Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationWed, 12 Oct 2016 16:26:36 +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/12/t1476286024ncsq1312lhsyd1y.htm/, Retrieved Sun, 05 May 2024 15:05:54 +0200
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Sun, 05 May 2024 15:05:54 +0200
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact0
Dataseries X:
95,9
89,2
100,2
102,3
102,2
100,5
104,1
94,9
97,3
100,3
98
115,1
94,4
91,6
104,1
107,8
101,7
104,1
102
99,9
101,6
101,3
101
115,9
97,5
97,6
109,2
101,6
108,8
108,8
100,9
107,4
101,7
104,5
106,1
116,7
103,7
96,5
114,1
102,8
114,5
107,2
107,9
111,3
99,8
106,7
106,9
115,3
106,1
97,3
109
109,8
116,5
108,3
110,8
108,7
104
111,3
106,5
120,5
110
99,7
109
112,2
116
112,3
113,2
109,9
107,6
114,9
105,7
123,3




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gertrude Mary Cox' @ cox.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 & 'Gertrude Mary Cox' @ cox.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]'Gertrude Mary Cox' @ cox.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'Gertrude Mary Cox' @ cox.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean105.7708333333330.812626389591818130.15924007398
Geometric Mean105.54906012541
Harmonic Mean105.327045198912
Quadratic Mean105.992239626829
Winsorized Mean ( 1 / 24 )105.7652777777780.792628300861367133.436161266057
Winsorized Mean ( 2 / 24 )105.73750.749745490202007141.031191760168
Winsorized Mean ( 3 / 24 )105.750.74367968099083142.198318312402
Winsorized Mean ( 4 / 24 )105.7777777777780.727073211378008145.484355801391
Winsorized Mean ( 5 / 24 )105.81250.717904645075494147.390744336071
Winsorized Mean ( 6 / 24 )105.8291666666670.69631951472612151.983628820588
Winsorized Mean ( 7 / 24 )105.8097222222220.692620276279539152.767289445505
Winsorized Mean ( 8 / 24 )105.8097222222220.684620794831745154.552305482083
Winsorized Mean ( 9 / 24 )105.7722222222220.673242865157888157.108567645075
Winsorized Mean ( 10 / 24 )105.7722222222220.653784642861754161.78450102351
Winsorized Mean ( 11 / 24 )105.8944444444440.588275140058088180.008362131346
Winsorized Mean ( 12 / 24 )105.7611111111110.560326152630952188.74919654298
Winsorized Mean ( 13 / 24 )105.7611111111110.554669873039567190.673977895257
Winsorized Mean ( 14 / 24 )105.6444444444440.518227571327722203.857243978314
Winsorized Mean ( 15 / 24 )105.6652777777780.515158178460738205.112297922746
Winsorized Mean ( 16 / 24 )105.5986111111110.491812833590835214.713004416969
Winsorized Mean ( 17 / 24 )105.5041666666670.450748974603843234.064130172216
Winsorized Mean ( 18 / 24 )105.5041666666670.443662720923679237.802640814656
Winsorized Mean ( 19 / 24 )105.5569444444440.428785390090021246.176634941511
Winsorized Mean ( 20 / 24 )105.4736111111110.394469756896828267.380728856984
Winsorized Mean ( 21 / 24 )105.4152777777780.386781084952362272.545069753764
Winsorized Mean ( 22 / 24 )105.4458333333330.38255144539324275.638308528521
Winsorized Mean ( 23 / 24 )105.3819444444440.374261538882966281.573000418294
Winsorized Mean ( 24 / 24 )105.4819444444440.360529770111288292.574852866892
Trimmed Mean ( 1 / 24 )105.7571428571430.760556000795504139.052407378978
Trimmed Mean ( 2 / 24 )105.7485294117650.722173253647516146.430969130545
Trimmed Mean ( 3 / 24 )105.7545454545450.704197146777793150.177469389713
Trimmed Mean ( 4 / 24 )105.756250.685394955510823154.299720401619
Trimmed Mean ( 5 / 24 )105.750.668869421892718158.102607981026
Trimmed Mean ( 6 / 24 )105.7350.651685450622977162.248520200847
Trimmed Mean ( 7 / 24 )105.7155172413790.636829914128541166.00275033569
Trimmed Mean ( 8 / 24 )105.6982142857140.61944933165659170.63254229857
Trimmed Mean ( 9 / 24 )105.679629629630.599891555711334176.16455611601
Trimmed Mean ( 10 / 24 )105.6653846153850.578282711599896182.722710701565
Trimmed Mean ( 11 / 24 )105.650.555839133974159190.072978929389
Trimmed Mean ( 12 / 24 )105.6166666666670.542717202763042194.607184236945
Trimmed Mean ( 13 / 24 )105.5978260869570.532049987939138198.473505273411
Trimmed Mean ( 14 / 24 )105.5772727272730.519135560110542203.371298057085
Trimmed Mean ( 15 / 24 )105.5690476190480.510192149077872206.920172742474
Trimmed Mean ( 16 / 24 )105.55750.498470577533586211.762749413004
Trimmed Mean ( 17 / 24 )105.5526315789470.487799028792421216.385489409952
Trimmed Mean ( 18 / 24 )105.5583333333330.482328594441459218.851493670142
Trimmed Mean ( 19 / 24 )105.5647058823530.475324869727519222.089590942019
