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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 computationSat, 24 Oct 2009 14:53:19 -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/2009/Oct/24/t1256417677vvkd4dyzq2pn2e6.htm/, Retrieved Fri, 03 May 2024 04:24:55 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=50251, Retrieved Fri, 03 May 2024 04:24:55 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP1W52
Estimated Impact158
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Robuustheid advie...] [2009-10-24 20:53:19] [8d07284ecb3aa8be600f3c4907b7b611] [Current]
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Dataseries X:
100,34 
115,78 
114,6 
114,2 
115,88 
125,22 
161,71 
165,01 
135,78 
153,67 
125,52 
135,29 
103,05 
120,79 
120,17 
119,62 
121,17 
129,86 
167,8 
167,14 
140,55 
158,44 
131,07 
140,55 
106,15 
123,65 
122,8 
122,25 
123,88 
132,96 
171,82 
173,69 
149,5 
164,44 
133,37 
143,77 
69,49 
84,5 
82,3 
78,8 
79,47 
88,93 
138,13 
139,69 
114,43 
128,65 
95,92 
98,22 
56,65 
69,6 
66,91 
63,76 
64 
35,24 
45,3 
43,02 
43,08 
43,17 
46,38 
70,85 
72,81 
59,51 
67,54 
56,51 
53,82 
112,55 
127,65 
126,51 
126,08 
127,34 




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\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 & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=50251&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=50251&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=50251&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'Gwilym Jenkins' @ 72.249.127.135







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean108.9757142857144.4823071854594124.3124154094639
Geometric Mean101.378443006876
Harmonic Mean92.6421133543394
Quadratic Mean115.160716677669
Winsorized Mean ( 1 / 23 )109.0601428571434.4515815343599124.4991902350553
Winsorized Mean ( 2 / 23 )108.9474.4284155916279924.6018011963390
Winsorized Mean ( 3 / 23 )108.9225714285714.4221618505116624.6310684933363
Winsorized Mean ( 4 / 23 )108.9225714285714.3732905193094824.9063196116616
Winsorized Mean ( 5 / 23 )108.9594.3495681094943725.0505331235441
Winsorized Mean ( 6 / 23 )109.3627142857144.1786786717670826.1716018091113
Winsorized Mean ( 7 / 23 )109.3047142857144.0691592913477126.8617437803749
Winsorized Mean ( 8 / 23 )108.7755714285713.9737683438192727.3734052961993
Winsorized Mean ( 9 / 23 )108.6071428571433.8190072428073828.4385799638612
Winsorized Mean ( 10 / 23 )108.3957142857143.5854233621969330.2323333496929
Winsorized Mean ( 11 / 23 )107.9274285714293.508305842349930.7634035974291
Winsorized Mean ( 12 / 23 )108.4262857142863.4191326020454031.7116351818069
Winsorized Mean ( 13 / 23 )108.3835714285713.3769797661554632.0948240539686
Winsorized Mean ( 14 / 23 )108.4615714285713.2675909895800733.1931296708926
Winsorized Mean ( 15 / 23 )107.9815714285713.1986442303657233.7585438241205
Winsorized Mean ( 16 / 23 )108.1552857142863.1350845182714234.4983636275041
Winsorized Mean ( 17 / 23 )108.1652.9956309576395636.1075851897424
Winsorized Mean ( 18 / 23 )109.5998571428572.7244863857169240.2277132737506
Winsorized Mean ( 19 / 23 )109.2687142857142.6319852611604841.5157014357809
Winsorized Mean ( 20 / 23 )109.7315714285712.4589865578624144.6247138186721
Winsorized Mean ( 21 / 23 )110.0285714285712.3100176770201447.6310517114767
Winsorized Mean ( 22 / 23 )111.1065714285712.0526601120595554.1280900699589
Winsorized Mean ( 23 / 23 )113.3014285714291.6886540180816267.0957030618644
Trimmed Mean ( 1 / 23 )109.1083823529414.3802427290830124.9092091697354
Trimmed Mean ( 2 / 23 )109.1595454545454.294334645022625.4194315249903
Trimmed Mean ( 3 / 23 )109.275781254.2053898876769325.9846968220976
