Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationThu, 13 Oct 2016 12:56:32 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Oct/13/t14763600111tjhqfev20d6hmc.htm/, Retrieved Tue, 30 Apr 2024 20:05:31 +0200
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Tue, 30 Apr 2024 20:05:31 +0200
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact0
Dataseries X:
92.1
93.91
95.46
94.54
95.63
96.32
96.42
96.95
96.52
96.82
96.4
96.69
96.72
98.57
98.6
96.44
97.09
97.36
97.74
96.78
96.45
97.66
98.69
98.21
97.33
99.05
100.09
98.1
97.68
97.44
99.19
98.32
97.83
97.71
97.51
97.62
96.49
98.92
99.69
97.06
97.63
97.97
99.01
97.89
97.23
96.93
96.97
97.68
97.73
99.03
100.35
99.38
99.3
99.77
101.11
101.15
101.59
100.95
99.23
100.41




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Herman Ole Andreas Wold' @ wold.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 & 'Herman Ole Andreas Wold' @ wold.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]'Herman Ole Andreas Wold' @ wold.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'Herman Ole Andreas Wold' @ wold.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean97.82350.225347669244433434.100340722369
Geometric Mean97.8081204441613
Harmonic Mean97.7926709997122
Quadratic Mean97.8388126716591
Winsorized Mean ( 1 / 20 )97.84633333333330.212046520674875461.438051527185
Winsorized Mean ( 2 / 20 )97.8660.205501481155397476.230144180786
Winsorized Mean ( 3 / 20 )97.9040.192039926404207509.810651530509
Winsorized Mean ( 4 / 20 )97.87933333333330.180485670380798542.310827927904
Winsorized Mean ( 5 / 20 )97.93183333333330.168501285291862581.193390683669
Winsorized Mean ( 6 / 20 )97.91383333333330.161072165401237607.887980455385
Winsorized Mean ( 7 / 20 )97.87883333333330.152489342346244641.873273419255
Winsorized Mean ( 8 / 20 )97.87083333333330.14983857447015653.175149853222
Winsorized Mean ( 9 / 20 )97.82583333333330.14043360851038696.598445137175
Winsorized Mean ( 10 / 20 )97.81916666666670.136857856827871714.750098634792
Winsorized Mean ( 11 / 20 )97.81183333333330.133623235332466731.997194125474
Winsorized Mean ( 12 / 20 )97.83783333333330.126781784961866771.70260193735
Winsorized Mean ( 13 / 20 )97.8140.120399335546339812.413121352762
Winsorized Mean ( 14 / 20 )97.82333333333330.117454803584708832.859366733207
Winsorized Mean ( 15 / 20 )97.82833333333330.115089050922252850.022939188378
Winsorized Mean ( 16 / 20 )97.83366666666670.106641054481572917.410908418698
Winsorized Mean ( 17 / 20 )97.77416666666670.09484161392859141030.92052756803
Winsorized Mean ( 18 / 20 )97.75316666666670.0895814156935731091.22149845283
Winsorized Mean ( 19 / 20 )97.77216666666670.0838909339245121165.46761482767
Winsorized Mean ( 20 / 20 )97.69883333333330.06935094232601681408.75999743527
Trimmed Mean ( 1 / 20 )97.85724137931030.20038963756221488.334838915665
Trimmed Mean ( 2 / 20 )97.86892857142860.185798675881137526.747180017793
Trimmed Mean ( 3 / 20 )97.87055555555560.172070349618394568.782220601086
Trimmed Mean ( 4 / 20 )97.85769230769230.161810461944265604.767399659231
Trimmed Mean ( 5 / 20 )97.85120.153805241279021636.201986267075
Trimmed Mean ( 6 / 20 )97.83104166666670.147900867575982661.463609173269
Trimmed Mean ( 7 / 20 )97.81304347826090.142753417199881685.188805962556
Trimmed Mean ( 8 / 20 )97.80022727272730.138715981539617705.039363072927
Trimmed Mean ( 9 / 20 )97.7876190476190.134125034634319729.078052536791
Trimmed Mean ( 10 / 20 )97.781250.130706751194008748.096399816895
Trimmed Mean ( 11 / 20 )97.77526315789470.126996565203776769.904784440482
Trimmed Mean ( 12 / 20 )97.76972222222220.122743432314592796.537300436882
Trimmed Mean ( 13 / 20 )97.75970588235290.118655183776764823.897471401475
Trimmed Mean ( 14 / 20 )97.7518750.114691414080173852.303337472747
Trimmed Mean ( 15 / 20 )97.74166666666670.109689303466742891.077466786009
Trimmed Mean ( 16 / 20 )97.72928571428570.102902235118783949.729474792008
Trimmed Mean ( 17 / 20 )97.71423076923080.0956164985392131021.9390195423
Trimmed Mean ( 18 / 20 )97.70541666666670.08932715308223861093.79302144237
Trimmed Mean ( 19 / 20 )97.69818181818180.0814150723774911200.00116643258
Trimmed Mean ( 20 / 20 )97.68650.07056641142252141384.32007566738
Median97.68
Midrange96.845
Midmean - Weighted Average at Xnp97.7106451612903
Midmean - Weighted Average at X(n+1)p97.7416666666667
Midmean - Empirical Distribution Function97.7106451612903
Midmean - Empirical Distribution Function - Averaging97.7416666666667
Midmean - Empirical Distribution Function - Interpolation97.7416666666667
Midmean - Closest Observation97.7106451612903
Midmean - True Basic - Statistics Graphics Toolkit97.7416666666667
Midmean - MS Excel (old versions)97.751875
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 97.8235 & 0.225347669244433 & 434.100340722369 \tabularnewline
