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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationThu, 15 Oct 2009 11:22:44 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Oct/15/t1255627417tylhdg17ulvo6xg.htm/, Retrieved Sat, 04 May 2024 06:17:06 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=46821, Retrieved Sat, 04 May 2024 06:17:06 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact134
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Shw3 Part 2: Cent...] [2009-10-15 17:22:44] [7a39e26d7a09dd77604df90cb29f8d39] [Current]
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Dataseries X:
96.14
96.97
95.86
97.00
97.33
96.82
95.18
93.38
93.79
93.57
93.72
94.29
93.79
94.33
93.28
93.24
92.13
90.75
88.89
84.03
81.41
84.86
82.98
84.50
82.93
88.68
87.72
87.43
88.05
88.43
88.81
88.39
88.07
90.11
88.48
87.90
88.20
90.32
91.30
90.88
91.17
93.52
97.38
95.78
100.40
97.47
96.92
94.56
94.20
94.34
94.68
95.71
96.74
95.25
95.06
95.33
95.78
94.73
94.61
94.83
94.43
94.82
93.71
93.61
92.45
93.17
95.06
88.28
84.90
86.07
87.62
85.09
86.48
86.39
87.70
89.69
93.39
91.43
92.09
86.45




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'George Udny Yule' @ 72.249.76.132

\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 & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=46821&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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=46821&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=46821&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'George Udny Yule' @ 72.249.76.132







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean91.6903750.471407246999592194.503532950734
Geometric Mean91.5931448709851
Harmonic Mean91.4944335956882
Quadratic Mean91.7860589972682
Winsorized Mean ( 1 / 26 )91.672750.459264752765669199.607632521223
Winsorized Mean ( 2 / 26 )91.671750.458607198482536199.891650857920
Winsorized Mean ( 3 / 26 )91.709250.449324027275798204.10493192635
Winsorized Mean ( 4 / 26 )91.716250.44179590249574207.598688629495
Winsorized Mean ( 5 / 26 )91.7368750.436944098680638209.951056157988
Winsorized Mean ( 6 / 26 )91.7361250.435780817255981210.509782366380
Winsorized Mean ( 7 / 26 )91.7440.431195592788825212.766553124143
Winsorized Mean ( 8 / 26 )91.8340.411721017440854223.049094192022
Winsorized Mean ( 9 / 26 )91.80250.395630105502282232.041239337562
Winsorized Mean ( 10 / 26 )91.7750.389579658255641235.574414770336
Winsorized Mean ( 11 / 26 )91.7681250.38741544989181236.872651892503
Winsorized Mean ( 12 / 26 )91.9106250.363964125012186252.526605463994
Winsorized Mean ( 13 / 26 )91.9301250.35767703829889257.019923440485
Winsorized Mean ( 14 / 26 )91.8776250.346901713534033264.852035650110
Winsorized Mean ( 15 / 26 )91.8663750.344452750877425266.702398996636
Winsorized Mean ( 16 / 26 )91.8883750.337279953758415272.439479358496
Winsorized Mean ( 17 / 26 )91.894750.329413218965351278.964973805942
Winsorized Mean ( 18 / 26 )91.899250.328749056647826279.542247016841
Winsorized Mean ( 19 / 26 )91.87550.317670411757735289.216422428624
Winsorized Mean ( 20 / 26 )91.8930.314456956061064292.22759499763
Winsorized Mean ( 21 / 26 )91.898250.307503101507463298.853083268072
Winsorized Mean ( 22 / 26 )91.89550.304318282540842301.971670031579
Winsorized Mean ( 23 / 26 )91.889750.299927099528611306.373615936743
Winsorized Mean ( 24 / 26 )91.934750.289619838939937317.432501642493
Winsorized Mean ( 25 / 26 )91.934750.279223719058411329.251219452343
Winsorized Mean ( 26 / 26 )91.93150.272251460225536337.671283466553
Trimmed Mean ( 1 / 26 )91.71051282051280.451232334053351203.244550311126
Trimmed Mean ( 2 / 26 )91.75026315789470.441785888192984207.680384570853
Trimmed Mean ( 3 / 26 )91.79270270270270.431058094670565212.947405088994
Trimmed Mean ( 4 / 26 )91.82361111111110.422554980428534217.305712544171
Trimmed Mean ( 5 / 26 )91.85428571428570.415104395631273221.279963982549
