Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationThu, 16 Mar 2017 09:52:15 +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/2017/Mar/16/t1489657945elrcqkxp6m4ogza.htm/, Retrieved Tue, 14 May 2024 01:50:17 +0200
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Tue, 14 May 2024 01:50:17 +0200
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact0
Dataseries X:
74.16
73.21
77.14
80.9
82.76
83.33
81.94
82.38
82.81
83.17
84.07
87.33
90.75
92.82
97.78
99.32
98.33
98.66
98.13
97.8
99.36
100.37
103.22
101.68
104.39
103.99
106.71
106.06
103.5
100.17
101.1
105.93
108.09
107.27
104.9
102.7
102.06
103.05
102.08
100.13
97.56
97.38
99.66
99.58
102.7
98.92
97.85
99.01
97.71
97.95
97.24
96.69
96.41
96.99
98.36
97.8
96.79
94.73
92.67
87.15
79.54
82.35
86.38
84.75
87.54
86.73
84.74
80.75
79.28
78.52
78.54
77.33




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Sir Ronald Aylmer Fisher' @ fisher.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&T=0

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Sir Ronald Aylmer Fisher' @ fisher.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean93.65486111111111.1163517177788483.8936865681114
Geometric Mean93.1626584789085
Harmonic Mean92.6518550875454
Quadratic Mean94.1260651039044
Winsorized Mean ( 1 / 24 )93.65666666666671.1109992647149684.2994857343091
Winsorized Mean ( 2 / 24 )93.72388888888891.0892317854594786.0458629100264
Winsorized Mean ( 3 / 24 )93.70472222222221.0830901672240186.5160861559569
Winsorized Mean ( 4 / 24 )93.76361111111111.0682456459065387.7734549823901
Winsorized Mean ( 5 / 24 )93.69347222222221.0568857454154588.6505212400157
Winsorized Mean ( 6 / 24 )93.71263888888891.0383694481442690.2498037248388
Winsorized Mean ( 7 / 24 )93.69902777777781.0278846039257491.1571468430589
Winsorized Mean ( 8 / 24 )93.77902777777780.99484585589147394.264882566901
Winsorized Mean ( 9 / 24 )93.76277777777780.98662384562861595.0339667880599
Winsorized Mean ( 10 / 24 )93.88361111111110.95747923371891398.0528953578042
Winsorized Mean ( 11 / 24 )93.89277777777780.93941973445799799.9476318559028
Winsorized Mean ( 12 / 24 )93.89777777777780.938554982248526100.04504749719
Winsorized Mean ( 13 / 24 )93.85444444444450.912242651104886102.883201449494
Winsorized Mean ( 14 / 24 )93.86027777777780.910084971101755103.133532316383
Winsorized Mean ( 15 / 24 )93.85611111111110.887370823228308105.768759411829
Winsorized Mean ( 16 / 24 )93.76277777777780.865637620888366108.316431166142
Winsorized Mean ( 17 / 24 )93.76513888888890.816057643782331114.900141679083
Winsorized Mean ( 18 / 24 )93.88263888888890.782578949330278119.965709490694
Winsorized Mean ( 19 / 24 )93.87472222222220.78095207865014120.205483522731
Winsorized Mean ( 20 / 24 )94.19694444444440.693035910353476135.919283600182
Winsorized Mean ( 21 / 24 )94.27569444444450.674293632211427139.814006748449
Winsorized Mean ( 22 / 24 )94.33680555555560.646733904180434145.86649152885
Winsorized Mean ( 23 / 24 )94.38152777777780.636349675889586148.317083128607
Winsorized Mean ( 24 / 24 )94.34819444444440.61425089326298153.598790786049
Trimmed Mean ( 1 / 24 )93.74071428571431.0905108556787385.960367838219
Trimmed Mean ( 2 / 24 )93.82970588235291.0659671436300888.0230750479065
Trimmed Mean ( 3 / 24 )93.88742424242421.0502803113593989.3927299474026
Trimmed Mean ( 4 / 24 )93.95593751.0338552761778990.8791971806254
Trimmed Mean ( 5 / 24 )94.01177419354841.0190920338533992.2505240651047
Trimmed Mean ( 6 / 24 )94.08816666666671.004159611293493.6984176703511
Trimmed Mean ( 7 / 24 )94.16586206896550.99054080429111295.0651014688446
Trimmed Mean ( 8 / 24 )94.25160714285710.97582970946226296.5861217679007
Trimmed Mean ( 9 / 24 )94.33037037037040.96492454754619597.7593228509448
Trimmed Mean ( 10 / 24 )94.41769230769230.95228397412452899.148672951778
Trimmed Mean ( 11 / 24 )94.49460.942087790440975100.303390999016
Trimmed Mean ( 12 / 24 )94.57666666666670.931925832081707101.485186278616
Trimmed Mean ( 13 / 24 )94.66521739130440.917936129630071103.128327054143
Trimmed Mean ( 14 / 24 )94.76727272727270.904248976665655104.80218963224
Trimmed Mean ( 15 / 24 )94.87833333333330.885535522185891107.142323437384
Trimmed Mean ( 16 / 24 )95.0010.864690755451972109.867024021025
Trimmed Mean ( 17 / 24 )95.14763157894740.840040593259026113.265516383931
Trimmed Mean ( 18 / 24 )95.31027777777780.817094201609185116.645397299447
Trimmed Mean ( 19 / 24 )95.47823529411770.792637294527115120.456400365415
Trimmed Mean ( 20 / 24 )95.6681250.756047851881531126.537129577072
