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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, 11 Oct 2014 14:05:18 +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/11/t1413032746okx5bm3ld9am5n4.htm/, Retrieved Tue, 14 May 2024 03:24:21 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=240442, Retrieved Tue, 14 May 2024 03:24:21 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact71
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Gemiddelde consum...] [2014-10-11 13:05:18] [1ab96e54865215824aa8065210e49a0c] [Current]
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Dataseries X:
48,74
48,79
48,82
48,82
49,20
49,30
49,30
49,34
49,47
49,65
49,70
49,75
49,75
49,70
50,09
50,19
50,53
50,55
50,55
50,55
50,58
50,61
50,94
51,01
51,01
51,04
51,15
51,31
51,31
51,34
51,34
51,34
51,47
51,95
51,97
51,92
51,92
51,91
51,97
52,14
52,33
52,40
52,40
52,41
52,71
53,17
53,33
53,32
53,32
53,30
53,31
53,72
53,87
53,91
53,91
53,96
54,02
54,33
54,48
54,54
52,40
52,45
52,38
52,45
52,83
52,76
52,86
52,88
53,32
53,20
53,22
53,22




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=240442&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=240442&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=240442&T=0

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean51.71847222222220.190086326213204272.078866757696
Geometric Mean51.6935514305941
Harmonic Mean51.6685178696365
Quadratic Mean51.7432681477611
Winsorized Mean ( 1 / 24 )51.71833333333330.189761711212387272.543565310963
Winsorized Mean ( 2 / 24 )51.7150.188747519130956273.990356207645
Winsorized Mean ( 3 / 24 )51.70208333333330.18635505276887277.438591361715
Winsorized Mean ( 4 / 24 )51.71986111111110.181405624253441285.106160980177
Winsorized Mean ( 5 / 24 )51.72333333333330.179465930873489288.20697656423
Winsorized Mean ( 6 / 24 )51.72333333333330.179465930873489288.20697656423
Winsorized Mean ( 7 / 24 )51.72333333333330.178065702385937290.473306427247
Winsorized Mean ( 8 / 24 )51.72111111111110.172601896097935299.655521059655
Winsorized Mean ( 9 / 24 )51.69486111111110.161042912789129321.000534676126
Winsorized Mean ( 10 / 24 )51.70041666666670.159610421339449323.916297149004
Winsorized Mean ( 11 / 24 )51.70041666666670.159610421339449323.916297149004
Winsorized Mean ( 12 / 24 )51.708750.15814801825138326.964261530029
Winsorized Mean ( 13 / 24 )51.70694444444440.157889374973784327.488435830655
Winsorized Mean ( 14 / 24 )51.77111111111110.146477758671508353.440082512549
Winsorized Mean ( 15 / 24 )51.77527777777780.140709827532585367.957794318154
Winsorized Mean ( 16 / 24 )51.85083333333330.129254324337476401.153567581644
Winsorized Mean ( 17 / 24 )51.85083333333330.127873046576238405.486806810534
Winsorized Mean ( 18 / 24 )51.84333333333330.126762997716149408.97844219038
Winsorized Mean ( 19 / 24 )51.76680555555560.115926867425609446.547092189607
Winsorized Mean ( 20 / 24 )51.76958333333330.113948111200519454.325945273742
Winsorized Mean ( 21 / 24 )51.76958333333330.111488091657258464.350789073383
Winsorized Mean ( 22 / 24 )51.84902777777780.0943286466183889549.663645525791
Winsorized Mean ( 23 / 24 )51.85541666666670.0891524466525259581.648834257736
Winsorized Mean ( 24 / 24 )51.768750.0779322308775143664.27907192038
Trimmed Mean ( 1 / 24 )51.72071428571430.186433378486846277.421965452198
Trimmed Mean ( 2 / 24 )51.72323529411770.182458991649451283.478686506669
Trimmed Mean ( 3 / 24 )51.72772727272730.17834368688171290.045182855486
Trimmed Mean ( 4 / 24 )51.737343750.174470889773475296.538544723267
Trimmed Mean ( 5 / 24 )51.74241935483870.171590482794074301.545974533651
Trimmed Mean ( 6 / 24 )51.7470.168651564719945306.827867775366
Trimmed Mean ( 7 / 24 )51.75189655172410.165014519681695313.620259911377
Trimmed Mean ( 8 / 24 )51.75714285714290.160878819097286321.715084357031
Trimmed Mean ( 9 / 24 )51.76314814814810.157094919401908329.502369301445
Trimmed Mean ( 10 / 24 )51.77365384615380.154988207804766334.048987206636
Trimmed Mean ( 11 / 24 )51.78420.152540149281614339.479148564342
Trimmed Mean ( 12 / 24 )51.7956250.149317271998917346.883011634285
Trimmed Mean ( 13 / 24 )51.80695652173910.145437494107577356.214584413965
Trimmed Mean ( 14 / 24 )51.81954545454550.14038528776805369.123761317238
Trimmed Mean ( 15 / 24 )51.82547619047620.136538934550531379.565552939746
Trimmed Mean ( 16 / 24 )51.83150.132728057242948390.50899317487
Trimmed Mean ( 17 / 24 )51.82921052631580.130269652265656397.860972412988
Trimmed Mean ( 18 / 24 )51.82666666666670.127068285604037407.864688032117
