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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationTue, 08 Mar 2016 19:36:45 +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/2016/Mar/08/t1457465844qcx0tj47i39h5lw.htm/, Retrieved Mon, 29 Apr 2024 07:46:35 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=293735, Retrieved Mon, 29 Apr 2024 07:46:35 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact87
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Data Series] [] [2016-02-22 13:43:50] [8fa711874ea7227c6cf9e3601ab440d2]
- RMPD    [Central Tendency] [] [2016-03-08 19:36:45] [1bc968f9226c7cafc5c8ae51fcf2ca2f] [Current]
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Dataseries X:
105.95
108.55
110.81
111.54
110.38
106.67
106.45
105.44
105.37
103.72
106.57
108.54
110.36
106.64
103.45
101.36
101.9
100.86
100.37
100.16
99.5
99.52
99.2
99.35
99.37
99.85
99.76
100.07
99.77
99.93
99.16
99.4
99.81
99.67
99.37
99.49
99.28
99.33
99.19
98.11
99.12
99.06
97.41
98.45
100.33
103.18
103.06
103.48
102.8
103.92
103.9
103.96
103.62
103.83
104.09
104.07
103.22
104.01
104.01
104.24
102.93
104.73
106.48
119.5
122.45
125.29
126.56
126.38
127.95
128.23
128.7
127.86




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=293735&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=293735&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=293735&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 Mean105.570.996868375022751105.901644234216
Geometric Mean105.262342819023
Harmonic Mean104.979304311983
Quadratic Mean105.903639718168
Winsorized Mean ( 1 / 24 )105.5731944444440.993678805018302106.244788468141
Winsorized Mean ( 2 / 24 )105.5748611111110.99021410942983106.618215298812
Winsorized Mean ( 3 / 24 )105.5965277777780.986547408248345107.036445380024
Winsorized Mean ( 4 / 24 )105.5276388888890.963652912800053109.507933289239
Winsorized Mean ( 5 / 24 )105.5179166666670.959558085263484109.965116533506
Winsorized Mean ( 6 / 24 )105.4295833333330.931777930095633113.148830776141
Winsorized Mean ( 7 / 24 )105.1544444444440.850616063426221123.621512649185
Winsorized Mean ( 8 / 24 )104.8355555555560.757997704422369138.305901118059
Winsorized Mean ( 9 / 24 )103.8468055555560.510247026092753203.522608158579
Winsorized Mean ( 10 / 24 )103.7481944444440.488807646976717212.247486482932
Winsorized Mean ( 11 / 24 )103.6855555555560.475215332498173218.186469301165
Winsorized Mean ( 12 / 24 )103.6822222222220.474554326058831218.483356970533
Winsorized Mean ( 13 / 24 )103.3608333333330.412247919372074250.724936321741
Winsorized Mean ( 14 / 24 )103.3763888888890.409549320298862252.414993177016
Winsorized Mean ( 15 / 24 )102.9888888888890.344938335395152298.571884655579
Winsorized Mean ( 16 / 24 )102.9866666666670.343305071994231299.985858258445
Winsorized Mean ( 17 / 24 )103.0055555555560.335834855883085306.714903921155
Winsorized Mean ( 18 / 24 )103.0055555555560.32934609948034312.757781914172
Winsorized Mean ( 19 / 24 )103.0002777777780.32780497586159314.212063154489
Winsorized Mean ( 20 / 24 )102.87250.306109270306801336.064634360452
Winsorized Mean ( 21 / 24 )102.7354166666670.283921919542528361.843907057969
Winsorized Mean ( 22 / 24 )102.7384722222220.27756765869505370.13848337099
Winsorized Mean ( 23 / 24 )102.578750.24479079387518419.046600471035
Winsorized Mean ( 24 / 24 )102.4454166666670.220951486462774463.655702465376
Trimmed Mean ( 1 / 24 )105.3561428571430.962575958506499109.45228989576
Trimmed Mean ( 2 / 24 )105.1263235294120.924728204484477113.683483449083
Trimmed Mean ( 3 / 24 )104.8816666666670.880571561135876119.106352391595
Trimmed Mean ( 4 / 24 )104.613593750.827359251900726126.442767769463
Trimmed Mean ( 5 / 24 )104.3482258064520.770250617637599135.473082938243
Trimmed Mean ( 6 / 24 )104.06750.698416798202405149.004863954948
Trimmed Mean ( 7 / 24 )103.7856896551720.614399657901188168.922114979211
Trimmed Mean ( 8 / 24 )103.5342857142860.533016218725904194.242280210101
Trimmed Mean ( 9 / 24 )103.3174074074070.457679421858287225.741867501742
Trimmed Mean ( 10 / 24 )103.2359615384620.440951020391457234.121153516808
Trimmed Mean ( 11 / 24 )103.16220.425181957687361242.630709358217
Trimmed Mean ( 12 / 24 )103.0908333333330.408350538789348252.456709470668
Trimmed Mean ( 13 / 24 )103.0136956521740.386505008522667266.526159766783
Trimmed Mean ( 14 / 24 )102.970.374558090572785274.910628262055
Trimmed Mean ( 15 / 24 )102.9202380952380.359212987992874286.515915447021
Trimmed Mean ( 16 / 24 )102.9120.354851937342742290.013916143848
Trimmed Mean ( 17 / 24 )102.9031578947370.348771896433125295.044293841112