Trimmed Mean ( 4 / 23 )109.4087096774194.10039944968226.6824515562513
Trimmed Mean ( 5 / 23 )109.55053.9909916954657827.4494432359911
Trimmed Mean ( 6 / 23 )109.6932758620693.8647984179161428.3826642428648
Trimmed Mean ( 7 / 23 )109.7621428571433.7603878781894529.1890481547853
Trimmed Mean ( 8 / 23 )109.8468518518523.6604235188174730.0093285072484
Trimmed Mean ( 9 / 23 )110.0271153846153.5591859180769530.9135622350584
Trimmed Mean ( 10 / 23 )110.2483.4689579803433431.7813016544779
Trimmed Mean ( 11 / 23 )110.5181253.4074730874749632.4340419316113
Trimmed Mean ( 12 / 23 )110.8765217391303.3421890367296533.1748206102739
Trimmed Mean ( 13 / 23 )111.2013636363643.2759097084082933.9451857757077
Trimmed Mean ( 14 / 23 )111.5626190476193.195230858514234.9153547858186
Trimmed Mean ( 15 / 23 )111.950253.1110656614220635.9845346204708
Trimmed Mean ( 16 / 23 )112.4376315789473.0088053430470737.369526692305
Trimmed Mean ( 17 / 23 )112.9580555555562.8821947605960039.1916802777746
Trimmed Mean ( 18 / 23 )113.5385294117652.7405498990316741.4291049587828
Trimmed Mean ( 19 / 23 )114.01718752.6250226663527943.4347439972454
Trimmed Mean ( 20 / 23 )114.6003333333332.4777422278947346.2519192041645
Trimmed Mean ( 21 / 23 )115.2089285714292.3158557070542449.747887236884
Trimmed Mean ( 22 / 23 )115.8730769230772.1192889786784554.6754492137894
Trimmed Mean ( 23 / 23 )116.5051.9248525258774560.5267148696966
Median119.895
Midrange104.465
Midmean - Weighted Average at Xnp112.374857142857
Midmean - Weighted Average at X(n+1)p112.958055555556
Midmean - Empirical Distribution Function112.958055555556
Midmean - Empirical Distribution Function - Averaging112.958055555556
Midmean - Empirical Distribution Function - Interpolation113.538529411765
Midmean - Closest Observation112.958055555556
Midmean - True Basic - Statistics Graphics Toolkit112.958055555556
Midmean - MS Excel (old versions)112.958055555556
Number of observations70

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 108.975714285714 & 4.48230718545941 & 24.3124154094639 \tabularnewline
Geometric Mean & 101.378443006876 &  &  \tabularnewline
Harmonic Mean & 92.6421133543394 &  &  \tabularnewline
Quadratic Mean & 115.160716677669 &  &  \tabularnewline
Winsorized Mean ( 1 / 23 ) & 109.060142857143 & 4.45158153435991 & 24.4991902350553 \tabularnewline
Winsorized Mean ( 2 / 23 ) & 108.947 & 4.42841559162799 & 24.6018011963390 \tabularnewline
Winsorized Mean ( 3 / 23 ) & 108.922571428571 & 4.42216185051166 & 24.6310684933363 \tabularnewline
Winsorized Mean ( 4 / 23 ) & 108.922571428571 & 4.37329051930948 & 24.9063196116616 \tabularnewline
Winsorized Mean ( 5 / 23 ) & 108.959 & 4.34956810949437 & 25.0505331235441 \tabularnewline
Winsorized Mean ( 6 / 23 ) & 109.362714285714 & 4.17867867176708 & 26.1716018091113 \tabularnewline
Winsorized Mean ( 7 / 23 ) & 109.304714285714 & 4.06915929134771 & 26.8617437803749 \tabularnewline
Winsorized Mean ( 8 / 23 ) & 108.775571428571 & 3.97376834381927 & 27.3734052961993 \tabularnewline
Winsorized Mean ( 9 / 23 ) & 108.607142857143 & 3.81900724280738 & 28.4385799638612 \tabularnewline
Winsorized Mean ( 10 / 23 ) & 108.395714285714 & 3.58542336219693 & 30.2323333496929 \tabularnewline
Winsorized Mean ( 11 / 23 ) & 107.927428571429 & 3.5083058423499 & 30.7634035974291 \tabularnewline
Winsorized Mean ( 12 / 23 ) & 108.426285714286 & 3.41913260204540 & 31.7116351818069 \tabularnewline
Winsorized Mean ( 13 / 23 ) & 108.383571428571 & 3.37697976615546 & 32.0948240539686 \tabularnewline
Winsorized Mean ( 14 / 23 ) & 108.461571428571 & 3.26759098958007 & 33.1931296708926 \tabularnewline
Winsorized Mean ( 15 / 23 ) & 107.981571428571 & 3.19864423036572 & 33.7585438241205 \tabularnewline
