Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationThu, 09 Mar 2017 10:48:52 +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/09/t14890566541q9g01sv9dr830c.htm/, Retrieved Thu, 16 May 2024 01:20:30 +0200
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Thu, 16 May 2024 01:20:30 +0200
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact0
Dataseries X:
62,38
62,62
64,15
64,97
66,12
67,08
68,66
69,04
70,8
73,2
74,19
75,36
75,54
76,81
77,69
79,34
80,36
80,74
81,12
82,95
87,31
88,93
90,8
91,29
91,36
92,72
95,75
97,19
98,73
99,03
99,4
99,66
100,5
101,21
101,26
101,44
101,97
102,23
102,58
101,91
101,63
101,1
100,71
100,75
100,14
97,72
94,91
94,34
97,11
96,51
95,8
95,25
95,09
94,97
95,21
95,46
95,33
95,14
95,6
95,66
95,66
96,33
97,66
98,27
99,53
100,86
101,26
101,29
101,38
101,49
101,29
101,26




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ jenkins.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 & 'Gwilym Jenkins' @ jenkins.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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.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 time2 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean90.73751.4407754545406762.9782383604859
Geometric Mean89.829610569183
Harmonic Mean88.8222901733173
Quadratic Mean91.5460436823399
Winsorized Mean ( 1 / 24 )90.73597222222221.4393001100251563.0417322907291
Winsorized Mean ( 2 / 24 )90.771251.4270638479187963.6069998776717
Winsorized Mean ( 3 / 24 )90.80291666666671.4179152939473764.0397328770452
Winsorized Mean ( 4 / 24 )90.851251.4000674717910264.8906226524781
Winsorized Mean ( 5 / 24 )90.90819444444441.3826309140119165.7501532210506
Winsorized Mean ( 6 / 24 )91.03569444444451.3508343336484967.3921976787223
Winsorized Mean ( 7 / 24 )91.06680555555551.3416209105776167.8781948295278
Winsorized Mean ( 8 / 24 )91.25236111111111.2961789349841770.4010523919103
Winsorized Mean ( 9 / 24 )91.55236111111111.2313067109673574.3538228904683
Winsorized Mean ( 10 / 24 )91.68569444444441.2023139503258976.2576982655763
Winsorized Mean ( 11 / 24 )91.86444444444441.1661731835072778.774272761239
Winsorized Mean ( 12 / 24 )91.89444444444441.1602050923749779.2053448553087
Winsorized Mean ( 13 / 24 )92.11472222222221.1142173574877682.6721299961747
Winsorized Mean ( 14 / 24 )92.26444444444441.0789204613177585.51552014479
Winsorized Mean ( 15 / 24 )92.55819444444451.0086829860997791.7614312127297
Winsorized Mean ( 16 / 24 )92.76041666666670.96438857432100996.1857275548665
Winsorized Mean ( 17 / 24 )92.84069444444440.94708704889478398.0276253938709
Winsorized Mean ( 18 / 24 )92.88319444444440.923900603407147100.5337523343
Winsorized Mean ( 19 / 24 )93.27111111111110.827043222098409112.776586058537
Winsorized Mean ( 20 / 24 )94.34888888888890.604154000370887156.16695218598
Winsorized Mean ( 21 / 24 )94.78347222222220.523290687824743181.129675011466
Winsorized Mean ( 22 / 24 )95.31513888888890.430637288105329221.33508063885
Winsorized Mean ( 23 / 24 )95.35347222222220.39193808195049243.287081846432
Winsorized Mean ( 24 / 24 )95.27680555555560.375434376820331253.777521287433
Trimmed Mean ( 1 / 24 )90.97342857142861.4144605141156564.3166971884733
Trimmed Mean ( 2 / 24 )91.22485294117651.3841292907252965.9077541039353
Trimmed Mean ( 3 / 24 )91.47227272727271.3549444942648767.5099777994239
Trimmed Mean ( 4 / 24 )91.723281251.3233023913612969.313923898863
Trimmed Mean ( 5 / 24 )91.97645161290321.2909508934279571.2470567867008
Trimmed Mean ( 6 / 24 )92.23283333333331.2564661252190573.4065419529345
Trimmed Mean ( 7 / 24 )92.48051724137931.2229671806262575.6197866193126
Trimmed Mean ( 8 / 24 )92.74017857142861.1832406933423478.378117903858
Trimmed Mean ( 9 / 24 )92.98814814814811.1453410342954481.1881748437921
Trimmed Mean ( 10 / 24 )93.20903846153851.1140404246903783.6675549609831
Trimmed Mean ( 11 / 24 )93.42841.0808938991522286.4362358537493
Trimmed Mean ( 12 / 24 )93.64166666666671.0468689103065589.4492765471903
Trimmed Mean ( 13 / 24 )93.86956521739131.0034553325857993.5463315297756
Trimmed Mean ( 14 / 24 )94.09045454545450.95823795273065298.1911165982612
Trimmed Mean ( 15 / 24 )94.31404761904760.907147963959641103.96765617747
Trimmed Mean ( 16 / 24 )94.524750.857925493410465110.178273901433
Trimmed Mean ( 17 / 24 )94.73368421052630.803248952218022117.938136052262
Trimmed Mean ( 18 / 24 )94.95638888888890.731295127792453129.846877519247
Trimmed Mean ( 19 / 24 )95.20029411764710.633046208293643150.38443145289