Geometric Mean & 97.8081204441613 &  &  \tabularnewline
Harmonic Mean & 97.7926709997122 &  &  \tabularnewline
Quadratic Mean & 97.8388126716591 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 97.8463333333333 & 0.212046520674875 & 461.438051527185 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 97.866 & 0.205501481155397 & 476.230144180786 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 97.904 & 0.192039926404207 & 509.810651530509 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 97.8793333333333 & 0.180485670380798 & 542.310827927904 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 97.9318333333333 & 0.168501285291862 & 581.193390683669 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 97.9138333333333 & 0.161072165401237 & 607.887980455385 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 97.8788333333333 & 0.152489342346244 & 641.873273419255 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 97.8708333333333 & 0.14983857447015 & 653.175149853222 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 97.8258333333333 & 0.14043360851038 & 696.598445137175 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 97.8191666666667 & 0.136857856827871 & 714.750098634792 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 97.8118333333333 & 0.133623235332466 & 731.997194125474 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 97.8378333333333 & 0.126781784961866 & 771.70260193735 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 97.814 & 0.120399335546339 & 812.413121352762 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 97.8233333333333 & 0.117454803584708 & 832.859366733207 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 97.8283333333333 & 0.115089050922252 & 850.022939188378 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 97.8336666666667 & 0.106641054481572 & 917.410908418698 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 97.7741666666667 & 0.0948416139285914 & 1030.92052756803 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 97.7531666666667 & 0.089581415693573 & 1091.22149845283 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 97.7721666666667 & 0.083890933924512 & 1165.46761482767 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 97.6988333333333 & 0.0693509423260168 & 1408.75999743527 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 97.8572413793103 & 0.20038963756221 & 488.334838915665 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 97.8689285714286 & 0.185798675881137 & 526.747180017793 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 97.8705555555556 & 0.172070349618394 & 568.782220601086 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 97.8576923076923 & 0.161810461944265 & 604.767399659231 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 97.8512 & 0.153805241279021 & 636.201986267075 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 97.8310416666667 & 0.147900867575982 & 661.463609173269 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 97.8130434782609 & 0.142753417199881 & 685.188805962556 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 97.8002272727273 & 0.138715981539617 & 705.039363072927 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 97.787619047619 & 0.134125034634319 & 729.078052536791 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 97.78125 & 0.130706751194008 & 748.096399816895 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 97.7752631578947 & 0.126996565203776 & 769.904784440482 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 97.7697222222222 & 0.122743432314592 & 796.537300436882 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 97.7597058823529 & 0.118655183776764 & 823.897471401475 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 97.751875 & 0.114691414080173 & 852.303337472747 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 97.7416666666667 & 0.109689303466742 & 891.077466786009 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 97.7292857142857 & 0.102902235118783 & 949.729474792008 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 97.7142307692308 & 0.095616498539213 & 1021.9390195423 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 97.7054166666667 & 0.0893271530822386 & 1093.79302144237 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 97.6981818181818 & 0.081415072377491 & 1200.00116643258 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 97.6865 & 0.0705664114225214 & 1384.32007566738 \tabularnewline
Median & 97.68 &  &  \tabularnewline
Midrange & 96.845 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 97.7106451612903 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 97.7416666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 97.7106451612903 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 97.7416666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 97.7416666666667 &  &  \tabularnewline