Trimmed Mean ( 19 / 24 )51.82470588235290.122764672999047422.14673502006
Trimmed Mean ( 20 / 24 )51.83156250.119516085244022433.678549579102
Trimmed Mean ( 21 / 24 )51.8390.115191345061213450.025129687066
Trimmed Mean ( 22 / 24 )51.84750.109408734404622473.888124948547
Trimmed Mean ( 23 / 24 )51.84730769230770.10665048262332486.142269748821
Trimmed Mean ( 24 / 24 )51.846250.10380411544856499.462374646335
Median51.935
Midrange51.64
Midmean - Weighted Average at Xnp51.7921621621622
Midmean - Weighted Average at X(n+1)p51.7921621621622
Midmean - Empirical Distribution Function51.7921621621622
Midmean - Empirical Distribution Function - Averaging51.7921621621622
Midmean - Empirical Distribution Function - Interpolation51.7921621621622
Midmean - Closest Observation51.7921621621622
Midmean - True Basic - Statistics Graphics Toolkit51.7921621621622
Midmean - MS Excel (old versions)51.8292105263158
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 51.7184722222222 & 0.190086326213204 & 272.078866757696 \tabularnewline
Geometric Mean & 51.6935514305941 &  &  \tabularnewline
Harmonic Mean & 51.6685178696365 &  &  \tabularnewline
Quadratic Mean & 51.7432681477611 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 51.7183333333333 & 0.189761711212387 & 272.543565310963 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 51.715 & 0.188747519130956 & 273.990356207645 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 51.7020833333333 & 0.18635505276887 & 277.438591361715 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 51.7198611111111 & 0.181405624253441 & 285.106160980177 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 51.7233333333333 & 0.179465930873489 & 288.20697656423 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 51.7233333333333 & 0.179465930873489 & 288.20697656423 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 51.7233333333333 & 0.178065702385937 & 290.473306427247 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 51.7211111111111 & 0.172601896097935 & 299.655521059655 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 51.6948611111111 & 0.161042912789129 & 321.000534676126 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 51.7004166666667 & 0.159610421339449 & 323.916297149004 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 51.7004166666667 & 0.159610421339449 & 323.916297149004 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 51.70875 & 0.15814801825138 & 326.964261530029 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 51.7069444444444 & 0.157889374973784 & 327.488435830655 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 51.7711111111111 & 0.146477758671508 & 353.440082512549 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 51.7752777777778 & 0.140709827532585 & 367.957794318154 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 51.8508333333333 & 0.129254324337476 & 401.153567581644 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 51.8508333333333 & 0.127873046576238 & 405.486806810534 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 51.8433333333333 & 0.126762997716149 & 408.97844219038 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 51.7668055555556 & 0.115926867425609 & 446.547092189607 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 51.7695833333333 & 0.113948111200519 & 454.325945273742 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 51.7695833333333 & 0.111488091657258 & 464.350789073383 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 51.8490277777778 & 0.0943286466183889 & 549.663645525791 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 51.8554166666667 & 0.0891524466525259 & 581.648834257736 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 51.76875 & 0.0779322308775143 & 664.27907192038 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 51.7207142857143 & 0.186433378486846 & 277.421965452198 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 51.7232352941177 & 0.182458991649451 & 283.478686506669 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 51.7277272727273 & 0.17834368688171 & 290.045182855486 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 51.73734375 & 0.174470889773475 & 296.538544723267 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 51.7424193548387 & 0.171590482794074 & 301.545974533651 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 51.747 & 0.168651564719945 & 306.827867775366 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 