Trimmed Mean ( 20 / 24 )95.428750.525075023441351181.743076207583
Trimmed Mean ( 21 / 24 )95.55833333333330.466309571913592204.924666120816
Trimmed Mean ( 22 / 24 )95.65321428571430.413425186149448231.36765124691
Trimmed Mean ( 23 / 24 )95.69576923076920.375349344181543254.951209357874
Trimmed Mean ( 24 / 24 )95.74041666666670.332428743136458288.002823592683
Median95.63
Midrange82.48
Midmean - Weighted Average at Xnp94.5721621621622
Midmean - Weighted Average at X(n+1)p94.9563888888889
Midmean - Empirical Distribution Function94.5721621621622
Midmean - Empirical Distribution Function - Averaging94.9563888888889
Midmean - Empirical Distribution Function - Interpolation94.9563888888889
Midmean - Closest Observation94.5721621621622
Midmean - True Basic - Statistics Graphics Toolkit94.9563888888889
Midmean - MS Excel (old versions)94.7336842105263
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 90.7375 & 1.44077545454067 & 62.9782383604859 \tabularnewline
Geometric Mean & 89.829610569183 &  &  \tabularnewline
Harmonic Mean & 88.8222901733173 &  &  \tabularnewline
Quadratic Mean & 91.5460436823399 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 90.7359722222222 & 1.43930011002515 & 63.0417322907291 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 90.77125 & 1.42706384791879 & 63.6069998776717 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 90.8029166666667 & 1.41791529394737 & 64.0397328770452 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 90.85125 & 1.40006747179102 & 64.8906226524781 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 90.9081944444444 & 1.38263091401191 & 65.7501532210506 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 91.0356944444445 & 1.35083433364849 & 67.3921976787223 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 91.0668055555555 & 1.34162091057761 & 67.8781948295278 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 91.2523611111111 & 1.29617893498417 & 70.4010523919103 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 91.5523611111111 & 1.23130671096735 & 74.3538228904683 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 91.6856944444444 & 1.20231395032589 & 76.2576982655763 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 91.8644444444444 & 1.16617318350727 & 78.774272761239 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 91.8944444444444 & 1.16020509237497 & 79.2053448553087 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 92.1147222222222 & 1.11421735748776 & 82.6721299961747 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 92.2644444444444 & 1.07892046131775 & 85.51552014479 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 92.5581944444445 & 1.00868298609977 & 91.7614312127297 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 92.7604166666667 & 0.964388574321009 & 96.1857275548665 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 92.8406944444444 & 0.947087048894783 & 98.0276253938709 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 92.8831944444444 & 0.923900603407147 & 100.5337523343 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 93.2711111111111 & 0.827043222098409 & 112.776586058537 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 94.3488888888889 & 0.604154000370887 & 156.16695218598 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 94.7834722222222 & 0.523290687824743 & 181.129675011466 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 95.3151388888889 & 0.430637288105329 & 221.33508063885 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 95.3534722222222 & 0.39193808195049 & 243.287081846432 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 95.2768055555556 & 0.375434376820331 & 253.777521287433 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 90.9734285714286 & 1.41446051411565 & 64.3166971884733 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 91.2248529411765 & 1.38412929072529 & 65.9077541039353 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 91.4722727272727 & 1.35494449426487 & 67.5099777994239 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 91.72328125 & 1.32330239136129 & 69.313923898863 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 91.9764516129032 & 1.29095089342795 & 71.2470567867008 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 92.2328333333333 & 1.25646612521905 & 73.4065419529345 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 