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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationSun, 21 Oct 2012 05:35:55 -0400
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/Oct/21/t1350812192mo38h0vu07d66j9.htm/, Retrieved Mon, 29 Apr 2024 05:08:18 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=180691, Retrieved Mon, 29 Apr 2024 05:08:18 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact112
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2012-10-21 09:35:55] [094ed89fe81fbe7ca359945eca8d835d] [Current]
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Dataseries X:
96,24
95,56
95,56
95,56
95,96
95,96
95,96
95,96
95,61
95,30
95,68
97,94
97,32
97,32
97,45
98,08
98,25
98,25
97,95
97,81
97,68
98,03
98,03
98,03
98,11
98,11
98,11
97,95
97,95
97,95
97,95
97,95
97,95
97,89
97,16
97,16
97,16
97,18
97,18
96,47
97,47
97,47
97,47
97,47
96,63
96,78
96,25
96,25
96,28
95,62
95,62
96,85
96,85
96,85
96,85
96,85
96,85
96,85
96,75
97,15
98,28
98,28
98,28
98,51
98,51
98,51
96,03
96,03
96,77
96,92
96,92
96,92




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=180691&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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=180691&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=180691&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 time2 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean97.12277777777780.106690179007461910.325380286275
Geometric Mean97.1186091759488
Harmonic Mean97.1144326727083
Quadratic Mean97.1269382903974
Winsorized Mean ( 1 / 24 )97.12638888888890.105879265393191917.331533499053
Winsorized Mean ( 2 / 24 )97.12638888888890.105879265393191917.331533499053
Winsorized Mean ( 3 / 24 )97.11680555555560.104243272561685931.636192619412
Winsorized Mean ( 4 / 24 )97.11958333333330.103666251055882936.848611232019
Winsorized Mean ( 5 / 24 )97.12027777777780.103524163528904938.141149536183
Winsorized Mean ( 6 / 24 )97.11777777777780.103133651953127941.669144247088
Winsorized Mean ( 7 / 24 )97.12361111111110.101955317462232952.609569845036
Winsorized Mean ( 8 / 24 )97.13916666666670.09373441445826691036.32339550076
Winsorized Mean ( 9 / 24 )97.13916666666670.09373441445826691036.32339550076
Winsorized Mean ( 10 / 24 )97.13916666666670.09373441445826691036.32339550076
Winsorized Mean ( 11 / 24 )97.13458333333330.09307222394101861043.64738716128
Winsorized Mean ( 12 / 24 )97.13791666666670.08984270237362951081.1998537477
Winsorized Mean ( 13 / 24 )97.13791666666670.08984270237362951081.1998537477
Winsorized Mean ( 14 / 24 )97.178750.0830339546051551170.34953305677
Winsorized Mean ( 15 / 24 )97.16416666666670.08034908919574211209.27527168305
Winsorized Mean ( 16 / 24 )97.16416666666670.08034908919574211209.27527168305
Winsorized Mean ( 17 / 24 )97.171250.07922031478508471226.59510080986
Winsorized Mean ( 18 / 24 )97.218750.07196301255545361350.95442155211
Winsorized Mean ( 19 / 24 )97.26097222222220.0660165364717351473.28195964756
Winsorized Mean ( 20 / 24 )97.29430555555560.06169610589926561576.99265030459
Winsorized Mean ( 21 / 24 )97.30013888888890.0609764998267781595.69898510572
Winsorized Mean ( 22 / 24 )97.30013888888890.06014506884003791617.75754464042
Winsorized Mean ( 23 / 24 )97.30652777777780.0550874818997821766.39999546182
Winsorized Mean ( 24 / 24 )97.27986111111110.05115049332845951901.83622446092
Trimmed Mean ( 1 / 24 )97.1290.104692421433407927.755788529374
Trimmed Mean ( 2 / 24 )97.13176470588230.103250282186417940.740912751333
Trimmed Mean ( 3 / 24 )97.1346969696970.101502975646662956.964033328727
Trimmed Mean ( 4 / 24 )97.141406250.100105318346653970.392061624645
Trimmed Mean ( 5 / 24 )97.14774193548390.0985898509881501985.372641928026
Trimmed Mean ( 6 / 24 )97.15433333333330.09675858672728441004.09004119877
Trimmed Mean ( 7 / 24 )97.16189655172410.09459739150167031027.10968039757
Trimmed Mean ( 8 / 24 )97.16892857142860.09223335684570891053.51178678204
Trimmed Mean ( 9 / 24 )97.17388888888890.09129299353471881064.4178170358
Trimmed Mean ( 10 / 24 )97.17923076923080.09004307924654511079.25263754193
Trimmed Mean ( 11 / 24 )97.1850.08840364292059851099.33252510068
Trimmed Mean ( 12 / 24 )97.1918750.08640610872502031124.82643222951
Trimmed Mean ( 13 / 24 )97.19891304347830.08452380293100761149.95906091467
Trimmed Mean ( 14 / 24 )97.20659090909090.0820231385789931185.11181836178
Trimmed Mean ( 15 / 24 )97.210.08034550825568381209.89962115428
Trimmed Mean ( 16 / 24 )97.21550.07863331811610621236.31435540411
Trimmed Mean ( 17 / 24 )97.22157894736840.07624129390009341275.18269921766
