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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 computationFri, 10 Oct 2014 16:31:36 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2014/Oct/10/t1412955214l2o8fizl2x3n0hv.htm/, Retrieved Mon, 13 May 2024 14:36:47 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=240347, Retrieved Mon, 13 May 2024 14:36:47 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact62
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2014-10-10 15:31:36] [bdd4dd5e616b71837cf1c04213e8fe07] [Current]
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Dataseries X:
204,12
203,27
203,73
203,7
203,44
203,34
203,34
203,05
202,71
202,51
203,45
203,04
203,04
202,87
202,92
202,87
203,17
203,88
203,88
203,45
203,22
202,11
202,5
202,86
202,86
203,8
203,78
204,53
204,44
204,14
204,14
204,04
204,68
205,01
204,93
204,34
204,34
203,87
202,47
201,95
201,86
200,33
200,33
200,33
200,75
201,86
202,77
202,85
202,85
202,84
202,94
203,05
203,45
204,19
204,18
204,47
204,78
206,05
206,32
206,36
205,21
205,35
205,94
204,57
204,27
204,86
204,66
204,79
205,58
205,63
205,12
204,96




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'George Udny Yule' @ yule.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 & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=240347&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]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=240347&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=240347&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'George Udny Yule' @ yule.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean203.6568055555560.1560272921620091305.26398768808
Geometric Mean203.652555163609
Harmonic Mean203.648297866875
Quadratic Mean203.661049073509
Winsorized Mean ( 1 / 24 )203.656250.1558926586756141306.38768836302
Winsorized Mean ( 2 / 24 )203.648750.1541670711198861320.96139934861
Winsorized Mean ( 3 / 24 )203.6616666666670.1480869135315861375.28470146167
Winsorized Mean ( 4 / 24 )203.7061111111110.129530202572771572.6533817213
Winsorized Mean ( 5 / 24 )203.7026388888890.1288106168068981581.41187379191
Winsorized Mean ( 6 / 24 )203.6909722222220.1235271855112771648.95663557094
Winsorized Mean ( 7 / 24 )203.6929166666670.1179908814379481726.34456310753
Winsorized Mean ( 8 / 24 )203.7229166666670.1091501237331171866.446960379
Winsorized Mean ( 9 / 24 )203.7129166666670.1061214125697081919.62123132175
Winsorized Mean ( 10 / 24 )203.7073611111110.1047149407708371945.35144279853
Winsorized Mean ( 11 / 24 )203.7333333333330.09925426162490062052.64066245616
Winsorized Mean ( 12 / 24 )203.7316666666670.09586338577577152125.22920005354
Winsorized Mean ( 13 / 24 )203.7316666666670.0920359611965052213.60937635759
Winsorized Mean ( 14 / 24 )203.7316666666670.09145686618541552227.62571214315
Winsorized Mean ( 15 / 24 )203.7108333333330.08816103978423412310.66731780724
Winsorized Mean ( 16 / 24 )203.7086111111110.08717019345721942336.90672272152
Winsorized Mean ( 17 / 24 )203.6873611111110.08396264564014942425.9283346559
Winsorized Mean ( 18 / 24 )203.6798611111110.08214635710096412479.47527193169
Winsorized Mean ( 19 / 24 )203.6640277777780.07986678553699152550.0466358878
Winsorized Mean ( 20 / 24 )203.6695833333330.07675755928171392653.4140121083
Winsorized Mean ( 21 / 24 )203.646250.07190712947930192832.07314037781
Winsorized Mean ( 22 / 24 )203.6768055555560.06776900445732223005.45665657257
Winsorized Mean ( 23 / 24 )203.6544444444440.06472945045507813146.24089981699
Winsorized Mean ( 24 / 24 )203.6311111111110.06076731434565613350.99737916371
Trimmed Mean ( 1 / 24 )203.6657142857140.1481904056693481374.35155377161
Trimmed Mean ( 2 / 24 )203.6757352941180.1388919395046771466.43308474542
Trimmed Mean ( 3 / 24 )203.6904545454550.1286873719982011582.83172142409
Trimmed Mean ( 4 / 24 )203.701250.1192425041735841708.29396289319
Trimmed Mean ( 5 / 24 )203.6998387096770.1152328459034681767.72375196148
Trimmed Mean ( 6 / 24 )203.6991666666670.1105963014845961841.82620876376
Trimmed Mean ( 7 / 24 )203.7008620689660.1065243921700971912.24618060902
Trimmed Mean ( 8 / 24 )203.7023214285710.1030480253285761976.77074139997
Trimmed Mean ( 9 / 24 )203.6988888888890.1009686373826912017.44714169837
Trimmed Mean ( 10 / 24 )203.6967307692310.09905386545702982056.42384403056
Trimmed Mean ( 11 / 24 )203.69520.09692464567268482101.58312765857
Trimmed Mean ( 12 / 24 )203.690.09537068404854042135.77161611139
Trimmed Mean ( 13 / 24 )203.6845652173910.09403191282814422166.12168242979
Trimmed Mean ( 14 / 24 )203.6786363636360.09300628028369022189.94497728939
