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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationTue, 27 Oct 2009 11:00:53 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Oct/27/t1256662889x1bm80pz4hce1eg.htm/, Retrieved Tue, 07 May 2024 11:52:09 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=51053, Retrieved Tue, 07 May 2024 11:52:09 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP1W52
Estimated Impact84
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2009-10-27 17:00:53] [d7e29fbdd9c070952bc7bcf8a141229f] [Current]
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Dataseries X:
104,28
104,33
104,46
104,46
104,5
104,61
104,66
104,66
105,03
105,32
105,52
105,67
105,71
105,81
106
106,02
106,19
106,22
106,34
106,42
106,84
107,23
107,42
107,63
107,69
107,81
107,92
108,06
108,21
108,44
108,55
108,66
109,23
109,7
109,94
110,13
110,39
110,46
110,67
110,89
110,98
111,12
111,33
111,43
111,87
112,22
112,47
112,64
112,84
113,03
113,09
113,27
113,44
113,51
113,66
113,62
114,01
114,55
114,77
114,87
115,11
115,09
115,24
115,27
115,41
115,59
115,6
115,68
116,2
116,55
116,73
117,04
117,12
117,28
117,48
117,66
117,92
118,12
118,17
118,39




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'RServer@AstonUniversity' @ vre.aston.ac.uk

\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 & 3 seconds \tabularnewline
R Server & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=51053&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=51053&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=51053&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 time3 seconds
R Server'RServer@AstonUniversity' @ vre.aston.ac.uk







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean110.9056250.492962140808571224.977976641552
Geometric Mean110.819114607763
Harmonic Mean110.732700002519
Quadratic Mean110.992141968475
Winsorized Mean ( 1 / 26 )110.90350.492335017023309225.260231682341
Winsorized Mean ( 2 / 26 )110.90550.491557776327823225.620477064809
Winsorized Mean ( 3 / 26 )110.8980.490181069618828226.238846975947
Winsorized Mean ( 4 / 26 )110.8870.487527162501963227.447839892518
Winsorized Mean ( 5 / 26 )110.8826250.484434739884826228.890737741811
Winsorized Mean ( 6 / 26 )110.8713750.481263886656462230.375430349177
Winsorized Mean ( 7 / 26 )110.8573750.478925245341066231.471145191048
Winsorized Mean ( 8 / 26 )110.8863750.47166367428249235.096279501880
Winsorized Mean ( 9 / 26 )110.8841250.46092623774055240.568047381185
Winsorized Mean ( 10 / 26 )110.8866250.453559199649864244.481040370478
Winsorized Mean ( 11 / 26 )110.8591250.443008528997175250.241513974795
Winsorized Mean ( 12 / 26 )110.7871250.430549222172806257.315817320265
Winsorized Mean ( 13 / 26 )110.7903750.426271309417599259.905774919192
Winsorized Mean ( 14 / 26 )110.8218750.421152506043261263.139535939545
Winsorized Mean ( 15 / 26 )110.7918750.41581737006197266.443595137665
Winsorized Mean ( 16 / 26 )110.7978750.406995540584144272.233633913965
Winsorized Mean ( 17 / 26 )110.7978750.405197197410788273.441859193496
Winsorized Mean ( 18 / 26 )110.7956250.397310015252493278.86441505782
Winsorized Mean ( 19 / 26 )110.8098750.393968389054715281.265903759123
Winsorized Mean ( 20 / 26 )110.8598750.37183582763581298.141993752631
Winsorized Mean ( 21 / 26 )110.9360.354462402712486312.969723025839
Winsorized Mean ( 22 / 26 )110.927750.339355726834605326.877495289962
Winsorized Mean ( 23 / 26 )110.8328750.310920753556415356.466635733565
Winsorized Mean ( 24 / 26 )110.7458750.295211289584964375.141056277681
Winsorized Mean ( 25 / 26 )110.7708750.288758976722211383.610152167019
Winsorized Mean ( 26 / 26 )110.7708750.279683545955361396.057889718259
Trimmed Mean ( 1 / 26 )110.8946153846150.488957234564561226.798189177776
Trimmed Mean ( 2 / 26 )110.8852631578950.484836289016008228.706608127333
Trimmed Mean ( 3 / 26 )110.8743243243240.480312748333639230.837771241724
Trimmed Mean ( 4 / 26 )110.8655555555560.475423494965587233.193261859262