Trimmed Mean ( 18 / 24 )97.22750.07321567942924351327.9600866637
Trimmed Mean ( 19 / 24 )97.22852941176470.07101521560360591369.12249840199
Trimmed Mean ( 20 / 24 )97.22468750.06940993290071891400.73161631011
Trimmed Mean ( 21 / 24 )97.21633333333330.06802380133374471429.15172964771
Trimmed Mean ( 22 / 24 )97.20607142857140.06592110742112991474.58189389297
Trimmed Mean ( 23 / 24 )97.19423076923080.06277474523288251548.30147710928
Trimmed Mean ( 24 / 24 )97.17958333333330.05949205027475321633.48855661432
Median97.16
Midrange96.905
Midmean - Weighted Average at Xnp97.258
Midmean - Weighted Average at X(n+1)p97.2830769230769
Midmean - Empirical Distribution Function97.258
Midmean - Empirical Distribution Function - Averaging97.2830769230769
Midmean - Empirical Distribution Function - Interpolation97.2830769230769
Midmean - Closest Observation97.258
Midmean - True Basic - Statistics Graphics Toolkit97.2830769230769
Midmean - MS Excel (old versions)97.258
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 97.1227777777778 & 0.106690179007461 & 910.325380286275 \tabularnewline
Geometric Mean & 97.1186091759488 &  &  \tabularnewline
Harmonic Mean & 97.1144326727083 &  &  \tabularnewline
Quadratic Mean & 97.1269382903974 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 97.1263888888889 & 0.105879265393191 & 917.331533499053 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 97.1263888888889 & 0.105879265393191 & 917.331533499053 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 97.1168055555556 & 0.104243272561685 & 931.636192619412 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 97.1195833333333 & 0.103666251055882 & 936.848611232019 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 97.1202777777778 & 0.103524163528904 & 938.141149536183 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 97.1177777777778 & 0.103133651953127 & 941.669144247088 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 97.1236111111111 & 0.101955317462232 & 952.609569845036 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 97.1391666666667 & 0.0937344144582669 & 1036.32339550076 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 97.1391666666667 & 0.0937344144582669 & 1036.32339550076 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 97.1391666666667 & 0.0937344144582669 & 1036.32339550076 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 97.1345833333333 & 0.0930722239410186 & 1043.64738716128 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 97.1379166666667 & 0.0898427023736295 & 1081.1998537477 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 97.1379166666667 & 0.0898427023736295 & 1081.1998537477 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 97.17875 & 0.083033954605155 & 1170.34953305677 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 97.1641666666667 & 0.0803490891957421 & 1209.27527168305 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 97.1641666666667 & 0.0803490891957421 & 1209.27527168305 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 97.17125 & 0.0792203147850847 & 1226.59510080986 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 97.21875 & 0.0719630125554536 & 1350.95442155211 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 97.2609722222222 & 0.066016536471735 & 1473.28195964756 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 97.2943055555556 & 0.0616961058992656 & 1576.99265030459 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 97.3001388888889 & 0.060976499826778 & 1595.69898510572 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 97.3001388888889 & 0.0601450688400379 & 1617.75754464042 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 97.3065277777778 & 0.055087481899782 & 1766.39999546182 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 97.2798611111111 & 0.0511504933284595 & 1901.83622446092 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 97.129 & 0.104692421433407 & 927.755788529374 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 97.1317647058823 & 0.103250282186417 & 940.740912751333 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 97.134696969697 & 0.101502975646662 & 956.964033328727 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 97.14140625 & 0.100105318346653 & 970.392061624645 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 97.1477419354839 & 0.0985898509881501 & 985.372641928026 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 97.1543333333333 & 0.0967585867272844 & 1004.09004119877 