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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationSat, 24 Oct 2009 09:07:33 -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/24/t1256396919k8adhfm66g09biz.htm/, Retrieved Fri, 03 May 2024 11:23:34 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=50168, Retrieved Fri, 03 May 2024 11:23:34 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP1W52
Estimated Impact107
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Centrummaten Verk...] [2009-10-24 15:07:33] [a00bf033610db033bc2faa6c748d42a9] [Current]
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Dataseries X:
76,3
71
85,9
109
83,4
101,3
81,6
84,8
88
88,4
85,2
139,5
85,3
79,4
131
91,4
88,2
113,2
81,9
89
95,7
93,2
98
140,5
93
82,1
86,3
84,8
85,7
110,8
87,4
100,4
100,4
99,4
108
161,7
109,3
99,9
110,3
97,5
102,4
122,3
104,4
122,7
127,3
128,4
125,3
187,1
131,4
125,6
142,9
116,6
129,7
155,4
138,7
167,7
155,8
157,1
159,9
244,6
154,3
143,2
147,3
155,1
152,2
166,5
161,2
180,1
169,2
164,5
166,2
267,3




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=50168&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=50168&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=50168&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 Mean121.8138888888894.5105771648164427.0062753474358
Geometric Mean116.663496264052
Harmonic Mean112.171840320145
Quadratic Mean127.605408497359
Winsorized Mean ( 1 / 24 )121.5722222222224.3650134051882927.8515117680327
Winsorized Mean ( 2 / 24 )120.0611111111113.8305825788527131.3427810625794
Winsorized Mean ( 3 / 24 )119.8611111111113.7481479806227231.9787563700186
Winsorized Mean ( 4 / 24 )119.2722222222223.6181836362456232.9646679696955
Winsorized Mean ( 5 / 24 )119.1819444444443.5961444350969333.1415899987988
Winsorized Mean ( 6 / 24 )119.1902777777783.5617546359273833.4639215670577
Winsorized Mean ( 7 / 24 )119.2972222222223.5373222303205333.7252911820285
Winsorized Mean ( 8 / 24 )119.1083333333333.5024431166833434.0072142116968
Winsorized Mean ( 9 / 24 )118.8083333333333.4327947239222534.6097983970289
Winsorized Mean ( 10 / 24 )118.7527777777783.4186974224983934.7362644603374
Winsorized Mean ( 11 / 24 )118.6152777777783.3758170979372435.1367607712682
Winsorized Mean ( 12 / 24 )118.1819444444443.2921691399864235.8978957092502
Winsorized Mean ( 13 / 24 )118.0194444444443.2434107024393836.3874499013281
Winsorized Mean ( 14 / 24 )118.1555555555563.2014557335873436.9068215799311
Winsorized Mean ( 15 / 24 )118.2180555555563.1743847914735237.2412493510845
Winsorized Mean ( 16 / 24 )118.0847222222223.1394373291765537.6133395385201
Winsorized Mean ( 17 / 24 )117.6361111111113.0532694357176338.52791690605
Winsorized Mean ( 18 / 24 )116.5611111111112.8417876872854241.0168260044981
Winsorized Mean ( 19 / 24 )116.11252.5938909944331844.7638317297034
Winsorized Mean ( 20 / 24 )116.4736111111112.5226625346864446.1709045540601
Winsorized Mean ( 21 / 24 )115.8319444444442.4129231377758648.004821467796
Winsorized Mean ( 22 / 24 )116.2902777777782.2696086607808951.2380304971899
Winsorized Mean ( 23 / 24 )116.6097222222222.1602216889458653.9804422939227
Winsorized Mean ( 24 / 24 )114.3430555555561.8004638013023363.5075559268938
Trimmed Mean ( 1 / 24 )120.4614285714294.0730621872479429.5751508407047
Trimmed Mean ( 2 / 24 )119.2852941176473.7089640983220832.1613504351825
Trimmed Mean ( 3 / 24 )118.8621212121213.6281962134019332.7606651407289
Trimmed Mean ( 4 / 24 )118.48753.5678378278549933.2098894952396
Trimmed Mean ( 5 / 24 )118.2596774193553.5406377389540533.4006713305525
Trimmed Mean ( 6 / 24 )118.0383333333333.5117551518726833.6123471678793
Trimmed Mean ( 7 / 24 )117.83.4829608573652233.8217984135236
Trimmed Mean ( 8 / 24 )117.5253.4504538097917634.0607370736236
Trimmed Mean ( 9 / 24 )117.2611111111113.4155483844272934.3315619962366
Trimmed Mean ( 10 / 24 )117.0230769230773.3847281621139634.5738479777913
Trimmed Mean ( 11 / 24 )116.7743.345498114280334.9048171635634
Trimmed Mean ( 12 / 24 )116.5229166666673.3016762339382935.2920481629648
Trimmed Mean ( 13 / 24 )116.3065217391303.2605375837450035.6709649104989
Trimmed Mean ( 14 / 24 )116.0909090909093.2140199256165536.1201584861485
Trimmed Mean ( 15 / 24 )115.8380952380953.1579737994133336.6811451252746
Trimmed Mean ( 16 / 24 )115.55253.0856823778832937.4479566750698
Trimmed Mean ( 17 / 24 )115.2526315789472.9936507891770938.4990233315184
Trimmed Mean ( 18 / 24 )114.9722222222222.8883306847763839.8057683727871
