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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationFri, 04 Mar 2016 09:24:55 +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/04/t1457083629ggmz427h6vi563c.htm/, Retrieved Sat, 18 May 2024 16:47:16 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=293337, Retrieved Sat, 18 May 2024 16:47:16 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact100
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2016-03-04 09:24:55] [1af9caed13b550360754d0d82088541b] [Current]
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Dataseries X:
103,71
103,07
103,93
102,9
101,54
102,13
101,08
101,33
101,24
100,58
99,87
99,1
98,98
98,77
98,05
97,94
97,65
97,2
97,39
97,35
98,01
97,81
97,56
98,05
97,82
99,05
98,86
97,64
97,77
98,07
98,36
100
99,52
98,82
98,98
98,6
98,8
99,62
99,35
99,87
99,53
99,88
99,26
99,51
100,64
100,85
101,44
101,26
101,67
102,93
103,81
106,19
106,94
108,51
108,41
108,97
109,25
109,97
108,92
109,01
108,86
107,36
107,99
107,94
108,54
108,37
108,77
107,15
108,61
109,02
109,16
109,55




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=293337&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=293337&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=293337&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 Mean102.2866666666670.50789182704708201.394590776089
Geometric Mean102.198494715829
Harmonic Mean102.11173506204
Quadratic Mean102.376154056716
Winsorized Mean ( 1 / 24 )102.2829166666670.506390941373061201.984096297872
Winsorized Mean ( 2 / 24 )102.2756944444440.504585577579549202.692464844223
Winsorized Mean ( 3 / 24 )102.2790277777780.502908137405151203.37516967911
Winsorized Mean ( 4 / 24 )102.2756944444440.50083771085355204.209252274837
Winsorized Mean ( 5 / 24 )102.2756944444440.500615615789848204.299848463733
Winsorized Mean ( 6 / 24 )102.2823611111110.498697108932439205.099165964822
Winsorized Mean ( 7 / 24 )102.2813888888890.497286978542567205.678799772019
Winsorized Mean ( 8 / 24 )102.2758333333330.495896216472497206.244431669314
Winsorized Mean ( 9 / 24 )102.2795833333330.491917873181489207.920038911858
Winsorized Mean ( 10 / 24 )102.2670833333330.48661004548346210.162293776176
Winsorized Mean ( 11 / 24 )102.26250.483900175542905211.329743547351
Winsorized Mean ( 12 / 24 )102.25750.482987562494374211.718702386236
Winsorized Mean ( 13 / 24 )102.2430555555560.479262386393197213.334195335065
Winsorized Mean ( 14 / 24 )102.2916666666670.471077661064823217.143955490156
Winsorized Mean ( 15 / 24 )102.26250.451001526339505226.74535234947
Winsorized Mean ( 16 / 24 )102.2891666666670.444747679956052229.993704917751
Winsorized Mean ( 17 / 24 )102.1593055555560.419742651911479243.385572303241
Winsorized Mean ( 18 / 24 )102.1118055555560.410054260235879249.020228437127
Winsorized Mean ( 19 / 24 )102.0669444444440.399302435518871255.61312770811
Winsorized Mean ( 20 / 24 )101.8919444444440.360082184959531282.968579675486
Winsorized Mean ( 21 / 24 )101.2327777777780.254390955623237397.94173314757
Winsorized Mean ( 22 / 24 )101.21750.246274967355933410.993862213018
Winsorized Mean ( 23 / 24 )101.2015277777780.239574533189858422.421892804347
Winsorized Mean ( 24 / 24 )101.0415277777780.202106343709286499.942386386042
Trimmed Mean ( 1 / 24 )102.2495714285710.505386572239684202.319525379235
Trimmed Mean ( 2 / 24 )102.2142647058820.503776445926597202.896077282612
Trimmed Mean ( 3 / 24 )102.1807575757580.502539300698168203.328888773077
Trimmed Mean ( 4 / 24 )102.143906250.501306112383314203.755557187177
Trimmed Mean ( 5 / 24 )102.105645161290.500030809255324204.198707902323
Trimmed Mean ( 6 / 24 )102.0648333333330.498016885997081204.942515410876
Trimmed Mean ( 7 / 24 )102.0198275862070.495518115456206205.885162225161
Trimmed Mean ( 8 / 24 )101.9717857142860.492240115830326207.158625302768
Trimmed Mean ( 9 / 24 )101.9211111111110.487961837834534208.871069843114
Trimmed Mean ( 10 / 24 )101.8659615384620.482947075567343210.925723939408
Trimmed Mean ( 11 / 24 )101.80820.477249576602585213.322766517146
Trimmed Mean ( 12 / 24 )101.746250.470025333650272216.469714961589
Trimmed Mean ( 13 / 24 )101.6795652173910.460407817177383220.846739398903
Trimmed Mean ( 14 / 24 )101.6086363636360.448299534476621226.653450537847
Trimmed Mean ( 15 / 24 )101.5250.433549787358346234.171490703755
Trimmed Mean ( 16 / 24 )101.43650.418338678584708242.474591025559
Trimmed Mean ( 17 / 24 )101.3355263157890.398448394878181254.325347067269
Trimmed Mean ( 18 / 24 )101.2386111111110.378129093765645267.735577029828
