Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationTue, 14 Mar 2017 12:35:41 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2017/Mar/14/t14894950770lpukku0c1bc7gj.htm/, Retrieved Tue, 14 May 2024 20:34:03 +0200
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Tue, 14 May 2024 20:34:03 +0200
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact0
Dataseries X:
78,46
78,59
81,37
83,61
84,65
84,56
83,85
84,08
85,41
85,75
86,38
88,87
90,37
92,21
95,75
97,29
98,29
99,51
99,04
98,9
100,74
100,3
101,68
101,3
103,13
104,17
105,98
106,25
104,01
101,68
101,93
104,41
105,51
104,71
103,14
102,66
102,68
101,89
101,37
101,16
99,34
99,35
99,88
99,31
99,91
98,39
98,02
98,7
98,01
98,42
98,2
93,5
93,17
93,42
93,13
92,31
92,09
92,62
91,43
89,38
86,21
86,65
88,62
87,3
88,33
88,67
88,23
88,85
90,38
89,65
89,2
87,87




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ jenkins.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 & 'Gwilym Jenkins' @ jenkins.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]'Gwilym Jenkins' @ jenkins.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'Gwilym Jenkins' @ jenkins.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean94.64138888888890.863548931368901109.595861277789
Geometric Mean94.3561344285358
Harmonic Mean94.0657170700433
Quadratic Mean94.9206952174053
Winsorized Mean ( 1 / 24 )94.63944444444450.862371736145372109.743212210854
Winsorized Mean ( 2 / 24 )94.70361111111110.84122203440707112.578614488935
Winsorized Mean ( 3 / 24 )94.76361111111110.815917671902138116.143594353325
Winsorized Mean ( 4 / 24 )94.76027777777780.810541897700123116.909783499972
Winsorized Mean ( 5 / 24 )94.75958333333330.804765234614597117.748107469769
Winsorized Mean ( 6 / 24 )94.786250.795216809775849119.195480823296
Winsorized Mean ( 7 / 24 )94.71041666666670.780281349420027121.379828874628
Winsorized Mean ( 8 / 24 )94.793750.765147388235618123.889529595845
Winsorized Mean ( 9 / 24 )94.780.749376396979881126.478496496527
Winsorized Mean ( 10 / 24 )94.84111111111110.738280277546559128.462203306156
Winsorized Mean ( 11 / 24 )94.75555555555550.71783347228413132.00214146332
Winsorized Mean ( 12 / 24 )94.79388888888890.709559627685248133.595381121287
Winsorized Mean ( 13 / 24 )94.87333333333330.68561659077517138.376659214253
Winsorized Mean ( 14 / 24 )94.98416666666670.668687101235228142.045758758032
Winsorized Mean ( 15 / 24 )94.99458333333330.64853053886428146.47665397483
Winsorized Mean ( 16 / 24 )95.001250.643125009980518147.718170691073
Winsorized Mean ( 17 / 24 )95.03666666666670.628652893172295151.17510425681
Winsorized Mean ( 18 / 24 )94.94416666666670.612652611053757154.972271322509
Winsorized Mean ( 19 / 24 )94.87555555555560.590563505364912160.652588068292
Winsorized Mean ( 20 / 24 )94.77277777777780.575948500615121164.550784795097
Winsorized Mean ( 21 / 24 )94.86027777777780.561061200115223169.072959880841
Winsorized Mean ( 22 / 24 )94.80222222222220.539180144095155175.82661984209
Winsorized Mean ( 23 / 24 )94.83736111111110.520758369931299182.113944944606
Winsorized Mean ( 24 / 24 )95.07402777777780.487177029154302195.152936382937
Trimmed Mean ( 1 / 24 )94.70671428571430.840881936736147112.627837688267
Trimmed Mean ( 2 / 24 )94.77794117647060.815244851880265116.257025061706
Trimmed Mean ( 3 / 24 )94.81848484848480.798157734334252118.796674854718
Trimmed Mean ( 4 / 24 )94.83906250.788915951737731120.214405972017
Trimmed Mean ( 5 / 24 )94.8619354838710.779339773958645121.720895883475
Trimmed Mean ( 6 / 24 )94.88650.769134219587266123.367934469121
Trimmed Mean ( 7 / 24 )94.90724137931030.75894523525825125.051501702907
Trimmed Mean ( 8 / 24 )94.94339285714290.749715629066518126.639207155596
Trimmed Mean ( 9 / 24 )94.96833333333330.741418821801924128.089995210163
Trimmed Mean ( 10 / 24 )94.99730769230770.733993504199448129.425270317507
Trimmed Mean ( 11 / 24 )95.01980.726410436070857130.807316747761
Trimmed Mean ( 12 / 24 )95.05583333333330.72025451282083131.975338774419
Trimmed Mean ( 13 / 24 )95.090.713201870589639133.328309867421
Trimmed Mean ( 14 / 24 )95.11727272727270.708143089095604134.319284042933
Trimmed Mean ( 15 / 24 )95.13357142857140.703884758991556135.155038112869
Trimmed Mean ( 16 / 24 )95.150250.701010213128351135.733043853069
Trimmed Mean ( 17 / 24 )95.16789473684210.69659853904085136.617993583333
Trimmed Mean ( 18 / 24 )95.18333333333330.692059268954641137.536389733076
Trimmed Mean ( 19 / 24 )95.21147058823530.687386371404267138.512304795521
