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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationSun, 20 Apr 2008 11:31:49 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/Apr/20/t1208712770c9yqy92nw0a8kfi.htm/, Retrieved Thu, 16 May 2024 18:31:13 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=10385, Retrieved Thu, 16 May 2024 18:31:13 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact202
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Centrummaten Inkt...] [2008-04-20 17:31:49] [10bf337d6aaebcf0c700ebf73b3b2ad5] [Current]
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Dataseries X:
58,1
57,9
57,3
55,9
55
55,9
56,6
57,3
56,2
57,7
56,8
57,9
58,3
58,2
56,9
57,1
56,7
54,2
54,2
52,1
51,5
51,8
53
52,4
52,41
52,36
52,94
52,34
51,84
51,42
50,85
50,66
51,53
51,59
52,32
51,98
51,17
50,57
49,84
50,12
49,08
48,57
47,22
46,78
46,04
45,05
44,42
44,09
44,46
44,34
43,04
42,87
42,32
42,49
41,94
41,6
41,42
41,12
41,28
40,21
39,69
39,16
38,8
38,44
37,02
36,75
35,95
36,29
36,35
36,07
36,6
36,5




Summary of compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001

\begin{tabular}{lllllllll}
\hline
Summary of compuational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 3 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=10385&T=0

[TABLE]
[ROW][C]Summary of compuational 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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ 193.190.124.10:1001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=10385&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=10385&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 compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean48.45694444444440.84076883826242657.6340870869905
Geometric Mean47.9145496583969
Harmonic Mean47.3515472007045
Quadratic Mean48.9720819844214
Winsorized Mean ( 1 / 24 )48.45722222222220.84019327230627557.6738993508129
Winsorized Mean ( 2 / 24 )48.46055555555560.83848237619132257.7955565097029
Winsorized Mean ( 3 / 24 )48.45472222222220.836634891102657.9162102101238
Winsorized Mean ( 4 / 24 )48.46305555555550.83494495894254758.0434135645704
Winsorized Mean ( 5 / 24 )48.45611111111110.83135374158331958.2857918204904
Winsorized Mean ( 6 / 24 )48.43527777777780.82371277613460658.8011733957405
Winsorized Mean ( 7 / 24 )48.46152777777780.81850616008979359.2072853458566
Winsorized Mean ( 8 / 24 )48.59708333333330.78519281439066761.8919104233603
Winsorized Mean ( 9 / 24 )48.61708333333330.77327716116364762.8714848634261
Winsorized Mean ( 10 / 24 )48.65319444444440.76232855704640563.8218180267944
Winsorized Mean ( 11 / 24 )48.71888888888890.7460233530738865.3047772407524
Winsorized Mean ( 12 / 24 )48.78888888888890.72893805418366866.9314609230097
Winsorized Mean ( 13 / 24 )48.88097222222220.69148173781333670.6901853645447
Winsorized Mean ( 14 / 24 )48.853750.67795655861113272.0602955742212
Winsorized Mean ( 15 / 24 )48.88291666666670.67338552177415872.5927645992086
Winsorized Mean ( 16 / 24 )48.72291666666670.63857836890668776.2990402416628
Winsorized Mean ( 17 / 24 )48.61430555555560.60051841930489480.9538958219252
Winsorized Mean ( 18 / 24 )48.70930555555560.58578399796233483.1523321309428
Winsorized Mean ( 19 / 24 )48.43750.53898954721138189.8672344400841
Winsorized Mean ( 20 / 24 )48.52638888888890.5207217929598993.190624139341
Winsorized Mean ( 21 / 24 )48.42138888888890.49512554744134497.7961834914714
Winsorized Mean ( 22 / 24 )48.73916666666670.446647779626613109.122151480102
Winsorized Mean ( 23 / 24 )48.806250.433523677836533112.580356033986
Winsorized Mean ( 24 / 24 )48.826250.428890160595044113.843250524233
Trimmed Mean ( 1 / 24 )48.4950.83408525290268258.1415386871229
Trimmed Mean ( 2 / 24 )48.5350.82641130250806858.7298356795237
Trimmed Mean ( 3 / 24 )48.57560606060610.81792389204838959.3889071255206
Trimmed Mean ( 4 / 24 )48.62093750.80817170447018960.161642917051
Trimmed Mean ( 5 / 24 )48.66677419354840.79666115705745461.0884235567652
Trimmed Mean ( 6 / 24 )48.71733333333330.78347310449140162.1812453472269
Trimmed Mean ( 7 / 24 )48.77568965517240.76916564942372263.4137648914982
Trimmed Mean ( 8 / 24 )48.83339285714290.75266523304722564.8806278183423
Trimmed Mean ( 9 / 24 )48.87277777777780.74027401657313666.0198476288804
Trimmed Mean ( 10 / 24 )48.91211538461540.72719591699880567.2612623933307
Trimmed Mean ( 11 / 24 )48.94940.7128621477064568.6660108935352
Trimmed Mean ( 12 / 24 )48.98083333333330.69801096801248170.1720110112331
Trimmed Mean ( 13 / 24 )49.00586956521740.68247868619455971.8057143124422
Trimmed Mean ( 14 / 24 )49.02159090909090.67034960926744273.1283948425982