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 97.1618965517241 & 0.0945973915016703 & 1027.10968039757 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 97.1689285714286 & 0.0922333568457089 & 1053.51178678204 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 97.1738888888889 & 0.0912929935347188 & 1064.4178170358 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 97.1792307692308 & 0.0900430792465451 & 1079.25263754193 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 97.185 & 0.0884036429205985 & 1099.33252510068 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 97.191875 & 0.0864061087250203 & 1124.82643222951 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 97.1989130434783 & 0.0845238029310076 & 1149.95906091467 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 97.2065909090909 & 0.082023138578993 & 1185.11181836178 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 97.21 & 0.0803455082556838 & 1209.89962115428 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 97.2155 & 0.0786333181161062 & 1236.31435540411 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 97.2215789473684 & 0.0762412939000934 & 1275.18269921766 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 97.2275 & 0.0732156794292435 & 1327.9600866637 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 97.2285294117647 & 0.0710152156036059 & 1369.12249840199 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 97.2246875 & 0.0694099329007189 & 1400.73161631011 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 97.2163333333333 & 0.0680238013337447 & 1429.15172964771 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 97.2060714285714 & 0.0659211074211299 & 1474.58189389297 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 97.1942307692308 & 0.0627747452328825 & 1548.30147710928 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 97.1795833333333 & 0.0594920502747532 & 1633.48855661432 \tabularnewline
Median & 97.16 &  &  \tabularnewline
Midrange & 96.905 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 97.258 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 97.2830769230769 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 97.258 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 97.2830769230769 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 97.2830769230769 &  &  \tabularnewline
Midmean - Closest Observation & 97.258 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 97.2830769230769 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 97.258 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=180691&T=1

[TABLE]
[ROW][C]Central Tendency - Ungrouped Data[/C][/ROW]
[ROW][C]Measure[/C][C]Value[/C][C]S.E.[/C][C]Value/S.E.[/C][/ROW]
[ROW][C]Arithmetic Mean[/C][C]97.1227777777778[/C][C]0.106690179007461[/C][C]910.325380286275[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]97.1186091759488[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]97.1144326727083[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]97.1269382903974[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]97.1263888888889[/C][C]0.105879265393191[/C][C]917.331533499053[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]97.1263888888889[/C][C]0.105879265393191[/C][C]917.331533499053[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]97.1168055555556[/C][C]0.104243272561685[/C][C]931.636192619412[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]97.1195833333333[/C][C]0.103666251055882[/C][C]936.848611232019[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]97.1202777777778[/C][C]0.103524163528904[/C][C]938.141149536183[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]97.1177777777778[/C][C]0.103133651953127[/C][C]941.669144247088[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]97.1236111111111[/C][C]0.101955317462232[/C][C]952.609569845036[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]97.1391666666667[/C][C]0.0937344144582669[/C][C]1036.32339550076[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]97.1391666666667[/C][C]0.0937344144582669[/C][C]1036.32339550076[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]97.1391666666667[/C][C]0.0937344144582669[/C][C]1036.32339550076[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]97.1345833333333[/C][C]0.0930722239410186[/C][C]1043.64738716128[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]97.1379166666667[/C][C]0.0898427023736295[/C][C]1081.1998537477[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]97.1379166666667[/C][C]0.0898427023736