92.4805172413793 & 1.22296718062625 & 75.6197866193126 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 92.7401785714286 & 1.18324069334234 & 78.378117903858 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 92.9881481481481 & 1.14534103429544 & 81.1881748437921 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 93.2090384615385 & 1.11404042469037 & 83.6675549609831 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 93.4284 & 1.08089389915222 & 86.4362358537493 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 93.6416666666667 & 1.04686891030655 & 89.4492765471903 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 93.8695652173913 & 1.00345533258579 & 93.5463315297756 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 94.0904545454545 & 0.958237952730652 & 98.1911165982612 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 94.3140476190476 & 0.907147963959641 & 103.96765617747 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 94.52475 & 0.857925493410465 & 110.178273901433 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 94.7336842105263 & 0.803248952218022 & 117.938136052262 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 94.9563888888889 & 0.731295127792453 & 129.846877519247 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 95.2002941176471 & 0.633046208293643 & 150.38443145289 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 95.42875 & 0.525075023441351 & 181.743076207583 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 95.5583333333333 & 0.466309571913592 & 204.924666120816 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 95.6532142857143 & 0.413425186149448 & 231.36765124691 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 95.6957692307692 & 0.375349344181543 & 254.951209357874 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 95.7404166666667 & 0.332428743136458 & 288.002823592683 \tabularnewline
Median & 95.63 &  &  \tabularnewline
Midrange & 82.48 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 94.5721621621622 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 94.9563888888889 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 94.5721621621622 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 94.9563888888889 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 94.9563888888889 &  &  \tabularnewline
Midmean - Closest Observation & 94.5721621621622 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 94.9563888888889 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 94.7336842105263 &  &  \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]90.7375[/C][C]1.44077545454067[/C][C]62.9782383604859[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]89.829610569183[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]88.8222901733173[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]91.5460436823399[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]90.7359722222222[/C][C]1.43930011002515[/C][C]63.0417322907291[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]90.77125[/C][C]1.42706384791879[/C][C]63.6069998776717[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]90.8029166666667[/C][C]1.41791529394737[/C][C]64.0397328770452[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]90.85125[/C][C]1.40006747179102[/C][C]64.8906226524781[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]90.9081944444444[/C][C]1.38263091401191[/C][C]65.7501532210506[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]91.0356944444445[/C][C]1.35083433364849[/C][C]67.3921976787223[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]91.0668055555555[/C][C]1.34162091057761[/C][C]67.8781948295278[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]91.2523611111111[/C][C]1.29617893498417[/C][C]70.4010523919103[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]91.5523611111111[/C][C]1.23130671096735[/C][C]74.3538228904683[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]91.6856944444444[/C][C]1.20231395032589[/C][C]76.2576982655763[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]91.8644444444444[/C][C]1.16617318350727[/C][C]78.774272761239[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]91.8944444444444[/C][C]1.16020509237497[/C][C]79.2053448553087[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]92.1147222222222[/C][C]1.11421735748776[/C][C]82.6721299961747[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]92.2644444444444[/C][C]1.07892046131775[/