Trimmed Mean ( 19 / 24 )101.1358823529410.351979155325695287.334862939136
Trimmed Mean ( 20 / 24 )101.0256250.317099041176921318.593284372734
Trimmed Mean ( 21 / 24 )100.9216666666670.280737568514581359.487571259723
Trimmed Mean ( 22 / 24 )100.8835714285710.271452693163745371.643288017469
Trimmed Mean ( 23 / 24 )100.8415384615380.259393192667747388.759386568425
Trimmed Mean ( 24 / 24 )100.7945833333330.242351089171692415.903158008612
Median100.745
Midrange103.585
Midmean - Weighted Average at Xnp101.172702702703
Midmean - Weighted Average at X(n+1)p101.238611111111
Midmean - Empirical Distribution Function101.172702702703
Midmean - Empirical Distribution Function - Averaging101.238611111111
Midmean - Empirical Distribution Function - Interpolation101.238611111111
Midmean - Closest Observation101.172702702703
Midmean - True Basic - Statistics Graphics Toolkit101.238611111111
Midmean - MS Excel (old versions)101.335526315789
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 102.286666666667 & 0.50789182704708 & 201.394590776089 \tabularnewline
Geometric Mean & 102.198494715829 &  &  \tabularnewline
Harmonic Mean & 102.11173506204 &  &  \tabularnewline
Quadratic Mean & 102.376154056716 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 102.282916666667 & 0.506390941373061 & 201.984096297872 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 102.275694444444 & 0.504585577579549 & 202.692464844223 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 102.279027777778 & 0.502908137405151 & 203.37516967911 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 102.275694444444 & 0.50083771085355 & 204.209252274837 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 102.275694444444 & 0.500615615789848 & 204.299848463733 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 102.282361111111 & 0.498697108932439 & 205.099165964822 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 102.281388888889 & 0.497286978542567 & 205.678799772019 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 102.275833333333 & 0.495896216472497 & 206.244431669314 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 102.279583333333 & 0.491917873181489 & 207.920038911858 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 102.267083333333 & 0.48661004548346 & 210.162293776176 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 102.2625 & 0.483900175542905 & 211.329743547351 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 102.2575 & 0.482987562494374 & 211.718702386236 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 102.243055555556 & 0.479262386393197 & 213.334195335065 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 102.291666666667 & 0.471077661064823 & 217.143955490156 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 102.2625 & 0.451001526339505 & 226.74535234947 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 102.289166666667 & 0.444747679956052 & 229.993704917751 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 102.159305555556 & 0.419742651911479 & 243.385572303241 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 102.111805555556 & 0.410054260235879 & 249.020228437127 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 102.066944444444 & 0.399302435518871 & 255.61312770811 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 101.891944444444 & 0.360082184959531 & 282.968579675486 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 101.232777777778 & 0.254390955623237 & 397.94173314757 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 101.2175 & 0.246274967355933 & 410.993862213018 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 101.201527777778 & 0.239574533189858 & 422.421892804347 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 101.041527777778 & 0.202106343709286 & 499.942386386042 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 102.249571428571 & 0.505386572239684 & 202.319525379235 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 102.214264705882 & 0.503776445926597 & 202.896077282612 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 102.180757575758 & 0.502539300698168 & 203.328888773077 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 102.14390625 & 0.501306112383314 & 203.755557187177 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 102.10564516129 & 0.500030809255324 & 204.198707902323 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 102.064833333333 & 0.498016885997081 & 204.942515410876 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 