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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationTue, 16 Dec 2014 23:03:30 +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/2014/Dec/16/t1418771042lyvqldzbkdrakov.htm/, Retrieved Thu, 16 May 2024 20:16:15 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=269970, Retrieved Thu, 16 May 2024 20:16:15 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact59
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Pearson Correlation] [Connected vs Sepa...] [2010-10-04 07:35:56] [b98453cac15ba1066b407e146608df68]
- RM D    [Central Tendency] [] [2014-12-16 23:03:30] [6993448de96b8662e47595bfdf466bf3] [Current]
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Dataseries X:
109
68
131
71
68
89
115
78
118
87
162
49
122
96
100
82
100
115
141
110
146
90
121
104
147
110
108
113
115
61
60
109
111
77
73
89
78
110
65
117
63
52
131
101
42
77
96
57
112
56
86
88
48
85
63
102
162
86
114
94
81
110
104
49
88
102
99
63
76
109
117
57
120
73
91
108
105
119




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Sir Ronald Aylmer Fisher' @ fisher.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 & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=269970&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]'Sir Ronald Aylmer Fisher' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=269970&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=269970&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'Sir Ronald Aylmer Fisher' @ fisher.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean94.88461538461543.0306998830790931.3078229600932
Geometric Mean90.9467411154527
Harmonic Mean86.7890706842974
Quadratic Mean98.5410886577074
Winsorized Mean ( 1 / 26 )94.96153846153853.0141989605626431.5047346588603
Winsorized Mean ( 2 / 26 )94.60256410256412.9082621258414832.5288987061962
Winsorized Mean ( 3 / 26 )94.56410256410262.8993316110336832.6158284910322
Winsorized Mean ( 4 / 26 )94.46153846153852.8114041762889633.5994159993841
Winsorized Mean ( 5 / 26 )94.07692307692312.634574366919335.7085851354921
Winsorized Mean ( 6 / 26 )94.15384615384622.6202722150973435.9328491182542
Winsorized Mean ( 7 / 26 )93.34615384615382.4857118787478537.5530867612766
Winsorized Mean ( 8 / 26 )93.55128205128212.4134465854620238.7625243561681
Winsorized Mean ( 9 / 26 )93.55128205128212.3759007220542939.3750804412376
Winsorized Mean ( 10 / 26 )93.67948717948722.3126066923569940.5081795746297
Winsorized Mean ( 11 / 26 )93.53846153846152.2928091493701240.7964446426596
Winsorized Mean ( 12 / 26 )93.38461538461542.2717649541864741.1066361476013
Winsorized Mean ( 13 / 26 )93.71794871794872.2147371742973542.3156073802219
Winsorized Mean ( 14 / 26 )93.89743589743592.0775499273974345.196235555726
Winsorized Mean ( 15 / 26 )93.89743589743592.0775499273974345.196235555726
Winsorized Mean ( 16 / 26 )94.51282051282051.980233960094447.7281081010826
Winsorized Mean ( 17 / 26 )94.73076923076921.88485322698850.2589633369752
Winsorized Mean ( 18 / 26 )94.51.8545827534723850.9548575403634
Winsorized Mean ( 19 / 26 )94.98717948717951.7154848609862255.3704562758845
Winsorized Mean ( 20 / 26 )94.98717948717951.646143394474757.7028585759935
Winsorized Mean ( 21 / 26 )94.71794871794871.6125648658330958.7374503344491
Winsorized Mean ( 22 / 26 )951.5726390155383660.4080142113723
Winsorized Mean ( 23 / 26 )951.5726390155383660.4080142113723
Winsorized Mean ( 24 / 26 )95.92307692307691.445855886437366.3434563727085
Winsorized Mean ( 25 / 26 )95.92307692307691.3628642673594370.3834411250132
Winsorized Mean ( 26 / 26 )96.92307692307691.2335861038374478.57017570283
Trimmed Mean ( 1 / 26 )94.69736842105262.8977317043630732.6798261821369
Trimmed Mean ( 2 / 26 )94.41891891891892.7598570780001134.2115248182845
Trimmed Mean ( 3 / 26 )94.31944444444442.6654065676603335.3865131079186
Trimmed Mean ( 4 / 26 )94.22857142857142.5575100653561736.8438711952631
Trimmed Mean ( 5 / 26 )94.16176470588232.4622354253359838.2423889027726
