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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationTue, 08 Mar 2016 18:42:22 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Mar/08/t1457462575maqrtbw0wqw8iso.htm/, Retrieved Sun, 28 Apr 2024 23:33:52 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=293705, Retrieved Sun, 28 Apr 2024 23:33:52 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact85
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2016-03-08 18:42:22] [3d038f408b3fdbe799ace9817e748893] [Current]
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Dataseries X:
90,4
89,5
88,9
88,4
87,6
87,1
86,5
85,7
85,3
84,9
84,5
84,4
84,3
84,2
84,1
83,8
83,5
83,2
82,8
82,2
81,5
80,8
80,3
79,8
79,2
78,8
78,1
77,8
77,3
76,7
76,2
76,1
76,3
76,2
76,2
76,6
75,5
75,4
75,5
75,5
75,2
74,9
74,6
74,4
74
73,3
72,7
72
71,2
70,9
70,4
70
69,7
69,2
68,7
68,6
68,4
67,9
67,4
66,5
65,6
64,6
63,8
63
62,1
61,7
61,4
61,1
61,1
61
60,5
60,2
59,9
59,4
59,6
59,5
59,3
59,3
59,1
58,8




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Herman Ole Andreas Wold' @ wold.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 & 2 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=293705&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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=293705&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=293705&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 time2 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean73.776251.0402824040718670.9194442886146
Geometric Mean73.1852127892199
Harmonic Mean72.5855926770118
Quadratic Mean74.3533985437115
Winsorized Mean ( 1 / 26 )73.768751.0373874710211471.110122360921
Winsorized Mean ( 2 / 26 )73.758751.0336669605268571.3563969989
Winsorized Mean ( 3 / 26 )73.741.0302399253559771.5755603963043
Winsorized Mean ( 4 / 26 )73.7051.0223095285440272.096559742499
Winsorized Mean ( 5 / 26 )73.681.0159026665227872.5266331391676
Winsorized Mean ( 6 / 26 )73.64251.0071795670980273.1175476605289
Winsorized Mean ( 7 / 26 )73.598750.99150265348464374.229503815584
Winsorized Mean ( 8 / 26 )73.588750.98017047366093875.0775012892868
Winsorized Mean ( 9 / 26 )73.57750.96762951738327776.0389164222406
Winsorized Mean ( 10 / 26 )73.590.94969948611339777.4876696007953
Winsorized Mean ( 11 / 26 )73.590.94540126100180277.8399638710231
Winsorized Mean ( 12 / 26 )73.5750.94323624837744978.002727446664
Winsorized Mean ( 13 / 26 )73.60750.93277993219126178.9119678283422
Winsorized Mean ( 14 / 26 )73.64250.92161075112125279.9062943985896
Winsorized Mean ( 15 / 26 )73.661250.90132548973684781.7254708080056
Winsorized Mean ( 16 / 26 )73.781250.86394388177382885.4005121820114
Winsorized Mean ( 17 / 26 )73.88750.82833211823595689.2003320568485
Winsorized Mean ( 18 / 26 )73.97750.78811378531757493.8665220405838
Winsorized Mean ( 19 / 26 )74.07250.732725048592883101.091808096704
Winsorized Mean ( 20 / 26 )74.12250.675795300349657109.681881424226
Winsorized Mean ( 21 / 26 )74.1750.617312212003462120.1579987528
Winsorized Mean ( 22 / 26 )74.1750.579801089855364127.931805058358
Winsorized Mean ( 23 / 26 )74.1750.541167572727849137.064753577359
Winsorized Mean ( 24 / 26 )74.0550.509699899295431145.29137655779
Winsorized Mean ( 25 / 26 )73.961250.489650785370476151.048976555894
Winsorized Mean ( 26 / 26 )73.896250.439585692996646168.104310893858
Trimmed Mean ( 1 / 26 )73.75512820512821.0273282928864471.7931441349696
Trimmed Mean ( 2 / 26 )73.74078947368421.0153267171541172.6276460845771
Trimmed Mean ( 3 / 26 )73.73108108108111.0033005983338673.4885249779807
Trimmed Mean ( 4 / 26 )73.72777777777780.99039641733359674.4426943468475
Trimmed Mean ( 5 / 26 )73.73428571428570.97765487293663775.4195450310659
Trimmed Mean ( 6 / 26 )73.74705882352940.96416128442760776.4883012983775
Trimmed Mean ( 7 / 26 )73.76818181818180.95009301247748977.6431158311772