Trimmed Mean ( 20 / 24 )95.251250.683719775825476139.313287940224
Trimmed Mean ( 21 / 24 )95.30866666666670.679088085856681140.348017660232
Trimmed Mean ( 22 / 24 )95.36357142857140.67348933724089141.596260186169
Trimmed Mean ( 23 / 24 )95.43423076923080.667701723613154142.929435995469
Trimmed Mean ( 24 / 24 )95.51208333333330.660547911340524144.595239336235
Median96.52
Midrange92.355
Midmean - Weighted Average at Xnp95.0059459459459
Midmean - Weighted Average at X(n+1)p95.1833333333333
Midmean - Empirical Distribution Function95.0059459459459
Midmean - Empirical Distribution Function - Averaging95.1833333333333
Midmean - Empirical Distribution Function - Interpolation95.1833333333333
Midmean - Closest Observation95.0059459459459
Midmean - True Basic - Statistics Graphics Toolkit95.1833333333333
Midmean - MS Excel (old versions)95.1678947368421
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 94.6413888888889 & 0.863548931368901 & 109.595861277789 \tabularnewline
Geometric Mean & 94.3561344285358 &  &  \tabularnewline
Harmonic Mean & 94.0657170700433 &  &  \tabularnewline
Quadratic Mean & 94.9206952174053 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 94.6394444444445 & 0.862371736145372 & 109.743212210854 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 94.7036111111111 & 0.84122203440707 & 112.578614488935 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 94.7636111111111 & 0.815917671902138 & 116.143594353325 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 94.7602777777778 & 0.810541897700123 & 116.909783499972 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 94.7595833333333 & 0.804765234614597 & 117.748107469769 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 94.78625 & 0.795216809775849 & 119.195480823296 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 94.7104166666667 & 0.780281349420027 & 121.379828874628 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 94.79375 & 0.765147388235618 & 123.889529595845 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 94.78 & 0.749376396979881 & 126.478496496527 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 94.8411111111111 & 0.738280277546559 & 128.462203306156 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 94.7555555555555 & 0.71783347228413 & 132.00214146332 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 94.7938888888889 & 0.709559627685248 & 133.595381121287 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 94.8733333333333 & 0.68561659077517 & 138.376659214253 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 94.9841666666667 & 0.668687101235228 & 142.045758758032 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 94.9945833333333 & 0.64853053886428 & 146.47665397483 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 95.00125 & 0.643125009980518 & 147.718170691073 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 95.0366666666667 & 0.628652893172295 & 151.17510425681 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 94.9441666666667 & 0.612652611053757 & 154.972271322509 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 94.8755555555556 & 0.590563505364912 & 160.652588068292 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 94.7727777777778 & 0.575948500615121 & 164.550784795097 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 94.8602777777778 & 0.561061200115223 & 169.072959880841 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 94.8022222222222 & 0.539180144095155 & 175.82661984209 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 94.8373611111111 & 0.520758369931299 & 182.113944944606 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 95.0740277777778 & 0.487177029154302 & 195.152936382937 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 94.7067142857143 & 0.840881936736147 & 112.627837688267 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 94.7779411764706 & 0.815244851880265 & 116.257025061706 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 94.8184848484848 & 0.798157734334252 & 118.796674854718 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 94.8390625 & 0.788915951737731 & 120.214405972017 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 94.861935483871 & 0.779339773958645 & 121.720895883475 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 94.8865 & 0.769134219587266 & 123.367934469121 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 