Trimmed Mean ( 20 / 24 )105.5656250.468108095435335225.515486763426
Trimmed Mean ( 21 / 24 )105.5766666666670.465392760424933226.854982811225
Trimmed Mean ( 22 / 24 )105.5964285714290.461320916397982228.90015348953
Trimmed Mean ( 23 / 24 )105.6153846153850.454234514411708232.512900857325
Trimmed Mean ( 24 / 24 )105.6458333333330.443592839761783238.159464859863
Median106.1
Midrange106.25
Midmean - Weighted Average at Xnp105.432432432432
Midmean - Weighted Average at X(n+1)p105.558333333333
Midmean - Empirical Distribution Function105.432432432432
Midmean - Empirical Distribution Function - Averaging105.558333333333
Midmean - Empirical Distribution Function - Interpolation105.558333333333
Midmean - Closest Observation105.432432432432
Midmean - True Basic - Statistics Graphics Toolkit105.558333333333
Midmean - MS Excel (old versions)105.552631578947
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 105.770833333333 & 0.812626389591818 & 130.15924007398 \tabularnewline
Geometric Mean & 105.54906012541 &  &  \tabularnewline
Harmonic Mean & 105.327045198912 &  &  \tabularnewline
Quadratic Mean & 105.992239626829 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 105.765277777778 & 0.792628300861367 & 133.436161266057 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 105.7375 & 0.749745490202007 & 141.031191760168 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 105.75 & 0.74367968099083 & 142.198318312402 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 105.777777777778 & 0.727073211378008 & 145.484355801391 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 105.8125 & 0.717904645075494 & 147.390744336071 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 105.829166666667 & 0.69631951472612 & 151.983628820588 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 105.809722222222 & 0.692620276279539 & 152.767289445505 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 105.809722222222 & 0.684620794831745 & 154.552305482083 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 105.772222222222 & 0.673242865157888 & 157.108567645075 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 105.772222222222 & 0.653784642861754 & 161.78450102351 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 105.894444444444 & 0.588275140058088 & 180.008362131346 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 105.761111111111 & 0.560326152630952 & 188.74919654298 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 105.761111111111 & 0.554669873039567 & 190.673977895257 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 105.644444444444 & 0.518227571327722 & 203.857243978314 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 105.665277777778 & 0.515158178460738 & 205.112297922746 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 105.598611111111 & 0.491812833590835 & 214.713004416969 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 105.504166666667 & 0.450748974603843 & 234.064130172216 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 105.504166666667 & 0.443662720923679 & 237.802640814656 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 105.556944444444 & 0.428785390090021 & 246.176634941511 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 105.473611111111 & 0.394469756896828 & 267.380728856984 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 105.415277777778 & 0.386781084952362 & 272.545069753764 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 105.445833333333 & 0.38255144539324 & 275.638308528521 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 105.381944444444 & 0.374261538882966 & 281.573000418294 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 105.481944444444 & 0.360529770111288 & 292.574852866892 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 105.757142857143 & 0.760556000795504 & 139.052407378978 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 105.748529411765 & 0.722173253647516 & 146.430969130545 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 105.754545454545 & 0.704197146777793 & 150.177469389713 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 105.75625 & 0.685394955510823 & 154.299720401619 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 105.75 & 0.668869421892718 & 158.102607981026 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 105.735 & 0.651685450622977 & 162.248520200847 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 105.715517241379 & 0.636829914128541 & 166.00275033569 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 105.698214285714 & 0.61944933165659 & 170.63254229857 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 105.67962962963 & 0.599891555711334 & 176.16455611601 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 105.665384615385 & 0.578282711599896 & 182.722710701565 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 105.65 & 0.555839133974159 & 190.072978929389 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 105.616666666667 & 0.542717202763042 & 194.607184236945 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 105.597826086957 & 0.532049987939138 & 198.473505273411 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 105.577272727273 & 0.519135560110542 & 203.371298057085 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 105.569047619048 & 0.510192149077872 & 206.920172742474 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 105.5575 & 0.498470577533586 & 211.762749413004 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 105.552631578947 & 0.487799028792421 & 216.385489409952 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 105.558333333333 & 0.482328594441459 & 218.851493670142 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 105.564705882353 & 0.475324869727519 & 222.089590942019 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 105.565625 & 0.468108095435335 & 225.515486763426 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 105.576666666667 & 0.465392760424933 & 226.854982811225 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 105.596428571429 & 0.461320916397982 & 228.90015348953 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 105.615384615385 & 0.454234514411708 & 232.512900857325 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 105.645833333333 & 0.443592839761783 & 238.159464859863 \tabularnewline
Median & 106.1 &  &  \tabularnewline
Midrange & 106.25 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 105.432432432432 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 105.558333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 105.432432432432 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 105.558333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 105.558333333333 &  &  \tabularnewline
Midmean - Closest Observation & 105.432432432432 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 105.558333333333 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 105.552631578947 &  &  \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]105.770833333333[/C][C]0.812626389591818[/C][C]130.15924007398[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]105.54906012541[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]105.327045198912[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]105.992239626829[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]105.765277777778[/C][C]0.792628300861367[/C][C]133.436161266057[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]105.7375[/C][C]0.749745490202007[/C][C]141.031191760168[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]105.75[/C][C]0.74367968099083[/C][C]142.198318312402[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]105.777777777778[/C][C]0.727073211378008[/C][C]145.484355801391[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]105.8125[/C][C]0.717904645075494[/C][C]147.390744336071[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]105.829166666667[/C][C]0.69631951472612[/C][C]151.983628820588[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]105.809722222222[/C][C]0.692620276279539[/C][C]152.767289445505[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]105.809722222222[/C][C]0.684620794831745[/C][C]154.552305482083[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]105.772222222222[/C][C]0.673242865157888[/C][C]157.108567645075[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]105.772222222222[/C][C]0.653784642861754[/C][C]161.78450102351[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]105.894444444444[/C][C]0.588275140058088[/C][C]180.008362131346[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]105.761111111111[/C][C]0.560326152630952[/C][C]188.74919654298[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]105.761111111111[/C][C]0.554669873039567[/C][C]190.673977895257[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]105.644444444444[/C][C]0.518227571327722