Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationMon, 23 Feb 2015 18:24:33 +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/2015/Feb/23/t1424715892n753uru4vmve3m5.htm/, Retrieved Sat, 18 May 2024 07:05:35 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=277432, Retrieved Sat, 18 May 2024 07:05:35 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsGlenn Waem
Estimated Impact83
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2015-02-23 18:24:33] [3d92bf785db8aeb0f2ab1bed7b74f49c] [Current]
Feedback Forum

Post a new message
Dataseries X:
105
101
95
93
84
87
116
120
117
109
105
107
109
109
108
107
99
103
131
137
135
124
118
121
121
118
113
107
100
102
130
136
133
120
112
109
110
106
102
98
92
92
120
127
124
114
108
106
111
110
104
100
96
98
122
134
133
125
118
116
118
116
111
108
102
102
129
136
137
126
119
117
120
116
110
104
98
98
124
130
131
121
114
111




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=277432&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=277432&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=277432&T=0

As an alternative you can also use a QR Code:  

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

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







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean113.1547619047621.3765403980542582.2022819415306
Geometric Mean112.454758288805
Harmonic Mean111.749854987048
Quadratic Mean113.847590266653
Winsorized Mean ( 1 / 28 )113.1904761904761.3678628663484182.7498713322374
Winsorized Mean ( 2 / 28 )113.2857142857141.3377620899206184.6830054007865
Winsorized Mean ( 3 / 28 )113.2857142857141.3377620899206184.6830054007865
Winsorized Mean ( 4 / 28 )113.2857142857141.3191918705077985.8750852081191
Winsorized Mean ( 5 / 28 )113.3452380952381.2862633227760788.1197777221938
Winsorized Mean ( 6 / 28 )113.3452380952381.2605827463819789.9149527633571
Winsorized Mean ( 7 / 28 )113.5119047619051.2341355930235591.9768503587258
Winsorized Mean ( 8 / 28 )113.3214285714291.1990817765250794.5068391413911
Winsorized Mean ( 9 / 28 )113.3214285714291.1990817765250794.5068391413911
Winsorized Mean ( 10 / 28 )113.2023809523811.1782816336171796.0741283939598
Winsorized Mean ( 11 / 28 )113.3333333333331.1583384411119297.8412951784127
Winsorized Mean ( 12 / 28 )113.3333333333331.11286913894017101.838867992391
Winsorized Mean ( 13 / 28 )113.023809523811.06204213792032106.421210127436
Winsorized Mean ( 14 / 28 )113.023809523811.01168959272873111.717873086904
Winsorized Mean ( 15 / 28 )113.023809523810.959294328286931117.819741231706
Winsorized Mean ( 16 / 28 )112.8333333333330.931200949041963121.169693232614
Winsorized Mean ( 17 / 28 )112.8333333333330.931200949041963121.169693232614
Winsorized Mean ( 18 / 28 )112.8333333333330.931200949041963121.169693232614
Winsorized Mean ( 19 / 28 )112.6071428571430.836285852277271134.651498109773
Winsorized Mean ( 20 / 28 )112.6071428571430.77207758869622145.849516299649
Winsorized Mean ( 21 / 28 )112.6071428571430.77207758869622145.849516299649
Winsorized Mean ( 22 / 28 )112.8690476190480.737640514712766153.013622988155
Winsorized Mean ( 23 / 28 )112.5952380952380.702041741558253160.382540567063
Winsorized Mean ( 24 / 28 )112.8809523809520.665605458139415169.591386309378
Winsorized Mean ( 25 / 28 )112.8809523809520.665605458139415169.591386309378
Winsorized Mean ( 26 / 28 )113.1904761904760.627920871988751180.262324824431
Winsorized Mean ( 27 / 28 )112.8690476190480.586660805996313192.392344034923
Winsorized Mean ( 28 / 28 )112.5357142857140.545530640776691206.286697527188
Trimmed Mean ( 1 / 28 )113.2195121951221.3324324407063484.972047164435
