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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationThu, 08 Mar 2012 08:05:00 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/Mar/08/t1331211927h9bzg2d1pkia18a.htm/, Retrieved Sat, 04 May 2024 08:21:59 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=163742, Retrieved Sat, 04 May 2024 08:21:59 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact130
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2012-03-08 13:05:00] [41122821deba20d6652b4f9148627213] [Current]
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Dataseries X:
100,17
102,01
100,3
99,94
100,16
100,18
99,98
100,04
100,05
100,11
100,11
101,03
100,84
102,68
101,27
100,28
100,82
100,87
101,23
101,09
101,22
101,33
101,3
102,39
101,69
103,75
102,99
100,8
102,21
102,45
102,49
102,4
102,99
103,19
103,35
104,44
103,42
105,81
104,25
103,78
104,53
105,01
104,83
104,55
105,16
105,06
105,2
105,87
105,41
107,89
106,06
105,5
106,71
106,34
106,11
106,15
106,61
106,63
106,27
105,59
107,09
108,53
108,01
106,52
107,27
107,58
107,36
107,23
107,54
107,64
108,23
108,42




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 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 & 1 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=163742&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]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=163742&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=163742&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'Herman Ole Andreas Wold' @ wold.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean103.8376388888890.321156915236231323.323689955453
Geometric Mean103.802403292107
Harmonic Mean103.767204662608
Quadratic Mean103.872894998059
Winsorized Mean ( 1 / 24 )103.8366666666670.320751452876977323.729372806591
Winsorized Mean ( 2 / 24 )103.8330555555560.31942820092062325.059137722655
Winsorized Mean ( 3 / 24 )103.8243055555560.31761907840478326.883089255866
Winsorized Mean ( 4 / 24 )103.8209722222220.315840729144161328.713058963445
Winsorized Mean ( 5 / 24 )103.8036111111110.312765587019938331.889489825791
Winsorized Mean ( 6 / 24 )103.8027777777780.311216328898929333.538982819532
Winsorized Mean ( 7 / 24 )103.7998611111110.310393730794316334.413523254741
Winsorized Mean ( 8 / 24 )103.7809722222220.30687028602668338.191662561944
Winsorized Mean ( 9 / 24 )103.7822222222220.302983612967771342.534110032089
Winsorized Mean ( 10 / 24 )103.7794444444440.301633910555856344.057616907854
Winsorized Mean ( 11 / 24 )103.8344444444440.286276954836496362.706262904565
Winsorized Mean ( 12 / 24 )103.7744444444440.275954233527795376.056721862149
Winsorized Mean ( 13 / 24 )103.7636111111110.27326070442056379.723866009708
Winsorized Mean ( 14 / 24 )103.7655555555560.271809698290651381.758105792815
Winsorized Mean ( 15 / 24 )103.7801388888890.264112140449853392.939675972955
Winsorized Mean ( 16 / 24 )103.7534722222220.256393837047897404.66445456269
Winsorized Mean ( 17 / 24 )103.7676388888890.249600345110276415.735157910312
Winsorized Mean ( 18 / 24 )103.7401388888890.245044189194287423.35278069637
Winsorized Mean ( 19 / 24 )103.7401388888890.242065357793072428.562516481893
Winsorized Mean ( 20 / 24 )103.7345833333330.238959168588985434.110078076808
Winsorized Mean ( 21 / 24 )103.6879166666670.230201393210027450.422628728688
Winsorized Mean ( 22 / 24 )103.7795833333330.212166099403997489.143098849741
Winsorized Mean ( 23 / 24 )103.8115277777780.188791111320692549.875081785165
Winsorized Mean ( 24 / 24 )103.8481944444440.175962735952843590.171514906857
Trimmed Mean ( 1 / 24 )103.8262857142860.318524624958757325.959996743515
Trimmed Mean ( 2 / 24 )103.8152941176470.315719802104808328.82097804934
Trimmed Mean ( 3 / 24 )103.8056060606060.313037910286956331.607139740517
Trimmed Mean ( 4 / 24 )103.798593750.310451289790707334.347439239105
Trimmed Mean ( 5 / 24 )103.7920967741940.307776964399128337.231530555987
Trimmed Mean ( 6 / 24 )103.7893333333330.305269896945584339.992034497375
Trimmed Mean ( 7 / 24 )103.7865517241380.302415117529854343.192339628631
Trimmed Mean ( 8 / 24 )103.7841071428570.298905881115287347.213332690593
Trimmed Mean ( 9 / 24 )103.784629629630.295201042838147351.572706626692
Trimmed Mean ( 10 / 24 )103.7850.291259616844188356.33158185304
Trimmed Mean ( 11 / 24 )103.78580.286400332060006362.380166438686
Trimmed Mean ( 12 / 24 )103.7791666666670.283349055675585366.259087820947
Trimmed Mean ( 13 / 24 )103.7797826086960.281284405583027368.949648643295
Trimmed Mean ( 14 / 24 )103.7818181818180.278752558123487372.308038643515