Trimmed Mean ( 6 / 26 )94.18181818181822.4047262216081939.16529762745
Trimmed Mean ( 7 / 26 )94.18752.3395829358011840.2582437060501
Trimmed Mean ( 8 / 26 )94.33870967741942.2945390240379341.1144498695002
Trimmed Mean ( 9 / 26 )94.46666666666672.256248907747141.8689030019268
Trimmed Mean ( 10 / 26 )94.60344827586212.2169041562992442.6736753625774
Trimmed Mean ( 11 / 26 )94.73214285714292.1811606393601343.4319880652779
Trimmed Mean ( 12 / 26 )94.88888888888892.1397157322554344.3464930684359
Trimmed Mean ( 13 / 26 )95.07692307692312.0910363451808745.4688046413172
Trimmed Mean ( 14 / 26 )95.242.0413201010870546.6560829677239
Trimmed Mean ( 15 / 26 )95.39583333333332.0056965821257347.562444979703
Trimmed Mean ( 16 / 26 )95.56521739130431.9584209783441448.7970760362799
Trimmed Mean ( 17 / 26 )95.68181818181821.9176416782069949.8955666583557
Trimmed Mean ( 18 / 26 )95.78571428571431.8832150932487450.8628645921025
Trimmed Mean ( 19 / 26 )95.9251.8416086543827552.0876136043959
Trimmed Mean ( 20 / 26 )96.02631578947371.8156451588805152.8882614093392
Trimmed Mean ( 21 / 26 )96.13888888888891.7924678287510753.6349313202876
Trimmed Mean ( 22 / 26 )96.29411764705881.7634279389408854.60621073345
Trimmed Mean ( 23 / 26 )96.43751.7291018902234255.7731736604251
Trimmed Mean ( 24 / 26 )96.61.6751050747622557.6680242066071
Trimmed Mean ( 25 / 26 )96.67857142857141.6338463491614459.172376569064
Trimmed Mean ( 26 / 26 )96.76923076923081.5935520964259960.7254892929226
Median97.5
Midrange102
Midmean - Weighted Average at Xnp95.5128205128205
Midmean - Weighted Average at X(n+1)p95.925
Midmean - Empirical Distribution Function95.925
Midmean - Empirical Distribution Function - Averaging95.925
Midmean - Empirical Distribution Function - Interpolation96.0263157894737
Midmean - Closest Observation95.925
Midmean - True Basic - Statistics Graphics Toolkit95.925
Midmean - MS Excel (old versions)95.925
Number of observations78

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 94.8846153846154 & 3.03069988307909 & 31.3078229600932 \tabularnewline
Geometric Mean & 90.9467411154527 &  &  \tabularnewline
Harmonic Mean & 86.7890706842974 &  &  \tabularnewline
Quadratic Mean & 98.5410886577074 &  &  \tabularnewline
Winsorized Mean ( 1 / 26 ) & 94.9615384615385 & 3.01419896056264 & 31.5047346588603 \tabularnewline
Winsorized Mean ( 2 / 26 ) & 94.6025641025641 & 2.90826212584148 & 32.5288987061962 \tabularnewline
Winsorized Mean ( 3 / 26 ) & 94.5641025641026 & 2.89933161103368 & 32.6158284910322 \tabularnewline
Winsorized Mean ( 4 / 26 ) & 94.4615384615385 & 2.81140417628896 & 33.5994159993841 \tabularnewline
Winsorized Mean ( 5 / 26 ) & 94.0769230769231 & 2.6345743669193 & 35.7085851354921 \tabularnewline
Winsorized Mean ( 6 / 26 ) & 94.1538461538462 & 2.62027221509734 & 35.9328491182542 \tabularnewline
Winsorized Mean ( 7 / 26 ) & 93.3461538461538 & 2.48571187874785 & 37.5530867612766 \tabularnewline
Winsorized Mean ( 8 / 26 ) & 93.5512820512821 & 2.41344658546202 & 38.7625243561681 \tabularnewline
Winsorized Mean ( 9 / 26 ) & 93.5512820512821 & 2.37590072205429 & 39.3750804412376 \tabularnewline
Winsorized Mean ( 10 / 26 ) & 93.6794871794872 & 2.31260669235699 & 40.5081795746297 \tabularnewline
Winsorized Mean ( 11 / 26 ) & 93.5384615384615 & 2.29280914937012 & 40.7964446426596 \tabularnewline
Winsorized Mean ( 12 / 26 ) & 93.3846153846154 & 2.27176495418647 & 41.1066361476013 \tabularnewline
Winsorized Mean ( 13 / 26 ) & 93.7179487179487 & 2.21473717429735 & 42.3156073802219 \tabularnewline
Winsorized Mean ( 14 / 26 ) & 93.8974358974359 & 2.07754992739743 & 45.196235555726 \tabularnewline
Winsorized Mean ( 15 / 26 ) & 93.8974358974359 & 2.07754992739743 & 45.196235555726 \tabularnewline
Winsorized Mean ( 16 / 26 ) & 94.5128205128205 & 1.9802339600944 & 47.7281081010826 \tabularnewline
Winsorized Mean ( 17 / 26 ) & 94.7307692307692 & 1.884853226988 & 50.2589633369752 \tabularnewline
Winsorized Mean ( 18 / 26 ) & 94.5 & 1.85458275347238 & 50.9548575403634 \tabularnewline