51.7518965517241 & 0.165014519681695 & 313.620259911377 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 51.7571428571429 & 0.160878819097286 & 321.715084357031 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 51.7631481481481 & 0.157094919401908 & 329.502369301445 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 51.7736538461538 & 0.154988207804766 & 334.048987206636 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 51.7842 & 0.152540149281614 & 339.479148564342 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 51.795625 & 0.149317271998917 & 346.883011634285 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 51.8069565217391 & 0.145437494107577 & 356.214584413965 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 51.8195454545455 & 0.14038528776805 & 369.123761317238 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 51.8254761904762 & 0.136538934550531 & 379.565552939746 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 51.8315 & 0.132728057242948 & 390.50899317487 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 51.8292105263158 & 0.130269652265656 & 397.860972412988 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 51.8266666666667 & 0.127068285604037 & 407.864688032117 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 51.8247058823529 & 0.122764672999047 & 422.14673502006 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 51.8315625 & 0.119516085244022 & 433.678549579102 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 51.839 & 0.115191345061213 & 450.025129687066 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 51.8475 & 0.109408734404622 & 473.888124948547 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 51.8473076923077 & 0.10665048262332 & 486.142269748821 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 51.84625 & 0.10380411544856 & 499.462374646335 \tabularnewline
Median & 51.935 &  &  \tabularnewline
Midrange & 51.64 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 51.7921621621622 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 51.7921621621622 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 51.7921621621622 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 51.7921621621622 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 51.7921621621622 &  &  \tabularnewline
Midmean - Closest Observation & 51.7921621621622 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 51.7921621621622 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 51.8292105263158 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=240442&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]51.7184722222222[/C][C]0.190086326213204[/C][C]272.078866757696[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]51.6935514305941[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]51.6685178696365[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]51.7432681477611[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]51.7183333333333[/C][C]0.189761711212387[/C][C]272.543565310963[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]51.715[/C][C]0.188747519130956[/C][C]273.990356207645[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]51.7020833333333[/C][C]0.18635505276887[/C][C]277.438591361715[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]51.7198611111111[/C][C]0.181405624253441[/C][C]285.106160980177[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]51.7233333333333[/C][C]0.179465930873489[/C][C]288.20697656423[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]51.7233333333333[/C][C]0.179465930873489[/C][C]288.20697656423[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]51.7233333333333[/C][C]0.178065702385937[/C][C]290.473306427247[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]51.7211111111111[/C][C]0.172601896097935[/C][C]299.655521059655[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]51.6948611111111[/C][C]0.161042912789129[/C][C]321.000534676126[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]51.7004166666667[/C][C]0.159610421339449[/C][C]323.916297149004[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]51.7004166666667[/C][C]0.159610421339449[/C][C]323.916297149004[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]51.70875[/C][C]0.15814801825138[/C][C]326.964261530029[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]51.7069444444444[/C][C]0.157889374973784[/C][C]327.488435830655[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]51.7711111111111[/C][C]0.146