Trimmed Mean ( 5 / 26 )110.8594285714290.470400291444497235.670407922162
Trimmed Mean ( 6 / 26 )110.8539705882350.465178090440149238.304367437739
Trimmed Mean ( 7 / 26 )110.8504545454550.459607587350881241.184996932671
Trimmed Mean ( 8 / 26 )110.849218750.453324049312295244.52534322448
Trimmed Mean ( 9 / 26 )110.8432258064520.447212281420447247.853716034784
Trimmed Mean ( 10 / 26 )110.8371666666670.441886434503388250.827266945252
Trimmed Mean ( 11 / 26 )110.8303448275860.436646252150496253.82181635991
Trimmed Mean ( 12 / 26 )110.8266071428570.432021319578677256.530412089245
Trimmed Mean ( 13 / 26 )110.8314814814810.428346683214407258.742476187228
Trimmed Mean ( 14 / 26 )110.8363461538460.42417829613439261.296599010173
Trimmed Mean ( 15 / 26 )110.8380.419513518061975264.206027286172
Trimmed Mean ( 16 / 26 )110.8431250.414210044132758267.601248617897
Trimmed Mean ( 17 / 26 )110.8480434782610.408728394463957271.202209045537
Trimmed Mean ( 18 / 26 )110.8534090909090.401571035209751276.049314744544
Trimmed Mean ( 19 / 26 )110.8595238095240.393480250576324281.741011517477
Trimmed Mean ( 20 / 26 )110.864750.383141700288549289.35704444728
Trimmed Mean ( 21 / 26 )110.8652631578950.374093068657212296.357437350657
Trimmed Mean ( 22 / 26 )110.8577777777780.365473624243442303.326342652665
Trimmed Mean ( 23 / 26 )110.8502941176470.356811360181742310.669184022575
Trimmed Mean ( 24 / 26 )110.85218750.351397766064270315.460706371495
Trimmed Mean ( 25 / 26 )110.8640.346750299372535319.722867436928
Trimmed Mean ( 26 / 26 )110.8746428571430.340555678089594325.569796630946
Median110.935
Midrange111.335
Midmean - Weighted Average at Xnp110.756341463415
Midmean - Weighted Average at X(n+1)p110.86475
Midmean - Empirical Distribution Function110.756341463415
Midmean - Empirical Distribution Function - Averaging110.86475
Midmean - Empirical Distribution Function - Interpolation110.86475
Midmean - Closest Observation110.756341463415
Midmean - True Basic - Statistics Graphics Toolkit110.86475
Midmean - MS Excel (old versions)110.859523809524
Number of observations80

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 110.905625 & 0.492962140808571 & 224.977976641552 \tabularnewline
Geometric Mean & 110.819114607763 &  &  \tabularnewline
Harmonic Mean & 110.732700002519 &  &  \tabularnewline
Quadratic Mean & 110.992141968475 &  &  \tabularnewline
Winsorized Mean ( 1 / 26 ) & 110.9035 & 0.492335017023309 & 225.260231682341 \tabularnewline
Winsorized Mean ( 2 / 26 ) & 110.9055 & 0.491557776327823 & 225.620477064809 \tabularnewline
Winsorized Mean ( 3 / 26 ) & 110.898 & 0.490181069618828 & 226.238846975947 \tabularnewline
Winsorized Mean ( 4 / 26 ) & 110.887 & 0.487527162501963 & 227.447839892518 \tabularnewline
Winsorized Mean ( 5 / 26 ) & 110.882625 & 0.484434739884826 & 228.890737741811 \tabularnewline
Winsorized Mean ( 6 / 26 ) & 110.871375 & 0.481263886656462 & 230.375430349177 \tabularnewline
Winsorized Mean ( 7 / 26 ) & 110.857375 & 0.478925245341066 & 231.471145191048 \tabularnewline
Winsorized Mean ( 8 / 26 ) & 110.886375 & 0.47166367428249 & 235.096279501880 \tabularnewline
Winsorized Mean ( 9 / 26 ) & 110.884125 & 0.46092623774055 & 240.568047381185 \tabularnewline
Winsorized Mean ( 10 / 26 ) & 110.886625 & 0.453559199649864 & 244.481040370478 \tabularnewline
Winsorized Mean ( 11 / 26 ) & 110.859125 & 0.443008528997175 & 250.241513974795 \tabularnewline
Winsorized Mean ( 12 / 26 ) & 110.787125 & 0.430549222172806 & 257.315817320265 \tabularnewline
Winsorized Mean ( 13 / 26 ) & 110.790375 & 0.426271309417599 & 259.905774919192 \tabularnewline
Winsorized Mean ( 14 / 26 ) & 110.821875 & 0.421152506043261 & 263.139535939545 \tabularnewline
Winsorized Mean ( 15 / 26 ) & 110.791875 & 0.41581737006197 & 266.443595137665 \tabularnewline
Winsorized Mean ( 16 / 26 ) & 110.797875 & 0.406995540584144 & 272.233633913965 \tabularnewline
Winsorized Mean ( 17 / 26 ) & 110.797875 & 0.405197197410788 & 273.441859193496 \tabularnewline