Winsorized Mean ( 19 / 26 ) & 94.9871794871795 & 1.71548486098622 & 55.3704562758845 \tabularnewline
Winsorized Mean ( 20 / 26 ) & 94.9871794871795 & 1.6461433944747 & 57.7028585759935 \tabularnewline
Winsorized Mean ( 21 / 26 ) & 94.7179487179487 & 1.61256486583309 & 58.7374503344491 \tabularnewline
Winsorized Mean ( 22 / 26 ) & 95 & 1.57263901553836 & 60.4080142113723 \tabularnewline
Winsorized Mean ( 23 / 26 ) & 95 & 1.57263901553836 & 60.4080142113723 \tabularnewline
Winsorized Mean ( 24 / 26 ) & 95.9230769230769 & 1.4458558864373 & 66.3434563727085 \tabularnewline
Winsorized Mean ( 25 / 26 ) & 95.9230769230769 & 1.36286426735943 & 70.3834411250132 \tabularnewline
Winsorized Mean ( 26 / 26 ) & 96.9230769230769 & 1.23358610383744 & 78.57017570283 \tabularnewline
Trimmed Mean ( 1 / 26 ) & 94.6973684210526 & 2.89773170436307 & 32.6798261821369 \tabularnewline
Trimmed Mean ( 2 / 26 ) & 94.4189189189189 & 2.75985707800011 & 34.2115248182845 \tabularnewline
Trimmed Mean ( 3 / 26 ) & 94.3194444444444 & 2.66540656766033 & 35.3865131079186 \tabularnewline
Trimmed Mean ( 4 / 26 ) & 94.2285714285714 & 2.55751006535617 & 36.8438711952631 \tabularnewline
Trimmed Mean ( 5 / 26 ) & 94.1617647058823 & 2.46223542533598 & 38.2423889027726 \tabularnewline
Trimmed Mean ( 6 / 26 ) & 94.1818181818182 & 2.40472622160819 & 39.16529762745 \tabularnewline
Trimmed Mean ( 7 / 26 ) & 94.1875 & 2.33958293580118 & 40.2582437060501 \tabularnewline
Trimmed Mean ( 8 / 26 ) & 94.3387096774194 & 2.29453902403793 & 41.1144498695002 \tabularnewline
Trimmed Mean ( 9 / 26 ) & 94.4666666666667 & 2.2562489077471 & 41.8689030019268 \tabularnewline
Trimmed Mean ( 10 / 26 ) & 94.6034482758621 & 2.21690415629924 & 42.6736753625774 \tabularnewline
Trimmed Mean ( 11 / 26 ) & 94.7321428571429 & 2.18116063936013 & 43.4319880652779 \tabularnewline
Trimmed Mean ( 12 / 26 ) & 94.8888888888889 & 2.13971573225543 & 44.3464930684359 \tabularnewline
Trimmed Mean ( 13 / 26 ) & 95.0769230769231 & 2.09103634518087 & 45.4688046413172 \tabularnewline
Trimmed Mean ( 14 / 26 ) & 95.24 & 2.04132010108705 & 46.6560829677239 \tabularnewline
Trimmed Mean ( 15 / 26 ) & 95.3958333333333 & 2.00569658212573 & 47.562444979703 \tabularnewline
Trimmed Mean ( 16 / 26 ) & 95.5652173913043 & 1.95842097834414 & 48.7970760362799 \tabularnewline
Trimmed Mean ( 17 / 26 ) & 95.6818181818182 & 1.91764167820699 & 49.8955666583557 \tabularnewline
Trimmed Mean ( 18 / 26 ) & 95.7857142857143 & 1.88321509324874 & 50.8628645921025 \tabularnewline
Trimmed Mean ( 19 / 26 ) & 95.925 & 1.84160865438275 & 52.0876136043959 \tabularnewline
Trimmed Mean ( 20 / 26 ) & 96.0263157894737 & 1.81564515888051 & 52.8882614093392 \tabularnewline
Trimmed Mean ( 21 / 26 ) & 96.1388888888889 & 1.79246782875107 & 53.6349313202876 \tabularnewline
Trimmed Mean ( 22 / 26 ) & 96.2941176470588 & 1.76342793894088 & 54.60621073345 \tabularnewline
Trimmed Mean ( 23 / 26 ) & 96.4375 & 1.72910189022342 & 55.7731736604251 \tabularnewline
Trimmed Mean ( 24 / 26 ) & 96.6 & 1.67510507476225 & 57.6680242066071 \tabularnewline
Trimmed Mean ( 25 / 26 ) & 96.6785714285714 & 1.63384634916144 & 59.172376569064 \tabularnewline
Trimmed Mean ( 26 / 26 ) & 96.7692307692308 & 1.59355209642599 & 60.7254892929226 \tabularnewline
Median & 97.5 &  &  \tabularnewline
Midrange & 102 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 95.5128205128205 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 95.925 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 95.925 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 95.925 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 96.0263157894737 &  &  \tabularnewline
Midmean - Closest Observation & 95.925 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 95.925 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 95.925 &  &  \tabularnewline