Trimmed Mean ( 19 / 24 )114.7852941176472.7990739885642641.0083101006287
Trimmed Mean ( 20 / 24 )114.6281252.73780372587841.8686423414956
Trimmed Mean ( 21 / 24 )114.4066666666672.6624374509228642.9706495553579
Trimmed Mean ( 22 / 24 )114.2321428571432.5808669925253044.2611506861771
Trimmed Mean ( 23 / 24 )113.9730769230772.4967582532451845.648423020106
Trimmed Mean ( 24 / 24 )113.6291666666672.3950241229509447.4438505974891
Median110.55
Midrange169.15
Midmean - Weighted Average at Xnp114.254054054054
Midmean - Weighted Average at X(n+1)p114.972222222222
Midmean - Empirical Distribution Function114.254054054054
Midmean - Empirical Distribution Function - Averaging114.972222222222
Midmean - Empirical Distribution Function - Interpolation114.972222222222
Midmean - Closest Observation114.254054054054
Midmean - True Basic - Statistics Graphics Toolkit114.972222222222
Midmean - MS Excel (old versions)115.252631578947
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 121.813888888889 & 4.51057716481644 & 27.0062753474358 \tabularnewline
Geometric Mean & 116.663496264052 &  &  \tabularnewline
Harmonic Mean & 112.171840320145 &  &  \tabularnewline
Quadratic Mean & 127.605408497359 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 121.572222222222 & 4.36501340518829 & 27.8515117680327 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 120.061111111111 & 3.83058257885271 & 31.3427810625794 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 119.861111111111 & 3.74814798062272 & 31.9787563700186 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 119.272222222222 & 3.61818363624562 & 32.9646679696955 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 119.181944444444 & 3.59614443509693 & 33.1415899987988 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 119.190277777778 & 3.56175463592738 & 33.4639215670577 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 119.297222222222 & 3.53732223032053 & 33.7252911820285 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 119.108333333333 & 3.50244311668334 & 34.0072142116968 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 118.808333333333 & 3.43279472392225 & 34.6097983970289 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 118.752777777778 & 3.41869742249839 & 34.7362644603374 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 118.615277777778 & 3.37581709793724 & 35.1367607712682 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 118.181944444444 & 3.29216913998642 & 35.8978957092502 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 118.019444444444 & 3.24341070243938 & 36.3874499013281 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 118.155555555556 & 3.20145573358734 & 36.9068215799311 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 118.218055555556 & 3.17438479147352 & 37.2412493510845 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 118.084722222222 & 3.13943732917655 & 37.6133395385201 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 117.636111111111 & 3.05326943571763 & 38.52791690605 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 116.561111111111 & 2.84178768728542 & 41.0168260044981 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 116.1125 & 2.59389099443318 & 44.7638317297034 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 116.473611111111 & 2.52266253468644 & 46.1709045540601 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 115.831944444444 & 2.41292313777586 & 48.004821467796 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 116.290277777778 & 2.26960866078089 & 51.2380304971899 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 116.609722222222 & 2.16022168894586 & 53.9804422939227 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 114.343055555556 & 1.80046380130233 & 63.5075559268938 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 120.461428571429 & 4.07306218724794 & 29.5751508407047 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 119.285294117647 & 3.70896409832208 & 32.1613504351825 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 118.862121212121 & 3.62819621340193 & 32.7606651407289 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 118.4875 & 3.56783782785499 & 33.2098894952396 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 118.259677419355 & 3.54063773895405 & 33.4006713305525 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 118.038333333333 & 3.51175515187268 & 33.6123471678793 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 