295[/C][C]1081.1998537477[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]97.17875[/C][C]0.083033954605155[/C][C]1170.34953305677[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]97.1641666666667[/C][C]0.0803490891957421[/C][C]1209.27527168305[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]97.1641666666667[/C][C]0.0803490891957421[/C][C]1209.27527168305[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]97.17125[/C][C]0.0792203147850847[/C][C]1226.59510080986[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]97.21875[/C][C]0.0719630125554536[/C][C]1350.95442155211[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]97.2609722222222[/C][C]0.066016536471735[/C][C]1473.28195964756[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]97.2943055555556[/C][C]0.0616961058992656[/C][C]1576.99265030459[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]97.3001388888889[/C][C]0.060976499826778[/C][C]1595.69898510572[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]97.3001388888889[/C][C]0.0601450688400379[/C][C]1617.75754464042[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]97.3065277777778[/C][C]0.055087481899782[/C][C]1766.39999546182[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]97.2798611111111[/C][C]0.0511504933284595[/C][C]1901.83622446092[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]97.129[/C][C]0.104692421433407[/C][C]927.755788529374[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]97.1317647058823[/C][C]0.103250282186417[/C][C]940.740912751333[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]97.134696969697[/C][C]0.101502975646662[/C][C]956.964033328727[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]97.14140625[/C][C]0.100105318346653[/C][C]970.392061624645[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]97.1477419354839[/C][C]0.0985898509881501[/C][C]985.372641928026[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]97.1543333333333[/C][C]0.0967585867272844[/C][C]1004.09004119877[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]97.1618965517241[/C][C]0.0945973915016703[/C][C]1027.10968039757[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]97.1689285714286[/C][C]0.0922333568457089[/C][C]1053.51178678204[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]97.1738888888889[/C][C]0.0912929935347188[/C][C]1064.4178170358[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]97.1792307692308[/C][C]0.0900430792465451[/C][C]1079.25263754193[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]97.185[/C][C]0.0884036429205985[/C][C]1099.33252510068[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]97.191875[/C][C]0.0864061087250203[/C][C]1124.82643222951[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]97.1989130434783[/C][C]0.0845238029310076[/C][C]1149.95906091467[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]97.2065909090909[/C][C]0.082023138578993[/C][C]1185.11181836178[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]97.21[/C][C]0.0803455082556838[/C][C]1209.89962115428[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]97.2155[/C][C]0.0786333181161062[/C][C]1236.31435540411[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]97.2215789473684[/C][C]0.0762412939000934[/C][C]1275.18269921766[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]97.2275[/C][C]0.0732156794292435[/C][C]1327.9600866637[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]97.2285294117647[/C][C]0.0710152156036059[/C][C]1369.12249840199[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]97.2246875[/C][C]0.0694099329007189[/C][C]1400.73161631011[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]97.2163333333333[/C][C]0.0680238013337447[/C][C]1429.15172964771[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]97.2060714285714[/C][C]0.0659211074211299[/C][C]1474.58189389297[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]97.1942307692308[/C][C]0.0627747452328825[/C][C]1548.30147710928[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]97.1795833333333[/C][C]0.0594920502747532[/C][C]1633.48855661432[/C][/ROW]
[ROW][C]Median[/C][C]97.16[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]96.905[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]97.258[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]97.2830769230769[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]97.258[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]97.2830769230769[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]97.2830769230769[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]97.258[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]97.2830769230769[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]97.258[/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=180691&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=180691&T=1