Trimmed Mean ( 18 / 24 )102.8911111111110.341709237249843301.107198445097
Trimmed Mean ( 19 / 24 )102.8776470588240.333022152117522308.921332724192
Trimmed Mean ( 20 / 24 )102.8631250.32067231462497320.773326254559
Trimmed Mean ( 21 / 24 )102.8620.309165878178503332.708126155534
Trimmed Mean ( 22 / 24 )102.87750.298658209648548344.465669037068
Trimmed Mean ( 23 / 24 )102.8950.284265450158556361.968012442623
Trimmed Mean ( 24 / 24 )102.936250.272985913330361377.075317712196
Median103.465
Midrange113.055
Midmean - Weighted Average at Xnp102.804054054054
Midmean - Weighted Average at X(n+1)p102.891111111111
Midmean - Empirical Distribution Function102.804054054054
Midmean - Empirical Distribution Function - Averaging102.891111111111
Midmean - Empirical Distribution Function - Interpolation102.891111111111
Midmean - Closest Observation102.804054054054
Midmean - True Basic - Statistics Graphics Toolkit102.891111111111
Midmean - MS Excel (old versions)102.903157894737
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 105.57 & 0.996868375022751 & 105.901644234216 \tabularnewline
Geometric Mean & 105.262342819023 &  &  \tabularnewline
Harmonic Mean & 104.979304311983 &  &  \tabularnewline
Quadratic Mean & 105.903639718168 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 105.573194444444 & 0.993678805018302 & 106.244788468141 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 105.574861111111 & 0.99021410942983 & 106.618215298812 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 105.596527777778 & 0.986547408248345 & 107.036445380024 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 105.527638888889 & 0.963652912800053 & 109.507933289239 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 105.517916666667 & 0.959558085263484 & 109.965116533506 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 105.429583333333 & 0.931777930095633 & 113.148830776141 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 105.154444444444 & 0.850616063426221 & 123.621512649185 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 104.835555555556 & 0.757997704422369 & 138.305901118059 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 103.846805555556 & 0.510247026092753 & 203.522608158579 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 103.748194444444 & 0.488807646976717 & 212.247486482932 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 103.685555555556 & 0.475215332498173 & 218.186469301165 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 103.682222222222 & 0.474554326058831 & 218.483356970533 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 103.360833333333 & 0.412247919372074 & 250.724936321741 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 103.376388888889 & 0.409549320298862 & 252.414993177016 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 102.988888888889 & 0.344938335395152 & 298.571884655579 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 102.986666666667 & 0.343305071994231 & 299.985858258445 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 103.005555555556 & 0.335834855883085 & 306.714903921155 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 103.005555555556 & 0.32934609948034 & 312.757781914172 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 103.000277777778 & 0.32780497586159 & 314.212063154489 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 102.8725 & 0.306109270306801 & 336.064634360452 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 102.735416666667 & 0.283921919542528 & 361.843907057969 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 102.738472222222 & 0.27756765869505 & 370.13848337099 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 102.57875 & 0.24479079387518 & 419.046600471035 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 102.445416666667 & 0.220951486462774 & 463.655702465376 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 105.356142857143 & 0.962575958506499 & 109.45228989576 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 105.126323529412 & 0.924728204484477 & 113.683483449083 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 104.881666666667 & 0.880571561135876 & 119.106352391595 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 104.61359375 & 0.827359251900726 & 126.442767769463 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 104.348225806452 & 0.770250617637599 & 135.473082938243 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 104.0675 & 0.698416798202405 & 149.004863954948 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 