Trimmed Mean ( 21 / 24 )95.84466666666670.730215010586487131.255404609783
Trimmed Mean ( 22 / 24 )96.03678571428570.695633405090753138.056604256601
Trimmed Mean ( 23 / 24 )96.25076923076920.649998324986462148.078488098833
Trimmed Mean ( 24 / 24 )96.49458333333330.577658623414655167.044305100017
Median97.635
Midrange90.65
Midmean - Weighted Average at Xnp95.0064864864865
Midmean - Weighted Average at X(n+1)p95.3102777777778
Midmean - Empirical Distribution Function95.0064864864865
Midmean - Empirical Distribution Function - Averaging95.3102777777778
Midmean - Empirical Distribution Function - Interpolation95.3102777777778
Midmean - Closest Observation95.0064864864865
Midmean - True Basic - Statistics Graphics Toolkit95.3102777777778
Midmean - MS Excel (old versions)95.1476315789474
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 93.6548611111111 & 1.11635171777884 & 83.8936865681114 \tabularnewline
Geometric Mean & 93.1626584789085 &  &  \tabularnewline
Harmonic Mean & 92.6518550875454 &  &  \tabularnewline
Quadratic Mean & 94.1260651039044 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 93.6566666666667 & 1.11099926471496 & 84.2994857343091 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 93.7238888888889 & 1.08923178545947 & 86.0458629100264 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 93.7047222222222 & 1.08309016722401 & 86.5160861559569 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 93.7636111111111 & 1.06824564590653 & 87.7734549823901 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 93.6934722222222 & 1.05688574541545 & 88.6505212400157 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 93.7126388888889 & 1.03836944814426 & 90.2498037248388 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 93.6990277777778 & 1.02788460392574 & 91.1571468430589 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 93.7790277777778 & 0.994845855891473 & 94.264882566901 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 93.7627777777778 & 0.986623845628615 & 95.0339667880599 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 93.8836111111111 & 0.957479233718913 & 98.0528953578042 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 93.8927777777778 & 0.939419734457997 & 99.9476318559028 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 93.8977777777778 & 0.938554982248526 & 100.04504749719 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 93.8544444444445 & 0.912242651104886 & 102.883201449494 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 93.8602777777778 & 0.910084971101755 & 103.133532316383 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 93.8561111111111 & 0.887370823228308 & 105.768759411829 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 93.7627777777778 & 0.865637620888366 & 108.316431166142 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 93.7651388888889 & 0.816057643782331 & 114.900141679083 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 93.8826388888889 & 0.782578949330278 & 119.965709490694 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 93.8747222222222 & 0.78095207865014 & 120.205483522731 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 94.1969444444444 & 0.693035910353476 & 135.919283600182 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 94.2756944444445 & 0.674293632211427 & 139.814006748449 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 94.3368055555556 & 0.646733904180434 & 145.86649152885 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 94.3815277777778 & 0.636349675889586 & 148.317083128607 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 94.3481944444444 & 0.61425089326298 & 153.598790786049 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 93.7407142857143 & 1.09051085567873 & 85.960367838219 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 93.8297058823529 & 1.06596714363008 & 88.0230750479065 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 93.8874242424242 & 1.05028031135939 & 89.3927299474026 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 93.9559375 & 1.03385527617789 & 90.8791971806254 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 94.0117741935484 & 1.01909203385339 & 92.2505240651047 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 94.0881666666667 & 1.0041596112934 & 93.6984176703511 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 94.1658620689655 & 0.990540804291112 & 95.0651014688446 