Trimmed Mean ( 2 / 28 )113.251.2913416632089487.6994859118673
Trimmed Mean ( 3 / 28 )113.2307692307691.2622919543419389.7025199608438
Trimmed Mean ( 4 / 28 )113.2105263157891.2283658791861192.1635224765447
Trimmed Mean ( 5 / 28 )113.1891891891891.195244754983494.6995907886344
Trimmed Mean ( 6 / 28 )113.1527777777781.1662741999532697.0207330165691
Trimmed Mean ( 7 / 28 )113.1142857142861.1389114081017499.3178968176435
Trimmed Mean ( 8 / 28 )113.0441176470591.11270770984775101.593721915099
Trimmed Mean ( 9 / 28 )1131.08947069118283103.720091705558
Trimmed Mean ( 10 / 28 )112.9531251.06146183816422106.412798782621
Trimmed Mean ( 11 / 28 )112.919354838711.03208659667893109.408798837291
Trimmed Mean ( 12 / 28 )112.8666666666671.00041422682577112.819933623678
Trimmed Mean ( 13 / 28 )112.8103448275860.970981534365967116.18176127443
Trimmed Mean ( 14 / 28 )112.7857142857140.945156582133107119.330189746095
Trimmed Mean ( 15 / 28 )112.7592592592590.922933669599399122.174824663405
Trimmed Mean ( 16 / 28 )112.7307692307690.905036762757304124.559326062426
Trimmed Mean ( 17 / 28 )112.720.887574084289329126.997849526278
Trimmed Mean ( 18 / 28 )112.7083333333330.864979775382252130.301697844352
Trimmed Mean ( 19 / 28 )112.6956521739130.835718074887178134.848886915754
Trimmed Mean ( 20 / 28 )112.7045454545450.817733903703987137.825452685821
Trimmed Mean ( 21 / 28 )112.7142857142860.80668354645309139.725529558499
Trimmed Mean ( 22 / 28 )112.7250.790964600977819142.515859572787
Trimmed Mean ( 23 / 28 )112.7105263157890.776529734002937145.146439834026
Trimmed Mean ( 24 / 28 )112.7222222222220.763878066301401147.565727038098
Trimmed Mean ( 25 / 28 )112.7058823529410.75351749334127149.573013697635
Trimmed Mean ( 26 / 28 )112.68750.737035118653808152.892985894381
Trimmed Mean ( 27 / 28 )112.6333333333330.721561737480701156.096599199657
Trimmed Mean ( 28 / 28 )112.6071428571430.709607697182201158.689291709063
Median111.5
Midrange110.5
Midmean - Weighted Average at Xnp112.704545454545
Midmean - Weighted Average at X(n+1)p112.704545454545
Midmean - Empirical Distribution Function112.704545454545
Midmean - Empirical Distribution Function - Averaging112.704545454545
Midmean - Empirical Distribution Function - Interpolation112.704545454545
Midmean - Closest Observation112.704545454545
Midmean - True Basic - Statistics Graphics Toolkit112.704545454545
Midmean - MS Excel (old versions)112.704545454545
Number of observations84

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 113.154761904762 & 1.37654039805425 & 82.2022819415306 \tabularnewline
Geometric Mean & 112.454758288805 &  &  \tabularnewline
Harmonic Mean & 111.749854987048 &  &  \tabularnewline
Quadratic Mean & 113.847590266653 &  &  \tabularnewline
Winsorized Mean ( 1 / 28 ) & 113.190476190476 & 1.36786286634841 & 82.7498713322374 \tabularnewline
Winsorized Mean ( 2 / 28 ) & 113.285714285714 & 1.33776208992061 & 84.6830054007865 \tabularnewline
Winsorized Mean ( 3 / 28 ) & 113.285714285714 & 1.33776208992061 & 84.6830054007865 \tabularnewline
Winsorized Mean ( 4 / 28 ) & 113.285714285714 & 1.31919187050779 & 85.8750852081191 \tabularnewline
Winsorized Mean ( 5 / 28 ) & 113.345238095238 & 1.28626332277607 & 88.1197777221938 \tabularnewline
Winsorized Mean ( 6 / 28 ) & 113.345238095238 & 1.26058274638197 & 89.9149527633571 \tabularnewline
Winsorized Mean ( 7 / 28 ) & 113.511904761905 & 1.23413559302355 & 91.9768503587258 \tabularnewline
Winsorized Mean ( 8 / 28 ) & 113.321428571429 & 1.19908177652507 & 94.5068391413911 \tabularnewline
Winsorized Mean ( 9 / 28 ) & 113.321428571429 & 1.19908177652507 & 94.5068391413911 \tabularnewline
Winsorized Mean ( 10 / 28 ) & 113.202380952381 & 1.17828163361717 & 96.0741283939598 \tabularnewline