Trimmed Mean ( 15 / 24 )103.783809523810.27532747946794376.946789780548
Trimmed Mean ( 16 / 24 )103.784250.272060487123445381.474910588206
Trimmed Mean ( 17 / 24 )103.7878947368420.268914671775759385.951030680052
Trimmed Mean ( 18 / 24 )103.7902777777780.26565268114921390.699153980989
Trimmed Mean ( 19 / 24 )103.7961764705880.261620145746816396.743821750782
Trimmed Mean ( 20 / 24 )103.80281250.256092392276804405.333448514949
Trimmed Mean ( 21 / 24 )103.8110.248438040102789417.854689068748
Trimmed Mean ( 22 / 24 )103.8260714285710.239312473825532433.851481992805
Trimmed Mean ( 23 / 24 )103.8319230769230.231373171259544448.763884385062
Trimmed Mean ( 24 / 24 )103.8345833333330.226769993898775457.885020624391
Median103.765
Midrange104.235
Midmean - Weighted Average at Xnp103.720810810811
Midmean - Weighted Average at X(n+1)p103.790277777778
Midmean - Empirical Distribution Function103.720810810811
Midmean - Empirical Distribution Function - Averaging103.790277777778
Midmean - Empirical Distribution Function - Interpolation103.790277777778
Midmean - Closest Observation103.720810810811
Midmean - True Basic - Statistics Graphics Toolkit103.790277777778
Midmean - MS Excel (old versions)103.787894736842
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 103.837638888889 & 0.321156915236231 & 323.323689955453 \tabularnewline
Geometric Mean & 103.802403292107 &  &  \tabularnewline
Harmonic Mean & 103.767204662608 &  &  \tabularnewline
Quadratic Mean & 103.872894998059 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 103.836666666667 & 0.320751452876977 & 323.729372806591 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 103.833055555556 & 0.31942820092062 & 325.059137722655 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 103.824305555556 & 0.31761907840478 & 326.883089255866 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 103.820972222222 & 0.315840729144161 & 328.713058963445 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 103.803611111111 & 0.312765587019938 & 331.889489825791 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 103.802777777778 & 0.311216328898929 & 333.538982819532 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 103.799861111111 & 0.310393730794316 & 334.413523254741 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 103.780972222222 & 0.30687028602668 & 338.191662561944 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 103.782222222222 & 0.302983612967771 & 342.534110032089 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 103.779444444444 & 0.301633910555856 & 344.057616907854 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 103.834444444444 & 0.286276954836496 & 362.706262904565 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 103.774444444444 & 0.275954233527795 & 376.056721862149 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 103.763611111111 & 0.27326070442056 & 379.723866009708 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 103.765555555556 & 0.271809698290651 & 381.758105792815 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 103.780138888889 & 0.264112140449853 & 392.939675972955 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 103.753472222222 & 0.256393837047897 & 404.66445456269 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 103.767638888889 & 0.249600345110276 & 415.735157910312 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 103.740138888889 & 0.245044189194287 & 423.35278069637 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 103.740138888889 & 0.242065357793072 & 428.562516481893 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 103.734583333333 & 0.238959168588985 & 434.110078076808 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 103.687916666667 & 0.230201393210027 & 450.422628728688 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 103.779583333333 & 0.212166099403997 & 489.143098849741 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 103.811527777778 & 0.188791111320692 & 549.875081785165 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 103.848194444444 & 0.175962735952843 & 590.171514906857 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 103.826285714286 & 0.318524624958757 & 325.959996743515 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 103.815294117647 & 0.315719802104808 & 328.82097804934 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 103.805606060606 & 0.313037910286956 & 331.607139740517 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 103.79859375 & 0.310451289790707 & 334.347439239105 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 103.792096774194 & 