Trimmed Mean ( 15 / 24 )49.04214285714290.65684235099961474.6634908399378
Trimmed Mean ( 16 / 24 )49.061250.63941130652363176.728780832384
Trimmed Mean ( 17 / 24 )49.10131578947370.62362282650430378.7355973877824
Trimmed Mean ( 18 / 24 )49.15861111111110.61036147925762280.5401598588797
Trimmed Mean ( 19 / 24 )49.21147058823530.59493152324739582.7178736800123
Trimmed Mean ( 20 / 24 )49.3031250.5831338164461684.5485609126084
Trimmed Mean ( 21 / 24 )49.39633333333330.5697873132805686.6925819196169
Trimmed Mean ( 22 / 24 )49.51571428571430.55464355982743589.2748386028677
Trimmed Mean ( 23 / 24 )49.61346153846150.54710706090734690.6832777046972
Trimmed Mean ( 24 / 24 )49.718750.53660071805388292.6550195093245
Median50.755
Midrange47.125
Midmean - Weighted Average at Xnp49.1013157894737
Midmean - Weighted Average at X(n+1)p49.2948648648649
Midmean - Empirical Distribution Function49.1013157894737
Midmean - Empirical Distribution Function - Averaging49.2948648648649
Midmean - Empirical Distribution Function - Interpolation49.2948648648649
Midmean - Closest Observation49.1013157894737
Midmean - True Basic - Statistics Graphics Toolkit49.2948648648649
Midmean - MS Excel (old versions)49.1013157894737
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 48.4569444444444 & 0.840768838262426 & 57.6340870869905 \tabularnewline
Geometric Mean & 47.9145496583969 &  &  \tabularnewline
Harmonic Mean & 47.3515472007045 &  &  \tabularnewline
Quadratic Mean & 48.9720819844214 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 48.4572222222222 & 0.840193272306275 & 57.6738993508129 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 48.4605555555556 & 0.838482376191322 & 57.7955565097029 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 48.4547222222222 & 0.8366348911026 & 57.9162102101238 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 48.4630555555555 & 0.834944958942547 & 58.0434135645704 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 48.4561111111111 & 0.831353741583319 & 58.2857918204904 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 48.4352777777778 & 0.823712776134606 & 58.8011733957405 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 48.4615277777778 & 0.818506160089793 & 59.2072853458566 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 48.5970833333333 & 0.785192814390667 & 61.8919104233603 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 48.6170833333333 & 0.773277161163647 & 62.8714848634261 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 48.6531944444444 & 0.762328557046405 & 63.8218180267944 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 48.7188888888889 & 0.74602335307388 & 65.3047772407524 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 48.7888888888889 & 0.728938054183668 & 66.9314609230097 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 48.8809722222222 & 0.691481737813336 & 70.6901853645447 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 48.85375 & 0.677956558611132 & 72.0602955742212 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 48.8829166666667 & 0.673385521774158 & 72.5927645992086 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 48.7229166666667 & 0.638578368906687 & 76.2990402416628 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 48.6143055555556 & 0.600518419304894 & 80.9538958219252 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 48.7093055555556 & 0.585783997962334 & 83.1523321309428 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 48.4375 & 0.538989547211381 & 89.8672344400841 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 48.5263888888889 & 0.52072179295989 & 93.190624139341 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 48.4213888888889 & 0.495125547441344 & 97.7961834914714 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 48.7391666666667 & 0.446647779626613 & 109.122151480102 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 48.80625 & 0.433523677836533 & 112.580356033986 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 48.82625 & 0.428890160595044 & 113.843250524233 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 48.495 & 0.834085252902682 & 58.1415386871229 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 48.535 & 0.826411302508068 & 58.7298356795237 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 48.5756060606061 & 0.817923892048389 & 59.3889071255206 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 48.6209375 & 0.808171704470189 & 60.161642917051 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 