Trimmed Mean ( 6 / 26 )91.88191176470590.40765363517988225.392107013010
Trimmed Mean ( 7 / 26 )91.91136363636360.398989451132301230.360385156867
Trimmed Mean ( 8 / 26 )91.941250.389677477802284235.941914114548
Trimmed Mean ( 9 / 26 )91.95854838709680.3829852850233240.109873624785
Trimmed Mean ( 10 / 26 )91.98166666666670.378149610683739243.24146863553
Trimmed Mean ( 11 / 26 )92.01017241379310.373227571067788246.525657658559
Trimmed Mean ( 12 / 26 )92.04160714285710.367366971840246250.544045050633
Trimmed Mean ( 13 / 26 )92.05777777777780.364581230402241252.502789779416
Trimmed Mean ( 14 / 26 )92.07288461538460.361917898631456254.402683491328
Trimmed Mean ( 15 / 26 )92.09520.36005399141614255.781638853044
Trimmed Mean ( 16 / 26 )92.1206250.357598050613122257.609416052615
Trimmed Mean ( 17 / 26 )92.14586956521740.355281962744916259.359830297312
Trimmed Mean ( 18 / 26 )92.17272727272730.353169186024676260.987455644806
Trimmed Mean ( 19 / 26 )92.20166666666670.349865067181940263.534931936257
Trimmed Mean ( 20 / 26 )92.2360.346977572614479265.826979262668
Trimmed Mean ( 21 / 26 )92.27210526315790.343023573271604268.996396903887
Trimmed Mean ( 22 / 26 )92.31166666666670.338377196312232272.806996667375
Trimmed Mean ( 23 / 26 )92.35617647058820.331803803115922278.345744091191
Trimmed Mean ( 24 / 26 )92.4068750.322756661277802286.305090138679
Trimmed Mean ( 25 / 26 )92.45933333333330.312075710432814296.272123213635
Trimmed Mean ( 26 / 26 )92.51928571428570.298649043100463309.792674216481
Median93.26
Midrange90.905
Midmean - Weighted Average at Xnp92.1375609756097
Midmean - Weighted Average at X(n+1)p92.236
Midmean - Empirical Distribution Function92.1375609756097
Midmean - Empirical Distribution Function - Averaging92.236
Midmean - Empirical Distribution Function - Interpolation92.236
Midmean - Closest Observation92.1375609756097
Midmean - True Basic - Statistics Graphics Toolkit92.236
Midmean - MS Excel (old versions)92.2016666666667
Number of observations80

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 91.690375 & 0.471407246999592 & 194.503532950734 \tabularnewline
Geometric Mean & 91.5931448709851 &  &  \tabularnewline
Harmonic Mean & 91.4944335956882 &  &  \tabularnewline
Quadratic Mean & 91.7860589972682 &  &  \tabularnewline
Winsorized Mean ( 1 / 26 ) & 91.67275 & 0.459264752765669 & 199.607632521223 \tabularnewline
Winsorized Mean ( 2 / 26 ) & 91.67175 & 0.458607198482536 & 199.891650857920 \tabularnewline
Winsorized Mean ( 3 / 26 ) & 91.70925 & 0.449324027275798 & 204.10493192635 \tabularnewline
Winsorized Mean ( 4 / 26 ) & 91.71625 & 0.44179590249574 & 207.598688629495 \tabularnewline
Winsorized Mean ( 5 / 26 ) & 91.736875 & 0.436944098680638 & 209.951056157988 \tabularnewline
Winsorized Mean ( 6 / 26 ) & 91.736125 & 0.435780817255981 & 210.509782366380 \tabularnewline
Winsorized Mean ( 7 / 26 ) & 91.744 & 0.431195592788825 & 212.766553124143 \tabularnewline
Winsorized Mean ( 8 / 26 ) & 91.834 & 0.411721017440854 & 223.049094192022 \tabularnewline
Winsorized Mean ( 9 / 26 ) & 91.8025 & 0.395630105502282 & 232.041239337562 \tabularnewline
Winsorized Mean ( 10 / 26 ) & 91.775 & 0.389579658255641 & 235.574414770336 \tabularnewline
Winsorized Mean ( 11 / 26 ) & 91.768125 & 0.38741544989181 & 236.872651892503 \tabularnewline
Winsorized Mean ( 12 / 26 ) & 91.910625 & 0.363964125012186 & 252.526605463994 \tabularnewline
Winsorized Mean ( 13 / 26 ) & 91.930125 & 0.35767703829889 & 257.019923440485 \tabularnewline
Winsorized Mean ( 14 / 26 ) & 91.877625 & 0.346901713534033 & 264.852035650110 \tabularnewline
Winsorized Mean ( 15 / 26 ) & 91.866375 & 0.344452750877425 & 266.702398996636 \tabularnewline
Winsorized Mean ( 16 / 26 ) & 91.888375 & 0.337279953758415 & 272.439479358496 \tabularnewline
Winsorized Mean ( 17 / 26 ) & 91.89475 & 0.329413218965351 & 278.964973805942 \tabularnewline
Winsorized Mean ( 18 / 26 ) & 91.89925 & 0.328749056647826 & 279.542247016841 \tabularnewline