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 94.2516071428571 & 0.975829709462262 & 96.5861217679007 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 94.3303703703704 & 0.964924547546195 & 97.7593228509448 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 94.4176923076923 & 0.952283974124528 & 99.148672951778 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 94.4946 & 0.942087790440975 & 100.303390999016 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 94.5766666666667 & 0.931925832081707 & 101.485186278616 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 94.6652173913044 & 0.917936129630071 & 103.128327054143 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 94.7672727272727 & 0.904248976665655 & 104.80218963224 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 94.8783333333333 & 0.885535522185891 & 107.142323437384 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 95.001 & 0.864690755451972 & 109.867024021025 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 95.1476315789474 & 0.840040593259026 & 113.265516383931 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 95.3102777777778 & 0.817094201609185 & 116.645397299447 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 95.4782352941177 & 0.792637294527115 & 120.456400365415 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 95.668125 & 0.756047851881531 & 126.537129577072 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 95.8446666666667 & 0.730215010586487 & 131.255404609783 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 96.0367857142857 & 0.695633405090753 & 138.056604256601 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 96.2507692307692 & 0.649998324986462 & 148.078488098833 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 96.4945833333333 & 0.577658623414655 & 167.044305100017 \tabularnewline
Median & 97.635 &  &  \tabularnewline
Midrange & 90.65 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 95.0064864864865 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 95.3102777777778 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 95.0064864864865 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 95.3102777777778 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 95.3102777777778 &  &  \tabularnewline
Midmean - Closest Observation & 95.0064864864865 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 95.3102777777778 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 95.1476315789474 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]93.6548611111111[/C][C]1.11635171777884[/C][C]83.8936865681114[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]93.1626584789085[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]92.6518550875454[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]94.1260651039044[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]93.6566666666667[/C][C]1.11099926471496[/C][C]84.2994857343091[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]93.7238888888889[/C][C]1.08923178545947[/C][C]86.0458629100264[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]93.7047222222222[/C][C]1.08309016722401[/C][C]86.5160861559569[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]93.7636111111111[/C][C]1.06824564590653[/C][C]87.7734549823901[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]93.6934722222222[/C][C]1.05688574541545[/C][C]88.6505212400157[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]93.7126388888889[/C][C]1.03836944814426[/C][C]90.2498037248388[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]93.6990277777778[/C][C]1.02788460392574[/C][C]91.1571468430589[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]93.7790277777778[/C][C]0.994845855891473[/C][C]94.264882566901[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]93.7627777777778[/C][C]0.986623845628615[/C][C]95.0339667880599[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]93.8836111111111[/C][C]0.957479233718913[/C][C]98.0528953578042[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]93.8927777777778[/C][C]0.939419734457997[/C][C]99.9476318559028[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]93.8977777777778[/C][C]0.938554982248526[/C][C]100.04504749719[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]93.8544444444445[/C][C]0.912242651104886[/C][C]102.883201449494[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]93.8602777777778[/C][C]0.910084971101755[/C][C]103.133532316383[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]93.8561