Winsorized Mean ( 18 / 26 ) & 110.795625 & 0.397310015252493 & 278.86441505782 \tabularnewline
Winsorized Mean ( 19 / 26 ) & 110.809875 & 0.393968389054715 & 281.265903759123 \tabularnewline
Winsorized Mean ( 20 / 26 ) & 110.859875 & 0.37183582763581 & 298.141993752631 \tabularnewline
Winsorized Mean ( 21 / 26 ) & 110.936 & 0.354462402712486 & 312.969723025839 \tabularnewline
Winsorized Mean ( 22 / 26 ) & 110.92775 & 0.339355726834605 & 326.877495289962 \tabularnewline
Winsorized Mean ( 23 / 26 ) & 110.832875 & 0.310920753556415 & 356.466635733565 \tabularnewline
Winsorized Mean ( 24 / 26 ) & 110.745875 & 0.295211289584964 & 375.141056277681 \tabularnewline
Winsorized Mean ( 25 / 26 ) & 110.770875 & 0.288758976722211 & 383.610152167019 \tabularnewline
Winsorized Mean ( 26 / 26 ) & 110.770875 & 0.279683545955361 & 396.057889718259 \tabularnewline
Trimmed Mean ( 1 / 26 ) & 110.894615384615 & 0.488957234564561 & 226.798189177776 \tabularnewline
Trimmed Mean ( 2 / 26 ) & 110.885263157895 & 0.484836289016008 & 228.706608127333 \tabularnewline
Trimmed Mean ( 3 / 26 ) & 110.874324324324 & 0.480312748333639 & 230.837771241724 \tabularnewline
Trimmed Mean ( 4 / 26 ) & 110.865555555556 & 0.475423494965587 & 233.193261859262 \tabularnewline
Trimmed Mean ( 5 / 26 ) & 110.859428571429 & 0.470400291444497 & 235.670407922162 \tabularnewline
Trimmed Mean ( 6 / 26 ) & 110.853970588235 & 0.465178090440149 & 238.304367437739 \tabularnewline
Trimmed Mean ( 7 / 26 ) & 110.850454545455 & 0.459607587350881 & 241.184996932671 \tabularnewline
Trimmed Mean ( 8 / 26 ) & 110.84921875 & 0.453324049312295 & 244.52534322448 \tabularnewline
Trimmed Mean ( 9 / 26 ) & 110.843225806452 & 0.447212281420447 & 247.853716034784 \tabularnewline
Trimmed Mean ( 10 / 26 ) & 110.837166666667 & 0.441886434503388 & 250.827266945252 \tabularnewline
Trimmed Mean ( 11 / 26 ) & 110.830344827586 & 0.436646252150496 & 253.82181635991 \tabularnewline
Trimmed Mean ( 12 / 26 ) & 110.826607142857 & 0.432021319578677 & 256.530412089245 \tabularnewline
Trimmed Mean ( 13 / 26 ) & 110.831481481481 & 0.428346683214407 & 258.742476187228 \tabularnewline
Trimmed Mean ( 14 / 26 ) & 110.836346153846 & 0.42417829613439 & 261.296599010173 \tabularnewline
Trimmed Mean ( 15 / 26 ) & 110.838 & 0.419513518061975 & 264.206027286172 \tabularnewline
Trimmed Mean ( 16 / 26 ) & 110.843125 & 0.414210044132758 & 267.601248617897 \tabularnewline
Trimmed Mean ( 17 / 26 ) & 110.848043478261 & 0.408728394463957 & 271.202209045537 \tabularnewline
Trimmed Mean ( 18 / 26 ) & 110.853409090909 & 0.401571035209751 & 276.049314744544 \tabularnewline
Trimmed Mean ( 19 / 26 ) & 110.859523809524 & 0.393480250576324 & 281.741011517477 \tabularnewline
Trimmed Mean ( 20 / 26 ) & 110.86475 & 0.383141700288549 & 289.35704444728 \tabularnewline
Trimmed Mean ( 21 / 26 ) & 110.865263157895 & 0.374093068657212 & 296.357437350657 \tabularnewline
Trimmed Mean ( 22 / 26 ) & 110.857777777778 & 0.365473624243442 & 303.326342652665 \tabularnewline
Trimmed Mean ( 23 / 26 ) & 110.850294117647 & 0.356811360181742 & 310.669184022575 \tabularnewline
Trimmed Mean ( 24 / 26 ) & 110.8521875 & 0.351397766064270 & 315.460706371495 \tabularnewline
Trimmed Mean ( 25 / 26 ) & 110.864 & 0.346750299372535 & 319.722867436928 \tabularnewline
Trimmed Mean ( 26 / 26 ) & 110.874642857143 & 0.340555678089594 & 325.569796630946 \tabularnewline
Median & 110.935 &  &  \tabularnewline
Midrange & 111.335 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 110.756341463415 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 110.86475 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 110.756341463415 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 110.86475 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 110.86475 &  &  \tabularnewline
Midmean - Closest Observation & 110.756341463415 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 110.86475 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 110.859523809524 &  &  \tabularnewline