Midmean - Closest Observation & 97.7106451612903 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 97.7416666666667 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 97.751875 &  &  \tabularnewline
Number of observations & 60 &  &  \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]97.8235[/C][C]0.225347669244433[/C][C]434.100340722369[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]97.8081204441613[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]97.7926709997122[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]97.8388126716591[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]97.8463333333333[/C][C]0.212046520674875[/C][C]461.438051527185[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]97.866[/C][C]0.205501481155397[/C][C]476.230144180786[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]97.904[/C][C]0.192039926404207[/C][C]509.810651530509[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]97.8793333333333[/C][C]0.180485670380798[/C][C]542.310827927904[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]97.9318333333333[/C][C]0.168501285291862[/C][C]581.193390683669[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]97.9138333333333[/C][C]0.161072165401237[/C][C]607.887980455385[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]97.8788333333333[/C][C]0.152489342346244[/C][C]641.873273419255[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]97.8708333333333[/C][C]0.14983857447015[/C][C]653.175149853222[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]97.8258333333333[/C][C]0.14043360851038[/C][C]696.598445137175[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]97.8191666666667[/C][C]0.136857856827871[/C][C]714.750098634792[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]97.8118333333333[/C][C]0.133623235332466[/C][C]731.997194125474[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]97.8378333333333[/C][C]0.126781784961866[/C][C]771.70260193735[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]97.814[/C][C]0.120399335546339[/C][C]812.413121352762[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]97.8233333333333[/C][C]0.117454803584708[/C][C]832.859366733207[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]97.8283333333333[/C][C]0.115089050922252[/C][C]850.022939188378[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]97.8336666666667[/C][C]0.106641054481572[/C][C]917.410908418698[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]97.7741666666667[/C][C]0.0948416139285914[/C][C]1030.92052756803[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]97.7531666666667[/C][C]0.089581415693573[/C][C]1091.22149845283[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]97.7721666666667[/C][C]0.083890933924512[/C][C]1165.46761482767[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]97.6988333333333[/C][C]0.0693509423260168[/C][C]1408.75999743527[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]97.8572413793103[/C][C]0.20038963756221[/C][C]488.334838915665[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]97.8689285714286[/C][C]0.185798675881137[/C][C]526.747180017793[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]97.8705555555556[/C][C]0.172070349618394[/C][C]568.782220601086[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]97.8576923076923[/C][C]0.161810461944265[/C][C]604.767399659231[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]97.8512[/C][C]0.153805241279021[/C][C]636.201986267075[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]97.8310416666667[/C][C]0.147900867575982[/C][C]661.463609173269[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]97.8130434782609[/C][C]0.142753417199881[/C][C]685.188805962556[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]97.8002272727273[/C][C]0.138715981539617[/C][C]705.039363072927[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]97.787619047619[/C][C]0.134125034634319[/C][C]729.078052536791[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]97.78125[/C][C]0.130706751194008[/C][C]748.096399816895[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]97.7752631578947[/C][C]0.126996565203776[/C][C]769.904784440482[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]97.7697222222222[/C][C]0.122743432314592[/C][C]796.537300436882[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]97.7597058823529[/C][C]0.118655183776764[/C][C]823.897471401475[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]97.751875[/C][C]0.114691414080173[/C][C]852.303337472747[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]97.7416666666667[/C][C]0.109689303466742[/C][C]891.077466786009[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]97.7292857142857[/C][C]0.102902235118783[/C][C]949.729474792008[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]97.7142307692308[/C][C]0.095616498539213[/C][C]1021.9390195423[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]97.7054166666667[/C][C]0.0893271530822386[/C][C]1093.79302144237[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]97.6981818181818[/C][C]0.081415072377491[/C][C]1200.00116643258[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]97.6865[/C][C]0.0705664114225214[/C][C]1384.32007566738[/C][/ROW]