Number of observations & 78 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=269970&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]94.8846153846154[/C][C]3.03069988307909[/C][C]31.3078229600932[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]90.9467411154527[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]86.7890706842974[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]98.5410886577074[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 26 )[/C][C]94.9615384615385[/C][C]3.01419896056264[/C][C]31.5047346588603[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 26 )[/C][C]94.6025641025641[/C][C]2.90826212584148[/C][C]32.5288987061962[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 26 )[/C][C]94.5641025641026[/C][C]2.89933161103368[/C][C]32.6158284910322[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 26 )[/C][C]94.4615384615385[/C][C]2.81140417628896[/C][C]33.5994159993841[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 26 )[/C][C]94.0769230769231[/C][C]2.6345743669193[/C][C]35.7085851354921[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 26 )[/C][C]94.1538461538462[/C][C]2.62027221509734[/C][C]35.9328491182542[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 26 )[/C][C]93.3461538461538[/C][C]2.48571187874785[/C][C]37.5530867612766[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 26 )[/C][C]93.5512820512821[/C][C]2.41344658546202[/C][C]38.7625243561681[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 26 )[/C][C]93.5512820512821[/C][C]2.37590072205429[/C][C]39.3750804412376[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 26 )[/C][C]93.6794871794872[/C][C]2.31260669235699[/C][C]40.5081795746297[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 26 )[/C][C]93.5384615384615[/C][C]2.29280914937012[/C][C]40.7964446426596[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 26 )[/C][C]93.3846153846154[/C][C]2.27176495418647[/C][C]41.1066361476013[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 26 )[/C][C]93.7179487179487[/C][C]2.21473717429735[/C][C]42.3156073802219[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 26 )[/C][C]93.8974358974359[/C][C]2.07754992739743[/C][C]45.196235555726[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 26 )[/C][C]93.8974358974359[/C][C]2.07754992739743[/C][C]45.196235555726[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 26 )[/C][C]94.5128205128205[/C][C]1.9802339600944[/C][C]47.7281081010826[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 26 )[/C][C]94.7307692307692[/C][C]1.884853226988[/C][C]50.2589633369752[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 26 )[/C][C]94.5[/C][C]1.85458275347238[/C][C]50.9548575403634[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 26 )[/C][C]94.9871794871795[/C][C]1.71548486098622[/C][C]55.3704562758845[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 26 )[/C][C]94.9871794871795[/C][C]1.6461433944747[/C][C]57.7028585759935[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 26 )[/C][C]94.7179487179487[/C][C]1.61256486583309[/C][C]58.7374503344491[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 26 )[/C][C]95[/C][C]1.57263901553836[/C][C]60.4080142113723[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 26 )[/C][C]95[/C][C]1.57263901553836[/C][C]60.4080142113723[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 26 )[/C][C]95.9230769230769[/C][C]1.4458558864373[/C][C]66.3434563727085[/C][/ROW]
[ROW][C]Winsorized Mean ( 25 / 26 )[/C][C]95.9230769230769[/C][C]1.36286426735943[/C][C]70.3834411250132[/C][/ROW]