0.307776964399128 & 337.231530555987 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 103.789333333333 & 0.305269896945584 & 339.992034497375 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 103.786551724138 & 0.302415117529854 & 343.192339628631 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 103.784107142857 & 0.298905881115287 & 347.213332690593 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 103.78462962963 & 0.295201042838147 & 351.572706626692 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 103.785 & 0.291259616844188 & 356.33158185304 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 103.7858 & 0.286400332060006 & 362.380166438686 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 103.779166666667 & 0.283349055675585 & 366.259087820947 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 103.779782608696 & 0.281284405583027 & 368.949648643295 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 103.781818181818 & 0.278752558123487 & 372.308038643515 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 103.78380952381 & 0.27532747946794 & 376.946789780548 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 103.78425 & 0.272060487123445 & 381.474910588206 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 103.787894736842 & 0.268914671775759 & 385.951030680052 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 103.790277777778 & 0.26565268114921 & 390.699153980989 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 103.796176470588 & 0.261620145746816 & 396.743821750782 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 103.8028125 & 0.256092392276804 & 405.333448514949 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 103.811 & 0.248438040102789 & 417.854689068748 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 103.826071428571 & 0.239312473825532 & 433.851481992805 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 103.831923076923 & 0.231373171259544 & 448.763884385062 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 103.834583333333 & 0.226769993898775 & 457.885020624391 \tabularnewline
Median & 103.765 &  &  \tabularnewline
Midrange & 104.235 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 103.720810810811 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 103.790277777778 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 103.720810810811 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 103.790277777778 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 103.790277777778 &  &  \tabularnewline
Midmean - Closest Observation & 103.720810810811 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 103.790277777778 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 103.787894736842 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=163742&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]103.837638888889[/C][C]0.321156915236231[/C][C]323.323689955453[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]103.802403292107[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]103.767204662608[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]103.872894998059[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]103.836666666667[/C][C]0.320751452876977[/C][C]323.729372806591[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]103.833055555556[/C][C]0.31942820092062[/C][C]325.059137722655[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]103.824305555556[/C][C]0.31761907840478[/C][C]326.883089255866[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]103.820972222222[/C][C]0.315840729144161[/C][C]328.713058963445[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]103.803611111111[/C][C]0.312765587019938[/C][C]331.889489825791[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]103.802777777778[/C][C]0.311216328898929[/C][C]333.538982819532[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]103.799861111111[/C][C]0.310393730794316[/C][C]334.413523254741[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]103.780972222222[/C][C]0.30687028602668[/C][C]338.191662561944[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]103.782222222222[/C][C]0.302983612967771[/C][C]342.534110032089[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]103.779444444444[/C][C]0.301633910555856[/C][C]344.057616907854[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]103.834444444444[/C][C]0.286276954836496[/C][C]362.706262904565[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]103.774444444444[/C][C]0.275954233527795[/C][C]376.056721862149[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]103.763611111111[/C][C]0.27