Trimmed Mean ( 8 / 26 )73.79843750.93670334455043178.7852823728514
Trimmed Mean ( 9 / 26 )73.83225806451610.92277939378294580.010735569029
Trimmed Mean ( 10 / 26 )73.870.90823694611179881.3334012850288
Trimmed Mean ( 11 / 26 )73.90862068965520.89385305719507382.6854258591247
Trimmed Mean ( 12 / 26 )73.950.8766783532544584.3524876888759
Trimmed Mean ( 13 / 26 )73.99629629629630.85553634557225586.4911194939372
Trimmed Mean ( 14 / 26 )74.04230769230770.83112685029476289.086651052181
Trimmed Mean ( 15 / 26 )74.0880.80263159007589292.3063593759058
Trimmed Mean ( 16 / 26 )74.13541666666670.77075012728996396.1860582849781
Trimmed Mean ( 17 / 26 )74.17391304347830.738332334102171100.461417734976
Trimmed Mean ( 18 / 26 )74.20454545454550.704597965716856105.314731329163
Trimmed Mean ( 19 / 26 )74.22857142857140.670060632358744110.778887527346
Trimmed Mean ( 20 / 26 )74.2450.638075532061357116.357697904737
Trimmed Mean ( 21 / 26 )74.25789473684210.609615129138809121.811108660877
Trimmed Mean ( 22 / 26 )74.26666666666670.586000704263079126.734773740691
Trimmed Mean ( 23 / 26 )74.27647058823530.563080697659912131.910880442037
Trimmed Mean ( 24 / 26 )74.28750.541331058148458137.231180221008
Trimmed Mean ( 25 / 26 )74.31333333333330.518834532419201143.23127835541
Trimmed Mean ( 26 / 26 )74.35357142857140.491339873716918151.328185245983
Median75.3
Midrange74.6
Midmean - Weighted Average at Xnp74.0341463414634
Midmean - Weighted Average at X(n+1)p74.245
Midmean - Empirical Distribution Function74.0341463414634
Midmean - Empirical Distribution Function - Averaging74.245
Midmean - Empirical Distribution Function - Interpolation74.245
Midmean - Closest Observation74.0341463414634
Midmean - True Basic - Statistics Graphics Toolkit74.245
Midmean - MS Excel (old versions)74.2285714285714
Number of observations80

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 73.77625 & 1.04028240407186 & 70.9194442886146 \tabularnewline
Geometric Mean & 73.1852127892199 &  &  \tabularnewline
Harmonic Mean & 72.5855926770118 &  &  \tabularnewline
Quadratic Mean & 74.3533985437115 &  &  \tabularnewline
Winsorized Mean ( 1 / 26 ) & 73.76875 & 1.03738747102114 & 71.110122360921 \tabularnewline
Winsorized Mean ( 2 / 26 ) & 73.75875 & 1.03366696052685 & 71.3563969989 \tabularnewline
Winsorized Mean ( 3 / 26 ) & 73.74 & 1.03023992535597 & 71.5755603963043 \tabularnewline
Winsorized Mean ( 4 / 26 ) & 73.705 & 1.02230952854402 & 72.096559742499 \tabularnewline
Winsorized Mean ( 5 / 26 ) & 73.68 & 1.01590266652278 & 72.5266331391676 \tabularnewline
Winsorized Mean ( 6 / 26 ) & 73.6425 & 1.00717956709802 & 73.1175476605289 \tabularnewline
Winsorized Mean ( 7 / 26 ) & 73.59875 & 0.991502653484643 & 74.229503815584 \tabularnewline
Winsorized Mean ( 8 / 26 ) & 73.58875 & 0.980170473660938 & 75.0775012892868 \tabularnewline
Winsorized Mean ( 9 / 26 ) & 73.5775 & 0.967629517383277 & 76.0389164222406 \tabularnewline
Winsorized Mean ( 10 / 26 ) & 73.59 & 0.949699486113397 & 77.4876696007953 \tabularnewline
Winsorized Mean ( 11 / 26 ) & 73.59 & 0.945401261001802 & 77.8399638710231 \tabularnewline
Winsorized Mean ( 12 / 26 ) & 73.575 & 0.943236248377449 & 78.002727446664 \tabularnewline
Winsorized Mean ( 13 / 26 ) & 73.6075 & 0.932779932191261 & 78.9119678283422 \tabularnewline
Winsorized Mean ( 14 / 26 ) & 73.6425 & 0.921610751121252 & 79.9062943985896 \tabularnewline
Winsorized Mean ( 15 / 26 ) & 73.66125 & 0.901325489736847 & 81.7254708080056 \tabularnewline
Winsorized Mean ( 16 / 26 ) & 73.78125 & 0.863943881773828 & 85.4005121820114 \tabularnewline
Winsorized Mean ( 17 / 26 ) & 73.8875 & 0.828332118235956 & 89.2003320568485 \tabularnewline
Winsorized Mean ( 18 / 26 ) & 73.9775 & 0.788113785317574 & 93.8665220405838 \tabularnewline
Winsorized Mean ( 19 / 26 ) & 74.0725 & 0.732725048592883 & 101.091808096704 \tabularnewline
Winsorized Mean ( 20 / 26 ) & 74.1225 & 0.675795300349657 & 109.681881424226 \tabularnewline