C][C]85.51552014479[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]92.5581944444445[/C][C]1.00868298609977[/C][C]91.7614312127297[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]92.7604166666667[/C][C]0.964388574321009[/C][C]96.1857275548665[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]92.8406944444444[/C][C]0.947087048894783[/C][C]98.0276253938709[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]92.8831944444444[/C][C]0.923900603407147[/C][C]100.5337523343[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]93.2711111111111[/C][C]0.827043222098409[/C][C]112.776586058537[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]94.3488888888889[/C][C]0.604154000370887[/C][C]156.16695218598[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]94.7834722222222[/C][C]0.523290687824743[/C][C]181.129675011466[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]95.3151388888889[/C][C]0.430637288105329[/C][C]221.33508063885[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]95.3534722222222[/C][C]0.39193808195049[/C][C]243.287081846432[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]95.2768055555556[/C][C]0.375434376820331[/C][C]253.777521287433[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]90.9734285714286[/C][C]1.41446051411565[/C][C]64.3166971884733[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]91.2248529411765[/C][C]1.38412929072529[/C][C]65.9077541039353[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]91.4722727272727[/C][C]1.35494449426487[/C][C]67.5099777994239[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]91.72328125[/C][C]1.32330239136129[/C][C]69.313923898863[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]91.9764516129032[/C][C]1.29095089342795[/C][C]71.2470567867008[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]92.2328333333333[/C][C]1.25646612521905[/C][C]73.4065419529345[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]92.4805172413793[/C][C]1.22296718062625[/C][C]75.6197866193126[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]92.7401785714286[/C][C]1.18324069334234[/C][C]78.378117903858[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]92.9881481481481[/C][C]1.14534103429544[/C][C]81.1881748437921[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]93.2090384615385[/C][C]1.11404042469037[/C][C]83.6675549609831[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]93.4284[/C][C]1.08089389915222[/C][C]86.4362358537493[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]93.6416666666667[/C][C]1.04686891030655[/C][C]89.4492765471903[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]93.8695652173913[/C][C]1.00345533258579[/C][C]93.5463315297756[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]94.0904545454545[/C][C]0.958237952730652[/C][C]98.1911165982612[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]94.3140476190476[/C][C]0.907147963959641[/C][C]103.96765617747[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]94.52475[/C][C]0.857925493410465[/C][C]110.178273901433[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]94.7336842105263[/C][C]0.803248952218022[/C][C]117.938136052262[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]94.9563888888889[/C][C]0.731295127792453[/C][C]129.846877519247[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]95.2002941176471[/C][C]0.633046208293643[/C][C]150.38443145289[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]95.42875[/C][C]0.525075023441351[/C][C]181.743076207583[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]95.5583333333333[/C][C]0.466309571913592[/C][C]204.924666120816[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]95.6532142857143[/C][C]0.413425186149448[/C][C]231.36765124691[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]95.6957692307692[/C][C]0.375349344181543[/C][C]254.951209357874[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]95.7404166666667[/C][C]0.332428743136458[/C][C]288.002823592683[/C][/ROW]
[ROW][C]Median[/C][C]95.63[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]82.48[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]94.5721621621622[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]94.9563888888889[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]94.5721621621622[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]94.9563888888889[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]94.9563888888889[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]94.5721621621622[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]94.9563888888889[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]94.7336842105263[/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 Mean90.73751.4407754545406762.9782383604859