102.019827586207 & 0.495518115456206 & 205.885162225161 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 101.971785714286 & 0.492240115830326 & 207.158625302768 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 101.921111111111 & 0.487961837834534 & 208.871069843114 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 101.865961538462 & 0.482947075567343 & 210.925723939408 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 101.8082 & 0.477249576602585 & 213.322766517146 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 101.74625 & 0.470025333650272 & 216.469714961589 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 101.679565217391 & 0.460407817177383 & 220.846739398903 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 101.608636363636 & 0.448299534476621 & 226.653450537847 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 101.525 & 0.433549787358346 & 234.171490703755 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 101.4365 & 0.418338678584708 & 242.474591025559 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 101.335526315789 & 0.398448394878181 & 254.325347067269 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 101.238611111111 & 0.378129093765645 & 267.735577029828 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 101.135882352941 & 0.351979155325695 & 287.334862939136 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 101.025625 & 0.317099041176921 & 318.593284372734 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 100.921666666667 & 0.280737568514581 & 359.487571259723 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 100.883571428571 & 0.271452693163745 & 371.643288017469 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 100.841538461538 & 0.259393192667747 & 388.759386568425 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 100.794583333333 & 0.242351089171692 & 415.903158008612 \tabularnewline
Median & 100.745 &  &  \tabularnewline
Midrange & 103.585 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 101.172702702703 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 101.238611111111 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 101.172702702703 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 101.238611111111 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 101.238611111111 &  &  \tabularnewline
Midmean - Closest Observation & 101.172702702703 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 101.238611111111 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 101.335526315789 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=293337&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]102.286666666667[/C][C]0.50789182704708[/C][C]201.394590776089[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]102.198494715829[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]102.11173506204[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]102.376154056716[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]102.282916666667[/C][C]0.506390941373061[/C][C]201.984096297872[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]102.275694444444[/C][C]0.504585577579549[/C][C]202.692464844223[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]102.279027777778[/C][C]0.502908137405151[/C][C]203.37516967911[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]102.275694444444[/C][C]0.50083771085355[/C][C]204.209252274837[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]102.275694444444[/C][C]0.500615615789848[/C][C]204.299848463733[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]102.282361111111[/C][C]0.498697108932439[/C][C]205.099165964822[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]102.281388888889[/C][C]0.497286978542567[/C][C]205.678799772019[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]102.275833333333[/C][C]0.495896216472497[/C][C]206.244431669314[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]102.279583333333[/C][C]0.491917873181489[/C][C]207.920038911858[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]102.267083333333[/C][C]0.48661004548346[/C][C]210.162293776176[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]102.2625[/C][C]0.483900175542905[/C][C]211.329743547351[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]102.2575[/C][C]0.482987562494374[/C][C]211.718702386236[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]102.243055555556[/C][C]0.479262386393197[/C][C]213.334195335065[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]102.291666666667[/C][C]0.471077