Number of observations & 80 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=51053&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]110.905625[/C][C]0.492962140808571[/C][C]224.977976641552[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]110.819114607763[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]110.732700002519[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]110.992141968475[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 26 )[/C][C]110.9035[/C][C]0.492335017023309[/C][C]225.260231682341[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 26 )[/C][C]110.9055[/C][C]0.491557776327823[/C][C]225.620477064809[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 26 )[/C][C]110.898[/C][C]0.490181069618828[/C][C]226.238846975947[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 26 )[/C][C]110.887[/C][C]0.487527162501963[/C][C]227.447839892518[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 26 )[/C][C]110.882625[/C][C]0.484434739884826[/C][C]228.890737741811[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 26 )[/C][C]110.871375[/C][C]0.481263886656462[/C][C]230.375430349177[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 26 )[/C][C]110.857375[/C][C]0.478925245341066[/C][C]231.471145191048[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 26 )[/C][C]110.886375[/C][C]0.47166367428249[/C][C]235.096279501880[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 26 )[/C][C]110.884125[/C][C]0.46092623774055[/C][C]240.568047381185[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 26 )[/C][C]110.886625[/C][C]0.453559199649864[/C][C]244.481040370478[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 26 )[/C][C]110.859125[/C][C]0.443008528997175[/C][C]250.241513974795[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 26 )[/C][C]110.787125[/C][C]0.430549222172806[/C][C]257.315817320265[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 26 )[/C][C]110.790375[/C][C]0.426271309417599[/C][C]259.905774919192[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 26 )[/C][C]110.821875[/C][C]0.421152506043261[/C][C]263.139535939545[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 26 )[/C][C]110.791875[/C][C]0.41581737006197[/C][C]266.443595137665[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 26 )[/C][C]110.797875[/C][C]0.406995540584144[/C][C]272.233633913965[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 26 )[/C][C]110.797875[/C][C]0.405197197410788[/C][C]273.441859193496[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 26 )[/C][C]110.795625[/C][C]0.397310015252493[/C][C]278.86441505782[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 26 )[/C][C]110.809875[/C][C]0.393968389054715[/C][C]281.265903759123[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 26 )[/C][C]110.859875[/C][C]0.37183582763581[/C][C]298.141993752631[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 26 )[/C][C]110.936[/C][C]0.354462402712486[/C][C]312.969723025839[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 26 )[/C][C]110.92775[/C][C]0.339355726834605[/C][C]326.877495289962[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 26 )[/C][C]110.832875[/C][C]0.310920753556415[/C][C]356.466635733565[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 26 )[/C][C]110.745875[/C][C]0.295211289584964[/C][C]375.141056277681[/C][/ROW]
[ROW][C]Winsorized Mean ( 25 / 26 )[/C][C]110.770875[/C][C]0.288758976722211[/C][C]383.610152167019[/C][/ROW]