Winsorized Mean ( 19 / 26 ) & 91.8755 & 0.317670411757735 & 289.216422428624 \tabularnewline
Winsorized Mean ( 20 / 26 ) & 91.893 & 0.314456956061064 & 292.22759499763 \tabularnewline
Winsorized Mean ( 21 / 26 ) & 91.89825 & 0.307503101507463 & 298.853083268072 \tabularnewline
Winsorized Mean ( 22 / 26 ) & 91.8955 & 0.304318282540842 & 301.971670031579 \tabularnewline
Winsorized Mean ( 23 / 26 ) & 91.88975 & 0.299927099528611 & 306.373615936743 \tabularnewline
Winsorized Mean ( 24 / 26 ) & 91.93475 & 0.289619838939937 & 317.432501642493 \tabularnewline
Winsorized Mean ( 25 / 26 ) & 91.93475 & 0.279223719058411 & 329.251219452343 \tabularnewline
Winsorized Mean ( 26 / 26 ) & 91.9315 & 0.272251460225536 & 337.671283466553 \tabularnewline
Trimmed Mean ( 1 / 26 ) & 91.7105128205128 & 0.451232334053351 & 203.244550311126 \tabularnewline
Trimmed Mean ( 2 / 26 ) & 91.7502631578947 & 0.441785888192984 & 207.680384570853 \tabularnewline
Trimmed Mean ( 3 / 26 ) & 91.7927027027027 & 0.431058094670565 & 212.947405088994 \tabularnewline
Trimmed Mean ( 4 / 26 ) & 91.8236111111111 & 0.422554980428534 & 217.305712544171 \tabularnewline
Trimmed Mean ( 5 / 26 ) & 91.8542857142857 & 0.415104395631273 & 221.279963982549 \tabularnewline
Trimmed Mean ( 6 / 26 ) & 91.8819117647059 & 0.40765363517988 & 225.392107013010 \tabularnewline
Trimmed Mean ( 7 / 26 ) & 91.9113636363636 & 0.398989451132301 & 230.360385156867 \tabularnewline
Trimmed Mean ( 8 / 26 ) & 91.94125 & 0.389677477802284 & 235.941914114548 \tabularnewline
Trimmed Mean ( 9 / 26 ) & 91.9585483870968 & 0.3829852850233 & 240.109873624785 \tabularnewline
Trimmed Mean ( 10 / 26 ) & 91.9816666666667 & 0.378149610683739 & 243.24146863553 \tabularnewline
Trimmed Mean ( 11 / 26 ) & 92.0101724137931 & 0.373227571067788 & 246.525657658559 \tabularnewline
Trimmed Mean ( 12 / 26 ) & 92.0416071428571 & 0.367366971840246 & 250.544045050633 \tabularnewline
Trimmed Mean ( 13 / 26 ) & 92.0577777777778 & 0.364581230402241 & 252.502789779416 \tabularnewline
Trimmed Mean ( 14 / 26 ) & 92.0728846153846 & 0.361917898631456 & 254.402683491328 \tabularnewline
Trimmed Mean ( 15 / 26 ) & 92.0952 & 0.36005399141614 & 255.781638853044 \tabularnewline
Trimmed Mean ( 16 / 26 ) & 92.120625 & 0.357598050613122 & 257.609416052615 \tabularnewline
Trimmed Mean ( 17 / 26 ) & 92.1458695652174 & 0.355281962744916 & 259.359830297312 \tabularnewline
Trimmed Mean ( 18 / 26 ) & 92.1727272727273 & 0.353169186024676 & 260.987455644806 \tabularnewline
Trimmed Mean ( 19 / 26 ) & 92.2016666666667 & 0.349865067181940 & 263.534931936257 \tabularnewline
Trimmed Mean ( 20 / 26 ) & 92.236 & 0.346977572614479 & 265.826979262668 \tabularnewline
Trimmed Mean ( 21 / 26 ) & 92.2721052631579 & 0.343023573271604 & 268.996396903887 \tabularnewline
Trimmed Mean ( 22 / 26 ) & 92.3116666666667 & 0.338377196312232 & 272.806996667375 \tabularnewline
Trimmed Mean ( 23 / 26 ) & 92.3561764705882 & 0.331803803115922 & 278.345744091191 \tabularnewline
Trimmed Mean ( 24 / 26 ) & 92.406875 & 0.322756661277802 & 286.305090138679 \tabularnewline
Trimmed Mean ( 25 / 26 ) & 92.4593333333333 & 0.312075710432814 & 296.272123213635 \tabularnewline
Trimmed Mean ( 26 / 26 ) & 92.5192857142857 & 0.298649043100463 & 309.792674216481 \tabularnewline
Median & 93.26 &  &  \tabularnewline
Midrange & 90.905 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 92.1375609756097 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 92.236 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 92.1375609756097 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 92.236 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 92.236 &  &  \tabularnewline
Midmean - Closest Observation & 92.1375609756097 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 92.236 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 92.2016666666667 &  &  \tabularnewline