477758671508[/C][C]353.440082512549[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]51.7752777777778[/C][C]0.140709827532585[/C][C]367.957794318154[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]51.8508333333333[/C][C]0.129254324337476[/C][C]401.153567581644[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]51.8508333333333[/C][C]0.127873046576238[/C][C]405.486806810534[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]51.8433333333333[/C][C]0.126762997716149[/C][C]408.97844219038[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]51.7668055555556[/C][C]0.115926867425609[/C][C]446.547092189607[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]51.7695833333333[/C][C]0.113948111200519[/C][C]454.325945273742[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]51.7695833333333[/C][C]0.111488091657258[/C][C]464.350789073383[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]51.8490277777778[/C][C]0.0943286466183889[/C][C]549.663645525791[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]51.8554166666667[/C][C]0.0891524466525259[/C][C]581.648834257736[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]51.76875[/C][C]0.0779322308775143[/C][C]664.27907192038[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]51.7207142857143[/C][C]0.186433378486846[/C][C]277.421965452198[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]51.7232352941177[/C][C]0.182458991649451[/C][C]283.478686506669[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]51.7277272727273[/C][C]0.17834368688171[/C][C]290.045182855486[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]51.73734375[/C][C]0.174470889773475[/C][C]296.538544723267[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]51.7424193548387[/C][C]0.171590482794074[/C][C]301.545974533651[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]51.747[/C][C]0.168651564719945[/C][C]306.827867775366[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]51.7518965517241[/C][C]0.165014519681695[/C][C]313.620259911377[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]51.7571428571429[/C][C]0.160878819097286[/C][C]321.715084357031[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]51.7631481481481[/C][C]0.157094919401908[/C][C]329.502369301445[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]51.7736538461538[/C][C]0.154988207804766[/C][C]334.048987206636[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]51.7842[/C][C]0.152540149281614[/C][C]339.479148564342[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]51.795625[/C][C]0.149317271998917[/C][C]346.883011634285[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]51.8069565217391[/C][C]0.145437494107577[/C][C]356.214584413965[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]51.8195454545455[/C][C]0.14038528776805[/C][C]369.123761317238[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]51.8254761904762[/C][C]0.136538934550531[/C][C]379.565552939746[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]51.8315[/C][C]0.132728057242948[/C][C]390.50899317487[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]51.8292105263158[/C][C]0.130269652265656[/C][C]397.860972412988[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]51.8266666666667[/C][C]0.127068285604037[/C][C]407.864688032117[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]51.8247058823529[/C][C]0.122764672999047[/C][C]422.14673502006[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]51.8315625[/C][C]0.119516085244022[/C][C]433.678549579102[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]51.839[/C][C]0.115191345061213[/C][C]450.025129687066[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]51.8475[/C][C]0.109408734404622[/C][C]473.888124948547[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]51.8473076923077[/C][C]0.10665048262332[/C][C]486.142269748821[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]51.84625[/C][C]0.10380411544856[/C][C]499.462374646335[/C][/ROW]
[ROW][C]Median[/C][C]51.935[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]51.64[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]51.7921621621622[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]51.7921621621622[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]51.7921621621622[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]51.7921621621622[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]51.7921621621622[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]51.7921621621622[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]51.7921621621622[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]51.8292105263158[/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=240442&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=240442&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 Mean51.71847222222220.190086326213204272.078866757696