Geometric Mean89.829610569183
Harmonic Mean88.8222901733173
Quadratic Mean91.5460436823399
Winsorized Mean ( 1 / 24 )90.73597222222221.4393001100251563.0417322907291
Winsorized Mean ( 2 / 24 )90.771251.4270638479187963.6069998776717
Winsorized Mean ( 3 / 24 )90.80291666666671.4179152939473764.0397328770452
Winsorized Mean ( 4 / 24 )90.851251.4000674717910264.8906226524781
Winsorized Mean ( 5 / 24 )90.90819444444441.3826309140119165.7501532210506
Winsorized Mean ( 6 / 24 )91.03569444444451.3508343336484967.3921976787223
Winsorized Mean ( 7 / 24 )91.06680555555551.3416209105776167.8781948295278
Winsorized Mean ( 8 / 24 )91.25236111111111.2961789349841770.4010523919103
Winsorized Mean ( 9 / 24 )91.55236111111111.2313067109673574.3538228904683
Winsorized Mean ( 10 / 24 )91.68569444444441.2023139503258976.2576982655763
Winsorized Mean ( 11 / 24 )91.86444444444441.1661731835072778.774272761239
Winsorized Mean ( 12 / 24 )91.89444444444441.1602050923749779.2053448553087
Winsorized Mean ( 13 / 24 )92.11472222222221.1142173574877682.6721299961747
Winsorized Mean ( 14 / 24 )92.26444444444441.0789204613177585.51552014479
Winsorized Mean ( 15 / 24 )92.55819444444451.0086829860997791.7614312127297
Winsorized Mean ( 16 / 24 )92.76041666666670.96438857432100996.1857275548665
Winsorized Mean ( 17 / 24 )92.84069444444440.94708704889478398.0276253938709
Winsorized Mean ( 18 / 24 )92.88319444444440.923900603407147100.5337523343
Winsorized Mean ( 19 / 24 )93.27111111111110.827043222098409112.776586058537
Winsorized Mean ( 20 / 24 )94.34888888888890.604154000370887156.16695218598
Winsorized Mean ( 21 / 24 )94.78347222222220.523290687824743181.129675011466
Winsorized Mean ( 22 / 24 )95.31513888888890.430637288105329221.33508063885
Winsorized Mean ( 23 / 24 )95.35347222222220.39193808195049243.287081846432
Winsorized Mean ( 24 / 24 )95.27680555555560.375434376820331253.777521287433
Trimmed Mean ( 1 / 24 )90.97342857142861.4144605141156564.3166971884733
Trimmed Mean ( 2 / 24 )91.22485294117651.3841292907252965.9077541039353
Trimmed Mean ( 3 / 24 )91.47227272727271.3549444942648767.5099777994239
Trimmed Mean ( 4 / 24 )91.723281251.3233023913612969.313923898863
Trimmed Mean ( 5 / 24 )91.97645161290321.2909508934279571.2470567867008
Trimmed Mean ( 6 / 24 )92.23283333333331.2564661252190573.4065419529345
Trimmed Mean ( 7 / 24 )92.48051724137931.2229671806262575.6197866193126
Trimmed Mean ( 8 / 24 )92.74017857142861.1832406933423478.378117903858
Trimmed Mean ( 9 / 24 )92.98814814814811.1453410342954481.1881748437921
Trimmed Mean ( 10 / 24 )93.20903846153851.1140404246903783.6675549609831
Trimmed Mean ( 11 / 24 )93.42841.0808938991522286.4362358537493
Trimmed Mean ( 12 / 24 )93.64166666666671.0468689103065589.4492765471903
Trimmed Mean ( 13 / 24 )93.86956521739131.0034553325857993.5463315297756
Trimmed Mean ( 14 / 24 )94.09045454545450.95823795273065298.1911165982612
Trimmed Mean ( 15 / 24 )94.31404761904760.907147963959641103.96765617747
Trimmed Mean ( 16 / 24 )94.524750.857925493410465110.178273901433
Trimmed Mean ( 17 / 24 )94.73368421052630.803248952218022117.938136052262
Trimmed Mean ( 18 / 24 )94.95638888888890.731295127792453129.846877519247
Trimmed Mean ( 19 / 24 )95.20029411764710.633046208293643150.38443145289
Trimmed Mean ( 20 / 24 )95.428750.525075023441351181.743076207583
Trimmed Mean ( 21 / 24 )95.55833333333330.466309571913592204.924666120816
Trimmed Mean ( 22 / 24 )95.65321428571430.413425186149448231.36765124691
Trimmed Mean ( 23 / 24 )95.69576923076920.375349344181543254.951209357874
Trimmed Mean ( 24 / 24 )95.74041666666670.332428743136458288.002823592683
Median95.63
Midrange82.48
Midmean - Weighted Average at Xnp94.5721621621622
Midmean - Weighted Average at X(n+1)p94.9563888888889
Midmean - Empirical Distribution Function94.5721621621622
Midmean - Empirical Distribution Function - Averaging94.9563888888889
Midmean - Empirical Distribution Function - Interpolation94.9563888888889
Midmean - Closest Observation94.5721621621622
Midmean - True Basic - Statistics Graphics Toolkit94.9563888888889
Midmean - MS Excel (old versions)94.7336842105263
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')