Number of observations & 80 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=46821&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]91.690375[/C][C]0.471407246999592[/C][C]194.503532950734[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]91.5931448709851[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]91.4944335956882[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]91.7860589972682[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 26 )[/C][C]91.67275[/C][C]0.459264752765669[/C][C]199.607632521223[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 26 )[/C][C]91.67175[/C][C]0.458607198482536[/C][C]199.891650857920[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 26 )[/C][C]91.70925[/C][C]0.449324027275798[/C][C]204.10493192635[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 26 )[/C][C]91.71625[/C][C]0.44179590249574[/C][C]207.598688629495[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 26 )[/C][C]91.736875[/C][C]0.436944098680638[/C][C]209.951056157988[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 26 )[/C][C]91.736125[/C][C]0.435780817255981[/C][C]210.509782366380[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 26 )[/C][C]91.744[/C][C]0.431195592788825[/C][C]212.766553124143[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 26 )[/C][C]91.834[/C][C]0.411721017440854[/C][C]223.049094192022[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 26 )[/C][C]91.8025[/C][C]0.395630105502282[/C][C]232.041239337562[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 26 )[/C][C]91.775[/C][C]0.389579658255641[/C][C]235.574414770336[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 26 )[/C][C]91.768125[/C][C]0.38741544989181[/C][C]236.872651892503[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 26 )[/C][C]91.910625[/C][C]0.363964125012186[/C][C]252.526605463994[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 26 )[/C][C]91.930125[/C][C]0.35767703829889[/C][C]257.019923440485[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 26 )[/C][C]91.877625[/C][C]0.346901713534033[/C][C]264.852035650110[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 26 )[/C][C]91.866375[/C][C]0.344452750877425[/C][C]266.702398996636[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 26 )[/C][C]91.888375[/C][C]0.337279953758415[/C][C]272.439479358496[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 26 )[/C][C]91.89475[/C][C]0.329413218965351[/C][C]278.964973805942[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 26 )[/C][C]91.89925[/C][C]0.328749056647826[/C][C]279.542247016841[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 26 )[/C][C]91.8755[/C][C]0.317670411757735[/C][C]289.216422428624[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 26 )[/C][C]91.893[/C][C]0.314456956061064[/C][C]292.22759499763[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 26 )[/C][C]91.89825[/C][C]0.307503101507463[/C][C]298.853083268072[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 26 )[/C][C]91.8955[/C][C]0.304318282540842[/C][C]301.971670031579[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 26 )[/C][C]91.88975[/C][C]0.299927099528611[/C][C]306.373615936743[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 26 )[/C][C]91.93475[/C][C]0.289619838939937[/C][C]317.432501642493[/C][/ROW]
[ROW][C]Winsorized Mean ( 25 / 26 )[/C][C]91.93475[/C][C]0.279223719058411[/C][C]329.251219452343[/C][/ROW]
[ROW][C]Winsorized Mean ( 26 / 26 )[/C][C]91.9315[/C][C]0.272251460225536[/C][C]337.671283466553[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 26 )[/C][C]91.7105128205128[/C][C]0.451232334053351[/C][C]203.244550311126[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 26 )[/C][C]91.7502631578947[/C][C]0.441785888192984[/C][C]207.680384570853[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 26 )[/C][C]91.7927027027027[/C][C]0.431058094670565[/C][C]212.947405088994[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 26 )[/C][C]91.8236111111111[/C][C]0.422554980428534[/C][C]217.305712544171[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 