326070442056[/C][C]379.723866009708[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]103.765555555556[/C][C]0.271809698290651[/C][C]381.758105792815[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]103.780138888889[/C][C]0.264112140449853[/C][C]392.939675972955[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]103.753472222222[/C][C]0.256393837047897[/C][C]404.66445456269[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]103.767638888889[/C][C]0.249600345110276[/C][C]415.735157910312[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]103.740138888889[/C][C]0.245044189194287[/C][C]423.35278069637[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]103.740138888889[/C][C]0.242065357793072[/C][C]428.562516481893[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]103.734583333333[/C][C]0.238959168588985[/C][C]434.110078076808[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]103.687916666667[/C][C]0.230201393210027[/C][C]450.422628728688[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]103.779583333333[/C][C]0.212166099403997[/C][C]489.143098849741[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]103.811527777778[/C][C]0.188791111320692[/C][C]549.875081785165[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]103.848194444444[/C][C]0.175962735952843[/C][C]590.171514906857[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]103.826285714286[/C][C]0.318524624958757[/C][C]325.959996743515[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]103.815294117647[/C][C]0.315719802104808[/C][C]328.82097804934[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]103.805606060606[/C][C]0.313037910286956[/C][C]331.607139740517[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]103.79859375[/C][C]0.310451289790707[/C][C]334.347439239105[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]103.792096774194[/C][C]0.307776964399128[/C][C]337.231530555987[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]103.789333333333[/C][C]0.305269896945584[/C][C]339.992034497375[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]103.786551724138[/C][C]0.302415117529854[/C][C]343.192339628631[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]103.784107142857[/C][C]0.298905881115287[/C][C]347.213332690593[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]103.78462962963[/C][C]0.295201042838147[/C][C]351.572706626692[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]103.785[/C][C]0.291259616844188[/C][C]356.33158185304[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]103.7858[/C][C]0.286400332060006[/C][C]362.380166438686[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]103.779166666667[/C][C]0.283349055675585[/C][C]366.259087820947[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]103.779782608696[/C][C]0.281284405583027[/C][C]368.949648643295[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]103.781818181818[/C][C]0.278752558123487[/C][C]372.308038643515[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]103.78380952381[/C][C]0.27532747946794[/C][C]376.946789780548[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]103.78425[/C][C]0.272060487123445[/C][C]381.474910588206[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]103.787894736842[/C][C]0.268914671775759[/C][C]385.951030680052[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]103.790277777778[/C][C]0.26565268114921[/C][C]390.699153980989[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]103.796176470588[/C][C]0.261620145746816[/C][C]396.743821750782[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]103.8028125[/C][C]0.256092392276804[/C][C]405.333448514949[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]103.811[/C][C]0.248438040102789[/C][C]417.854689068748[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]103.826071428571[/C][C]0.239312473825532[/C][C]433.851481992805[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]103.831923076923[/C][C]0.231373171259544[/C][C]448.763884385062[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]103.834583333333[/C][C]0.226769993898775[/C][C]457.885020624391[/C][/ROW]
[ROW][C]Median[/C][C]103.765[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]104.235[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]103.720810810811[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]103.790277777778[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]103.720810810811[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]103.790277777778[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]103.790277777778[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]103.720810810811[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]103.790277777778[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]103.787894736842[/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=163742&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=163742&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 Mean103.8376388888890.321156915236231323.323689955453
