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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationMon, 05 Mar 2012 08:47:11 -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/05/t13309552535qp0t4xdq2tttcv.htm/, Retrieved Fri, 03 May 2024 00:07:17 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=163494, Retrieved Fri, 03 May 2024 00:07:17 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact151
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2012-03-05 13:47:11] [e0b098c2bb79809f51906d3408b0bcc0] [Current]
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Dataseries X:
23,15
23,18
23,32
23,37
23,43
23,65
23,76
23,81
23,85
23,83
23,85
23,71
23,74
23,87
24,13
24,23
24,27
24,41
24,39
24,34
24,31
24,34
24,41
24,39
24,54
24,9
25,63
26,7
27,12
27,68
27,84
27,84
27,77
27,8
27,82
27,72
27,87
27,83
28,07
28,05
28,15
28,3
28,41
28,43
28,43
28,29
28,19
27,53
27,92
27,98
27,92
27,89
27,95
28,02
27,97
27,81
27,78
27,56
27,52
27,18




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'AstonUniversity' @ aston.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 & 'AstonUniversity' @ aston.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=163494&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]'AstonUniversity' @ aston.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=163494&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=163494&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'AstonUniversity' @ aston.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean26.13583333333330.254893385452172102.536334110708
Geometric Mean26.0614560106331
Harmonic Mean25.9863032742793
Quadratic Mean26.2090643035318
Winsorized Mean ( 1 / 20 )26.13633333333330.254794585112472102.57805644416
Winsorized Mean ( 2 / 20 )26.14033333333330.253794810873598102.997903083024
Winsorized Mean ( 3 / 20 )26.13733333333330.252511102476352103.509640079216
Winsorized Mean ( 4 / 20 )26.14066666666670.251677857348382103.865580159012
Winsorized Mean ( 5 / 20 )26.15066666666670.247246402253896105.767632727018
Winsorized Mean ( 6 / 20 )26.15266666666670.245671323614915106.453884327421
Winsorized Mean ( 7 / 20 )26.14683333333330.243816580553741107.239767180518
Winsorized Mean ( 8 / 20 )26.14683333333330.243016296641079107.592921523081
Winsorized Mean ( 9 / 20 )26.14983333333330.241181003326026108.424100458626
Winsorized Mean ( 10 / 20 )26.14650.239763869832042109.051042670925
Winsorized Mean ( 11 / 20 )26.14833333333330.238927472467717109.440463514996
Winsorized Mean ( 12 / 20 )26.14433333333330.238412281973595109.66017822953
Winsorized Mean ( 13 / 20 )26.14216666666670.236875982673652110.362251046292
Winsorized Mean ( 14 / 20 )26.20283333333330.227249842804377115.304076825653
Winsorized Mean ( 15 / 20 )26.22033333333330.222464110819333117.863206054964
Winsorized Mean ( 16 / 20 )26.22566666666670.220175631828829119.11248510487
Winsorized Mean ( 17 / 20 )26.22850.217402985052194120.644617615085
Winsorized Mean ( 18 / 20 )26.23750.216060075475987121.436132715394
Winsorized Mean ( 19 / 20 )26.23433333333330.215662475181721121.645331721375
Winsorized Mean ( 20 / 20 )26.24766666666670.212770846558003123.361198638232
Trimmed Mean ( 1 / 20 )26.14775862068970.255495798460682102.341247011596
Trimmed Mean ( 2 / 20 )26.160.255958093160864102.204230688494
Trimmed Mean ( 3 / 20 )26.17092592592590.256740204080372101.935441002194
Trimmed Mean ( 4 / 20 )26.18384615384620.257806788915111101.563834932477
Trimmed Mean ( 5 / 20 )26.19680.258910975165644101.180724313599
Trimmed Mean ( 6 / 20 )26.20833333333330.261075641421668100.385976993556
Trimmed Mean ( 7 / 20 )26.22043478260870.26352459693642799.4990034608958
Trimmed Mean ( 8 / 20 )26.23477272727270.26629663804302898.5171007792961
Trimmed Mean ( 9 / 20 )26.25047619047620.26914411433932997.5331608306334
Trimmed Mean ( 10 / 20 )26.267250.27226589273383896.4764618008116
Trimmed Mean ( 11 / 20 )26.28631578947370.27554844342366695.3963501403546
Trimmed Mean ( 12 / 20 )26.30722222222220.2788398900863294.3452610531382
Trimmed Mean ( 13 / 20 )26.33117647058820.2819763345482393.3808027286222
Trimmed Mean ( 14 / 20 )26.35843750.28505344340982592.4684058704884
Trimmed Mean ( 15 / 20 )26.38066666666670.29003802102456690.9558911396386
Trimmed Mean ( 16 / 20 )26.40357142857140.29606779856213289.1808280292612
Trimmed Mean ( 17 / 20 )26.42923076923080.30267622868055687.3184884205894
Trimmed Mean ( 18 / 20 )26.458750.30999667629120585.3517215621536
Trimmed Mean ( 19 / 20 )26.49227272727270.31767685657390383.3937763455226