26 )[/C][C]91.8542857142857[/C][C]0.415104395631273[/C][C]221.279963982549[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 26 )[/C][C]91.8819117647059[/C][C]0.40765363517988[/C][C]225.392107013010[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 26 )[/C][C]91.9113636363636[/C][C]0.398989451132301[/C][C]230.360385156867[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 26 )[/C][C]91.94125[/C][C]0.389677477802284[/C][C]235.941914114548[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 26 )[/C][C]91.9585483870968[/C][C]0.3829852850233[/C][C]240.109873624785[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 26 )[/C][C]91.9816666666667[/C][C]0.378149610683739[/C][C]243.24146863553[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 26 )[/C][C]92.0101724137931[/C][C]0.373227571067788[/C][C]246.525657658559[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 26 )[/C][C]92.0416071428571[/C][C]0.367366971840246[/C][C]250.544045050633[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 26 )[/C][C]92.0577777777778[/C][C]0.364581230402241[/C][C]252.502789779416[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 26 )[/C][C]92.0728846153846[/C][C]0.361917898631456[/C][C]254.402683491328[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 26 )[/C][C]92.0952[/C][C]0.36005399141614[/C][C]255.781638853044[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 26 )[/C][C]92.120625[/C][C]0.357598050613122[/C][C]257.609416052615[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 26 )[/C][C]92.1458695652174[/C][C]0.355281962744916[/C][C]259.359830297312[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 26 )[/C][C]92.1727272727273[/C][C]0.353169186024676[/C][C]260.987455644806[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 26 )[/C][C]92.2016666666667[/C][C]0.349865067181940[/C][C]263.534931936257[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 26 )[/C][C]92.236[/C][C]0.346977572614479[/C][C]265.826979262668[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 26 )[/C][C]92.2721052631579[/C][C]0.343023573271604[/C][C]268.996396903887[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 26 )[/C][C]92.3116666666667[/C][C]0.338377196312232[/C][C]272.806996667375[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 26 )[/C][C]92.3561764705882[/C][C]0.331803803115922[/C][C]278.345744091191[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 26 )[/C][C]92.406875[/C][C]0.322756661277802[/C][C]286.305090138679[/C][/ROW]
[ROW][C]Trimmed Mean ( 25 / 26 )[/C][C]92.4593333333333[/C][C]0.312075710432814[/C][C]296.272123213635[/C][/ROW]
[ROW][C]Trimmed Mean ( 26 / 26 )[/C][C]92.5192857142857[/C][C]0.298649043100463[/C][C]309.792674216481[/C][/ROW]
[ROW][C]Median[/C][C]93.26[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]90.905[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]92.1375609756097[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]92.236[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]92.1375609756097[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]92.236[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]92.236[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]92.1375609756097[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]92.236[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]92.2016666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]80[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=46821&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=46821&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 Mean91.6903750.471407246999592194.503532950734
Geometric Mean91.5931448709851
Harmonic Mean91.4944335956882
Quadratic Mean91.7860589972682
Winsorized Mean ( 1 / 26 )91.672750.459264752765669199.607632521223
Winsorized Mean ( 2 / 26 )91.671750.458607198482536199.891650857920
Winsorized Mean ( 3 / 26 )91.709250.449324027275798204.10493192635