[ROW][C]Winsorized Mean ( 26 / 26 )[/C][C]96.9230769230769[/C][C]1.23358610383744[/C][C]78.57017570283[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 26 )[/C][C]94.6973684210526[/C][C]2.89773170436307[/C][C]32.6798261821369[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 26 )[/C][C]94.4189189189189[/C][C]2.75985707800011[/C][C]34.2115248182845[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 26 )[/C][C]94.3194444444444[/C][C]2.66540656766033[/C][C]35.3865131079186[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 26 )[/C][C]94.2285714285714[/C][C]2.55751006535617[/C][C]36.8438711952631[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 26 )[/C][C]94.1617647058823[/C][C]2.46223542533598[/C][C]38.2423889027726[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 26 )[/C][C]94.1818181818182[/C][C]2.40472622160819[/C][C]39.16529762745[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 26 )[/C][C]94.1875[/C][C]2.33958293580118[/C][C]40.2582437060501[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 26 )[/C][C]94.3387096774194[/C][C]2.29453902403793[/C][C]41.1144498695002[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 26 )[/C][C]94.4666666666667[/C][C]2.2562489077471[/C][C]41.8689030019268[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 26 )[/C][C]94.6034482758621[/C][C]2.21690415629924[/C][C]42.6736753625774[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 26 )[/C][C]94.7321428571429[/C][C]2.18116063936013[/C][C]43.4319880652779[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 26 )[/C][C]94.8888888888889[/C][C]2.13971573225543[/C][C]44.3464930684359[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 26 )[/C][C]95.0769230769231[/C][C]2.09103634518087[/C][C]45.4688046413172[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 26 )[/C][C]95.24[/C][C]2.04132010108705[/C][C]46.6560829677239[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 26 )[/C][C]95.3958333333333[/C][C]2.00569658212573[/C][C]47.562444979703[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 26 )[/C][C]95.5652173913043[/C][C]1.95842097834414[/C][C]48.7970760362799[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 26 )[/C][C]95.6818181818182[/C][C]1.91764167820699[/C][C]49.8955666583557[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 26 )[/C][C]95.7857142857143[/C][C]1.88321509324874[/C][C]50.8628645921025[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 26 )[/C][C]95.925[/C][C]1.84160865438275[/C][C]52.0876136043959[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 26 )[/C][C]96.0263157894737[/C][C]1.81564515888051[/C][C]52.8882614093392[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 26 )[/C][C]96.1388888888889[/C][C]1.79246782875107[/C][C]53.6349313202876[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 26 )[/C][C]96.2941176470588[/C][C]1.76342793894088[/C][C]54.60621073345[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 26 )[/C][C]96.4375[/C][C]1.72910189022342[/C][C]55.7731736604251[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 26 )[/C][C]96.6[/C][C]1.67510507476225[/C][C]57.6680242066071[/C][/ROW]
[ROW][C]Trimmed Mean ( 25 / 26 )[/C][C]96.6785714285714[/C][C]1.63384634916144[/C][C]59.172376569064[/C][/ROW]
[ROW][C]Trimmed Mean ( 26 / 26 )[/C][C]96.7692307692308[/C][C]1.59355209642599[/C][C]60.7254892929226[/C][/ROW]
[ROW][C]Median[/C][C]97.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]102[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]95.5128205128205[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]95.925[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]95.925[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]95.925[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]96.0263157894737[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]95.925[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]95.925[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]95.925[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]78[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=269970&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=269970&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 Mean94.88461538461543.0306998830790931.3078229600932
Geometric Mean90.9467411154527
Harmonic Mean86.7890706842974
Quadratic Mean98.5410886577074
Winsorized Mean ( 1 / 26 )94.96153846153853.0141989605626431.5047346588603
Winsorized Mean ( 2 / 26 )94.60256410256412.9082621258414832.5288987061962
Winsorized Mean ( 3 / 26 )94.56410256410262.8993316110336832.6158284910322
Winsorized Mean ( 4 / 26 )94.46153846153852.8114041762889633.5994159993841