[ROW][C]Winsorized Mean ( 26 / 26 )[/C][C]110.770875[/C][C]0.279683545955361[/C][C]396.057889718259[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 26 )[/C][C]110.894615384615[/C][C]0.488957234564561[/C][C]226.798189177776[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 26 )[/C][C]110.885263157895[/C][C]0.484836289016008[/C][C]228.706608127333[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 26 )[/C][C]110.874324324324[/C][C]0.480312748333639[/C][C]230.837771241724[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 26 )[/C][C]110.865555555556[/C][C]0.475423494965587[/C][C]233.193261859262[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 26 )[/C][C]110.859428571429[/C][C]0.470400291444497[/C][C]235.670407922162[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 26 )[/C][C]110.853970588235[/C][C]0.465178090440149[/C][C]238.304367437739[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 26 )[/C][C]110.850454545455[/C][C]0.459607587350881[/C][C]241.184996932671[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 26 )[/C][C]110.84921875[/C][C]0.453324049312295[/C][C]244.52534322448[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 26 )[/C][C]110.843225806452[/C][C]0.447212281420447[/C][C]247.853716034784[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 26 )[/C][C]110.837166666667[/C][C]0.441886434503388[/C][C]250.827266945252[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 26 )[/C][C]110.830344827586[/C][C]0.436646252150496[/C][C]253.82181635991[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 26 )[/C][C]110.826607142857[/C][C]0.432021319578677[/C][C]256.530412089245[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 26 )[/C][C]110.831481481481[/C][C]0.428346683214407[/C][C]258.742476187228[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 26 )[/C][C]110.836346153846[/C][C]0.42417829613439[/C][C]261.296599010173[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 26 )[/C][C]110.838[/C][C]0.419513518061975[/C][C]264.206027286172[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 26 )[/C][C]110.843125[/C][C]0.414210044132758[/C][C]267.601248617897[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 26 )[/C][C]110.848043478261[/C][C]0.408728394463957[/C][C]271.202209045537[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 26 )[/C][C]110.853409090909[/C][C]0.401571035209751[/C][C]276.049314744544[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 26 )[/C][C]110.859523809524[/C][C]0.393480250576324[/C][C]281.741011517477[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 26 )[/C][C]110.86475[/C][C]0.383141700288549[/C][C]289.35704444728[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 26 )[/C][C]110.865263157895[/C][C]0.374093068657212[/C][C]296.357437350657[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 26 )[/C][C]110.857777777778[/C][C]0.365473624243442[/C][C]303.326342652665[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 26 )[/C][C]110.850294117647[/C][C]0.356811360181742[/C][C]310.669184022575[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 26 )[/C][C]110.8521875[/C][C]0.351397766064270[/C][C]315.460706371495[/C][/ROW]
[ROW][C]Trimmed Mean ( 25 / 26 )[/C][C]110.864[/C][C]0.346750299372535[/C][C]319.722867436928[/C][/ROW]
[ROW][C]Trimmed Mean ( 26 / 26 )[/C][C]110.874642857143[/C][C]0.340555678089594[/C][C]325.569796630946[/C][/ROW]
[ROW][C]Median[/C][C]110.935[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]111.335[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]110.756341463415[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]110.86475[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]110.756341463415[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]110.86475[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]110.86475[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]110.756341463415[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]110.86475[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]110.859523809524[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]80[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=51053&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=51053&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 Mean110.9056250.492962140808571224.977976641552
Geometric Mean110.819114607763
Harmonic Mean110.732700002519
Quadratic Mean110.992141968475