Winsorized Mean ( 16 / 23 ) & 108.155285714286 & 3.13508451827142 & 34.4983636275041 \tabularnewline
Winsorized Mean ( 17 / 23 ) & 108.165 & 2.99563095763956 & 36.1075851897424 \tabularnewline
Winsorized Mean ( 18 / 23 ) & 109.599857142857 & 2.72448638571692 & 40.2277132737506 \tabularnewline
Winsorized Mean ( 19 / 23 ) & 109.268714285714 & 2.63198526116048 & 41.5157014357809 \tabularnewline
Winsorized Mean ( 20 / 23 ) & 109.731571428571 & 2.45898655786241 & 44.6247138186721 \tabularnewline
Winsorized Mean ( 21 / 23 ) & 110.028571428571 & 2.31001767702014 & 47.6310517114767 \tabularnewline
Winsorized Mean ( 22 / 23 ) & 111.106571428571 & 2.05266011205955 & 54.1280900699589 \tabularnewline
Winsorized Mean ( 23 / 23 ) & 113.301428571429 & 1.68865401808162 & 67.0957030618644 \tabularnewline
Trimmed Mean ( 1 / 23 ) & 109.108382352941 & 4.38024272908301 & 24.9092091697354 \tabularnewline
Trimmed Mean ( 2 / 23 ) & 109.159545454545 & 4.2943346450226 & 25.4194315249903 \tabularnewline
Trimmed Mean ( 3 / 23 ) & 109.27578125 & 4.20538988767693 & 25.9846968220976 \tabularnewline
Trimmed Mean ( 4 / 23 ) & 109.408709677419 & 4.100399449682 & 26.6824515562513 \tabularnewline
Trimmed Mean ( 5 / 23 ) & 109.5505 & 3.99099169546578 & 27.4494432359911 \tabularnewline
Trimmed Mean ( 6 / 23 ) & 109.693275862069 & 3.86479841791614 & 28.3826642428648 \tabularnewline
Trimmed Mean ( 7 / 23 ) & 109.762142857143 & 3.76038787818945 & 29.1890481547853 \tabularnewline
Trimmed Mean ( 8 / 23 ) & 109.846851851852 & 3.66042351881747 & 30.0093285072484 \tabularnewline
Trimmed Mean ( 9 / 23 ) & 110.027115384615 & 3.55918591807695 & 30.9135622350584 \tabularnewline
Trimmed Mean ( 10 / 23 ) & 110.248 & 3.46895798034334 & 31.7813016544779 \tabularnewline
Trimmed Mean ( 11 / 23 ) & 110.518125 & 3.40747308747496 & 32.4340419316113 \tabularnewline
Trimmed Mean ( 12 / 23 ) & 110.876521739130 & 3.34218903672965 & 33.1748206102739 \tabularnewline
Trimmed Mean ( 13 / 23 ) & 111.201363636364 & 3.27590970840829 & 33.9451857757077 \tabularnewline
Trimmed Mean ( 14 / 23 ) & 111.562619047619 & 3.1952308585142 & 34.9153547858186 \tabularnewline
Trimmed Mean ( 15 / 23 ) & 111.95025 & 3.11106566142206 & 35.9845346204708 \tabularnewline
Trimmed Mean ( 16 / 23 ) & 112.437631578947 & 3.00880534304707 & 37.369526692305 \tabularnewline
Trimmed Mean ( 17 / 23 ) & 112.958055555556 & 2.88219476059600 & 39.1916802777746 \tabularnewline
Trimmed Mean ( 18 / 23 ) & 113.538529411765 & 2.74054989903167 & 41.4291049587828 \tabularnewline
Trimmed Mean ( 19 / 23 ) & 114.0171875 & 2.62502266635279 & 43.4347439972454 \tabularnewline
Trimmed Mean ( 20 / 23 ) & 114.600333333333 & 2.47774222789473 & 46.2519192041645 \tabularnewline
Trimmed Mean ( 21 / 23 ) & 115.208928571429 & 2.31585570705424 & 49.747887236884 \tabularnewline
Trimmed Mean ( 22 / 23 ) & 115.873076923077 & 2.11928897867845 & 54.6754492137894 \tabularnewline
Trimmed Mean ( 23 / 23 ) & 116.505 & 1.92485252587745 & 60.5267148696966 \tabularnewline
Median & 119.895 &  &  \tabularnewline
Midrange & 104.465 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 112.374857142857 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 112.958055555556 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 112.958055555556 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 112.958055555556 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 113.538529411765 &  &  \tabularnewline
Midmean - Closest Observation & 112.958055555556 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 112.958055555556 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 112.958055555556 &  &  \tabularnewline