[/C][C]203.857243978314[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]105.665277777778[/C][C]0.515158178460738[/C][C]205.112297922746[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]105.598611111111[/C][C]0.491812833590835[/C][C]214.713004416969[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]105.504166666667[/C][C]0.450748974603843[/C][C]234.064130172216[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]105.504166666667[/C][C]0.443662720923679[/C][C]237.802640814656[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]105.556944444444[/C][C]0.428785390090021[/C][C]246.176634941511[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]105.473611111111[/C][C]0.394469756896828[/C][C]267.380728856984[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]105.415277777778[/C][C]0.386781084952362[/C][C]272.545069753764[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]105.445833333333[/C][C]0.38255144539324[/C][C]275.638308528521[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]105.381944444444[/C][C]0.374261538882966[/C][C]281.573000418294[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]105.481944444444[/C][C]0.360529770111288[/C][C]292.574852866892[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]105.757142857143[/C][C]0.760556000795504[/C][C]139.052407378978[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]105.748529411765[/C][C]0.722173253647516[/C][C]146.430969130545[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]105.754545454545[/C][C]0.704197146777793[/C][C]150.177469389713[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]105.75625[/C][C]0.685394955510823[/C][C]154.299720401619[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]105.75[/C][C]0.668869421892718[/C][C]158.102607981026[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]105.735[/C][C]0.651685450622977[/C][C]162.248520200847[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]105.715517241379[/C][C]0.636829914128541[/C][C]166.00275033569[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]105.698214285714[/C][C]0.61944933165659[/C][C]170.63254229857[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]105.67962962963[/C][C]0.599891555711334[/C][C]176.16455611601[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]105.665384615385[/C][C]0.578282711599896[/C][C]182.722710701565[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]105.65[/C][C]0.555839133974159[/C][C]190.072978929389[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]105.616666666667[/C][C]0.542717202763042[/C][C]194.607184236945[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]105.597826086957[/C][C]0.532049987939138[/C][C]198.473505273411[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]105.577272727273[/C][C]0.519135560110542[/C][C]203.371298057085[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]105.569047619048[/C][C]0.510192149077872[/C][C]206.920172742474[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]105.5575[/C][C]0.498470577533586[/C][C]211.762749413004[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]105.552631578947[/C][C]0.487799028792421[/C][C]216.385489409952[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]105.558333333333[/C][C]0.482328594441459[/C][C]218.851493670142[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]105.564705882353[/C][C]0.475324869727519[/C][C]222.089590942019[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]105.565625[/C][C]0.468108095435335[/C][C]225.515486763426[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]105.576666666667[/C][C]0.465392760424933[/C][C]226.854982811225[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]105.596428571429[/C][C]0.461320916397982[/C][C]228.90015348953[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]105.615384615385[/C][C]0.454234514411708[/C][C]232.512900857325[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]105.645833333333[/C][C]0.443592839761783[/C][C]238.159464859863[/C][/ROW]
[ROW][C]Median[/C][C]106.1[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]106.25[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]105.432432432432[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]105.558333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]105.432432432432[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]105.558333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]105.558333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]105.432432432432[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]105.558333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]105.552631578947[/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 Mean105.7708333333330.812626389591818130.15924007398
