0.113584879343025[/C][C]892.996347221722[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]101.427121212121[/C][C]0.107090307870029[/C][C]947.117654524056[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]101.424375[/C][C]0.102155313544218[/C][C]992.84483088683[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]101.422741935484[/C][C]0.0970580382543621[/C][C]1044.97003813[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]101.425[/C][C]0.0921701631931442[/C][C]1100.41033330344[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]101.426379310345[/C][C]0.0865919561208975[/C][C]1171.31410184031[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]101.421607142857[/C][C]0.0822412418996833[/C][C]1233.22076369627[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]101.414259259259[/C][C]0.0794352893165792[/C][C]1276.69024852526[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]101.405384615385[/C][C]0.0761341900680625[/C][C]1331.92964323558[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]101.3962[/C][C]0.072338145863291[/C][C]1401.69752472817[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]101.386875[/C][C]0.0676997675978391[/C][C]1497.5956136552[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]101.380217391304[/C][C]0.0632871602324165[/C][C]1601.90814406895[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]101.374090909091[/C][C]0.0597584268136726[/C][C]1696.39825400987[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]101.367619047619[/C][C]0.0553353303347251[/C][C]1831.8788093329[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]101.35675[/C][C]0.0508484267209911[/C][C]1993.31142645084[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]101.352368421053[/C][C]0.0484385405058179[/C][C]2092.39104569799[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]101.343333333333[/C][C]0.0462206577879329[/C][C]2192.59824899748[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]101.334411764706[/C][C]0.044198529541503[/C][C]2292.7100248788[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]101.3246875[/C][C]0.0416058317654527[/C][C]2435.34820001207[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]101.314[/C][C]0.0381515429554958[/C][C]2655.56756428394[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]101.303571428571[/C][C]0.0348170360816612[/C][C]2909.59779548638[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]101.291923076923[/C][C]0.0303974656371178[/C][C]3332.2489541114[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]101.287083333333[/C][C]0.0288077030677325[/C][C]3515.97220698879[/C][/ROW]
[ROW][C]Median[/C][C]101.255[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]101.49[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]101.333783783784[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]101.343333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]101.333783783784[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]101.343333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]101.343333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]101.333783783784[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]101.343333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]101.37[/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=&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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 Mean101.4345833333330.126638392183431800.978136128019
Geometric Mean101.42897775007
Harmonic Mean101.423379123337
Quadratic Mean101.440195894209
Winsorized Mean ( 1 / 24 )101.4350.126306164779657803.088275041483
Winsorized Mean ( 2 / 24 )101.4377777777780.123472232124153821.543241202449
Winsorized Mean ( 3 / 24 )101.4344444444440.117486204179434863.373237333683
Winsorized Mean ( 4 / 24 )101.430.115225165700213880.276451620779
Winsorized Mean ( 5 / 24 )101.4133333333330.111355638596621910.715744720361
Winsorized Mean ( 6 / 24 )101.4183333333330.109930444647545922.56820809283
Winsorized Mean ( 7 / 24 )101.4523611111110.1012734821888821001.76629576038
Winsorized Mean ( 8 / 24 )101.4656944444440.09155602080033971108.23617668701
Winsorized Mean ( 9 / 24 )101.4719444444440.09060517256825021119.93544704094
Winsorized Mean ( 10 / 24 )101.4691666666670.08906810840178581139.23118484722
Winsorized Mean ( 11 / 24 )101.4645833333330.08815153972222511151.02451588548
Winsorized Mean ( 12 / 24 )101.4379166666670.08240680644720011230.94099917172
Winsorized Mean ( 13 / 24 )101.4288888888890.07407028224514981369.36009711952
Winsorized Mean ( 14 / 24 )101.4269444444440.07308125659890831387.86535925491
Winsorized Mean ( 15 / 24 )101.4581944444440.06736788682183211506.03201660119
Winsorized Mean ( 16 / 24 )101.393750.05537729371885581830.96253339436
Winsorized Mean ( 17 / 24 )101.4291666666670.05070849752694112000.2400310279
Winsorized Mean ( 18 / 24 )101.4191666666670.04686650288139472164.00116141221
Winsorized Mean ( 19 / 24 )101.4165277777780.04568002945329362220.15022738707
Winsorized Mean ( 20 / 24 )101.413750.04443852354437972282.11339872083
Winsorized Mean ( 21 / 24 )101.3991666666670.03962744638558292558.81152875794
Winsorized Mean ( 22 / 24 )101.3961111111110.03745292065869852707.29516758159
Winsorized Mean ( 23 / 24 )101.3290277777780.02714301637834493733.15280679783
Winsorized Mean ( 24 / 24 )101.3290277777780.02624606664190743860.73193977129
Trimmed Mean ( 1 / 24 )101.4330.120528915458896841.565690803812
Trimmed Mean ( 2 / 24 )101.4308823529410.113584879343025892.996347221722
Trimmed Mean ( 3 / 24 )101.4271212121210.107090307870029947.117654524056
Trimmed Mean ( 4 / 24 )101.4243750.102155313544218992.84483088683
Trimmed Mean ( 5 / 24 )101.4227419354840.09705803825436211044.97003813
Trimmed Mean ( 6 / 24 )101.4250.09217016319314421100.41033330344
Trimmed Mean ( 7 / 24 )101.4263793103450.08659195612089751171.31410184031
Trimmed Mean ( 8 / 24 )101.4216071428570.08224124189968331233.22076369627
Trimmed Mean ( 9 / 24 )101.4142592592590.07943528931657921276.69024852526
Trimmed Mean ( 10 / 24 )101.4053846153850.07613419006806251331.92964323558
Trimmed Mean ( 11 / 24 )101.39620.0723381458632911401.69752472817
Trimmed Mean ( 12 / 24 )101.3868750.06769976759783911497.5956136552
Trimmed Mean ( 13 / 24 )101.3802173913040.06328716023241651601.90814406895
Trimmed Mean ( 14 / 24 )101.3740909090910.05975842681367261696.39825400987
Trimmed Mean ( 15 / 24 )101.3676190476190.05533533033472511831.8788093329
Trimmed Mean ( 16 / 24 )101.356750.05084842672099111993.31142645084
Trimmed Mean ( 17 / 24 )101.3523684210530.04843854050581792092.39104569799
Trimmed Mean ( 18 / 24 )101.3433333333330.04622065778793292192.59824899748
Trimmed Mean ( 19 / 24 )101.3344117647060.0441985295415032292.7100248788
Trimmed Mean ( 20 / 24 )101.32468750.04160583176545272435.34820001207
Trimmed Mean ( 21 / 24 )101.3140.03815154295549582655.56756428394
Trimmed Mean ( 22 / 24 )101.3035714285710.03481703608166122909.59779548638
Trimmed Mean ( 23 / 24 )101.2919230769230.03039746563711783332.2489541114
Trimmed Mean ( 24 / 24 )101.2870833333330.02880770306773253515.97220698879
Median101.255
Midrange101.49
Midmean - Weighted Average at Xnp101.333783783784
Midmean - Weighted Average at X(n+1)p101.343333333333
Midmean - Empirical Distribution Function101.333783783784
Midmean - Empirical Distribution Function - Averaging101.343333333333
Midmean - Empirical Distribution Function - Interpolation101.343333333333
Midmean - Closest Observation101.333783783784
Midmean - True Basic - Statistics Graphics Toolkit101.343333333333
Midmean - MS Excel (old versions)101.37
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')