94.9072413793103 & 0.75894523525825 & 125.051501702907 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 94.9433928571429 & 0.749715629066518 & 126.639207155596 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 94.9683333333333 & 0.741418821801924 & 128.089995210163 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 94.9973076923077 & 0.733993504199448 & 129.425270317507 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 95.0198 & 0.726410436070857 & 130.807316747761 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 95.0558333333333 & 0.72025451282083 & 131.975338774419 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 95.09 & 0.713201870589639 & 133.328309867421 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 95.1172727272727 & 0.708143089095604 & 134.319284042933 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 95.1335714285714 & 0.703884758991556 & 135.155038112869 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 95.15025 & 0.701010213128351 & 135.733043853069 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 95.1678947368421 & 0.69659853904085 & 136.617993583333 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 95.1833333333333 & 0.692059268954641 & 137.536389733076 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 95.2114705882353 & 0.687386371404267 & 138.512304795521 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 95.25125 & 0.683719775825476 & 139.313287940224 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 95.3086666666667 & 0.679088085856681 & 140.348017660232 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 95.3635714285714 & 0.67348933724089 & 141.596260186169 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 95.4342307692308 & 0.667701723613154 & 142.929435995469 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 95.5120833333333 & 0.660547911340524 & 144.595239336235 \tabularnewline
Median & 96.52 &  &  \tabularnewline
Midrange & 92.355 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 95.0059459459459 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 95.1833333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 95.0059459459459 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 95.1833333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 95.1833333333333 &  &  \tabularnewline
Midmean - Closest Observation & 95.0059459459459 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 95.1833333333333 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 95.1678947368421 &  &  \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]94.6413888888889[/C][C]0.863548931368901[/C][C]109.595861277789[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]94.3561344285358[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]94.0657170700433[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]94.9206952174053[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]94.6394444444445[/C][C]0.862371736145372[/C][C]109.743212210854[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]94.7036111111111[/C][C]0.84122203440707[/C][C]112.578614488935[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]94.7636111111111[/C][C]0.815917671902138[/C][C]116.143594353325[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]94.7602777777778[/C][C]0.810541897700123[/C][C]116.909783499972[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]94.7595833333333[/C][C]0.804765234614597[/C][C]117.748107469769[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]94.78625[/C][C]0.795216809775849[/C][C]119.195480823296[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]94.7104166666667[/C][C]0.780281349420027[/C][C]121.379828874628[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]94.79375[/C][C]0.765147388235618[/C][C]123.889529595845[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]94.78[/C][C]0.749376396979881[/C][C]126.478496496527[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]94.8411111111111[/C][C]0.738280277546559[/C][C]128.462203306156[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]94.7555555555555[/C][C]0.71783347228413[/C][C]132.00214146332[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]94.7938888888889[/C][C]0.709559627685248[/C][C]133.595381121287[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]94.8733333333333[/C][C]0.68561659077517[/C][C]138.376659214253[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]94.9841666666667[/C][