Winsorized Mean ( 1 / 26 )110.90350.492335017023309225.260231682341
Winsorized Mean ( 2 / 26 )110.90550.491557776327823225.620477064809
Winsorized Mean ( 3 / 26 )110.8980.490181069618828226.238846975947
Winsorized Mean ( 4 / 26 )110.8870.487527162501963227.447839892518
Winsorized Mean ( 5 / 26 )110.8826250.484434739884826228.890737741811
Winsorized Mean ( 6 / 26 )110.8713750.481263886656462230.375430349177
Winsorized Mean ( 7 / 26 )110.8573750.478925245341066231.471145191048
Winsorized Mean ( 8 / 26 )110.8863750.47166367428249235.096279501880
Winsorized Mean ( 9 / 26 )110.8841250.46092623774055240.568047381185
Winsorized Mean ( 10 / 26 )110.8866250.453559199649864244.481040370478
Winsorized Mean ( 11 / 26 )110.8591250.443008528997175250.241513974795
Winsorized Mean ( 12 / 26 )110.7871250.430549222172806257.315817320265
Winsorized Mean ( 13 / 26 )110.7903750.426271309417599259.905774919192
Winsorized Mean ( 14 / 26 )110.8218750.421152506043261263.139535939545
Winsorized Mean ( 15 / 26 )110.7918750.41581737006197266.443595137665
Winsorized Mean ( 16 / 26 )110.7978750.406995540584144272.233633913965
Winsorized Mean ( 17 / 26 )110.7978750.405197197410788273.441859193496
Winsorized Mean ( 18 / 26 )110.7956250.397310015252493278.86441505782
Winsorized Mean ( 19 / 26 )110.8098750.393968389054715281.265903759123
Winsorized Mean ( 20 / 26 )110.8598750.37183582763581298.141993752631
Winsorized Mean ( 21 / 26 )110.9360.354462402712486312.969723025839
Winsorized Mean ( 22 / 26 )110.927750.339355726834605326.877495289962
Winsorized Mean ( 23 / 26 )110.8328750.310920753556415356.466635733565
Winsorized Mean ( 24 / 26 )110.7458750.295211289584964375.141056277681
Winsorized Mean ( 25 / 26 )110.7708750.288758976722211383.610152167019
Winsorized Mean ( 26 / 26 )110.7708750.279683545955361396.057889718259
Trimmed Mean ( 1 / 26 )110.8946153846150.488957234564561226.798189177776
Trimmed Mean ( 2 / 26 )110.8852631578950.484836289016008228.706608127333
Trimmed Mean ( 3 / 26 )110.8743243243240.480312748333639230.837771241724
Trimmed Mean ( 4 / 26 )110.8655555555560.475423494965587233.193261859262
Trimmed Mean ( 5 / 26 )110.8594285714290.470400291444497235.670407922162
Trimmed Mean ( 6 / 26 )110.8539705882350.465178090440149238.304367437739
Trimmed Mean ( 7 / 26 )110.8504545454550.459607587350881241.184996932671
Trimmed Mean ( 8 / 26 )110.849218750.453324049312295244.52534322448
Trimmed Mean ( 9 / 26 )110.8432258064520.447212281420447247.853716034784
Trimmed Mean ( 10 / 26 )110.8371666666670.441886434503388250.827266945252
Trimmed Mean ( 11 / 26 )110.8303448275860.436646252150496253.82181635991
Trimmed Mean ( 12 / 26 )110.8266071428570.432021319578677256.530412089245
Trimmed Mean ( 13 / 26 )110.8314814814810.428346683214407258.742476187228
Trimmed Mean ( 14 / 26 )110.8363461538460.42417829613439261.296599010173
Trimmed Mean ( 15 / 26 )110.8380.419513518061975264.206027286172
Trimmed Mean ( 16 / 26 )110.8431250.414210044132758267.601248617897
Trimmed Mean ( 17 / 26 )110.8480434782610.408728394463957271.202209045537
Trimmed Mean ( 18 / 26 )110.8534090909090.401571035209751276.049314744544
Trimmed Mean ( 19 / 26 )110.8595238095240.393480250576324281.741011517477
Trimmed Mean ( 20 / 26 )110.864750.383141700288549289.35704444728
Trimmed Mean ( 21 / 26 )110.8652631578950.374093068657212296.357437350657
Trimmed Mean ( 22 / 26 )110.8577777777780.365473624243442303.326342652665
Trimmed Mean ( 23 / 26 )110.8502941176470.356811360181742310.669184022575
Trimmed Mean ( 24 / 26 )110.85218750.351397766064270315.460706371495
Trimmed Mean ( 25 / 26 )110.8640.346750299372535319.722867436928
Trimmed Mean ( 26 / 26 )110.8746428571430.340555678089594325.569796630946
Median110.935
Midrange111.335
Midmean - Weighted Average at Xnp110.756341463415
Midmean - Weighted Average at X(n+1)p110.86475
Midmean - Empirical Distribution Function110.756341463415
Midmean - Empirical Distribution Function - Averaging110.86475
Midmean - Empirical Distribution Function - Interpolation110.86475