103.785689655172 & 0.614399657901188 & 168.922114979211 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 103.534285714286 & 0.533016218725904 & 194.242280210101 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 103.317407407407 & 0.457679421858287 & 225.741867501742 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 103.235961538462 & 0.440951020391457 & 234.121153516808 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 103.1622 & 0.425181957687361 & 242.630709358217 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 103.090833333333 & 0.408350538789348 & 252.456709470668 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 103.013695652174 & 0.386505008522667 & 266.526159766783 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 102.97 & 0.374558090572785 & 274.910628262055 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 102.920238095238 & 0.359212987992874 & 286.515915447021 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 102.912 & 0.354851937342742 & 290.013916143848 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 102.903157894737 & 0.348771896433125 & 295.044293841112 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 102.891111111111 & 0.341709237249843 & 301.107198445097 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 102.877647058824 & 0.333022152117522 & 308.921332724192 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 102.863125 & 0.32067231462497 & 320.773326254559 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 102.862 & 0.309165878178503 & 332.708126155534 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 102.8775 & 0.298658209648548 & 344.465669037068 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 102.895 & 0.284265450158556 & 361.968012442623 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 102.93625 & 0.272985913330361 & 377.075317712196 \tabularnewline
Median & 103.465 &  &  \tabularnewline
Midrange & 113.055 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 102.804054054054 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 102.891111111111 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 102.804054054054 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 102.891111111111 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 102.891111111111 &  &  \tabularnewline
Midmean - Closest Observation & 102.804054054054 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 102.891111111111 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 102.903157894737 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=293735&T=1

[TABLE]
[ROW][C]Central Tendency - Ungrouped Data[/C][/ROW]
[ROW][C]Measure[/C][C]Value[/C][C]S.E.[/C][C]Value/S.E.[/C][/ROW]
[ROW][C]Arithmetic Mean[/C][C]105.57[/C][C]0.996868375022751[/C][C]105.901644234216[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]105.262342819023[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]104.979304311983[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]105.903639718168[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]105.573194444444[/C][C]0.993678805018302[/C][C]106.244788468141[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]105.574861111111[/C][C]0.99021410942983[/C][C]106.618215298812[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]105.596527777778[/C][C]0.986547408248345[/C][C]107.036445380024[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]105.527638888889[/C][C]0.963652912800053[/C][C]109.507933289239[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]105.517916666667[/C][C]0.959558085263484[/C][C]109.965116533506[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]105.429583333333[/C][C]0.931777930095633[/C][C]113.148830776141[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]105.154444444444[/C][C]0.850616063426221[/C][C]123.621512649185[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]104.835555555556[/C][C]0.757997704422369[/C][C]138.305901118059[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]103.846805555556[/C][C]0.510247026092753[/C][C]203.522608158579[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]103.748194444444[/C][C]0.488807646976717[/C][C]212.247486482932[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]103.685555555556[/C][C]0.475215332498173[/C][C]218.186469301165[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]103.682222222222[/C][C]0.474554326058831[/C][C]218.483356970533[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]103.360833333333[/C][C]0.412247919372074[/C][C]250.724936321741[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