Number of observations & 70 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=50251&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]108.975714285714[/C][C]4.48230718545941[/C][C]24.3124154094639[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]101.378443006876[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]92.6421133543394[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]115.160716677669[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 23 )[/C][C]109.060142857143[/C][C]4.45158153435991[/C][C]24.4991902350553[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 23 )[/C][C]108.947[/C][C]4.42841559162799[/C][C]24.6018011963390[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 23 )[/C][C]108.922571428571[/C][C]4.42216185051166[/C][C]24.6310684933363[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 23 )[/C][C]108.922571428571[/C][C]4.37329051930948[/C][C]24.9063196116616[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 23 )[/C][C]108.959[/C][C]4.34956810949437[/C][C]25.0505331235441[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 23 )[/C][C]109.362714285714[/C][C]4.17867867176708[/C][C]26.1716018091113[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 23 )[/C][C]109.304714285714[/C][C]4.06915929134771[/C][C]26.8617437803749[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 23 )[/C][C]108.775571428571[/C][C]3.97376834381927[/C][C]27.3734052961993[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 23 )[/C][C]108.607142857143[/C][C]3.81900724280738[/C][C]28.4385799638612[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 23 )[/C][C]108.395714285714[/C][C]3.58542336219693[/C][C]30.2323333496929[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 23 )[/C][C]107.927428571429[/C][C]3.5083058423499[/C][C]30.7634035974291[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 23 )[/C][C]108.426285714286[/C][C]3.41913260204540[/C][C]31.7116351818069[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 23 )[/C][C]108.383571428571[/C][C]3.37697976615546[/C][C]32.0948240539686[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 23 )[/C][C]108.461571428571[/C][C]3.26759098958007[/C][C]33.1931296708926[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 23 )[/C][C]107.981571428571[/C][C]3.19864423036572[/C][C]33.7585438241205[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 23 )[/C][C]108.155285714286[/C][C]3.13508451827142[/C][C]34.4983636275041[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 23 )[/C][C]108.165[/C][C]2.99563095763956[/C][C]36.1075851897424[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 23 )[/C][C]109.599857142857[/C][C]2.72448638571692[/C][C]40.2277132737506[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 23 )[/C][C]109.268714285714[/C][C]2.63198526116048[/C][C]41.5157014357809[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 23 )[/C][C]109.731571428571[/C][C]2.45898655786241[/C][C]44.6247138186721[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 23 )[/C][C]110.028571428571[/C][C]2.31001767702014[/C][C]47.6310517114767[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 23 )[/C][C]111.106571428571[/C][C]2.05266011205955[/C][C]54.1280900699589[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 23 )[/C][C]113.301428571429[/C][C]1.68865401808162[/C][C]67.0957030618644[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 23 )[/C][C]109.108382352941[/C][C]4.38024272908301[/C][C]24.9092091697354[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 23 )[/C][C]109.159545454545[/C][C]4.2943346450226[/C][C]25.4194315249903[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 23 )[/C][C]109.27578125[/C][C]4.20538988767693[/C][C]25.9846968220976[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 23 )[/C][C]109.408709677419[/C][C]4.100399449682[/C][C]26.6824515562513[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 23 )[/C][C]109.5505[/C][C]3.99099169546578[/C][C]27.4494432359911[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 23 )[/C][C]109.693275862069[/C][C]3.86479841791614[/C][C]28.3826642428648[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 23 )[/C][C]109.762142857143[/C][C]3.76038787818945[/C][C]29.1890481547853[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 23 )[/C][C]109.846851851852[/C][C]3.66042351881747[/C][C]30.0093285072484[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 23 )[/C][C]110.027115384615[/C][C]3.55918591807695[/C][C]30.9135622350584[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 23 )[/C][C]110.248[/C][C]3.46895798034334[/C][C]31.7813016544779[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 23 )[/C][C]110.518125[/C][C]3.40747308747496[/C][C]32.4340419316113[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 23 )[/C][C]110.876521739130[/C][C]3.34218903672965[/C][C]33.1748206102739[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 23 )[/C][C]111.201363636364[/C][C]3.27590970840829[/C][C]33.9451857757077[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 23 )[/C][C]111.562619047619[/C][C]3.1952308585142[/C][C]34.9153547858186[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 23 )[/C][C]111.95025[/C][C]3.11106566142206[/C][C]35.9845346204708[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 23 )[/C][C]112.437631578947[/C][C]3.00880534304707[/C][C]37.369526692305[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 23 )[/C][C]112.958055555556[/C][C]2.88219476059600[/C][C]39.1916802777746[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 23 )[/C][C]113.538529411765[/C][C]2.74054989903167[/C][C]41.4291049587828[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 23 )[/C][C]114.0171875[/C][C]2.62502266635279[/C][C]43.4347439972454[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 23 )[/C][C]114.600333333333[/C][C]2.47774222789473[/C][C]46.2519192041645[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 23 )[/C][C]115.208928571429[/C][C]2.31585570705424[/C][C]49.747887236884[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 23 )[/C][C]115.873076923077[/C][C]2.11928897867845[/C][C]54.6754492137894[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 23 )[/C][C]116.505[/C][C]1.92485252587745[/C][C]60.5267148696966[/C][/ROW]
[ROW][C]Median[/C][C]119.895[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]104.465[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]112.374857142857[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]112.958055555556[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]112.958055555556[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]112.958055555556[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]113.538529411765[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]112.958055555556[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]112.958055555556[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]112.958055555556[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]70[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=50251&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=50251&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 Mean108.9757142857144.4823071854594124.3124154094639
Geometric Mean101.378443006876
Harmonic Mean92.6421133543394
Quadratic Mean115.160716677669
Winsorized Mean ( 1 / 23 )109.0601428571434.4515815343599124.4991902350553
Winsorized Mean ( 2 / 23 )108.9474.4284155916279924.6018011963390
Winsorized Mean ( 3 / 23 )108.9225714285714.4221618505116624.6310684933363