Midmean - Closest Observation110.756341463415
Midmean - True Basic - Statistics Graphics Toolkit110.86475
Midmean - MS Excel (old versions)110.859523809524
Number of observations80



Parameters (Session):
Parameters (R input):
R code (references can be found in the software module):
geomean <- function(x) {
return(exp(mean(log(x))))
}
harmean <- function(x) {
return(1/mean(1/x))
}
quamean <- function(x) {
return(sqrt(mean(x*x)))
}
winmean <- function(x) {
x <-sort(x[!is.na(x)])
n<-length(x)
denom <- 3
nodenom <- n/denom
if (nodenom>40) denom <- n/40
sqrtn = sqrt(n)
roundnodenom = floor(nodenom)
win <- array(NA,dim=c(roundnodenom,2))
for (j in 1:roundnodenom) {
win[j,1] <- (j*x[j+1]+sum(x[(j+1):(n-j)])+j*x[n-j])/n
win[j,2] <- sd(c(rep(x[j+1],j),x[(j+1):(n-j)],rep(x[n-j],j)))/sqrtn
}
return(win)
}
trimean <- function(x) {
x <-sort(x[!is.na(x)])
n<-length(x)
denom <- 3
nodenom <- n/denom
if (nodenom>40) denom <- n/40
sqrtn = sqrt(n)
roundnodenom = floor(nodenom)
tri <- array(NA,dim=c(roundnodenom,2))
for (j in 1:roundnodenom) {
tri[j,1] <- mean(x,trim=j/n)
tri[j,2] <- sd(x[(j+1):(n-j)]) / sqrt(n-j*2)
}
return(tri)
}
midrange <- function(x) {
return((max(x)+min(x))/2)
}
q1 <- function(data,n,p,i,f) {
np <- n*p;
i <<- floor(np)
f <<- np - i
qvalue <- (1-f)*data[i] + f*data[i+1]
}
q2 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
qvalue <- (1-f)*data[i] + f*data[i+1]
}
q3 <- function(data,n,p,i,f) {
np <- n*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
qvalue <- data[i+1]
}
}
q4 <- function(data,n,p,i,f) {
np <- n*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- (data[i]+data[i+1])/2
} else {
qvalue <- data[i+1]
}
}
q5 <- function(data,n,p,i,f) {
np <- (n-1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i+1]
} else {
qvalue <- data[i+1] + f*(data[i+2]-data[i+1])
}
}
q6 <- function(data,n,p,i,f) {
np <- n*p+0.5
i <<- floor(np)
f <<- np - i
qvalue <- data[i]
}
q7 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
qvalue <- f*data[i] + (1-f)*data[i+1]
}
}
q8 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
if (f == 0.5) {
qvalue <- (data[i]+data[i+1])/2
} else {
if (f < 0.5) {
qvalue <- data[i]
} else {
qvalue <- data[i+1]
}
}
}
}
midmean <- function(x,def) {
x <-sort(x[!is.na(x)])
n<-length(x)
if (def==1) {
qvalue1 <- q1(x,n,0.25,i,f)
qvalue3 <- q1(x,n,0.75,i,f)
}
if (def==2) {
qvalue1 <- q2(x,n,0.25,i,f)
qvalue3 <- q2(x,n,0.75,i,f)
}
if (def==3) {
qvalue1 <- q3(x,n,0.25,i,f)
qvalue3 <- q3(x,n,0.75,i,f)
}
if (def==4) {
qvalue1 <- q4(x,n,0.25,i,f)
qvalue3 <- q4(x,n,0.75,i,f)
}
if (def==5) {
qvalue1 <- q5(x,n,0.25,i,f)
qvalue3 <- q5(x,n,0.75,i,f)
}
if (def==6) {
qvalue1 <- q6(x,n,0.25,i,f)
qvalue3 <- q6(x,n,0.75,i,f)
}
if (def==7) {
qvalue1 <- q7(x,n,0.25,i,f)
qvalue3 <- q7(x,n,0.75,i,f)
}
if (def==8) {
qvalue1 <- q8(x,n,0.25,i,f)
qvalue3 <- q8(x,n,0.75,i,f)
}
midm <- 0
myn <- 0
roundno4 <- round(n/4)
round3no4 <- round(3*n/4)
for (i in 1:n) {
if ((x[i]>=qvalue1) & (x[i]<=qvalue3)){
midm = midm + x[i]
myn = myn + 1
}
}
midm = midm / myn
return(midm)
}
(arm <- mean(x))
sqrtn <- sqrt(length(x))
(armse <- sd(x) / sqrtn)
(armose <- arm / armse)
(geo <- geomean(x))
(har <- harmean(x))
(qua <- quamean(x))
(win <- winmean(x))
(tri <- trimean(x))
(midr <- midrange(x))
midm <- array(NA,dim=8)
for (j in 1:8) midm[j] <- midmean(x,j)
midm
bitmap(file='test1.png')
lb <- win[,1] - 2*win[,2]
ub <- win[,1] + 2*win[,2]
if ((ylimmin == '') | (ylimmax == '')) plot(win[,1],type='b',main=main, xlab='j', pch=19, ylab='Winsorized Mean(j/n)', ylim=c(min(lb),max(ub))) else plot(win[,1],type='l',main=main, xlab='j', pch=19, ylab='Winsorized Mean(j/n)', ylim=c(ylimmin,ylimmax))
lines(ub,lty=3)
lines(lb,lty=3)
grid()
dev.off()
bitmap(file='test2.png')
lb <- tri[,1] - 2*tri[,2]
ub <- tri[,1] + 2*tri[,2]
if ((ylimmin == '') | (ylimmax == '')) plot(tri[,1],type='b',main=main, xlab='j', pch=19, ylab='Trimmed Mean(j/n)', ylim=c(min(lb),max(ub))) else plot(tri[,1],type='l',main=main, xlab='j', pch=19, ylab='Trimmed Mean(j/n)', ylim=c(ylimmin,ylimmax))