Trimmed Mean ( 15 / 24 )203.6721428571430.09165121971905972222.25239862015
Trimmed Mean ( 16 / 24 )203.66750.09048356558527972250.87836318791
Trimmed Mean ( 17 / 24 )203.6626315789470.08898885461766012288.63077802251
Trimmed Mean ( 18 / 24 )203.6597222222220.08758803835045712325.20017639097
Trimmed Mean ( 19 / 24 )203.6573529411760.08593131280929122370.00164763172
Trimmed Mean ( 20 / 24 )203.65656250.0840310155093962423.58802003563
Trimmed Mean ( 21 / 24 )203.6550.08198927600186722483.92240950343
Trimmed Mean ( 22 / 24 )203.6560714285710.08024324673774342537.98393893725
Trimmed Mean ( 23 / 24 )203.6534615384620.0786461252558032589.49135607205
Trimmed Mean ( 24 / 24 )203.6533333333330.07689553111406372648.44172844378
Median203.715
Midrange203.345
Midmean - Weighted Average at Xnp203.617631578947
Midmean - Weighted Average at X(n+1)p203.659722222222
Midmean - Empirical Distribution Function203.617631578947
Midmean - Empirical Distribution Function - Averaging203.659722222222
Midmean - Empirical Distribution Function - Interpolation203.659722222222
Midmean - Closest Observation203.617631578947
Midmean - True Basic - Statistics Graphics Toolkit203.659722222222
Midmean - MS Excel (old versions)203.642051282051
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 203.656805555556 & 0.156027292162009 & 1305.26398768808 \tabularnewline
Geometric Mean & 203.652555163609 &  &  \tabularnewline
Harmonic Mean & 203.648297866875 &  &  \tabularnewline
Quadratic Mean & 203.661049073509 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 203.65625 & 0.155892658675614 & 1306.38768836302 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 203.64875 & 0.154167071119886 & 1320.96139934861 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 203.661666666667 & 0.148086913531586 & 1375.28470146167 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 203.706111111111 & 0.12953020257277 & 1572.6533817213 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 203.702638888889 & 0.128810616806898 & 1581.41187379191 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 203.690972222222 & 0.123527185511277 & 1648.95663557094 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 203.692916666667 & 0.117990881437948 & 1726.34456310753 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 203.722916666667 & 0.109150123733117 & 1866.446960379 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 203.712916666667 & 0.106121412569708 & 1919.62123132175 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 203.707361111111 & 0.104714940770837 & 1945.35144279853 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 203.733333333333 & 0.0992542616249006 & 2052.64066245616 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 203.731666666667 & 0.0958633857757715 & 2125.22920005354 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 203.731666666667 & 0.092035961196505 & 2213.60937635759 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 203.731666666667 & 0.0914568661854155 & 2227.62571214315 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 203.710833333333 & 0.0881610397842341 & 2310.66731780724 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 203.708611111111 & 0.0871701934572194 & 2336.90672272152 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 203.687361111111 & 0.0839626456401494 & 2425.9283346559 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 203.679861111111 & 0.0821463571009641 & 2479.47527193169 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 203.664027777778 & 0.0798667855369915 & 2550.0466358878 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 203.669583333333 & 0.0767575592817139 & 2653.4140121083 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 203.64625 & 0.0719071294793019 & 2832.07314037781 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 203.676805555556 & 0.0677690044573222 & 3005.45665657257 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 203.654444444444 & 0.0647294504550781 & 3146.24089981699 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 203.631111111111 & 0.0607673143456561 & 3350.99737916371 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 203.665714285714 & 0.148190405669348 & 1374.35155377161 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 203.675735294118 & 0.138891939504677 & 1466.43308474542 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 203.690454545455 & 0.128687371998201 & 1582.83172142409 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 203.70125 & 0.119242504173584 & 1708.29396289319 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 203.699838709677 & 