C]0.668687101235228[/C][C]142.045758758032[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]94.9945833333333[/C][C]0.64853053886428[/C][C]146.47665397483[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]95.00125[/C][C]0.643125009980518[/C][C]147.718170691073[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]95.0366666666667[/C][C]0.628652893172295[/C][C]151.17510425681[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]94.9441666666667[/C][C]0.612652611053757[/C][C]154.972271322509[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]94.8755555555556[/C][C]0.590563505364912[/C][C]160.652588068292[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]94.7727777777778[/C][C]0.575948500615121[/C][C]164.550784795097[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]94.8602777777778[/C][C]0.561061200115223[/C][C]169.072959880841[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]94.8022222222222[/C][C]0.539180144095155[/C][C]175.82661984209[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]94.8373611111111[/C][C]0.520758369931299[/C][C]182.113944944606[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]95.0740277777778[/C][C]0.487177029154302[/C][C]195.152936382937[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]94.7067142857143[/C][C]0.840881936736147[/C][C]112.627837688267[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]94.7779411764706[/C][C]0.815244851880265[/C][C]116.257025061706[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]94.8184848484848[/C][C]0.798157734334252[/C][C]118.796674854718[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]94.8390625[/C][C]0.788915951737731[/C][C]120.214405972017[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]94.861935483871[/C][C]0.779339773958645[/C][C]121.720895883475[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]94.8865[/C][C]0.769134219587266[/C][C]123.367934469121[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]94.9072413793103[/C][C]0.75894523525825[/C][C]125.051501702907[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]94.9433928571429[/C][C]0.749715629066518[/C][C]126.639207155596[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]94.9683333333333[/C][C]0.741418821801924[/C][C]128.089995210163[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]94.9973076923077[/C][C]0.733993504199448[/C][C]129.425270317507[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]95.0198[/C][C]0.726410436070857[/C][C]130.807316747761[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]95.0558333333333[/C][C]0.72025451282083[/C][C]131.975338774419[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]95.09[/C][C]0.713201870589639[/C][C]133.328309867421[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]95.1172727272727[/C][C]0.708143089095604[/C][C]134.319284042933[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]95.1335714285714[/C][C]0.703884758991556[/C][C]135.155038112869[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]95.15025[/C][C]0.701010213128351[/C][C]135.733043853069[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]95.1678947368421[/C][C]0.69659853904085[/C][C]136.617993583333[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]95.1833333333333[/C][C]0.692059268954641[/C][C]137.536389733076[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]95.2114705882353[/C][C]0.687386371404267[/C][C]138.512304795521[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]95.25125[/C][C]0.683719775825476[/C][C]139.313287940224[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]95.3086666666667[/C][C]0.679088085856681[/C][C]140.348017660232[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]95.3635714285714[/C][C]0.67348933724089[/C][C]141.596260186169[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]95.4342307692308[/C][C]0.667701723613154[/C][C]142.929435995469[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]95.5120833333333[/C][C]0.660547911340524[/C][C]144.595239336235[/C][/ROW]
[ROW][C]Median[/C][C]96.52[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]92.355[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]95.0059459459459[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]95.1833333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]95.0059459459459[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]95.1833333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]95.1833333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]95.0059459459459[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]95.1833333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]95.1678947368421[/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 Mean94.64138888888890.863548931368901109.595861277789