lines(ub,lty=3)
lines(lb,lty=3)
grid()
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Central Tendency - Ungrouped Data',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Measure',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.element(a,'S.E.',header=TRUE)
a<-table.element(a,'Value/S.E.',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('arithmetic_mean.htm', 'Arithmetic Mean', 'click to view the definition of the Arithmetic Mean'),header=TRUE)
a<-table.element(a,arm)
a<-table.element(a,hyperlink('arithmetic_mean_standard_error.htm', armse, 'click to view the definition of the Standard Error of the Arithmetic Mean'))
a<-table.element(a,armose)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('geometric_mean.htm', 'Geometric Mean', 'click to view the definition of the Geometric Mean'),header=TRUE)
a<-table.element(a,geo)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('harmonic_mean.htm', 'Harmonic Mean', 'click to view the definition of the Harmonic Mean'),header=TRUE)
a<-table.element(a,har)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('quadratic_mean.htm', 'Quadratic Mean', 'click to view the definition of the Quadratic Mean'),header=TRUE)
a<-table.element(a,qua)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
for (j in 1:length(win[,1])) {
a<-table.row.start(a)
mylabel <- paste('Winsorized Mean (',j)
mylabel <- paste(mylabel,'/')
mylabel <- paste(mylabel,length(win[,1]))
mylabel <- paste(mylabel,')')
a<-table.element(a,hyperlink('winsorized_mean.htm', mylabel, 'click to view the definition of the Winsorized Mean'),header=TRUE)
a<-table.element(a,win[j,1])
a<-table.element(a,win[j,2])
a<-table.element(a,win[j,1]/win[j,2])
a<-table.row.end(a)
}
for (j in 1:length(tri[,1])) {
a<-table.row.start(a)
mylabel <- paste('Trimmed Mean (',j)
mylabel <- paste(mylabel,'/')
mylabel <- paste(mylabel,length(tri[,1]))
mylabel <- paste(mylabel,')')
a<-table.element(a,hyperlink('arithmetic_mean.htm', mylabel, 'click to view the definition of the Trimmed Mean'),header=TRUE)
a<-table.element(a,tri[j,1])
a<-table.element(a,tri[j,2])
a<-table.element(a,tri[j,1]/tri[j,2])
a<-table.row.end(a)
}
a<-table.row.start(a)
a<-table.element(a,hyperlink('median_1.htm', 'Median', 'click to view the definition of the Median'),header=TRUE)
a<-table.element(a,median(x))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('midrange.htm', 'Midrange', 'click to view the definition of the Midrange'),header=TRUE)
a<-table.element(a,midr)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_1.htm','Weighted Average at Xnp',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[1])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_2.htm','Weighted Average at X(n+1)p',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[2])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_3.htm','Empirical Distribution Function',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[3])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_4.htm','Empirical Distribution Function - Averaging',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[4])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_5.htm','Empirical Distribution Function - Interpolation',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[5])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_6.htm','Closest Observation',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[6])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_7.htm','True Basic - Statistics Graphics Toolkit',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[7])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_8.htm','MS Excel (old versions)',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[8])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Number of observations',header=TRUE)
a<-table.element(a,length(x))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')