0.115232845903468 & 1767.72375196148 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 203.699166666667 & 0.110596301484596 & 1841.82620876376 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 203.700862068966 & 0.106524392170097 & 1912.24618060902 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 203.702321428571 & 0.103048025328576 & 1976.77074139997 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 203.698888888889 & 0.100968637382691 & 2017.44714169837 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 203.696730769231 & 0.0990538654570298 & 2056.42384403056 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 203.6952 & 0.0969246456726848 & 2101.58312765857 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 203.69 & 0.0953706840485404 & 2135.77161611139 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 203.684565217391 & 0.0940319128281442 & 2166.12168242979 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 203.678636363636 & 0.0930062802836902 & 2189.94497728939 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 203.672142857143 & 0.0916512197190597 & 2222.25239862015 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 203.6675 & 0.0904835655852797 & 2250.87836318791 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 203.662631578947 & 0.0889888546176601 & 2288.63077802251 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 203.659722222222 & 0.0875880383504571 & 2325.20017639097 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 203.657352941176 & 0.0859313128092912 & 2370.00164763172 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 203.6565625 & 0.084031015509396 & 2423.58802003563 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 203.655 & 0.0819892760018672 & 2483.92240950343 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 203.656071428571 & 0.0802432467377434 & 2537.98393893725 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 203.653461538462 & 0.078646125255803 & 2589.49135607205 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 203.653333333333 & 0.0768955311140637 & 2648.44172844378 \tabularnewline
Median & 203.715 &  &  \tabularnewline
Midrange & 203.345 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 203.617631578947 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 203.659722222222 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 203.617631578947 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 203.659722222222 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 203.659722222222 &  &  \tabularnewline
Midmean - Closest Observation & 203.617631578947 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 203.659722222222 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 203.642051282051 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=240347&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]203.656805555556[/C][C]0.156027292162009[/C][C]1305.26398768808[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]203.652555163609[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]203.648297866875[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]203.661049073509[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]203.65625[/C][C]0.155892658675614[/C][C]1306.38768836302[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]203.64875[/C][C]0.154167071119886[/C][C]1320.96139934861[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]203.661666666667[/C][C]0.148086913531586[/C][C]1375.28470146167[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]203.706111111111[/C][C]0.12953020257277[/C][C]1572.6533817213[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]203.702638888889[/C][C]0.128810616806898[/C][C]1581.41187379191[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]203.690972222222[/C][C]0.123527185511277[/C][C]1648.95663557094[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]203.692916666667[/C][C]0.117990881437948[/C][C]1726.34456310753[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]203.722916666667[/C][C]0.109150123733117[/C][C]1866.446960379[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]203.712916666667[/C][C]0.106121412569708[/C][C]1919.62123132175[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]203.707361111111[/C][C]0.104714940770837[/C][C]1945.35144279853[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]203.733333333333[/C][C]0.0992542616249006[/C][C]2052.64066245616[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]203.731666666667[/C][C]0.0958633857757715[/C][C]2125.22920005354[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]203.731666666667[/C][C]0.092035