Geometric Mean103.802403292107
Harmonic Mean103.767204662608
Quadratic Mean103.872894998059
Winsorized Mean ( 1 / 24 )103.8366666666670.320751452876977323.729372806591
Winsorized Mean ( 2 / 24 )103.8330555555560.31942820092062325.059137722655
Winsorized Mean ( 3 / 24 )103.8243055555560.31761907840478326.883089255866
Winsorized Mean ( 4 / 24 )103.8209722222220.315840729144161328.713058963445
Winsorized Mean ( 5 / 24 )103.8036111111110.312765587019938331.889489825791
Winsorized Mean ( 6 / 24 )103.8027777777780.311216328898929333.538982819532
Winsorized Mean ( 7 / 24 )103.7998611111110.310393730794316334.413523254741
Winsorized Mean ( 8 / 24 )103.7809722222220.30687028602668338.191662561944
Winsorized Mean ( 9 / 24 )103.7822222222220.302983612967771342.534110032089
Winsorized Mean ( 10 / 24 )103.7794444444440.301633910555856344.057616907854
Winsorized Mean ( 11 / 24 )103.8344444444440.286276954836496362.706262904565
Winsorized Mean ( 12 / 24 )103.7744444444440.275954233527795376.056721862149
Winsorized Mean ( 13 / 24 )103.7636111111110.27326070442056379.723866009708
Winsorized Mean ( 14 / 24 )103.7655555555560.271809698290651381.758105792815
Winsorized Mean ( 15 / 24 )103.7801388888890.264112140449853392.939675972955
Winsorized Mean ( 16 / 24 )103.7534722222220.256393837047897404.66445456269
Winsorized Mean ( 17 / 24 )103.7676388888890.249600345110276415.735157910312
Winsorized Mean ( 18 / 24 )103.7401388888890.245044189194287423.35278069637
Winsorized Mean ( 19 / 24 )103.7401388888890.242065357793072428.562516481893
Winsorized Mean ( 20 / 24 )103.7345833333330.238959168588985434.110078076808
Winsorized Mean ( 21 / 24 )103.6879166666670.230201393210027450.422628728688
Winsorized Mean ( 22 / 24 )103.7795833333330.212166099403997489.143098849741
Winsorized Mean ( 23 / 24 )103.8115277777780.188791111320692549.875081785165
Winsorized Mean ( 24 / 24 )103.8481944444440.175962735952843590.171514906857
Trimmed Mean ( 1 / 24 )103.8262857142860.318524624958757325.959996743515
Trimmed Mean ( 2 / 24 )103.8152941176470.315719802104808328.82097804934
Trimmed Mean ( 3 / 24 )103.8056060606060.313037910286956331.607139740517
Trimmed Mean ( 4 / 24 )103.798593750.310451289790707334.347439239105
Trimmed Mean ( 5 / 24 )103.7920967741940.307776964399128337.231530555987
Trimmed Mean ( 6 / 24 )103.7893333333330.305269896945584339.992034497375
Trimmed Mean ( 7 / 24 )103.7865517241380.302415117529854343.192339628631
Trimmed Mean ( 8 / 24 )103.7841071428570.298905881115287347.213332690593
Trimmed Mean ( 9 / 24 )103.784629629630.295201042838147351.572706626692
Trimmed Mean ( 10 / 24 )103.7850.291259616844188356.33158185304
Trimmed Mean ( 11 / 24 )103.78580.286400332060006362.380166438686
Trimmed Mean ( 12 / 24 )103.7791666666670.283349055675585366.259087820947
Trimmed Mean ( 13 / 24 )103.7797826086960.281284405583027368.949648643295
Trimmed Mean ( 14 / 24 )103.7818181818180.278752558123487372.308038643515
Trimmed Mean ( 15 / 24 )103.783809523810.27532747946794376.946789780548
Trimmed Mean ( 16 / 24 )103.784250.272060487123445381.474910588206
Trimmed Mean ( 17 / 24 )103.7878947368420.268914671775759385.951030680052
Trimmed Mean ( 18 / 24 )103.7902777777780.26565268114921390.699153980989
Trimmed Mean ( 19 / 24 )103.7961764705880.261620145746816396.743821750782
Trimmed Mean ( 20 / 24 )103.80281250.256092392276804405.333448514949
Trimmed Mean ( 21 / 24 )103.8110.248438040102789417.854689068748
Trimmed Mean ( 22 / 24 )103.8260714285710.239312473825532433.851481992805
Trimmed Mean ( 23 / 24 )103.8319230769230.231373171259544448.763884385062
Trimmed Mean ( 24 / 24 )103.8345833333330.226769993898775457.885020624391
Median103.765
Midrange104.235
Midmean - Weighted Average at Xnp103.720810810811
Midmean - Weighted Average at X(n+1)p103.790277777778
Midmean - Empirical Distribution Function103.720810810811
Midmean - Empirical Distribution Function - Averaging103.790277777778
Midmean - Empirical Distribution Function - Interpolation103.790277777778
Midmean - Closest Observation103.720810810811
Midmean - True Basic - Statistics Graphics Toolkit103.790277777778
Midmean - MS Excel (old versions)103.787894736842
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')