Geometric Mean51.6935514305941
Harmonic Mean51.6685178696365
Quadratic Mean51.7432681477611
Winsorized Mean ( 1 / 24 )51.71833333333330.189761711212387272.543565310963
Winsorized Mean ( 2 / 24 )51.7150.188747519130956273.990356207645
Winsorized Mean ( 3 / 24 )51.70208333333330.18635505276887277.438591361715
Winsorized Mean ( 4 / 24 )51.71986111111110.181405624253441285.106160980177
Winsorized Mean ( 5 / 24 )51.72333333333330.179465930873489288.20697656423
Winsorized Mean ( 6 / 24 )51.72333333333330.179465930873489288.20697656423
Winsorized Mean ( 7 / 24 )51.72333333333330.178065702385937290.473306427247
Winsorized Mean ( 8 / 24 )51.72111111111110.172601896097935299.655521059655
Winsorized Mean ( 9 / 24 )51.69486111111110.161042912789129321.000534676126
Winsorized Mean ( 10 / 24 )51.70041666666670.159610421339449323.916297149004
Winsorized Mean ( 11 / 24 )51.70041666666670.159610421339449323.916297149004
Winsorized Mean ( 12 / 24 )51.708750.15814801825138326.964261530029
Winsorized Mean ( 13 / 24 )51.70694444444440.157889374973784327.488435830655
Winsorized Mean ( 14 / 24 )51.77111111111110.146477758671508353.440082512549
Winsorized Mean ( 15 / 24 )51.77527777777780.140709827532585367.957794318154
Winsorized Mean ( 16 / 24 )51.85083333333330.129254324337476401.153567581644
Winsorized Mean ( 17 / 24 )51.85083333333330.127873046576238405.486806810534
Winsorized Mean ( 18 / 24 )51.84333333333330.126762997716149408.97844219038
Winsorized Mean ( 19 / 24 )51.76680555555560.115926867425609446.547092189607
Winsorized Mean ( 20 / 24 )51.76958333333330.113948111200519454.325945273742
Winsorized Mean ( 21 / 24 )51.76958333333330.111488091657258464.350789073383
Winsorized Mean ( 22 / 24 )51.84902777777780.0943286466183889549.663645525791
Winsorized Mean ( 23 / 24 )51.85541666666670.0891524466525259581.648834257736
Winsorized Mean ( 24 / 24 )51.768750.0779322308775143664.27907192038
Trimmed Mean ( 1 / 24 )51.72071428571430.186433378486846277.421965452198
Trimmed Mean ( 2 / 24 )51.72323529411770.182458991649451283.478686506669
Trimmed Mean ( 3 / 24 )51.72772727272730.17834368688171290.045182855486
Trimmed Mean ( 4 / 24 )51.737343750.174470889773475296.538544723267
Trimmed Mean ( 5 / 24 )51.74241935483870.171590482794074301.545974533651
Trimmed Mean ( 6 / 24 )51.7470.168651564719945306.827867775366
Trimmed Mean ( 7 / 24 )51.75189655172410.165014519681695313.620259911377
Trimmed Mean ( 8 / 24 )51.75714285714290.160878819097286321.715084357031
Trimmed Mean ( 9 / 24 )51.76314814814810.157094919401908329.502369301445
Trimmed Mean ( 10 / 24 )51.77365384615380.154988207804766334.048987206636
Trimmed Mean ( 11 / 24 )51.78420.152540149281614339.479148564342
Trimmed Mean ( 12 / 24 )51.7956250.149317271998917346.883011634285
Trimmed Mean ( 13 / 24 )51.80695652173910.145437494107577356.214584413965
Trimmed Mean ( 14 / 24 )51.81954545454550.14038528776805369.123761317238
Trimmed Mean ( 15 / 24 )51.82547619047620.136538934550531379.565552939746
Trimmed Mean ( 16 / 24 )51.83150.132728057242948390.50899317487
Trimmed Mean ( 17 / 24 )51.82921052631580.130269652265656397.860972412988
Trimmed Mean ( 18 / 24 )51.82666666666670.127068285604037407.864688032117
Trimmed Mean ( 19 / 24 )51.82470588235290.122764672999047422.14673502006
Trimmed Mean ( 20 / 24 )51.83156250.119516085244022433.678549579102
Trimmed Mean ( 21 / 24 )51.8390.115191345061213450.025129687066
Trimmed Mean ( 22 / 24 )51.84750.109408734404622473.888124948547
Trimmed Mean ( 23 / 24 )51.84730769230770.10665048262332486.142269748821
Trimmed Mean ( 24 / 24 )51.846250.10380411544856499.462374646335
Median51.935
Midrange51.64
Midmean - Weighted Average at Xnp51.7921621621622
Midmean - Weighted Average at X(n+1)p51.7921621621622
Midmean - Empirical Distribution Function51.7921621621622
Midmean - Empirical Distribution Function - Averaging51.7921621621622
Midmean - Empirical Distribution Function - Interpolation51.7921621621622
Midmean - Closest Observation51.7921621621622
Midmean - True Basic - Statistics Graphics Toolkit51.7921621621622
Midmean - MS Excel (old versions)51.8292105263158
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')