48.6667741935484 & 0.796661157057454 & 61.0884235567652 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 48.7173333333333 & 0.783473104491401 & 62.1812453472269 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 48.7756896551724 & 0.769165649423722 & 63.4137648914982 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 48.8333928571429 & 0.752665233047225 & 64.8806278183423 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 48.8727777777778 & 0.740274016573136 & 66.0198476288804 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 48.9121153846154 & 0.727195916998805 & 67.2612623933307 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 48.9494 & 0.71286214770645 & 68.6660108935352 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 48.9808333333333 & 0.698010968012481 & 70.1720110112331 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 49.0058695652174 & 0.682478686194559 & 71.8057143124422 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 49.0215909090909 & 0.670349609267442 & 73.1283948425982 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 49.0421428571429 & 0.656842350999614 & 74.6634908399378 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 49.06125 & 0.639411306523631 & 76.728780832384 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 49.1013157894737 & 0.623622826504303 & 78.7355973877824 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 49.1586111111111 & 0.610361479257622 & 80.5401598588797 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 49.2114705882353 & 0.594931523247395 & 82.7178736800123 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 49.303125 & 0.58313381644616 & 84.5485609126084 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 49.3963333333333 & 0.56978731328056 & 86.6925819196169 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 49.5157142857143 & 0.554643559827435 & 89.2748386028677 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 49.6134615384615 & 0.547107060907346 & 90.6832777046972 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 49.71875 & 0.536600718053882 & 92.6550195093245 \tabularnewline
Median & 50.755 &  &  \tabularnewline
Midrange & 47.125 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 49.1013157894737 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 49.2948648648649 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 49.1013157894737 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 49.2948648648649 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 49.2948648648649 &  &  \tabularnewline
Midmean - Closest Observation & 49.1013157894737 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 49.2948648648649 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 49.1013157894737 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=10385&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]48.4569444444444[/C][C]0.840768838262426[/C][C]57.6340870869905[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]47.9145496583969[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]47.3515472007045[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]48.9720819844214[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]48.4572222222222[/C][C]0.840193272306275[/C][C]57.6738993508129[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]48.4605555555556[/C][C]0.838482376191322[/C][C]57.7955565097029[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]48.4547222222222[/C][C]0.8366348911026[/C][C]57.9162102101238[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]48.4630555555555[/C][C]0.834944958942547[/C][C]58.0434135645704[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]48.4561111111111[/C][C]0.831353741583319[/C][C]58.2857918204904[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]48.4352777777778[/C][C]0.823712776134606[/C][C]58.8011733957405[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]48.4615277777778[/C][C]0.818506160089793[/C][C]59.2072853458566[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]48.5970833333333[/C][C]0.785192814390667[/C][C]61.8919104233603[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]48.6170833333333[/C][C]0.773277161163647[/C][C]62.8714848634261[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]48.6531944444444[/C][C]0.762328557046405[/C][C]63.8218180267944[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]48.7188888888889[/C][C]0.74602335307388[/C][C]65.3047772407524[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]48.7888888888889[/C][C]0.728938054183668[/C][C]66.9314609230097[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