Winsorized Mean ( 4 / 26 )91.716250.44179590249574207.598688629495
Winsorized Mean ( 5 / 26 )91.7368750.436944098680638209.951056157988
Winsorized Mean ( 6 / 26 )91.7361250.435780817255981210.509782366380
Winsorized Mean ( 7 / 26 )91.7440.431195592788825212.766553124143
Winsorized Mean ( 8 / 26 )91.8340.411721017440854223.049094192022
Winsorized Mean ( 9 / 26 )91.80250.395630105502282232.041239337562
Winsorized Mean ( 10 / 26 )91.7750.389579658255641235.574414770336
Winsorized Mean ( 11 / 26 )91.7681250.38741544989181236.872651892503
Winsorized Mean ( 12 / 26 )91.9106250.363964125012186252.526605463994
Winsorized Mean ( 13 / 26 )91.9301250.35767703829889257.019923440485
Winsorized Mean ( 14 / 26 )91.8776250.346901713534033264.852035650110
Winsorized Mean ( 15 / 26 )91.8663750.344452750877425266.702398996636
Winsorized Mean ( 16 / 26 )91.8883750.337279953758415272.439479358496
Winsorized Mean ( 17 / 26 )91.894750.329413218965351278.964973805942
Winsorized Mean ( 18 / 26 )91.899250.328749056647826279.542247016841
Winsorized Mean ( 19 / 26 )91.87550.317670411757735289.216422428624
Winsorized Mean ( 20 / 26 )91.8930.314456956061064292.22759499763
Winsorized Mean ( 21 / 26 )91.898250.307503101507463298.853083268072
Winsorized Mean ( 22 / 26 )91.89550.304318282540842301.971670031579
Winsorized Mean ( 23 / 26 )91.889750.299927099528611306.373615936743
Winsorized Mean ( 24 / 26 )91.934750.289619838939937317.432501642493
Winsorized Mean ( 25 / 26 )91.934750.279223719058411329.251219452343
Winsorized Mean ( 26 / 26 )91.93150.272251460225536337.671283466553
Trimmed Mean ( 1 / 26 )91.71051282051280.451232334053351203.244550311126
Trimmed Mean ( 2 / 26 )91.75026315789470.441785888192984207.680384570853
Trimmed Mean ( 3 / 26 )91.79270270270270.431058094670565212.947405088994
Trimmed Mean ( 4 / 26 )91.82361111111110.422554980428534217.305712544171
Trimmed Mean ( 5 / 26 )91.85428571428570.415104395631273221.279963982549
Trimmed Mean ( 6 / 26 )91.88191176470590.40765363517988225.392107013010
Trimmed Mean ( 7 / 26 )91.91136363636360.398989451132301230.360385156867
Trimmed Mean ( 8 / 26 )91.941250.389677477802284235.941914114548
Trimmed Mean ( 9 / 26 )91.95854838709680.3829852850233240.109873624785
Trimmed Mean ( 10 / 26 )91.98166666666670.378149610683739243.24146863553
Trimmed Mean ( 11 / 26 )92.01017241379310.373227571067788246.525657658559
Trimmed Mean ( 12 / 26 )92.04160714285710.367366971840246250.544045050633
Trimmed Mean ( 13 / 26 )92.05777777777780.364581230402241252.502789779416
Trimmed Mean ( 14 / 26 )92.07288461538460.361917898631456254.402683491328
Trimmed Mean ( 15 / 26 )92.09520.36005399141614255.781638853044
Trimmed Mean ( 16 / 26 )92.1206250.357598050613122257.609416052615
Trimmed Mean ( 17 / 26 )92.14586956521740.355281962744916259.359830297312
Trimmed Mean ( 18 / 26 )92.17272727272730.353169186024676260.987455644806
Trimmed Mean ( 19 / 26 )92.20166666666670.349865067181940263.534931936257
Trimmed Mean ( 20 / 26 )92.2360.346977572614479265.826979262668
Trimmed Mean ( 21 / 26 )92.27210526315790.343023573271604268.996396903887
Trimmed Mean ( 22 / 26 )92.31166666666670.338377196312232272.806996667375
Trimmed Mean ( 23 / 26 )92.35617647058820.331803803115922278.345744091191
Trimmed Mean ( 24 / 26 )92.4068750.322756661277802286.305090138679
Trimmed Mean ( 25 / 26 )92.45933333333330.312075710432814296.272123213635
Trimmed Mean ( 26 / 26 )92.51928571428570.298649043100463309.792674216481
Median93.26
Midrange90.905
Midmean - Weighted Average at Xnp92.1375609756097
Midmean - Weighted Average at X(n+1)p92.236
Midmean - Empirical Distribution Function92.1375609756097
Midmean - Empirical Distribution Function - Averaging92.236
Midmean - Empirical Distribution Function - Interpolation92.236
Midmean - Closest Observation92.1375609756097
Midmean - True Basic - Statistics Graphics Toolkit92.236
Midmean - MS Excel (old versions)92.2016666666667
Number of observations80



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')