Winsorized Mean ( 5 / 26 )94.07692307692312.634574366919335.7085851354921
Winsorized Mean ( 6 / 26 )94.15384615384622.6202722150973435.9328491182542
Winsorized Mean ( 7 / 26 )93.34615384615382.4857118787478537.5530867612766
Winsorized Mean ( 8 / 26 )93.55128205128212.4134465854620238.7625243561681
Winsorized Mean ( 9 / 26 )93.55128205128212.3759007220542939.3750804412376
Winsorized Mean ( 10 / 26 )93.67948717948722.3126066923569940.5081795746297
Winsorized Mean ( 11 / 26 )93.53846153846152.2928091493701240.7964446426596
Winsorized Mean ( 12 / 26 )93.38461538461542.2717649541864741.1066361476013
Winsorized Mean ( 13 / 26 )93.71794871794872.2147371742973542.3156073802219
Winsorized Mean ( 14 / 26 )93.89743589743592.0775499273974345.196235555726
Winsorized Mean ( 15 / 26 )93.89743589743592.0775499273974345.196235555726
Winsorized Mean ( 16 / 26 )94.51282051282051.980233960094447.7281081010826
Winsorized Mean ( 17 / 26 )94.73076923076921.88485322698850.2589633369752
Winsorized Mean ( 18 / 26 )94.51.8545827534723850.9548575403634
Winsorized Mean ( 19 / 26 )94.98717948717951.7154848609862255.3704562758845
Winsorized Mean ( 20 / 26 )94.98717948717951.646143394474757.7028585759935
Winsorized Mean ( 21 / 26 )94.71794871794871.6125648658330958.7374503344491
Winsorized Mean ( 22 / 26 )951.5726390155383660.4080142113723
Winsorized Mean ( 23 / 26 )951.5726390155383660.4080142113723
Winsorized Mean ( 24 / 26 )95.92307692307691.445855886437366.3434563727085
Winsorized Mean ( 25 / 26 )95.92307692307691.3628642673594370.3834411250132
Winsorized Mean ( 26 / 26 )96.92307692307691.2335861038374478.57017570283
Trimmed Mean ( 1 / 26 )94.69736842105262.8977317043630732.6798261821369
Trimmed Mean ( 2 / 26 )94.41891891891892.7598570780001134.2115248182845
Trimmed Mean ( 3 / 26 )94.31944444444442.6654065676603335.3865131079186
Trimmed Mean ( 4 / 26 )94.22857142857142.5575100653561736.8438711952631
Trimmed Mean ( 5 / 26 )94.16176470588232.4622354253359838.2423889027726
Trimmed Mean ( 6 / 26 )94.18181818181822.4047262216081939.16529762745
Trimmed Mean ( 7 / 26 )94.18752.3395829358011840.2582437060501
Trimmed Mean ( 8 / 26 )94.33870967741942.2945390240379341.1144498695002
Trimmed Mean ( 9 / 26 )94.46666666666672.256248907747141.8689030019268
Trimmed Mean ( 10 / 26 )94.60344827586212.2169041562992442.6736753625774
Trimmed Mean ( 11 / 26 )94.73214285714292.1811606393601343.4319880652779
Trimmed Mean ( 12 / 26 )94.88888888888892.1397157322554344.3464930684359
Trimmed Mean ( 13 / 26 )95.07692307692312.0910363451808745.4688046413172
Trimmed Mean ( 14 / 26 )95.242.0413201010870546.6560829677239
Trimmed Mean ( 15 / 26 )95.39583333333332.0056965821257347.562444979703
Trimmed Mean ( 16 / 26 )95.56521739130431.9584209783441448.7970760362799
Trimmed Mean ( 17 / 26 )95.68181818181821.9176416782069949.8955666583557
Trimmed Mean ( 18 / 26 )95.78571428571431.8832150932487450.8628645921025
Trimmed Mean ( 19 / 26 )95.9251.8416086543827552.0876136043959
Trimmed Mean ( 20 / 26 )96.02631578947371.8156451588805152.8882614093392
Trimmed Mean ( 21 / 26 )96.13888888888891.7924678287510753.6349313202876
Trimmed Mean ( 22 / 26 )96.29411764705881.7634279389408854.60621073345
Trimmed Mean ( 23 / 26 )96.43751.7291018902234255.7731736604251
Trimmed Mean ( 24 / 26 )96.61.6751050747622557.6680242066071
Trimmed Mean ( 25 / 26 )96.67857142857141.6338463491614459.172376569064
Trimmed Mean ( 26 / 26 )96.76923076923081.5935520964259960.7254892929226
Median97.5
Midrange102
Midmean - Weighted Average at Xnp95.5128205128205
Midmean - Weighted Average at X(n+1)p95.925
Midmean - Empirical Distribution Function95.925
Midmean - Empirical Distribution Function - Averaging95.925
Midmean - Empirical Distribution Function - Interpolation96.0263157894737
Midmean - Closest Observation95.925
Midmean - True Basic - Statistics Graphics Toolkit95.925
Midmean - MS Excel (old versions)95.925
Number of observations78



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')