Winsorized Mean ( 11 / 28 ) & 113.333333333333 & 1.15833844111192 & 97.8412951784127 \tabularnewline
Winsorized Mean ( 12 / 28 ) & 113.333333333333 & 1.11286913894017 & 101.838867992391 \tabularnewline
Winsorized Mean ( 13 / 28 ) & 113.02380952381 & 1.06204213792032 & 106.421210127436 \tabularnewline
Winsorized Mean ( 14 / 28 ) & 113.02380952381 & 1.01168959272873 & 111.717873086904 \tabularnewline
Winsorized Mean ( 15 / 28 ) & 113.02380952381 & 0.959294328286931 & 117.819741231706 \tabularnewline
Winsorized Mean ( 16 / 28 ) & 112.833333333333 & 0.931200949041963 & 121.169693232614 \tabularnewline
Winsorized Mean ( 17 / 28 ) & 112.833333333333 & 0.931200949041963 & 121.169693232614 \tabularnewline
Winsorized Mean ( 18 / 28 ) & 112.833333333333 & 0.931200949041963 & 121.169693232614 \tabularnewline
Winsorized Mean ( 19 / 28 ) & 112.607142857143 & 0.836285852277271 & 134.651498109773 \tabularnewline
Winsorized Mean ( 20 / 28 ) & 112.607142857143 & 0.77207758869622 & 145.849516299649 \tabularnewline
Winsorized Mean ( 21 / 28 ) & 112.607142857143 & 0.77207758869622 & 145.849516299649 \tabularnewline
Winsorized Mean ( 22 / 28 ) & 112.869047619048 & 0.737640514712766 & 153.013622988155 \tabularnewline
Winsorized Mean ( 23 / 28 ) & 112.595238095238 & 0.702041741558253 & 160.382540567063 \tabularnewline
Winsorized Mean ( 24 / 28 ) & 112.880952380952 & 0.665605458139415 & 169.591386309378 \tabularnewline
Winsorized Mean ( 25 / 28 ) & 112.880952380952 & 0.665605458139415 & 169.591386309378 \tabularnewline
Winsorized Mean ( 26 / 28 ) & 113.190476190476 & 0.627920871988751 & 180.262324824431 \tabularnewline
Winsorized Mean ( 27 / 28 ) & 112.869047619048 & 0.586660805996313 & 192.392344034923 \tabularnewline
Winsorized Mean ( 28 / 28 ) & 112.535714285714 & 0.545530640776691 & 206.286697527188 \tabularnewline
Trimmed Mean ( 1 / 28 ) & 113.219512195122 & 1.33243244070634 & 84.972047164435 \tabularnewline
Trimmed Mean ( 2 / 28 ) & 113.25 & 1.29134166320894 & 87.6994859118673 \tabularnewline
Trimmed Mean ( 3 / 28 ) & 113.230769230769 & 1.26229195434193 & 89.7025199608438 \tabularnewline
Trimmed Mean ( 4 / 28 ) & 113.210526315789 & 1.22836587918611 & 92.1635224765447 \tabularnewline
Trimmed Mean ( 5 / 28 ) & 113.189189189189 & 1.1952447549834 & 94.6995907886344 \tabularnewline
Trimmed Mean ( 6 / 28 ) & 113.152777777778 & 1.16627419995326 & 97.0207330165691 \tabularnewline
Trimmed Mean ( 7 / 28 ) & 113.114285714286 & 1.13891140810174 & 99.3178968176435 \tabularnewline
Trimmed Mean ( 8 / 28 ) & 113.044117647059 & 1.11270770984775 & 101.593721915099 \tabularnewline
Trimmed Mean ( 9 / 28 ) & 113 & 1.08947069118283 & 103.720091705558 \tabularnewline
Trimmed Mean ( 10 / 28 ) & 112.953125 & 1.06146183816422 & 106.412798782621 \tabularnewline
Trimmed Mean ( 11 / 28 ) & 112.91935483871 & 1.03208659667893 & 109.408798837291 \tabularnewline
Trimmed Mean ( 12 / 28 ) & 112.866666666667 & 1.00041422682577 & 112.819933623678 \tabularnewline
Trimmed Mean ( 13 / 28 ) & 112.810344827586 & 0.970981534365967 & 116.18176127443 \tabularnewline
Trimmed Mean ( 14 / 28 ) & 112.785714285714 & 0.945156582133107 & 119.330189746095 \tabularnewline
Trimmed Mean ( 15 / 28 ) & 112.759259259259 & 0.922933669599399 & 122.174824663405 \tabularnewline
Trimmed Mean ( 16 / 28 ) & 112.730769230769 & 0.905036762757304 & 124.559326062426 \tabularnewline
Trimmed Mean ( 17 / 28 ) & 112.72 & 0.887574084289329 & 126.997849526278 \tabularnewline
Trimmed Mean ( 18 / 28 ) & 112.708333333333 & 0.864979775382252 & 130.301697844352 \tabularnewline
Trimmed Mean ( 19 / 28 ) & 112.695652173913 & 0.835718074887178 & 134.848886915754 \tabularnewline