Winsorized Mean ( 21 / 26 ) & 74.175 & 0.617312212003462 & 120.1579987528 \tabularnewline
Winsorized Mean ( 22 / 26 ) & 74.175 & 0.579801089855364 & 127.931805058358 \tabularnewline
Winsorized Mean ( 23 / 26 ) & 74.175 & 0.541167572727849 & 137.064753577359 \tabularnewline
Winsorized Mean ( 24 / 26 ) & 74.055 & 0.509699899295431 & 145.29137655779 \tabularnewline
Winsorized Mean ( 25 / 26 ) & 73.96125 & 0.489650785370476 & 151.048976555894 \tabularnewline
Winsorized Mean ( 26 / 26 ) & 73.89625 & 0.439585692996646 & 168.104310893858 \tabularnewline
Trimmed Mean ( 1 / 26 ) & 73.7551282051282 & 1.02732829288644 & 71.7931441349696 \tabularnewline
Trimmed Mean ( 2 / 26 ) & 73.7407894736842 & 1.01532671715411 & 72.6276460845771 \tabularnewline
Trimmed Mean ( 3 / 26 ) & 73.7310810810811 & 1.00330059833386 & 73.4885249779807 \tabularnewline
Trimmed Mean ( 4 / 26 ) & 73.7277777777778 & 0.990396417333596 & 74.4426943468475 \tabularnewline
Trimmed Mean ( 5 / 26 ) & 73.7342857142857 & 0.977654872936637 & 75.4195450310659 \tabularnewline
Trimmed Mean ( 6 / 26 ) & 73.7470588235294 & 0.964161284427607 & 76.4883012983775 \tabularnewline
Trimmed Mean ( 7 / 26 ) & 73.7681818181818 & 0.950093012477489 & 77.6431158311772 \tabularnewline
Trimmed Mean ( 8 / 26 ) & 73.7984375 & 0.936703344550431 & 78.7852823728514 \tabularnewline
Trimmed Mean ( 9 / 26 ) & 73.8322580645161 & 0.922779393782945 & 80.010735569029 \tabularnewline
Trimmed Mean ( 10 / 26 ) & 73.87 & 0.908236946111798 & 81.3334012850288 \tabularnewline
Trimmed Mean ( 11 / 26 ) & 73.9086206896552 & 0.893853057195073 & 82.6854258591247 \tabularnewline
Trimmed Mean ( 12 / 26 ) & 73.95 & 0.87667835325445 & 84.3524876888759 \tabularnewline
Trimmed Mean ( 13 / 26 ) & 73.9962962962963 & 0.855536345572255 & 86.4911194939372 \tabularnewline
Trimmed Mean ( 14 / 26 ) & 74.0423076923077 & 0.831126850294762 & 89.086651052181 \tabularnewline
Trimmed Mean ( 15 / 26 ) & 74.088 & 0.802631590075892 & 92.3063593759058 \tabularnewline
Trimmed Mean ( 16 / 26 ) & 74.1354166666667 & 0.770750127289963 & 96.1860582849781 \tabularnewline
Trimmed Mean ( 17 / 26 ) & 74.1739130434783 & 0.738332334102171 & 100.461417734976 \tabularnewline
Trimmed Mean ( 18 / 26 ) & 74.2045454545455 & 0.704597965716856 & 105.314731329163 \tabularnewline
Trimmed Mean ( 19 / 26 ) & 74.2285714285714 & 0.670060632358744 & 110.778887527346 \tabularnewline
Trimmed Mean ( 20 / 26 ) & 74.245 & 0.638075532061357 & 116.357697904737 \tabularnewline
Trimmed Mean ( 21 / 26 ) & 74.2578947368421 & 0.609615129138809 & 121.811108660877 \tabularnewline
Trimmed Mean ( 22 / 26 ) & 74.2666666666667 & 0.586000704263079 & 126.734773740691 \tabularnewline
Trimmed Mean ( 23 / 26 ) & 74.2764705882353 & 0.563080697659912 & 131.910880442037 \tabularnewline
Trimmed Mean ( 24 / 26 ) & 74.2875 & 0.541331058148458 & 137.231180221008 \tabularnewline
Trimmed Mean ( 25 / 26 ) & 74.3133333333333 & 0.518834532419201 & 143.23127835541 \tabularnewline
Trimmed Mean ( 26 / 26 ) & 74.3535714285714 & 0.491339873716918 & 151.328185245983 \tabularnewline
Median & 75.3 &  &  \tabularnewline
Midrange & 74.6 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 74.0341463414634 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 74.245 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 74.0341463414634 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 74.245 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 74.245 &  &  \tabularnewline
Midmean - Closest Observation & 74.0341463414634 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 74.245 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 74.2285714285714 &  &  \tabularnewline