661064823[/C][C]217.143955490156[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]102.2625[/C][C]0.451001526339505[/C][C]226.74535234947[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]102.289166666667[/C][C]0.444747679956052[/C][C]229.993704917751[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]102.159305555556[/C][C]0.419742651911479[/C][C]243.385572303241[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]102.111805555556[/C][C]0.410054260235879[/C][C]249.020228437127[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]102.066944444444[/C][C]0.399302435518871[/C][C]255.61312770811[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]101.891944444444[/C][C]0.360082184959531[/C][C]282.968579675486[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]101.232777777778[/C][C]0.254390955623237[/C][C]397.94173314757[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]101.2175[/C][C]0.246274967355933[/C][C]410.993862213018[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]101.201527777778[/C][C]0.239574533189858[/C][C]422.421892804347[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]101.041527777778[/C][C]0.202106343709286[/C][C]499.942386386042[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]102.249571428571[/C][C]0.505386572239684[/C][C]202.319525379235[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]102.214264705882[/C][C]0.503776445926597[/C][C]202.896077282612[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]102.180757575758[/C][C]0.502539300698168[/C][C]203.328888773077[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]102.14390625[/C][C]0.501306112383314[/C][C]203.755557187177[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]102.10564516129[/C][C]0.500030809255324[/C][C]204.198707902323[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]102.064833333333[/C][C]0.498016885997081[/C][C]204.942515410876[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]102.019827586207[/C][C]0.495518115456206[/C][C]205.885162225161[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]101.971785714286[/C][C]0.492240115830326[/C][C]207.158625302768[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]101.921111111111[/C][C]0.487961837834534[/C][C]208.871069843114[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]101.865961538462[/C][C]0.482947075567343[/C][C]210.925723939408[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]101.8082[/C][C]0.477249576602585[/C][C]213.322766517146[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]101.74625[/C][C]0.470025333650272[/C][C]216.469714961589[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]101.679565217391[/C][C]0.460407817177383[/C][C]220.846739398903[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]101.608636363636[/C][C]0.448299534476621[/C][C]226.653450537847[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]101.525[/C][C]0.433549787358346[/C][C]234.171490703755[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]101.4365[/C][C]0.418338678584708[/C][C]242.474591025559[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]101.335526315789[/C][C]0.398448394878181[/C][C]254.325347067269[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]101.238611111111[/C][C]0.378129093765645[/C][C]267.735577029828[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]101.135882352941[/C][C]0.351979155325695[/C][C]287.334862939136[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]101.025625[/C][C]0.317099041176921[/C][C]318.593284372734[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]100.921666666667[/C][C]0.280737568514581[/C][C]359.487571259723[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]100.883571428571[/C][C]0.271452693163745[/C][C]371.643288017469[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]100.841538461538[/C][C]0.259393192667747[/C][C]388.759386568425[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]100.794583333333[/C][C]0.242351089171692[/C][C]415.903158008612[/C][/ROW]
[ROW][C]Median[/C][C]100.745[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]103.585[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]101.172702702703[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]101.238611111111[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]101.172702702703[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]101.238611111111[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]101.238611111111[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]101.172702702703[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]101.238611111111[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]101.335526315789[/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=293337&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=293337&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 Mean102.2866666666670.50789182704708201.394590776089