111111111[/C][C]0.887370823228308[/C][C]105.768759411829[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]93.7627777777778[/C][C]0.865637620888366[/C][C]108.316431166142[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]93.7651388888889[/C][C]0.816057643782331[/C][C]114.900141679083[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]93.8826388888889[/C][C]0.782578949330278[/C][C]119.965709490694[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]93.8747222222222[/C][C]0.78095207865014[/C][C]120.205483522731[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]94.1969444444444[/C][C]0.693035910353476[/C][C]135.919283600182[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]94.2756944444445[/C][C]0.674293632211427[/C][C]139.814006748449[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]94.3368055555556[/C][C]0.646733904180434[/C][C]145.86649152885[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]94.3815277777778[/C][C]0.636349675889586[/C][C]148.317083128607[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]94.3481944444444[/C][C]0.61425089326298[/C][C]153.598790786049[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]93.7407142857143[/C][C]1.09051085567873[/C][C]85.960367838219[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]93.8297058823529[/C][C]1.06596714363008[/C][C]88.0230750479065[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]93.8874242424242[/C][C]1.05028031135939[/C][C]89.3927299474026[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]93.9559375[/C][C]1.03385527617789[/C][C]90.8791971806254[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]94.0117741935484[/C][C]1.01909203385339[/C][C]92.2505240651047[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]94.0881666666667[/C][C]1.0041596112934[/C][C]93.6984176703511[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]94.1658620689655[/C][C]0.990540804291112[/C][C]95.0651014688446[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]94.2516071428571[/C][C]0.975829709462262[/C][C]96.5861217679007[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]94.3303703703704[/C][C]0.964924547546195[/C][C]97.7593228509448[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]94.4176923076923[/C][C]0.952283974124528[/C][C]99.148672951778[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]94.4946[/C][C]0.942087790440975[/C][C]100.303390999016[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]94.5766666666667[/C][C]0.931925832081707[/C][C]101.485186278616[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]94.6652173913044[/C][C]0.917936129630071[/C][C]103.128327054143[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]94.7672727272727[/C][C]0.904248976665655[/C][C]104.80218963224[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]94.8783333333333[/C][C]0.885535522185891[/C][C]107.142323437384[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]95.001[/C][C]0.864690755451972[/C][C]109.867024021025[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]95.1476315789474[/C][C]0.840040593259026[/C][C]113.265516383931[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]95.3102777777778[/C][C]0.817094201609185[/C][C]116.645397299447[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]95.4782352941177[/C][C]0.792637294527115[/C][C]120.456400365415[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]95.668125[/C][C]0.756047851881531[/C][C]126.537129577072[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]95.8446666666667[/C][C]0.730215010586487[/C][C]131.255404609783[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]96.0367857142857[/C][C]0.695633405090753[/C][C]138.056604256601[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]96.2507692307692[/C][C]0.649998324986462[/C][C]148.078488098833[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]96.4945833333333[/C][C]0.577658623414655[/C][C]167.044305100017[/C][/ROW]
[ROW][C]Median[/C][C]97.635[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]90.65[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]95.0064864864865[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]95.3102777777778[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]95.0064864864865[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]95.3102777777778[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]95.3102777777778[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]95.0064864864865[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]95.3102777777778[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]95.1476315789474[/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=&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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 Mean93.65486111111111.1163517177788483.8936865681114