Number of observations & 80 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=293705&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]73.77625[/C][C]1.04028240407186[/C][C]70.9194442886146[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]73.1852127892199[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]72.5855926770118[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]74.3533985437115[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 26 )[/C][C]73.76875[/C][C]1.03738747102114[/C][C]71.110122360921[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 26 )[/C][C]73.75875[/C][C]1.03366696052685[/C][C]71.3563969989[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 26 )[/C][C]73.74[/C][C]1.03023992535597[/C][C]71.5755603963043[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 26 )[/C][C]73.705[/C][C]1.02230952854402[/C][C]72.096559742499[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 26 )[/C][C]73.68[/C][C]1.01590266652278[/C][C]72.5266331391676[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 26 )[/C][C]73.6425[/C][C]1.00717956709802[/C][C]73.1175476605289[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 26 )[/C][C]73.59875[/C][C]0.991502653484643[/C][C]74.229503815584[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 26 )[/C][C]73.58875[/C][C]0.980170473660938[/C][C]75.0775012892868[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 26 )[/C][C]73.5775[/C][C]0.967629517383277[/C][C]76.0389164222406[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 26 )[/C][C]73.59[/C][C]0.949699486113397[/C][C]77.4876696007953[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 26 )[/C][C]73.59[/C][C]0.945401261001802[/C][C]77.8399638710231[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 26 )[/C][C]73.575[/C][C]0.943236248377449[/C][C]78.002727446664[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 26 )[/C][C]73.6075[/C][C]0.932779932191261[/C][C]78.9119678283422[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 26 )[/C][C]73.6425[/C][C]0.921610751121252[/C][C]79.9062943985896[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 26 )[/C][C]73.66125[/C][C]0.901325489736847[/C][C]81.7254708080056[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 26 )[/C][C]73.78125[/C][C]0.863943881773828[/C][C]85.4005121820114[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 26 )[/C][C]73.8875[/C][C]0.828332118235956[/C][C]89.2003320568485[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 26 )[/C][C]73.9775[/C][C]0.788113785317574[/C][C]93.8665220405838[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 26 )[/C][C]74.0725[/C][C]0.732725048592883[/C][C]101.091808096704[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 26 )[/C][C]74.1225[/C][C]0.675795300349657[/C][C]109.681881424226[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 26 )[/C][C]74.175[/C][C]0.617312212003462[/C][C]120.1579987528[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 26 )[/C][C]74.175[/C][C]0.579801089855364[/C][C]127.931805058358[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 26 )[/C][C]74.175[/C][C]0.541167572727849[/C][C]137.064753577359[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 26 )[/C][C]74.055[/C][C]0.509699899295431[/C][C]145.29137655779[/C][/ROW]
[ROW][C]Winsorized Mean ( 25 / 26 )[/C][C]73.96125[/C][C]0.489650785370476[/C][C]151.048976555894[/C][/ROW]
[ROW][C]Winsorized Mean ( 26 / 26 )[/C][C]73.89625[/C][C]0.439585692996646[/C][C]168.104310893858[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 26 )[/C][C]73.7551282051282[/C][C]1.02732829288644[/C][C]71.7931441349696[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 26 )[/C][C]73.7407894736842[/C][C]1.01532671715411[/C][C]72.6276460845771[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 26 )[/C][C]73.7310810810811[/C][C]1.00330059833386[/C][C]73.4885249779807[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 26 )[/C][C]73.7277777777778[/C][C]0.990396417333596[/C][C]74.4426943468475[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 26 )[/C][C]73.7342857142857[/C][C]0.977654872936637[/C][C]75.4195450310659[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 26 )[/C][C]73.7470588235294[/C][C]0.964161284427607[/C][C]76.4883012983775[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 26 )[/C][C]73.7681818181818[/C][C]0.950093012477489[/C][C]77.6431158311772[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 26 )[/C][C]73.7984375[/C][C]0.936703344550431[/C][C]78.7852823728514[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 26 )[/C][C]73.8322580645161[/C][C]0.922779393782945[/C][C]80.010735569029[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 26 )[/C][C]73.87[/C][C]0.908236946111798[/C][C]81.3334012850288[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 26 )[/C][C]73.9086206896552[/C][C]0.893853057195073[/C][C]82.6854258591247[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 26 )[/C][C]73.95[/C][C]0.87667835325445[/C][C]84.3524876888759[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 26 )[/C][C]73.9962962962963[/C][C]0.855536345572255[/C][C]86.4911194939372[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 26 )[/C][C]74.0423076923077[/C][C]0.831126850294762[/C][C]89.086651052181[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 26 )[/C][C]74.088[/C][C]0.802631590075892[/C][C]92.3063593759058[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 26 )[/C][C]74.1354166666667[/C][C]0.770750127289963[/C][C]96.1860582849781[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 26 )[/C][C]74.1739130434783[/C][C]0.738332334102171[/C][C]100.461417734976[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 26 )[/C][C]74.2045454545455[/C][C]0.704597965716856[/C][C]105.314731329163[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 26 )[/C][C]74.2285714285714[/C][C]0.670060632358744[/C][C]110.778887527346[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 26 )[/C][C]74.245[/C][C]0.638075532061357[/C][C]116.357697904737[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 26 )[/C][C]74.2578947368421[/C][C]0.609615129138809[/C][C]121.811108660877[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 26 )[/C][C]74.2666666666667[/C][C]0.586000704263079[/C][C]126.734773740691[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 26 )[/C][C]74.2764705882353[/C][C]0.563080697659912[/C][C]131.910880442037[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 26 )[/C][C]74.2875[/C][C]0.541331058148458[/C][C]137.231180221008[/C][/ROW]
[ROW][C]Trimmed Mean ( 25 / 26 )[/C][C]74.3133333333333[/C][C]0.518834532419201[/C][C]143.23127835541[/C][/ROW]
[ROW][C]Trimmed Mean ( 26 / 26 )[/C][C]74.3535714285714[/C][C]0.491339873716918[/C][C]151.328185245983[/C][/ROW]
[ROW][C]Median[/C][C]75.3[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]74.6[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]74.0341463414634[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]74.245[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]74.0341463414634[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]74.245[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]74.245[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]74.0341463414634[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]74.245[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]74.2285714285714[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]80[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=293705&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=293705&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 Mean73.776251.0402824040718670.9194442886146
Geometric Mean73.1852127892199
Harmonic Mean72.5855926770118
Quadratic Mean74.3533985437115
Winsorized Mean ( 1 / 26 )73.768751.0373874710211471.110122360921
Winsorized Mean ( 2 / 26 )73.758751.0336669605268571.3563969989
Winsorized Mean ( 3 / 26 )73.741.0302399253559771.5755603963043
Winsorized Mean ( 4 / 26 )73.7051.0223095285440272.096559742499