117.8 & 3.48296085736522 & 33.8217984135236 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 117.525 & 3.45045380979176 & 34.0607370736236 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 117.261111111111 & 3.41554838442729 & 34.3315619962366 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 117.023076923077 & 3.38472816211396 & 34.5738479777913 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 116.774 & 3.3454981142803 & 34.9048171635634 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 116.522916666667 & 3.30167623393829 & 35.2920481629648 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 116.306521739130 & 3.26053758374500 & 35.6709649104989 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 116.090909090909 & 3.21401992561655 & 36.1201584861485 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 115.838095238095 & 3.15797379941333 & 36.6811451252746 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 115.5525 & 3.08568237788329 & 37.4479566750698 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 115.252631578947 & 2.99365078917709 & 38.4990233315184 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 114.972222222222 & 2.88833068477638 & 39.8057683727871 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 114.785294117647 & 2.79907398856426 & 41.0083101006287 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 114.628125 & 2.737803725878 & 41.8686423414956 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 114.406666666667 & 2.66243745092286 & 42.9706495553579 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 114.232142857143 & 2.58086699252530 & 44.2611506861771 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 113.973076923077 & 2.49675825324518 & 45.648423020106 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 113.629166666667 & 2.39502412295094 & 47.4438505974891 \tabularnewline
Median & 110.55 &  &  \tabularnewline
Midrange & 169.15 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 114.254054054054 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 114.972222222222 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 114.254054054054 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 114.972222222222 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 114.972222222222 &  &  \tabularnewline
Midmean - Closest Observation & 114.254054054054 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 114.972222222222 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 115.252631578947 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=50168&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]121.813888888889[/C][C]4.51057716481644[/C][C]27.0062753474358[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]116.663496264052[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]112.171840320145[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]127.605408497359[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]121.572222222222[/C][C]4.36501340518829[/C][C]27.8515117680327[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]120.061111111111[/C][C]3.83058257885271[/C][C]31.3427810625794[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]119.861111111111[/C][C]3.74814798062272[/C][C]31.9787563700186[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]119.272222222222[/C][C]3.61818363624562[/C][C]32.9646679696955[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]119.181944444444[/C][C]3.59614443509693[/C][C]33.1415899987988[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]119.190277777778[/C][C]3.56175463592738[/C][C]33.4639215670577[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]119.297222222222[/C][C]3.53732223032053[/C][C]33.7252911820285[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]119.108333333333[/C][C]3.50244311668334[/C][C]34.0072142116968[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]118.808333333333[/C][C]3.43279472392225[/C][C]34.6097983970289[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]118.752777777778[/C][C]3.41869742249839[/C][C]34.7362644603374[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]118.615277777778[/C][C]3.37581709793724[/C][C]35.1367607712682[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]118.181944444444[/C][C]3.29216913998642[/C][C]35.8978957092502[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]118.019444444444[/C][C]3.24341070243938[/C][C]36.3874499013281[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]118.155555555556[/C][C]