]103.376388888889[/C][C]0.409549320298862[/C][C]252.414993177016[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]102.988888888889[/C][C]0.344938335395152[/C][C]298.571884655579[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]102.986666666667[/C][C]0.343305071994231[/C][C]299.985858258445[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]103.005555555556[/C][C]0.335834855883085[/C][C]306.714903921155[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]103.005555555556[/C][C]0.32934609948034[/C][C]312.757781914172[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]103.000277777778[/C][C]0.32780497586159[/C][C]314.212063154489[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]102.8725[/C][C]0.306109270306801[/C][C]336.064634360452[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]102.735416666667[/C][C]0.283921919542528[/C][C]361.843907057969[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]102.738472222222[/C][C]0.27756765869505[/C][C]370.13848337099[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]102.57875[/C][C]0.24479079387518[/C][C]419.046600471035[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]102.445416666667[/C][C]0.220951486462774[/C][C]463.655702465376[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]105.356142857143[/C][C]0.962575958506499[/C][C]109.45228989576[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]105.126323529412[/C][C]0.924728204484477[/C][C]113.683483449083[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]104.881666666667[/C][C]0.880571561135876[/C][C]119.106352391595[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]104.61359375[/C][C]0.827359251900726[/C][C]126.442767769463[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]104.348225806452[/C][C]0.770250617637599[/C][C]135.473082938243[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]104.0675[/C][C]0.698416798202405[/C][C]149.004863954948[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]103.785689655172[/C][C]0.614399657901188[/C][C]168.922114979211[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]103.534285714286[/C][C]0.533016218725904[/C][C]194.242280210101[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]103.317407407407[/C][C]0.457679421858287[/C][C]225.741867501742[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]103.235961538462[/C][C]0.440951020391457[/C][C]234.121153516808[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]103.1622[/C][C]0.425181957687361[/C][C]242.630709358217[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]103.090833333333[/C][C]0.408350538789348[/C][C]252.456709470668[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]103.013695652174[/C][C]0.386505008522667[/C][C]266.526159766783[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]102.97[/C][C]0.374558090572785[/C][C]274.910628262055[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]102.920238095238[/C][C]0.359212987992874[/C][C]286.515915447021[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]102.912[/C][C]0.354851937342742[/C][C]290.013916143848[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]102.903157894737[/C][C]0.348771896433125[/C][C]295.044293841112[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]102.891111111111[/C][C]0.341709237249843[/C][C]301.107198445097[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]102.877647058824[/C][C]0.333022152117522[/C][C]308.921332724192[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]102.863125[/C][C]0.32067231462497[/C][C]320.773326254559[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]102.862[/C][C]0.309165878178503[/C][C]332.708126155534[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]102.8775[/C][C]0.298658209648548[/C][C]344.465669037068[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]102.895[/C][C]0.284265450158556[/C][C]361.968012442623[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]102.93625[/C][C]0.272985913330361[/C][C]377.075317712196[/C][/ROW]
[ROW][C]Median[/C][C]103.465[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]113.055[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]102.804054054054[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]102.891111111111[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]102.804054054054[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]102.891111111111[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]102.891111111111[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]102.804054054054[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]102.891111111111[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]102.903157894737[/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=293735&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=293735&T=1