Geometric Mean102.198494715829
Harmonic Mean102.11173506204
Quadratic Mean102.376154056716
Winsorized Mean ( 1 / 24 )102.2829166666670.506390941373061201.984096297872
Winsorized Mean ( 2 / 24 )102.2756944444440.504585577579549202.692464844223
Winsorized Mean ( 3 / 24 )102.2790277777780.502908137405151203.37516967911
Winsorized Mean ( 4 / 24 )102.2756944444440.50083771085355204.209252274837
Winsorized Mean ( 5 / 24 )102.2756944444440.500615615789848204.299848463733
Winsorized Mean ( 6 / 24 )102.2823611111110.498697108932439205.099165964822
Winsorized Mean ( 7 / 24 )102.2813888888890.497286978542567205.678799772019
Winsorized Mean ( 8 / 24 )102.2758333333330.495896216472497206.244431669314
Winsorized Mean ( 9 / 24 )102.2795833333330.491917873181489207.920038911858
Winsorized Mean ( 10 / 24 )102.2670833333330.48661004548346210.162293776176
Winsorized Mean ( 11 / 24 )102.26250.483900175542905211.329743547351
Winsorized Mean ( 12 / 24 )102.25750.482987562494374211.718702386236
Winsorized Mean ( 13 / 24 )102.2430555555560.479262386393197213.334195335065
Winsorized Mean ( 14 / 24 )102.2916666666670.471077661064823217.143955490156
Winsorized Mean ( 15 / 24 )102.26250.451001526339505226.74535234947
Winsorized Mean ( 16 / 24 )102.2891666666670.444747679956052229.993704917751
Winsorized Mean ( 17 / 24 )102.1593055555560.419742651911479243.385572303241
Winsorized Mean ( 18 / 24 )102.1118055555560.410054260235879249.020228437127
Winsorized Mean ( 19 / 24 )102.0669444444440.399302435518871255.61312770811
Winsorized Mean ( 20 / 24 )101.8919444444440.360082184959531282.968579675486
Winsorized Mean ( 21 / 24 )101.2327777777780.254390955623237397.94173314757
Winsorized Mean ( 22 / 24 )101.21750.246274967355933410.993862213018
Winsorized Mean ( 23 / 24 )101.2015277777780.239574533189858422.421892804347
Winsorized Mean ( 24 / 24 )101.0415277777780.202106343709286499.942386386042
Trimmed Mean ( 1 / 24 )102.2495714285710.505386572239684202.319525379235
Trimmed Mean ( 2 / 24 )102.2142647058820.503776445926597202.896077282612
Trimmed Mean ( 3 / 24 )102.1807575757580.502539300698168203.328888773077
Trimmed Mean ( 4 / 24 )102.143906250.501306112383314203.755557187177
Trimmed Mean ( 5 / 24 )102.105645161290.500030809255324204.198707902323
Trimmed Mean ( 6 / 24 )102.0648333333330.498016885997081204.942515410876
Trimmed Mean ( 7 / 24 )102.0198275862070.495518115456206205.885162225161
Trimmed Mean ( 8 / 24 )101.9717857142860.492240115830326207.158625302768
Trimmed Mean ( 9 / 24 )101.9211111111110.487961837834534208.871069843114
Trimmed Mean ( 10 / 24 )101.8659615384620.482947075567343210.925723939408
Trimmed Mean ( 11 / 24 )101.80820.477249576602585213.322766517146
Trimmed Mean ( 12 / 24 )101.746250.470025333650272216.469714961589
Trimmed Mean ( 13 / 24 )101.6795652173910.460407817177383220.846739398903
Trimmed Mean ( 14 / 24 )101.6086363636360.448299534476621226.653450537847
Trimmed Mean ( 15 / 24 )101.5250.433549787358346234.171490703755
Trimmed Mean ( 16 / 24 )101.43650.418338678584708242.474591025559
Trimmed Mean ( 17 / 24 )101.3355263157890.398448394878181254.325347067269
Trimmed Mean ( 18 / 24 )101.2386111111110.378129093765645267.735577029828
Trimmed Mean ( 19 / 24 )101.1358823529410.351979155325695287.334862939136
Trimmed Mean ( 20 / 24 )101.0256250.317099041176921318.593284372734
Trimmed Mean ( 21 / 24 )100.9216666666670.280737568514581359.487571259723
Trimmed Mean ( 22 / 24 )100.8835714285710.271452693163745371.643288017469
Trimmed Mean ( 23 / 24 )100.8415384615380.259393192667747388.759386568425
Trimmed Mean ( 24 / 24 )100.7945833333330.242351089171692415.903158008612
Median100.745
Midrange103.585
Midmean - Weighted Average at Xnp101.172702702703
Midmean - Weighted Average at X(n+1)p101.238611111111
Midmean - Empirical Distribution Function101.172702702703
Midmean - Empirical Distribution Function - Averaging101.238611111111
Midmean - Empirical Distribution Function - Interpolation101.238611111111
Midmean - Closest Observation101.172702702703
Midmean - True Basic - Statistics Graphics Toolkit101.238611111111
Midmean - MS Excel (old versions)101.335526315789
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')