3.20145573358734[/C][C]36.9068215799311[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]118.218055555556[/C][C]3.17438479147352[/C][C]37.2412493510845[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]118.084722222222[/C][C]3.13943732917655[/C][C]37.6133395385201[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]117.636111111111[/C][C]3.05326943571763[/C][C]38.52791690605[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]116.561111111111[/C][C]2.84178768728542[/C][C]41.0168260044981[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]116.1125[/C][C]2.59389099443318[/C][C]44.7638317297034[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]116.473611111111[/C][C]2.52266253468644[/C][C]46.1709045540601[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]115.831944444444[/C][C]2.41292313777586[/C][C]48.004821467796[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]116.290277777778[/C][C]2.26960866078089[/C][C]51.2380304971899[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]116.609722222222[/C][C]2.16022168894586[/C][C]53.9804422939227[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]114.343055555556[/C][C]1.80046380130233[/C][C]63.5075559268938[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]120.461428571429[/C][C]4.07306218724794[/C][C]29.5751508407047[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]119.285294117647[/C][C]3.70896409832208[/C][C]32.1613504351825[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]118.862121212121[/C][C]3.62819621340193[/C][C]32.7606651407289[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]118.4875[/C][C]3.56783782785499[/C][C]33.2098894952396[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]118.259677419355[/C][C]3.54063773895405[/C][C]33.4006713305525[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]118.038333333333[/C][C]3.51175515187268[/C][C]33.6123471678793[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]117.8[/C][C]3.48296085736522[/C][C]33.8217984135236[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]117.525[/C][C]3.45045380979176[/C][C]34.0607370736236[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]117.261111111111[/C][C]3.41554838442729[/C][C]34.3315619962366[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]117.023076923077[/C][C]3.38472816211396[/C][C]34.5738479777913[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]116.774[/C][C]3.3454981142803[/C][C]34.9048171635634[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]116.522916666667[/C][C]3.30167623393829[/C][C]35.2920481629648[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]116.306521739130[/C][C]3.26053758374500[/C][C]35.6709649104989[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]116.090909090909[/C][C]3.21401992561655[/C][C]36.1201584861485[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]115.838095238095[/C][C]3.15797379941333[/C][C]36.6811451252746[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]115.5525[/C][C]3.08568237788329[/C][C]37.4479566750698[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]115.252631578947[/C][C]2.99365078917709[/C][C]38.4990233315184[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]114.972222222222[/C][C]2.88833068477638[/C][C]39.8057683727871[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]114.785294117647[/C][C]2.79907398856426[/C][C]41.0083101006287[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]114.628125[/C][C]2.737803725878[/C][C]41.8686423414956[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]114.406666666667[/C][C]2.66243745092286[/C][C]42.9706495553579[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]114.232142857143[/C][C]2.58086699252530[/C][C]44.2611506861771[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]113.973076923077[/C][C]2.49675825324518[/C][C]45.648423020106[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]113.629166666667[/C][C]2.39502412295094[/C][C]47.4438505974891[/C][/ROW]
[ROW][C]Median[/C][C]110.55[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]169.15[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]114.254054054054[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]114.972222222222[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]114.254054054054[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]114.972222222222[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]114.972222222222[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]114.254054054054[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]114.972222222222[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]115.252631578947[/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=50168&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=50168&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 Mean121.8138888888894.5105771648164427.0062753474358