Geometric Mean93.1626584789085
Harmonic Mean92.6518550875454
Quadratic Mean94.1260651039044
Winsorized Mean ( 1 / 24 )93.65666666666671.1109992647149684.2994857343091
Winsorized Mean ( 2 / 24 )93.72388888888891.0892317854594786.0458629100264
Winsorized Mean ( 3 / 24 )93.70472222222221.0830901672240186.5160861559569
Winsorized Mean ( 4 / 24 )93.76361111111111.0682456459065387.7734549823901
Winsorized Mean ( 5 / 24 )93.69347222222221.0568857454154588.6505212400157
Winsorized Mean ( 6 / 24 )93.71263888888891.0383694481442690.2498037248388
Winsorized Mean ( 7 / 24 )93.69902777777781.0278846039257491.1571468430589
Winsorized Mean ( 8 / 24 )93.77902777777780.99484585589147394.264882566901
Winsorized Mean ( 9 / 24 )93.76277777777780.98662384562861595.0339667880599
Winsorized Mean ( 10 / 24 )93.88361111111110.95747923371891398.0528953578042
Winsorized Mean ( 11 / 24 )93.89277777777780.93941973445799799.9476318559028
Winsorized Mean ( 12 / 24 )93.89777777777780.938554982248526100.04504749719
Winsorized Mean ( 13 / 24 )93.85444444444450.912242651104886102.883201449494
Winsorized Mean ( 14 / 24 )93.86027777777780.910084971101755103.133532316383
Winsorized Mean ( 15 / 24 )93.85611111111110.887370823228308105.768759411829
Winsorized Mean ( 16 / 24 )93.76277777777780.865637620888366108.316431166142
Winsorized Mean ( 17 / 24 )93.76513888888890.816057643782331114.900141679083
Winsorized Mean ( 18 / 24 )93.88263888888890.782578949330278119.965709490694
Winsorized Mean ( 19 / 24 )93.87472222222220.78095207865014120.205483522731
Winsorized Mean ( 20 / 24 )94.19694444444440.693035910353476135.919283600182
Winsorized Mean ( 21 / 24 )94.27569444444450.674293632211427139.814006748449
Winsorized Mean ( 22 / 24 )94.33680555555560.646733904180434145.86649152885
Winsorized Mean ( 23 / 24 )94.38152777777780.636349675889586148.317083128607
Winsorized Mean ( 24 / 24 )94.34819444444440.61425089326298153.598790786049
Trimmed Mean ( 1 / 24 )93.74071428571431.0905108556787385.960367838219
Trimmed Mean ( 2 / 24 )93.82970588235291.0659671436300888.0230750479065
Trimmed Mean ( 3 / 24 )93.88742424242421.0502803113593989.3927299474026
Trimmed Mean ( 4 / 24 )93.95593751.0338552761778990.8791971806254
Trimmed Mean ( 5 / 24 )94.01177419354841.0190920338533992.2505240651047
Trimmed Mean ( 6 / 24 )94.08816666666671.004159611293493.6984176703511
Trimmed Mean ( 7 / 24 )94.16586206896550.99054080429111295.0651014688446
Trimmed Mean ( 8 / 24 )94.25160714285710.97582970946226296.5861217679007
Trimmed Mean ( 9 / 24 )94.33037037037040.96492454754619597.7593228509448
Trimmed Mean ( 10 / 24 )94.41769230769230.95228397412452899.148672951778
Trimmed Mean ( 11 / 24 )94.49460.942087790440975100.303390999016
Trimmed Mean ( 12 / 24 )94.57666666666670.931925832081707101.485186278616
Trimmed Mean ( 13 / 24 )94.66521739130440.917936129630071103.128327054143
Trimmed Mean ( 14 / 24 )94.76727272727270.904248976665655104.80218963224
Trimmed Mean ( 15 / 24 )94.87833333333330.885535522185891107.142323437384
Trimmed Mean ( 16 / 24 )95.0010.864690755451972109.867024021025
Trimmed Mean ( 17 / 24 )95.14763157894740.840040593259026113.265516383931
Trimmed Mean ( 18 / 24 )95.31027777777780.817094201609185116.645397299447
Trimmed Mean ( 19 / 24 )95.47823529411770.792637294527115120.456400365415
Trimmed Mean ( 20 / 24 )95.6681250.756047851881531126.537129577072
Trimmed Mean ( 21 / 24 )95.84466666666670.730215010586487131.255404609783
Trimmed Mean ( 22 / 24 )96.03678571428570.695633405090753138.056604256601
Trimmed Mean ( 23 / 24 )96.25076923076920.649998324986462148.078488098833
Trimmed Mean ( 24 / 24 )96.49458333333330.577658623414655167.044305100017
Median97.635
Midrange90.65
Midmean - Weighted Average at Xnp95.0064864864865
Midmean - Weighted Average at X(n+1)p95.3102777777778
Midmean - Empirical Distribution Function95.0064864864865
Midmean - Empirical Distribution Function - Averaging95.3102777777778
Midmean - Empirical Distribution Function - Interpolation95.3102777777778
Midmean - Closest Observation95.0064864864865
Midmean - True Basic - Statistics Graphics Toolkit95.3102777777778
Midmean - MS Excel (old versions)95.1476315789474
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')