Winsorized Mean ( 4 / 23 )108.9225714285714.3732905193094824.9063196116616
Winsorized Mean ( 5 / 23 )108.9594.3495681094943725.0505331235441
Winsorized Mean ( 6 / 23 )109.3627142857144.1786786717670826.1716018091113
Winsorized Mean ( 7 / 23 )109.3047142857144.0691592913477126.8617437803749
Winsorized Mean ( 8 / 23 )108.7755714285713.9737683438192727.3734052961993
Winsorized Mean ( 9 / 23 )108.6071428571433.8190072428073828.4385799638612
Winsorized Mean ( 10 / 23 )108.3957142857143.5854233621969330.2323333496929
Winsorized Mean ( 11 / 23 )107.9274285714293.508305842349930.7634035974291
Winsorized Mean ( 12 / 23 )108.4262857142863.4191326020454031.7116351818069
Winsorized Mean ( 13 / 23 )108.3835714285713.3769797661554632.0948240539686
Winsorized Mean ( 14 / 23 )108.4615714285713.2675909895800733.1931296708926
Winsorized Mean ( 15 / 23 )107.9815714285713.1986442303657233.7585438241205
Winsorized Mean ( 16 / 23 )108.1552857142863.1350845182714234.4983636275041
Winsorized Mean ( 17 / 23 )108.1652.9956309576395636.1075851897424
Winsorized Mean ( 18 / 23 )109.5998571428572.7244863857169240.2277132737506
Winsorized Mean ( 19 / 23 )109.2687142857142.6319852611604841.5157014357809
Winsorized Mean ( 20 / 23 )109.7315714285712.4589865578624144.6247138186721
Winsorized Mean ( 21 / 23 )110.0285714285712.3100176770201447.6310517114767
Winsorized Mean ( 22 / 23 )111.1065714285712.0526601120595554.1280900699589
Winsorized Mean ( 23 / 23 )113.3014285714291.6886540180816267.0957030618644
Trimmed Mean ( 1 / 23 )109.1083823529414.3802427290830124.9092091697354
Trimmed Mean ( 2 / 23 )109.1595454545454.294334645022625.4194315249903
Trimmed Mean ( 3 / 23 )109.275781254.2053898876769325.9846968220976
Trimmed Mean ( 4 / 23 )109.4087096774194.10039944968226.6824515562513
Trimmed Mean ( 5 / 23 )109.55053.9909916954657827.4494432359911
Trimmed Mean ( 6 / 23 )109.6932758620693.8647984179161428.3826642428648
Trimmed Mean ( 7 / 23 )109.7621428571433.7603878781894529.1890481547853
Trimmed Mean ( 8 / 23 )109.8468518518523.6604235188174730.0093285072484
Trimmed Mean ( 9 / 23 )110.0271153846153.5591859180769530.9135622350584
Trimmed Mean ( 10 / 23 )110.2483.4689579803433431.7813016544779
Trimmed Mean ( 11 / 23 )110.5181253.4074730874749632.4340419316113
Trimmed Mean ( 12 / 23 )110.8765217391303.3421890367296533.1748206102739
Trimmed Mean ( 13 / 23 )111.2013636363643.2759097084082933.9451857757077
Trimmed Mean ( 14 / 23 )111.5626190476193.195230858514234.9153547858186
Trimmed Mean ( 15 / 23 )111.950253.1110656614220635.9845346204708
Trimmed Mean ( 16 / 23 )112.4376315789473.0088053430470737.369526692305
Trimmed Mean ( 17 / 23 )112.9580555555562.8821947605960039.1916802777746
Trimmed Mean ( 18 / 23 )113.5385294117652.7405498990316741.4291049587828
Trimmed Mean ( 19 / 23 )114.01718752.6250226663527943.4347439972454
Trimmed Mean ( 20 / 23 )114.6003333333332.4777422278947346.2519192041645
Trimmed Mean ( 21 / 23 )115.2089285714292.3158557070542449.747887236884
Trimmed Mean ( 22 / 23 )115.8730769230772.1192889786784554.6754492137894
Trimmed Mean ( 23 / 23 )116.5051.9248525258774560.5267148696966
Median119.895
Midrange104.465
Midmean - Weighted Average at Xnp112.374857142857
Midmean - Weighted Average at X(n+1)p112.958055555556
Midmean - Empirical Distribution Function112.958055555556
Midmean - Empirical Distribution Function - Averaging112.958055555556
Midmean - Empirical Distribution Function - Interpolation113.538529411765
Midmean - Closest Observation112.958055555556
Midmean - True Basic - Statistics Graphics Toolkit112.958055555556
Midmean - MS Excel (old versions)112.958055555556
Number of observations70



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')