961196505[/C][C]2213.60937635759[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]203.731666666667[/C][C]0.0914568661854155[/C][C]2227.62571214315[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]203.710833333333[/C][C]0.0881610397842341[/C][C]2310.66731780724[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]203.708611111111[/C][C]0.0871701934572194[/C][C]2336.90672272152[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]203.687361111111[/C][C]0.0839626456401494[/C][C]2425.9283346559[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]203.679861111111[/C][C]0.0821463571009641[/C][C]2479.47527193169[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]203.664027777778[/C][C]0.0798667855369915[/C][C]2550.0466358878[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]203.669583333333[/C][C]0.0767575592817139[/C][C]2653.4140121083[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]203.64625[/C][C]0.0719071294793019[/C][C]2832.07314037781[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]203.676805555556[/C][C]0.0677690044573222[/C][C]3005.45665657257[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]203.654444444444[/C][C]0.0647294504550781[/C][C]3146.24089981699[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]203.631111111111[/C][C]0.0607673143456561[/C][C]3350.99737916371[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]203.665714285714[/C][C]0.148190405669348[/C][C]1374.35155377161[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]203.675735294118[/C][C]0.138891939504677[/C][C]1466.43308474542[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]203.690454545455[/C][C]0.128687371998201[/C][C]1582.83172142409[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]203.70125[/C][C]0.119242504173584[/C][C]1708.29396289319[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]203.699838709677[/C][C]0.115232845903468[/C][C]1767.72375196148[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]203.699166666667[/C][C]0.110596301484596[/C][C]1841.82620876376[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]203.700862068966[/C][C]0.106524392170097[/C][C]1912.24618060902[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]203.702321428571[/C][C]0.103048025328576[/C][C]1976.77074139997[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]203.698888888889[/C][C]0.100968637382691[/C][C]2017.44714169837[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]203.696730769231[/C][C]0.0990538654570298[/C][C]2056.42384403056[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]203.6952[/C][C]0.0969246456726848[/C][C]2101.58312765857[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]203.69[/C][C]0.0953706840485404[/C][C]2135.77161611139[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]203.684565217391[/C][C]0.0940319128281442[/C][C]2166.12168242979[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]203.678636363636[/C][C]0.0930062802836902[/C][C]2189.94497728939[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]203.672142857143[/C][C]0.0916512197190597[/C][C]2222.25239862015[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]203.6675[/C][C]0.0904835655852797[/C][C]2250.87836318791[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]203.662631578947[/C][C]0.0889888546176601[/C][C]2288.63077802251[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]203.659722222222[/C][C]0.0875880383504571[/C][C]2325.20017639097[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]203.657352941176[/C][C]0.0859313128092912[/C][C]2370.00164763172[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]203.6565625[/C][C]0.084031015509396[/C][C]2423.58802003563[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]203.655[/C][C]0.0819892760018672[/C][C]2483.92240950343[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]203.656071428571[/C][C]0.0802432467377434[/C][C]2537.98393893725[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]203.653461538462[/C][C]0.078646125255803[/C][C]2589.49135607205[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]203.653333333333[/C][C]0.0768955311140637[/C][C]2648.44172844378[/C][/ROW]
[ROW][C]Median[/C][C]203.715[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]203.345[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]203.617631578947[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]203.659722222222[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]203.617631578947[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]203.659722222222[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]203.659722222222[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]203.617631578947[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]203.659722222222[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]203.642051282051[/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=240347&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=240347&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 Mean203.6568055555560.1560272921620091305.26398768808