Geometric Mean94.3561344285358
Harmonic Mean94.0657170700433
Quadratic Mean94.9206952174053
Winsorized Mean ( 1 / 24 )94.63944444444450.862371736145372109.743212210854
Winsorized Mean ( 2 / 24 )94.70361111111110.84122203440707112.578614488935
Winsorized Mean ( 3 / 24 )94.76361111111110.815917671902138116.143594353325
Winsorized Mean ( 4 / 24 )94.76027777777780.810541897700123116.909783499972
Winsorized Mean ( 5 / 24 )94.75958333333330.804765234614597117.748107469769
Winsorized Mean ( 6 / 24 )94.786250.795216809775849119.195480823296
Winsorized Mean ( 7 / 24 )94.71041666666670.780281349420027121.379828874628
Winsorized Mean ( 8 / 24 )94.793750.765147388235618123.889529595845
Winsorized Mean ( 9 / 24 )94.780.749376396979881126.478496496527
Winsorized Mean ( 10 / 24 )94.84111111111110.738280277546559128.462203306156
Winsorized Mean ( 11 / 24 )94.75555555555550.71783347228413132.00214146332
Winsorized Mean ( 12 / 24 )94.79388888888890.709559627685248133.595381121287
Winsorized Mean ( 13 / 24 )94.87333333333330.68561659077517138.376659214253
Winsorized Mean ( 14 / 24 )94.98416666666670.668687101235228142.045758758032
Winsorized Mean ( 15 / 24 )94.99458333333330.64853053886428146.47665397483
Winsorized Mean ( 16 / 24 )95.001250.643125009980518147.718170691073
Winsorized Mean ( 17 / 24 )95.03666666666670.628652893172295151.17510425681
Winsorized Mean ( 18 / 24 )94.94416666666670.612652611053757154.972271322509
Winsorized Mean ( 19 / 24 )94.87555555555560.590563505364912160.652588068292
Winsorized Mean ( 20 / 24 )94.77277777777780.575948500615121164.550784795097
Winsorized Mean ( 21 / 24 )94.86027777777780.561061200115223169.072959880841
Winsorized Mean ( 22 / 24 )94.80222222222220.539180144095155175.82661984209
Winsorized Mean ( 23 / 24 )94.83736111111110.520758369931299182.113944944606
Winsorized Mean ( 24 / 24 )95.07402777777780.487177029154302195.152936382937
Trimmed Mean ( 1 / 24 )94.70671428571430.840881936736147112.627837688267
Trimmed Mean ( 2 / 24 )94.77794117647060.815244851880265116.257025061706
Trimmed Mean ( 3 / 24 )94.81848484848480.798157734334252118.796674854718
Trimmed Mean ( 4 / 24 )94.83906250.788915951737731120.214405972017
Trimmed Mean ( 5 / 24 )94.8619354838710.779339773958645121.720895883475
Trimmed Mean ( 6 / 24 )94.88650.769134219587266123.367934469121
Trimmed Mean ( 7 / 24 )94.90724137931030.75894523525825125.051501702907
Trimmed Mean ( 8 / 24 )94.94339285714290.749715629066518126.639207155596
Trimmed Mean ( 9 / 24 )94.96833333333330.741418821801924128.089995210163
Trimmed Mean ( 10 / 24 )94.99730769230770.733993504199448129.425270317507
Trimmed Mean ( 11 / 24 )95.01980.726410436070857130.807316747761
Trimmed Mean ( 12 / 24 )95.05583333333330.72025451282083131.975338774419
Trimmed Mean ( 13 / 24 )95.090.713201870589639133.328309867421
Trimmed Mean ( 14 / 24 )95.11727272727270.708143089095604134.319284042933
Trimmed Mean ( 15 / 24 )95.13357142857140.703884758991556135.155038112869
Trimmed Mean ( 16 / 24 )95.150250.701010213128351135.733043853069
Trimmed Mean ( 17 / 24 )95.16789473684210.69659853904085136.617993583333
Trimmed Mean ( 18 / 24 )95.18333333333330.692059268954641137.536389733076
Trimmed Mean ( 19 / 24 )95.21147058823530.687386371404267138.512304795521
Trimmed Mean ( 20 / 24 )95.251250.683719775825476139.313287940224
Trimmed Mean ( 21 / 24 )95.30866666666670.679088085856681140.348017660232
Trimmed Mean ( 22 / 24 )95.36357142857140.67348933724089141.596260186169
Trimmed Mean ( 23 / 24 )95.43423076923080.667701723613154142.929435995469
Trimmed Mean ( 24 / 24 )95.51208333333330.660547911340524144.595239336235
Median96.52
Midrange92.355
Midmean - Weighted Average at Xnp95.0059459459459
Midmean - Weighted Average at X(n+1)p95.1833333333333
Midmean - Empirical Distribution Function95.0059459459459
Midmean - Empirical Distribution Function - Averaging95.1833333333333
Midmean - Empirical Distribution Function - Interpolation95.1833333333333
Midmean - Closest Observation95.0059459459459
Midmean - True Basic - Statistics Graphics Toolkit95.1833333333333
Midmean - MS Excel (old versions)95.1678947368421
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')