Geometric Mean105.54906012541
Harmonic Mean105.327045198912
Quadratic Mean105.992239626829
Winsorized Mean ( 1 / 24 )105.7652777777780.792628300861367133.436161266057
Winsorized Mean ( 2 / 24 )105.73750.749745490202007141.031191760168
Winsorized Mean ( 3 / 24 )105.750.74367968099083142.198318312402
Winsorized Mean ( 4 / 24 )105.7777777777780.727073211378008145.484355801391
Winsorized Mean ( 5 / 24 )105.81250.717904645075494147.390744336071
Winsorized Mean ( 6 / 24 )105.8291666666670.69631951472612151.983628820588
Winsorized Mean ( 7 / 24 )105.8097222222220.692620276279539152.767289445505
Winsorized Mean ( 8 / 24 )105.8097222222220.684620794831745154.552305482083
Winsorized Mean ( 9 / 24 )105.7722222222220.673242865157888157.108567645075
Winsorized Mean ( 10 / 24 )105.7722222222220.653784642861754161.78450102351
Winsorized Mean ( 11 / 24 )105.8944444444440.588275140058088180.008362131346
Winsorized Mean ( 12 / 24 )105.7611111111110.560326152630952188.74919654298
Winsorized Mean ( 13 / 24 )105.7611111111110.554669873039567190.673977895257
Winsorized Mean ( 14 / 24 )105.6444444444440.518227571327722203.857243978314
Winsorized Mean ( 15 / 24 )105.6652777777780.515158178460738205.112297922746
Winsorized Mean ( 16 / 24 )105.5986111111110.491812833590835214.713004416969
Winsorized Mean ( 17 / 24 )105.5041666666670.450748974603843234.064130172216
Winsorized Mean ( 18 / 24 )105.5041666666670.443662720923679237.802640814656
Winsorized Mean ( 19 / 24 )105.5569444444440.428785390090021246.176634941511
Winsorized Mean ( 20 / 24 )105.4736111111110.394469756896828267.380728856984
Winsorized Mean ( 21 / 24 )105.4152777777780.386781084952362272.545069753764
Winsorized Mean ( 22 / 24 )105.4458333333330.38255144539324275.638308528521
Winsorized Mean ( 23 / 24 )105.3819444444440.374261538882966281.573000418294
Winsorized Mean ( 24 / 24 )105.4819444444440.360529770111288292.574852866892
Trimmed Mean ( 1 / 24 )105.7571428571430.760556000795504139.052407378978
Trimmed Mean ( 2 / 24 )105.7485294117650.722173253647516146.430969130545
Trimmed Mean ( 3 / 24 )105.7545454545450.704197146777793150.177469389713
Trimmed Mean ( 4 / 24 )105.756250.685394955510823154.299720401619
Trimmed Mean ( 5 / 24 )105.750.668869421892718158.102607981026
Trimmed Mean ( 6 / 24 )105.7350.651685450622977162.248520200847
Trimmed Mean ( 7 / 24 )105.7155172413790.636829914128541166.00275033569
Trimmed Mean ( 8 / 24 )105.6982142857140.61944933165659170.63254229857
Trimmed Mean ( 9 / 24 )105.679629629630.599891555711334176.16455611601
Trimmed Mean ( 10 / 24 )105.6653846153850.578282711599896182.722710701565
Trimmed Mean ( 11 / 24 )105.650.555839133974159190.072978929389
Trimmed Mean ( 12 / 24 )105.6166666666670.542717202763042194.607184236945
Trimmed Mean ( 13 / 24 )105.5978260869570.532049987939138198.473505273411
Trimmed Mean ( 14 / 24 )105.5772727272730.519135560110542203.371298057085
Trimmed Mean ( 15 / 24 )105.5690476190480.510192149077872206.920172742474
Trimmed Mean ( 16 / 24 )105.55750.498470577533586211.762749413004
Trimmed Mean ( 17 / 24 )105.5526315789470.487799028792421216.385489409952
Trimmed Mean ( 18 / 24 )105.5583333333330.482328594441459218.851493670142
Trimmed Mean ( 19 / 24 )105.5647058823530.475324869727519222.089590942019
Trimmed Mean ( 20 / 24 )105.5656250.468108095435335225.515486763426
Trimmed Mean ( 21 / 24 )105.5766666666670.465392760424933226.854982811225
Trimmed Mean ( 22 / 24 )105.5964285714290.461320916397982228.90015348953
Trimmed Mean ( 23 / 24 )105.6153846153850.454234514411708232.512900857325
Trimmed Mean ( 24 / 24 )105.6458333333330.443592839761783238.159464859863
Median106.1
Midrange106.25
Midmean - Weighted Average at Xnp105.432432432432
Midmean - Weighted Average at X(n+1)p105.558333333333
Midmean - Empirical Distribution Function105.432432432432
Midmean - Empirical Distribution Function - Averaging105.558333333333
Midmean - Empirical Distribution Function - Interpolation105.558333333333
Midmean - Closest Observation105.432432432432
Midmean - True Basic - Statistics Graphics Toolkit105.558333333333
Midmean - MS Excel (old versions)105.552631578947
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')