As an alternative you can also use a QR Code:  

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

Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean105.570.996868375022751105.901644234216
Geometric Mean105.262342819023
Harmonic Mean104.979304311983
Quadratic Mean105.903639718168
Winsorized Mean ( 1 / 24 )105.5731944444440.993678805018302106.244788468141
Winsorized Mean ( 2 / 24 )105.5748611111110.99021410942983106.618215298812
Winsorized Mean ( 3 / 24 )105.5965277777780.986547408248345107.036445380024
Winsorized Mean ( 4 / 24 )105.5276388888890.963652912800053109.507933289239
Winsorized Mean ( 5 / 24 )105.5179166666670.959558085263484109.965116533506
Winsorized Mean ( 6 / 24 )105.4295833333330.931777930095633113.148830776141
Winsorized Mean ( 7 / 24 )105.1544444444440.850616063426221123.621512649185
Winsorized Mean ( 8 / 24 )104.8355555555560.757997704422369138.305901118059
Winsorized Mean ( 9 / 24 )103.8468055555560.510247026092753203.522608158579
Winsorized Mean ( 10 / 24 )103.7481944444440.488807646976717212.247486482932
Winsorized Mean ( 11 / 24 )103.6855555555560.475215332498173218.186469301165
Winsorized Mean ( 12 / 24 )103.6822222222220.474554326058831218.483356970533
Winsorized Mean ( 13 / 24 )103.3608333333330.412247919372074250.724936321741
Winsorized Mean ( 14 / 24 )103.3763888888890.409549320298862252.414993177016
Winsorized Mean ( 15 / 24 )102.9888888888890.344938335395152298.571884655579
Winsorized Mean ( 16 / 24 )102.9866666666670.343305071994231299.985858258445
Winsorized Mean ( 17 / 24 )103.0055555555560.335834855883085306.714903921155
Winsorized Mean ( 18 / 24 )103.0055555555560.32934609948034312.757781914172
Winsorized Mean ( 19 / 24 )103.0002777777780.32780497586159314.212063154489
Winsorized Mean ( 20 / 24 )102.87250.306109270306801336.064634360452
Winsorized Mean ( 21 / 24 )102.7354166666670.283921919542528361.843907057969
Winsorized Mean ( 22 / 24 )102.7384722222220.27756765869505370.13848337099
Winsorized Mean ( 23 / 24 )102.578750.24479079387518419.046600471035
Winsorized Mean ( 24 / 24 )102.4454166666670.220951486462774463.655702465376
Trimmed Mean ( 1 / 24 )105.3561428571430.962575958506499109.45228989576
Trimmed Mean ( 2 / 24 )105.1263235294120.924728204484477113.683483449083
Trimmed Mean ( 3 / 24 )104.8816666666670.880571561135876119.106352391595
Trimmed Mean ( 4 / 24 )104.613593750.827359251900726126.442767769463
Trimmed Mean ( 5 / 24 )104.3482258064520.770250617637599135.473082938243
Trimmed Mean ( 6 / 24 )104.06750.698416798202405149.004863954948
Trimmed Mean ( 7 / 24 )103.7856896551720.614399657901188168.922114979211
Trimmed Mean ( 8 / 24 )103.5342857142860.533016218725904194.242280210101
Trimmed Mean ( 9 / 24 )103.3174074074070.457679421858287225.741867501742
Trimmed Mean ( 10 / 24 )103.2359615384620.440951020391457234.121153516808
Trimmed Mean ( 11 / 24 )103.16220.425181957687361242.630709358217
Trimmed Mean ( 12 / 24 )103.0908333333330.408350538789348252.456709470668
Trimmed Mean ( 13 / 24 )103.0136956521740.386505008522667266.526159766783
Trimmed Mean ( 14 / 24 )102.970.374558090572785274.910628262055
Trimmed Mean ( 15 / 24 )102.9202380952380.359212987992874286.515915447021
Trimmed Mean ( 16 / 24 )102.9120.354851937342742290.013916143848
Trimmed Mean ( 17 / 24 )102.9031578947370.348771896433125295.044293841112
Trimmed Mean ( 18 / 24 )102.8911111111110.341709237249843301.107198445097
Trimmed Mean ( 19 / 24 )102.8776470588240.333022152117522308.921332724192
Trimmed Mean ( 20 / 24 )102.8631250.32067231462497320.773326254559
Trimmed Mean ( 21 / 24 )102.8620.309165878178503332.708126155534
Trimmed Mean ( 22 / 24 )102.87750.298658209648548344.465669037068
Trimmed Mean ( 23 / 24 )102.8950.284265450158556361.968012442623
Trimmed Mean ( 24 / 24 )102.936250.272985913330361377.075317712196
Median103.465
Midrange113.055
Midmean - Weighted Average at Xnp102.804054054054
Midmean - Weighted Average at X(n+1)p102.891111111111
Midmean - Empirical Distribution Function102.804054054054
Midmean - Empirical Distribution Function - Averaging102.891111111111
Midmean - Empirical Distribution Function - Interpolation102.891111111111
Midmean - Closest Observation102.804054054054
Midmean - True Basic - Statistics Graphics Toolkit102.891111111111
Midmean - MS Excel (old versions)102.903157894737
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')