Trimmed Mean ( 20 / 28 ) & 112.704545454545 & 0.817733903703987 & 137.825452685821 \tabularnewline
Trimmed Mean ( 21 / 28 ) & 112.714285714286 & 0.80668354645309 & 139.725529558499 \tabularnewline
Trimmed Mean ( 22 / 28 ) & 112.725 & 0.790964600977819 & 142.515859572787 \tabularnewline
Trimmed Mean ( 23 / 28 ) & 112.710526315789 & 0.776529734002937 & 145.146439834026 \tabularnewline
Trimmed Mean ( 24 / 28 ) & 112.722222222222 & 0.763878066301401 & 147.565727038098 \tabularnewline
Trimmed Mean ( 25 / 28 ) & 112.705882352941 & 0.75351749334127 & 149.573013697635 \tabularnewline
Trimmed Mean ( 26 / 28 ) & 112.6875 & 0.737035118653808 & 152.892985894381 \tabularnewline
Trimmed Mean ( 27 / 28 ) & 112.633333333333 & 0.721561737480701 & 156.096599199657 \tabularnewline
Trimmed Mean ( 28 / 28 ) & 112.607142857143 & 0.709607697182201 & 158.689291709063 \tabularnewline
Median & 111.5 &  &  \tabularnewline
Midrange & 110.5 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 112.704545454545 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 112.704545454545 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 112.704545454545 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 112.704545454545 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 112.704545454545 &  &  \tabularnewline
Midmean - Closest Observation & 112.704545454545 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 112.704545454545 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 112.704545454545 &  &  \tabularnewline
Number of observations & 84 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=277432&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]113.154761904762[/C][C]1.37654039805425[/C][C]82.2022819415306[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]112.454758288805[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]111.749854987048[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]113.847590266653[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 28 )[/C][C]113.190476190476[/C][C]1.36786286634841[/C][C]82.7498713322374[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 28 )[/C][C]113.285714285714[/C][C]1.33776208992061[/C][C]84.6830054007865[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 28 )[/C][C]113.285714285714[/C][C]1.33776208992061[/C][C]84.6830054007865[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 28 )[/C][C]113.285714285714[/C][C]1.31919187050779[/C][C]85.8750852081191[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 28 )[/C][C]113.345238095238[/C][C]1.28626332277607[/C][C]88.1197777221938[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 28 )[/C][C]113.345238095238[/C][C]1.26058274638197[/C][C]89.9149527633571[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 28 )[/C][C]113.511904761905[/C][C]1.23413559302355[/C][C]91.9768503587258[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 28 )[/C][C]113.321428571429[/C][C]1.19908177652507[/C][C]94.5068391413911[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 28 )[/C][C]113.321428571429[/C][C]1.19908177652507[/C][C]94.5068391413911[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 28 )[/C][C]113.202380952381[/C][C]1.17828163361717[/C][C]96.0741283939598[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 28 )[/C][C]113.333333333333[/C][C]1.15833844111192[/C][C]97.8412951784127[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 28 )[/C][C]113.333333333333[/C][C]1.11286913894017[/C][C]101.838867992391[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 28 )[/C][C]113.02380952381[/C][C]1.06204213792032[/C][C]106.421210127436[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 28 )[/C][C]113.02380952381[/C][C]1.01168959272873[/C][C]111.717873086904[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 28 )[/C][C]113.02380952381[/C][C]0.959294328286931[/C][C]117.819741231706[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 28 )[/C][C]112.833333333333[/C][C]0.931200949041963[/C][C]121.169693232614[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 28 )[/C][C]112.833333333333[/C][C]0.931200949041963[/C][C]121.169693232614[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 28 )[/C][C]112.833333333333[/C][C]0.931200949041963[/C][C]121.169693232614[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 28 )[/C][C]112.607142857143[/C][C]0.836285852277271[/C][C]134.651498109773[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 28 )[/C][C]112.607142857143[/C][C]0.77207758869622[/C][C]145.849516299649[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 28 )[/C][C]112.607142857143[/C][C]0.77207758869622[/C][C]145.849516299649[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 28 )[/C][C]112.869047619048[/C][C]0.737640514712766[/C][C]153.013622988155[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 28 )[/C][C]112.595238095238[/C][C]0.702041741558253[/C][C]160.382540567063[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 28 )[/C][C]112.880952380952[/C][C]0.665605458139415[/C][C]169.591386309378[/C][/ROW]
[ROW][C]Winsorized Mean ( 25 / 28 )[/C][C]112.880952380952[/C][C]0.665605458139415[/C][C]169.591386309378[/C][/ROW]
[ROW][C]Winsorized Mean ( 26 / 28 )[/C][C]113.190476190476[/C][C]0.627920871988751[/C][C]180.262324824431[/C][/ROW]
[ROW][C]Winsorized Mean ( 27 / 28 )[/C][C]112.869047619048[/C][C]0.586660805996313[/C][C]192.392344034923[/C][/ROW]
[ROW][C]Winsorized Mean ( 28 / 28 )[/C][C]112.535714285714[/C][C]0.545530640776691[/C][C]206.286697527188[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 28 )[/C][C]113.219512195122[/C][C]1.33243244070634[/C][C]84.972047164435[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 28 )[/C][C]113.25[/C][C]1.29134166320894[/C][C]87.6994859118673[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 28 )[/C][C]113.230769230769[/C][C]1.26229195434193[/C][C]89.7025199608438[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 28 )[/C][C]113.210526315789[/C][C]1.22836587918611[/C][C]92.1635224765447[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 28 )[/C][C]113.189189189189[/C][C]1.1952447549834[/C][C]94.6995907886344[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 28 )[/C][C]113.152777777778[/C][C]1.16627419995326[/C][C]97.0207330165691[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 28 )[/C][C]113.114285714286[/C][C]1.13891140810174[/C][C]99.3178968176435[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 28 )[/C][C]113.044117647059[/C][C]1.11270770984775[/C][C]101.593721915099[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 28 )[/C][C]113[/C][C]1.08947069118283[/C][C]103.720091705558[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 28 )[/C][C]112.953125[/C][C]1.06146183816422[/C][C]106.412798782621[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 28 )[/C][C]112.91935483871[/C][C]1.03208659667893[/C][C]109.408798837291[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 28 )[/C][C]112.866666666667[/C][C]1.00041422682577[/C][C]112.819933623678[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 28 )[/C][C]112.810344827586[/C][C]0.970981534365967[/C][C]116.18176127443[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 28 )[/C][C]112.785714285714[/C][C]0.945156582133107[/C][C]119.330189746095[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 28 )[/C][C]112.759259259259[/C][C]0.922933669599399[/C][C]122.174824663405[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 28 )[/C][C]112.730769230769[/C][C]0.905036762757304[/C][C]124.559326062426[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 28 )[/C][C]112.72[/C][C]0.887574084289329[/C][C]126.997849526278[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 28 )[/C][C]112.708333333333[/C][C]0.864979775382252[/C][C]130.301697844352[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 28 )[/C][C]112.695652173913[/C][C]0.835718074887178[/C][C]134.848886915754[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 28 )[/C][C]112.704545454545[/C][C]0.817733903703987[/C][C]137.825452685821[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 28 )[/C][C]112.714285714286[/C][C]0.80668354645309[/C][C]139.725529558499[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 28 )[/C][C]112.725[/C][C]0.790964600977819[/C][C]142.515859572787[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 28 )[/C][C]112.710526315789[/C][C]0.776529734002937[/C][C]145.146439834026[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 28 )[/C][C]112.722222222222[/C][C]0.763878066301401[/C][C]147.565727038098[/C][/ROW]
[ROW][C]Trimmed Mean ( 25 / 28 )[/C][C]112.705882352941[/C][C]0.75351749334127[/C][C]149.573013697635[/C][/ROW]
[ROW][C]Trimmed Mean ( 26 / 28 )[/C][C]112.6875[/C][C]0.737035118653808[/C][C]152.892985894381[/C][/ROW]
[ROW][C]Trimmed Mean ( 27 / 28 )[/C][C]112.633333333333[/C][C]0.721561737480701[/C][C]156.096599199657[/C][/ROW]
[ROW][C]Trimmed Mean ( 28 / 28 )[/C][C]112.607142857143[/C][C]0.709607697182201[/C][C]158.689291709063[/C][/ROW]
[ROW][C]Median[/C][C]111.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]110.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]112.704545454545[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]112.704545454545[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]112.704545454545[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]112.704545454545[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]112.704545454545[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]112.704545454545[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]112.704545454545[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]112.704545454545[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]84[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=277432&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=277432&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 Mean113.1547619047621.3765403980542582.2022819415306
Geometric Mean112.454758288805
Harmonic Mean111.749854987048
Quadratic Mean113.847590266653
Winsorized Mean ( 1 / 28 )113.1904761904761.3678628663484182.7498713322374
Winsorized Mean ( 2 / 28 )113.2857142857141.3377620899206184.6830054007865
Winsorized Mean ( 3 / 28 )113.2857142857141.3377620899206184.6830054007865
Winsorized Mean ( 4 / 28 )113.2857142857141.3191918705077985.8750852081191
Winsorized Mean ( 5 / 28 )113.3452380952381.2862633227760788.1197777221938
Winsorized Mean ( 6 / 28 )113.3452380952381.2605827463819789.9149527633571
Winsorized Mean ( 7 / 28 )113.5119047619051.2341355930235591.9768503587258
Winsorized Mean ( 8 / 28 )113.3214285714291.1990817765250794.5068391413911
Winsorized Mean ( 9 / 28 )113.3214285714291.1990817765250794.5068391413911
Winsorized Mean ( 10 / 28 )113.2023809523811.1782816336171796.0741283939598
Winsorized Mean ( 11 / 28 )113.3333333333331.1583384411119297.8412951784127
Winsorized Mean ( 12 / 28 )113.3333333333331.11286913894017101.838867992391
Winsorized Mean ( 13 / 28 )113.023809523811.06204213792032106.421210127436
Winsorized Mean ( 14 / 28 )113.023809523811.01168959272873111.717873086904