]48.8809722222222[/C][C]0.691481737813336[/C][C]70.6901853645447[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]48.85375[/C][C]0.677956558611132[/C][C]72.0602955742212[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]48.8829166666667[/C][C]0.673385521774158[/C][C]72.5927645992086[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]48.7229166666667[/C][C]0.638578368906687[/C][C]76.2990402416628[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]48.6143055555556[/C][C]0.600518419304894[/C][C]80.9538958219252[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]48.7093055555556[/C][C]0.585783997962334[/C][C]83.1523321309428[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]48.4375[/C][C]0.538989547211381[/C][C]89.8672344400841[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]48.5263888888889[/C][C]0.52072179295989[/C][C]93.190624139341[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]48.4213888888889[/C][C]0.495125547441344[/C][C]97.7961834914714[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]48.7391666666667[/C][C]0.446647779626613[/C][C]109.122151480102[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]48.80625[/C][C]0.433523677836533[/C][C]112.580356033986[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]48.82625[/C][C]0.428890160595044[/C][C]113.843250524233[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]48.495[/C][C]0.834085252902682[/C][C]58.1415386871229[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]48.535[/C][C]0.826411302508068[/C][C]58.7298356795237[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]48.5756060606061[/C][C]0.817923892048389[/C][C]59.3889071255206[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]48.6209375[/C][C]0.808171704470189[/C][C]60.161642917051[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]48.6667741935484[/C][C]0.796661157057454[/C][C]61.0884235567652[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]48.7173333333333[/C][C]0.783473104491401[/C][C]62.1812453472269[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]48.7756896551724[/C][C]0.769165649423722[/C][C]63.4137648914982[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]48.8333928571429[/C][C]0.752665233047225[/C][C]64.8806278183423[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]48.8727777777778[/C][C]0.740274016573136[/C][C]66.0198476288804[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]48.9121153846154[/C][C]0.727195916998805[/C][C]67.2612623933307[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]48.9494[/C][C]0.71286214770645[/C][C]68.6660108935352[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]48.9808333333333[/C][C]0.698010968012481[/C][C]70.1720110112331[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]49.0058695652174[/C][C]0.682478686194559[/C][C]71.8057143124422[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]49.0215909090909[/C][C]0.670349609267442[/C][C]73.1283948425982[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]49.0421428571429[/C][C]0.656842350999614[/C][C]74.6634908399378[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]49.06125[/C][C]0.639411306523631[/C][C]76.728780832384[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]49.1013157894737[/C][C]0.623622826504303[/C][C]78.7355973877824[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]49.1586111111111[/C][C]0.610361479257622[/C][C]80.5401598588797[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]49.2114705882353[/C][C]0.594931523247395[/C][C]82.7178736800123[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]49.303125[/C][C]0.58313381644616[/C][C]84.5485609126084[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]49.3963333333333[/C][C]0.56978731328056[/C][C]86.6925819196169[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]49.5157142857143[/C][C]0.554643559827435[/C][C]89.2748386028677[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]49.6134615384615[/C][C]0.547107060907346[/C][C]90.6832777046972[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]49.71875[/C][C]0.536600718053882[/C][C]92.6550195093245[/C][/ROW]
[ROW][C]Median[/C][C]50.755[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]47.125[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]49.1013157894737[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]49.2948648648649[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]49.1013157894737[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]49.2948648648649[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]49.2948648648649[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]49.1013157894737[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]49.2948648648649[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]49.1013157894737[/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=10385&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=10385&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 Mean48.45694444444440.84076883826242657.6340870869905