Geometric Mean203.652555163609
Harmonic Mean203.648297866875
Quadratic Mean203.661049073509
Winsorized Mean ( 1 / 24 )203.656250.1558926586756141306.38768836302
Winsorized Mean ( 2 / 24 )203.648750.1541670711198861320.96139934861
Winsorized Mean ( 3 / 24 )203.6616666666670.1480869135315861375.28470146167
Winsorized Mean ( 4 / 24 )203.7061111111110.129530202572771572.6533817213
Winsorized Mean ( 5 / 24 )203.7026388888890.1288106168068981581.41187379191
Winsorized Mean ( 6 / 24 )203.6909722222220.1235271855112771648.95663557094
Winsorized Mean ( 7 / 24 )203.6929166666670.1179908814379481726.34456310753
Winsorized Mean ( 8 / 24 )203.7229166666670.1091501237331171866.446960379
Winsorized Mean ( 9 / 24 )203.7129166666670.1061214125697081919.62123132175
Winsorized Mean ( 10 / 24 )203.7073611111110.1047149407708371945.35144279853
Winsorized Mean ( 11 / 24 )203.7333333333330.09925426162490062052.64066245616
Winsorized Mean ( 12 / 24 )203.7316666666670.09586338577577152125.22920005354
Winsorized Mean ( 13 / 24 )203.7316666666670.0920359611965052213.60937635759
Winsorized Mean ( 14 / 24 )203.7316666666670.09145686618541552227.62571214315
Winsorized Mean ( 15 / 24 )203.7108333333330.08816103978423412310.66731780724
Winsorized Mean ( 16 / 24 )203.7086111111110.08717019345721942336.90672272152
Winsorized Mean ( 17 / 24 )203.6873611111110.08396264564014942425.9283346559
Winsorized Mean ( 18 / 24 )203.6798611111110.08214635710096412479.47527193169
Winsorized Mean ( 19 / 24 )203.6640277777780.07986678553699152550.0466358878
Winsorized Mean ( 20 / 24 )203.6695833333330.07675755928171392653.4140121083
Winsorized Mean ( 21 / 24 )203.646250.07190712947930192832.07314037781
Winsorized Mean ( 22 / 24 )203.6768055555560.06776900445732223005.45665657257
Winsorized Mean ( 23 / 24 )203.6544444444440.06472945045507813146.24089981699
Winsorized Mean ( 24 / 24 )203.6311111111110.06076731434565613350.99737916371
Trimmed Mean ( 1 / 24 )203.6657142857140.1481904056693481374.35155377161
Trimmed Mean ( 2 / 24 )203.6757352941180.1388919395046771466.43308474542
Trimmed Mean ( 3 / 24 )203.6904545454550.1286873719982011582.83172142409
Trimmed Mean ( 4 / 24 )203.701250.1192425041735841708.29396289319
Trimmed Mean ( 5 / 24 )203.6998387096770.1152328459034681767.72375196148
Trimmed Mean ( 6 / 24 )203.6991666666670.1105963014845961841.82620876376
Trimmed Mean ( 7 / 24 )203.7008620689660.1065243921700971912.24618060902
Trimmed Mean ( 8 / 24 )203.7023214285710.1030480253285761976.77074139997
Trimmed Mean ( 9 / 24 )203.6988888888890.1009686373826912017.44714169837
Trimmed Mean ( 10 / 24 )203.6967307692310.09905386545702982056.42384403056
Trimmed Mean ( 11 / 24 )203.69520.09692464567268482101.58312765857
Trimmed Mean ( 12 / 24 )203.690.09537068404854042135.77161611139
Trimmed Mean ( 13 / 24 )203.6845652173910.09403191282814422166.12168242979
Trimmed Mean ( 14 / 24 )203.6786363636360.09300628028369022189.94497728939
Trimmed Mean ( 15 / 24 )203.6721428571430.09165121971905972222.25239862015
Trimmed Mean ( 16 / 24 )203.66750.09048356558527972250.87836318791
Trimmed Mean ( 17 / 24 )203.6626315789470.08898885461766012288.63077802251
Trimmed Mean ( 18 / 24 )203.6597222222220.08758803835045712325.20017639097
Trimmed Mean ( 19 / 24 )203.6573529411760.08593131280929122370.00164763172
Trimmed Mean ( 20 / 24 )203.65656250.0840310155093962423.58802003563
Trimmed Mean ( 21 / 24 )203.6550.08198927600186722483.92240950343
Trimmed Mean ( 22 / 24 )203.6560714285710.08024324673774342537.98393893725
Trimmed Mean ( 23 / 24 )203.6534615384620.0786461252558032589.49135607205
Trimmed Mean ( 24 / 24 )203.6533333333330.07689553111406372648.44172844378
Median203.715
Midrange203.345
Midmean - Weighted Average at Xnp203.617631578947
Midmean - Weighted Average at X(n+1)p203.659722222222
Midmean - Empirical Distribution Function203.617631578947
Midmean - Empirical Distribution Function - Averaging203.659722222222
Midmean - Empirical Distribution Function - Interpolation203.659722222222
Midmean - Closest Observation203.617631578947
Midmean - True Basic - Statistics Graphics Toolkit203.659722222222
Midmean - MS Excel (old versions)203.642051282051
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')