[ROW][C]Median[/C][C]97.68[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]96.845[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]97.7106451612903[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]97.7416666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]97.7106451612903[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]97.7416666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]97.7416666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]97.7106451612903[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]97.7416666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]97.751875[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]60[/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 Mean97.82350.225347669244433434.100340722369
Geometric Mean97.8081204441613
Harmonic Mean97.7926709997122
Quadratic Mean97.8388126716591
Winsorized Mean ( 1 / 20 )97.84633333333330.212046520674875461.438051527185
Winsorized Mean ( 2 / 20 )97.8660.205501481155397476.230144180786
Winsorized Mean ( 3 / 20 )97.9040.192039926404207509.810651530509
Winsorized Mean ( 4 / 20 )97.87933333333330.180485670380798542.310827927904
Winsorized Mean ( 5 / 20 )97.93183333333330.168501285291862581.193390683669
Winsorized Mean ( 6 / 20 )97.91383333333330.161072165401237607.887980455385
Winsorized Mean ( 7 / 20 )97.87883333333330.152489342346244641.873273419255
Winsorized Mean ( 8 / 20 )97.87083333333330.14983857447015653.175149853222
Winsorized Mean ( 9 / 20 )97.82583333333330.14043360851038696.598445137175
Winsorized Mean ( 10 / 20 )97.81916666666670.136857856827871714.750098634792
Winsorized Mean ( 11 / 20 )97.81183333333330.133623235332466731.997194125474
Winsorized Mean ( 12 / 20 )97.83783333333330.126781784961866771.70260193735
Winsorized Mean ( 13 / 20 )97.8140.120399335546339812.413121352762
Winsorized Mean ( 14 / 20 )97.82333333333330.117454803584708832.859366733207
Winsorized Mean ( 15 / 20 )97.82833333333330.115089050922252850.022939188378
Winsorized Mean ( 16 / 20 )97.83366666666670.106641054481572917.410908418698
Winsorized Mean ( 17 / 20 )97.77416666666670.09484161392859141030.92052756803
Winsorized Mean ( 18 / 20 )97.75316666666670.0895814156935731091.22149845283
Winsorized Mean ( 19 / 20 )97.77216666666670.0838909339245121165.46761482767
Winsorized Mean ( 20 / 20 )97.69883333333330.06935094232601681408.75999743527
Trimmed Mean ( 1 / 20 )97.85724137931030.20038963756221488.334838915665
Trimmed Mean ( 2 / 20 )97.86892857142860.185798675881137526.747180017793
Trimmed Mean ( 3 / 20 )97.87055555555560.172070349618394568.782220601086
Trimmed Mean ( 4 / 20 )97.85769230769230.161810461944265604.767399659231
Trimmed Mean ( 5 / 20 )97.85120.153805241279021636.201986267075
Trimmed Mean ( 6 / 20 )97.83104166666670.147900867575982661.463609173269
Trimmed Mean ( 7 / 20 )97.81304347826090.142753417199881685.188805962556
Trimmed Mean ( 8 / 20 )97.80022727272730.138715981539617705.039363072927
Trimmed Mean ( 9 / 20 )97.7876190476190.134125034634319729.078052536791
Trimmed Mean ( 10 / 20 )97.781250.130706751194008748.096399816895
Trimmed Mean ( 11 / 20 )97.77526315789470.126996565203776769.904784440482
Trimmed Mean ( 12 / 20 )97.76972222222220.122743432314592796.537300436882
Trimmed Mean ( 13 / 20 )97.75970588235290.118655183776764823.897471401475
Trimmed Mean ( 14 / 20 )97.7518750.114691414080173852.303337472747
Trimmed Mean ( 15 / 20 )97.74166666666670.109689303466742891.077466786009
Trimmed Mean ( 16 / 20 )97.72928571428570.102902235118783949.729474792008
Trimmed Mean ( 17 / 20 )97.71423076923080.0956164985392131021.9390195423
Trimmed Mean ( 18 / 20 )97.70541666666670.08932715308223861093.79302144237
Trimmed Mean ( 19 / 20 )97.69818181818180.0814150723774911200.00116643258
Trimmed Mean ( 20 / 20 )97.68650.07056641142252141384.32007566738
Median97.68
Midrange96.845
Midmean - Weighted Average at Xnp97.7106451612903
Midmean - Weighted Average at X(n+1)p97.7416666666667
Midmean - Empirical Distribution Function97.7106451612903
Midmean - Empirical Distribution Function - Averaging97.7416666666667
Midmean - Empirical Distribution Function - Interpolation97.7416666666667
Midmean - Closest Observation97.7106451612903
Midmean - True Basic - Statistics Graphics Toolkit97.7416666666667
Midmean - MS Excel (old versions)97.751875
Number of observations60



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')