Geometric Mean47.9145496583969
Harmonic Mean47.3515472007045
Quadratic Mean48.9720819844214
Winsorized Mean ( 1 / 24 )48.45722222222220.84019327230627557.6738993508129
Winsorized Mean ( 2 / 24 )48.46055555555560.83848237619132257.7955565097029
Winsorized Mean ( 3 / 24 )48.45472222222220.836634891102657.9162102101238
Winsorized Mean ( 4 / 24 )48.46305555555550.83494495894254758.0434135645704
Winsorized Mean ( 5 / 24 )48.45611111111110.83135374158331958.2857918204904
Winsorized Mean ( 6 / 24 )48.43527777777780.82371277613460658.8011733957405
Winsorized Mean ( 7 / 24 )48.46152777777780.81850616008979359.2072853458566
Winsorized Mean ( 8 / 24 )48.59708333333330.78519281439066761.8919104233603
Winsorized Mean ( 9 / 24 )48.61708333333330.77327716116364762.8714848634261
Winsorized Mean ( 10 / 24 )48.65319444444440.76232855704640563.8218180267944
Winsorized Mean ( 11 / 24 )48.71888888888890.7460233530738865.3047772407524
Winsorized Mean ( 12 / 24 )48.78888888888890.72893805418366866.9314609230097
Winsorized Mean ( 13 / 24 )48.88097222222220.69148173781333670.6901853645447
Winsorized Mean ( 14 / 24 )48.853750.67795655861113272.0602955742212
Winsorized Mean ( 15 / 24 )48.88291666666670.67338552177415872.5927645992086
Winsorized Mean ( 16 / 24 )48.72291666666670.63857836890668776.2990402416628
Winsorized Mean ( 17 / 24 )48.61430555555560.60051841930489480.9538958219252
Winsorized Mean ( 18 / 24 )48.70930555555560.58578399796233483.1523321309428
Winsorized Mean ( 19 / 24 )48.43750.53898954721138189.8672344400841
Winsorized Mean ( 20 / 24 )48.52638888888890.5207217929598993.190624139341
Winsorized Mean ( 21 / 24 )48.42138888888890.49512554744134497.7961834914714
Winsorized Mean ( 22 / 24 )48.73916666666670.446647779626613109.122151480102
Winsorized Mean ( 23 / 24 )48.806250.433523677836533112.580356033986
Winsorized Mean ( 24 / 24 )48.826250.428890160595044113.843250524233
Trimmed Mean ( 1 / 24 )48.4950.83408525290268258.1415386871229
Trimmed Mean ( 2 / 24 )48.5350.82641130250806858.7298356795237
Trimmed Mean ( 3 / 24 )48.57560606060610.81792389204838959.3889071255206
Trimmed Mean ( 4 / 24 )48.62093750.80817170447018960.161642917051
Trimmed Mean ( 5 / 24 )48.66677419354840.79666115705745461.0884235567652
Trimmed Mean ( 6 / 24 )48.71733333333330.78347310449140162.1812453472269
Trimmed Mean ( 7 / 24 )48.77568965517240.76916564942372263.4137648914982
Trimmed Mean ( 8 / 24 )48.83339285714290.75266523304722564.8806278183423
Trimmed Mean ( 9 / 24 )48.87277777777780.74027401657313666.0198476288804
Trimmed Mean ( 10 / 24 )48.91211538461540.72719591699880567.2612623933307
Trimmed Mean ( 11 / 24 )48.94940.7128621477064568.6660108935352
Trimmed Mean ( 12 / 24 )48.98083333333330.69801096801248170.1720110112331
Trimmed Mean ( 13 / 24 )49.00586956521740.68247868619455971.8057143124422
Trimmed Mean ( 14 / 24 )49.02159090909090.67034960926744273.1283948425982
Trimmed Mean ( 15 / 24 )49.04214285714290.65684235099961474.6634908399378
Trimmed Mean ( 16 / 24 )49.061250.63941130652363176.728780832384
Trimmed Mean ( 17 / 24 )49.10131578947370.62362282650430378.7355973877824
Trimmed Mean ( 18 / 24 )49.15861111111110.61036147925762280.5401598588797
Trimmed Mean ( 19 / 24 )49.21147058823530.59493152324739582.7178736800123
Trimmed Mean ( 20 / 24 )49.3031250.5831338164461684.5485609126084
Trimmed Mean ( 21 / 24 )49.39633333333330.5697873132805686.6925819196169
Trimmed Mean ( 22 / 24 )49.51571428571430.55464355982743589.2748386028677
Trimmed Mean ( 23 / 24 )49.61346153846150.54710706090734690.6832777046972
Trimmed Mean ( 24 / 24 )49.718750.53660071805388292.6550195093245
Median50.755
Midrange47.125
Midmean - Weighted Average at Xnp49.1013157894737
Midmean - Weighted Average at X(n+1)p49.2948648648649
Midmean - Empirical Distribution Function49.1013157894737
Midmean - Empirical Distribution Function - Averaging49.2948648648649
Midmean - Empirical Distribution Function - Interpolation49.2948648648649
Midmean - Closest Observation49.1013157894737
Midmean - True Basic - Statistics Graphics Toolkit49.2948648648649
Midmean - MS Excel (old versions)49.1013157894737
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')