Winsorized Mean ( 15 / 28 )113.023809523810.959294328286931117.819741231706
Winsorized Mean ( 16 / 28 )112.8333333333330.931200949041963121.169693232614
Winsorized Mean ( 17 / 28 )112.8333333333330.931200949041963121.169693232614
Winsorized Mean ( 18 / 28 )112.8333333333330.931200949041963121.169693232614
Winsorized Mean ( 19 / 28 )112.6071428571430.836285852277271134.651498109773
Winsorized Mean ( 20 / 28 )112.6071428571430.77207758869622145.849516299649
Winsorized Mean ( 21 / 28 )112.6071428571430.77207758869622145.849516299649
Winsorized Mean ( 22 / 28 )112.8690476190480.737640514712766153.013622988155
Winsorized Mean ( 23 / 28 )112.5952380952380.702041741558253160.382540567063
Winsorized Mean ( 24 / 28 )112.8809523809520.665605458139415169.591386309378
Winsorized Mean ( 25 / 28 )112.8809523809520.665605458139415169.591386309378
Winsorized Mean ( 26 / 28 )113.1904761904760.627920871988751180.262324824431
Winsorized Mean ( 27 / 28 )112.8690476190480.586660805996313192.392344034923
Winsorized Mean ( 28 / 28 )112.5357142857140.545530640776691206.286697527188
Trimmed Mean ( 1 / 28 )113.2195121951221.3324324407063484.972047164435
Trimmed Mean ( 2 / 28 )113.251.2913416632089487.6994859118673
Trimmed Mean ( 3 / 28 )113.2307692307691.2622919543419389.7025199608438
Trimmed Mean ( 4 / 28 )113.2105263157891.2283658791861192.1635224765447
Trimmed Mean ( 5 / 28 )113.1891891891891.195244754983494.6995907886344
Trimmed Mean ( 6 / 28 )113.1527777777781.1662741999532697.0207330165691
Trimmed Mean ( 7 / 28 )113.1142857142861.1389114081017499.3178968176435
Trimmed Mean ( 8 / 28 )113.0441176470591.11270770984775101.593721915099
Trimmed Mean ( 9 / 28 )1131.08947069118283103.720091705558
Trimmed Mean ( 10 / 28 )112.9531251.06146183816422106.412798782621
Trimmed Mean ( 11 / 28 )112.919354838711.03208659667893109.408798837291
Trimmed Mean ( 12 / 28 )112.8666666666671.00041422682577112.819933623678
Trimmed Mean ( 13 / 28 )112.8103448275860.970981534365967116.18176127443
Trimmed Mean ( 14 / 28 )112.7857142857140.945156582133107119.330189746095
Trimmed Mean ( 15 / 28 )112.7592592592590.922933669599399122.174824663405
Trimmed Mean ( 16 / 28 )112.7307692307690.905036762757304124.559326062426
Trimmed Mean ( 17 / 28 )112.720.887574084289329126.997849526278
Trimmed Mean ( 18 / 28 )112.7083333333330.864979775382252130.301697844352
Trimmed Mean ( 19 / 28 )112.6956521739130.835718074887178134.848886915754
Trimmed Mean ( 20 / 28 )112.7045454545450.817733903703987137.825452685821
Trimmed Mean ( 21 / 28 )112.7142857142860.80668354645309139.725529558499
Trimmed Mean ( 22 / 28 )112.7250.790964600977819142.515859572787
Trimmed Mean ( 23 / 28 )112.7105263157890.776529734002937145.146439834026
Trimmed Mean ( 24 / 28 )112.7222222222220.763878066301401147.565727038098
Trimmed Mean ( 25 / 28 )112.7058823529410.75351749334127149.573013697635
Trimmed Mean ( 26 / 28 )112.68750.737035118653808152.892985894381
Trimmed Mean ( 27 / 28 )112.6333333333330.721561737480701156.096599199657
Trimmed Mean ( 28 / 28 )112.6071428571430.709607697182201158.689291709063
Median111.5
Midrange110.5
Midmean - Weighted Average at Xnp112.704545454545
Midmean - Weighted Average at X(n+1)p112.704545454545
Midmean - Empirical Distribution Function112.704545454545
Midmean - Empirical Distribution Function - Averaging112.704545454545
Midmean - Empirical Distribution Function - Interpolation112.704545454545
Midmean - Closest Observation112.704545454545
Midmean - True Basic - Statistics Graphics Toolkit112.704545454545
Midmean - MS Excel (old versions)112.704545454545
Number of observations84



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')