Winsorized Mean ( 5 / 26 )73.681.0159026665227872.5266331391676
Winsorized Mean ( 6 / 26 )73.64251.0071795670980273.1175476605289
Winsorized Mean ( 7 / 26 )73.598750.99150265348464374.229503815584
Winsorized Mean ( 8 / 26 )73.588750.98017047366093875.0775012892868
Winsorized Mean ( 9 / 26 )73.57750.96762951738327776.0389164222406
Winsorized Mean ( 10 / 26 )73.590.94969948611339777.4876696007953
Winsorized Mean ( 11 / 26 )73.590.94540126100180277.8399638710231
Winsorized Mean ( 12 / 26 )73.5750.94323624837744978.002727446664
Winsorized Mean ( 13 / 26 )73.60750.93277993219126178.9119678283422
Winsorized Mean ( 14 / 26 )73.64250.92161075112125279.9062943985896
Winsorized Mean ( 15 / 26 )73.661250.90132548973684781.7254708080056
Winsorized Mean ( 16 / 26 )73.781250.86394388177382885.4005121820114
Winsorized Mean ( 17 / 26 )73.88750.82833211823595689.2003320568485
Winsorized Mean ( 18 / 26 )73.97750.78811378531757493.8665220405838
Winsorized Mean ( 19 / 26 )74.07250.732725048592883101.091808096704
Winsorized Mean ( 20 / 26 )74.12250.675795300349657109.681881424226
Winsorized Mean ( 21 / 26 )74.1750.617312212003462120.1579987528
Winsorized Mean ( 22 / 26 )74.1750.579801089855364127.931805058358
Winsorized Mean ( 23 / 26 )74.1750.541167572727849137.064753577359
Winsorized Mean ( 24 / 26 )74.0550.509699899295431145.29137655779
Winsorized Mean ( 25 / 26 )73.961250.489650785370476151.048976555894
Winsorized Mean ( 26 / 26 )73.896250.439585692996646168.104310893858
Trimmed Mean ( 1 / 26 )73.75512820512821.0273282928864471.7931441349696
Trimmed Mean ( 2 / 26 )73.74078947368421.0153267171541172.6276460845771
Trimmed Mean ( 3 / 26 )73.73108108108111.0033005983338673.4885249779807
Trimmed Mean ( 4 / 26 )73.72777777777780.99039641733359674.4426943468475
Trimmed Mean ( 5 / 26 )73.73428571428570.97765487293663775.4195450310659
Trimmed Mean ( 6 / 26 )73.74705882352940.96416128442760776.4883012983775
Trimmed Mean ( 7 / 26 )73.76818181818180.95009301247748977.6431158311772
Trimmed Mean ( 8 / 26 )73.79843750.93670334455043178.7852823728514
Trimmed Mean ( 9 / 26 )73.83225806451610.92277939378294580.010735569029
Trimmed Mean ( 10 / 26 )73.870.90823694611179881.3334012850288
Trimmed Mean ( 11 / 26 )73.90862068965520.89385305719507382.6854258591247
Trimmed Mean ( 12 / 26 )73.950.8766783532544584.3524876888759
Trimmed Mean ( 13 / 26 )73.99629629629630.85553634557225586.4911194939372
Trimmed Mean ( 14 / 26 )74.04230769230770.83112685029476289.086651052181
Trimmed Mean ( 15 / 26 )74.0880.80263159007589292.3063593759058
Trimmed Mean ( 16 / 26 )74.13541666666670.77075012728996396.1860582849781
Trimmed Mean ( 17 / 26 )74.17391304347830.738332334102171100.461417734976
Trimmed Mean ( 18 / 26 )74.20454545454550.704597965716856105.314731329163
Trimmed Mean ( 19 / 26 )74.22857142857140.670060632358744110.778887527346
Trimmed Mean ( 20 / 26 )74.2450.638075532061357116.357697904737
Trimmed Mean ( 21 / 26 )74.25789473684210.609615129138809121.811108660877
Trimmed Mean ( 22 / 26 )74.26666666666670.586000704263079126.734773740691
Trimmed Mean ( 23 / 26 )74.27647058823530.563080697659912131.910880442037
Trimmed Mean ( 24 / 26 )74.28750.541331058148458137.231180221008
Trimmed Mean ( 25 / 26 )74.31333333333330.518834532419201143.23127835541
Trimmed Mean ( 26 / 26 )74.35357142857140.491339873716918151.328185245983
Median75.3
Midrange74.6
Midmean - Weighted Average at Xnp74.0341463414634
Midmean - Weighted Average at X(n+1)p74.245
Midmean - Empirical Distribution Function74.0341463414634
Midmean - Empirical Distribution Function - Averaging74.245
Midmean - Empirical Distribution Function - Interpolation74.245
Midmean - Closest Observation74.0341463414634
Midmean - True Basic - Statistics Graphics Toolkit74.245
Midmean - MS Excel (old versions)74.2285714285714
Number of observations80



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')