Geometric Mean116.663496264052
Harmonic Mean112.171840320145
Quadratic Mean127.605408497359
Winsorized Mean ( 1 / 24 )121.5722222222224.3650134051882927.8515117680327
Winsorized Mean ( 2 / 24 )120.0611111111113.8305825788527131.3427810625794
Winsorized Mean ( 3 / 24 )119.8611111111113.7481479806227231.9787563700186
Winsorized Mean ( 4 / 24 )119.2722222222223.6181836362456232.9646679696955
Winsorized Mean ( 5 / 24 )119.1819444444443.5961444350969333.1415899987988
Winsorized Mean ( 6 / 24 )119.1902777777783.5617546359273833.4639215670577
Winsorized Mean ( 7 / 24 )119.2972222222223.5373222303205333.7252911820285
Winsorized Mean ( 8 / 24 )119.1083333333333.5024431166833434.0072142116968
Winsorized Mean ( 9 / 24 )118.8083333333333.4327947239222534.6097983970289
Winsorized Mean ( 10 / 24 )118.7527777777783.4186974224983934.7362644603374
Winsorized Mean ( 11 / 24 )118.6152777777783.3758170979372435.1367607712682
Winsorized Mean ( 12 / 24 )118.1819444444443.2921691399864235.8978957092502
Winsorized Mean ( 13 / 24 )118.0194444444443.2434107024393836.3874499013281
Winsorized Mean ( 14 / 24 )118.1555555555563.2014557335873436.9068215799311
Winsorized Mean ( 15 / 24 )118.2180555555563.1743847914735237.2412493510845
Winsorized Mean ( 16 / 24 )118.0847222222223.1394373291765537.6133395385201
Winsorized Mean ( 17 / 24 )117.6361111111113.0532694357176338.52791690605
Winsorized Mean ( 18 / 24 )116.5611111111112.8417876872854241.0168260044981
Winsorized Mean ( 19 / 24 )116.11252.5938909944331844.7638317297034
Winsorized Mean ( 20 / 24 )116.4736111111112.5226625346864446.1709045540601
Winsorized Mean ( 21 / 24 )115.8319444444442.4129231377758648.004821467796
Winsorized Mean ( 22 / 24 )116.2902777777782.2696086607808951.2380304971899
Winsorized Mean ( 23 / 24 )116.6097222222222.1602216889458653.9804422939227
Winsorized Mean ( 24 / 24 )114.3430555555561.8004638013023363.5075559268938
Trimmed Mean ( 1 / 24 )120.4614285714294.0730621872479429.5751508407047
Trimmed Mean ( 2 / 24 )119.2852941176473.7089640983220832.1613504351825
Trimmed Mean ( 3 / 24 )118.8621212121213.6281962134019332.7606651407289
Trimmed Mean ( 4 / 24 )118.48753.5678378278549933.2098894952396
Trimmed Mean ( 5 / 24 )118.2596774193553.5406377389540533.4006713305525
Trimmed Mean ( 6 / 24 )118.0383333333333.5117551518726833.6123471678793
Trimmed Mean ( 7 / 24 )117.83.4829608573652233.8217984135236
Trimmed Mean ( 8 / 24 )117.5253.4504538097917634.0607370736236
Trimmed Mean ( 9 / 24 )117.2611111111113.4155483844272934.3315619962366
Trimmed Mean ( 10 / 24 )117.0230769230773.3847281621139634.5738479777913
Trimmed Mean ( 11 / 24 )116.7743.345498114280334.9048171635634
Trimmed Mean ( 12 / 24 )116.5229166666673.3016762339382935.2920481629648
Trimmed Mean ( 13 / 24 )116.3065217391303.2605375837450035.6709649104989
Trimmed Mean ( 14 / 24 )116.0909090909093.2140199256165536.1201584861485
Trimmed Mean ( 15 / 24 )115.8380952380953.1579737994133336.6811451252746
Trimmed Mean ( 16 / 24 )115.55253.0856823778832937.4479566750698
Trimmed Mean ( 17 / 24 )115.2526315789472.9936507891770938.4990233315184
Trimmed Mean ( 18 / 24 )114.9722222222222.8883306847763839.8057683727871
Trimmed Mean ( 19 / 24 )114.7852941176472.7990739885642641.0083101006287
Trimmed Mean ( 20 / 24 )114.6281252.73780372587841.8686423414956
Trimmed Mean ( 21 / 24 )114.4066666666672.6624374509228642.9706495553579
Trimmed Mean ( 22 / 24 )114.2321428571432.5808669925253044.2611506861771
Trimmed Mean ( 23 / 24 )113.9730769230772.4967582532451845.648423020106
Trimmed Mean ( 24 / 24 )113.6291666666672.3950241229509447.4438505974891
Median110.55
Midrange169.15
Midmean - Weighted Average at Xnp114.254054054054
Midmean - Weighted Average at X(n+1)p114.972222222222
Midmean - Empirical Distribution Function114.254054054054
Midmean - Empirical Distribution Function - Averaging114.972222222222
Midmean - Empirical Distribution Function - Interpolation114.972222222222
Midmean - Closest Observation114.254054054054
Midmean - True Basic - Statistics Graphics Toolkit114.972222222222
Midmean - MS Excel (old versions)115.252631578947
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')