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean97.12277777777780.106690179007461910.325380286275
Geometric Mean97.1186091759488
Harmonic Mean97.1144326727083
Quadratic Mean97.1269382903974
Winsorized Mean ( 1 / 24 )97.12638888888890.105879265393191917.331533499053
Winsorized Mean ( 2 / 24 )97.12638888888890.105879265393191917.331533499053
Winsorized Mean ( 3 / 24 )97.11680555555560.104243272561685931.636192619412
Winsorized Mean ( 4 / 24 )97.11958333333330.103666251055882936.848611232019
Winsorized Mean ( 5 / 24 )97.12027777777780.103524163528904938.141149536183
Winsorized Mean ( 6 / 24 )97.11777777777780.103133651953127941.669144247088
Winsorized Mean ( 7 / 24 )97.12361111111110.101955317462232952.609569845036
Winsorized Mean ( 8 / 24 )97.13916666666670.09373441445826691036.32339550076
Winsorized Mean ( 9 / 24 )97.13916666666670.09373441445826691036.32339550076
Winsorized Mean ( 10 / 24 )97.13916666666670.09373441445826691036.32339550076
Winsorized Mean ( 11 / 24 )97.13458333333330.09307222394101861043.64738716128
Winsorized Mean ( 12 / 24 )97.13791666666670.08984270237362951081.1998537477
Winsorized Mean ( 13 / 24 )97.13791666666670.08984270237362951081.1998537477
Winsorized Mean ( 14 / 24 )97.178750.0830339546051551170.34953305677
Winsorized Mean ( 15 / 24 )97.16416666666670.08034908919574211209.27527168305
Winsorized Mean ( 16 / 24 )97.16416666666670.08034908919574211209.27527168305
Winsorized Mean ( 17 / 24 )97.171250.07922031478508471226.59510080986
Winsorized Mean ( 18 / 24 )97.218750.07196301255545361350.95442155211
Winsorized Mean ( 19 / 24 )97.26097222222220.0660165364717351473.28195964756
Winsorized Mean ( 20 / 24 )97.29430555555560.06169610589926561576.99265030459
Winsorized Mean ( 21 / 24 )97.30013888888890.0609764998267781595.69898510572
Winsorized Mean ( 22 / 24 )97.30013888888890.06014506884003791617.75754464042
Winsorized Mean ( 23 / 24 )97.30652777777780.0550874818997821766.39999546182
Winsorized Mean ( 24 / 24 )97.27986111111110.05115049332845951901.83622446092
Trimmed Mean ( 1 / 24 )97.1290.104692421433407927.755788529374
Trimmed Mean ( 2 / 24 )97.13176470588230.103250282186417940.740912751333
Trimmed Mean ( 3 / 24 )97.1346969696970.101502975646662956.964033328727
Trimmed Mean ( 4 / 24 )97.141406250.100105318346653970.392061624645
Trimmed Mean ( 5 / 24 )97.14774193548390.0985898509881501985.372641928026
Trimmed Mean ( 6 / 24 )97.15433333333330.09675858672728441004.09004119877
Trimmed Mean ( 7 / 24 )97.16189655172410.09459739150167031027.10968039757
Trimmed Mean ( 8 / 24 )97.16892857142860.09223335684570891053.51178678204
Trimmed Mean ( 9 / 24 )97.17388888888890.09129299353471881064.4178170358
Trimmed Mean ( 10 / 24 )97.17923076923080.09004307924654511079.25263754193
Trimmed Mean ( 11 / 24 )97.1850.08840364292059851099.33252510068
Trimmed Mean ( 12 / 24 )97.1918750.08640610872502031124.82643222951
Trimmed Mean ( 13 / 24 )97.19891304347830.08452380293100761149.95906091467
Trimmed Mean ( 14 / 24 )97.20659090909090.0820231385789931185.11181836178
Trimmed Mean ( 15 / 24 )97.210.08034550825568381209.89962115428
Trimmed Mean ( 16 / 24 )97.21550.07863331811610621236.31435540411
Trimmed Mean ( 17 / 24 )97.22157894736840.07624129390009341275.18269921766
Trimmed Mean ( 18 / 24 )97.22750.07321567942924351327.9600866637
Trimmed Mean ( 19 / 24 )97.22852941176470.07101521560360591369.12249840199
Trimmed Mean ( 20 / 24 )97.22468750.06940993290071891400.73161631011
Trimmed Mean ( 21 / 24 )97.21633333333330.06802380133374471429.15172964771
Trimmed Mean ( 22 / 24 )97.20607142857140.06592110742112991474.58189389297
Trimmed Mean ( 23 / 24 )97.19423076923080.06277474523288251548.30147710928
Trimmed Mean ( 24 / 24 )97.17958333333330.05949205027475321633.48855661432
Median97.16
Midrange96.905
Midmean - Weighted Average at Xnp97.258
Midmean - Weighted Average at X(n+1)p97.2830769230769
Midmean - Empirical Distribution Function97.258
Midmean - Empirical Distribution Function - Averaging97.2830769230769
Midmean - Empirical Distribution Function - Interpolation97.2830769230769
Midmean - Closest Observation97.258
Midmean - True Basic - Statistics Graphics Toolkit97.2830769230769
Midmean - MS Excel (old versions)97.258
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')