Trimmed Mean ( 20 / 20 )26.5330.32512920508622481.6075565803554
Median27.35
Midrange25.79
Midmean - Weighted Average at Xnp26.308064516129
Midmean - Weighted Average at X(n+1)p26.3806666666667
Midmean - Empirical Distribution Function26.308064516129
Midmean - Empirical Distribution Function - Averaging26.3806666666667
Midmean - Empirical Distribution Function - Interpolation26.3806666666667
Midmean - Closest Observation26.308064516129
Midmean - True Basic - Statistics Graphics Toolkit26.3806666666667
Midmean - MS Excel (old versions)26.4057575757576
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 26.1358333333333 & 0.254893385452172 & 102.536334110708 \tabularnewline
Geometric Mean & 26.0614560106331 &  &  \tabularnewline
Harmonic Mean & 25.9863032742793 &  &  \tabularnewline
Quadratic Mean & 26.2090643035318 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 26.1363333333333 & 0.254794585112472 & 102.57805644416 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 26.1403333333333 & 0.253794810873598 & 102.997903083024 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 26.1373333333333 & 0.252511102476352 & 103.509640079216 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 26.1406666666667 & 0.251677857348382 & 103.865580159012 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 26.1506666666667 & 0.247246402253896 & 105.767632727018 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 26.1526666666667 & 0.245671323614915 & 106.453884327421 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 26.1468333333333 & 0.243816580553741 & 107.239767180518 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 26.1468333333333 & 0.243016296641079 & 107.592921523081 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 26.1498333333333 & 0.241181003326026 & 108.424100458626 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 26.1465 & 0.239763869832042 & 109.051042670925 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 26.1483333333333 & 0.238927472467717 & 109.440463514996 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 26.1443333333333 & 0.238412281973595 & 109.66017822953 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 26.1421666666667 & 0.236875982673652 & 110.362251046292 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 26.2028333333333 & 0.227249842804377 & 115.304076825653 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 26.2203333333333 & 0.222464110819333 & 117.863206054964 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 26.2256666666667 & 0.220175631828829 & 119.11248510487 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 26.2285 & 0.217402985052194 & 120.644617615085 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 26.2375 & 0.216060075475987 & 121.436132715394 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 26.2343333333333 & 0.215662475181721 & 121.645331721375 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 26.2476666666667 & 0.212770846558003 & 123.361198638232 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 26.1477586206897 & 0.255495798460682 & 102.341247011596 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 26.16 & 0.255958093160864 & 102.204230688494 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 26.1709259259259 & 0.256740204080372 & 101.935441002194 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 26.1838461538462 & 0.257806788915111 & 101.563834932477 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 26.1968 & 0.258910975165644 & 101.180724313599 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 26.2083333333333 & 0.261075641421668 & 100.385976993556 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 26.2204347826087 & 0.263524596936427 & 99.4990034608958 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 26.2347727272727 & 0.266296638043028 & 98.5171007792961 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 26.2504761904762 & 0.269144114339329 & 97.5331608306334 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 26.26725 & 0.272265892733838 & 96.4764618008116 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 26.2863157894737 & 0.275548443423666 & 95.3963501403546 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 26.3072222222222 & 0.27883989008632 & 94.3452610531382 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 26.3311764705882 & 0.28197633454823 & 93.3808027286222 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 26.3584375 & 0.285053443409825 & 92.4684058704884 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 26.3806666666667 & 0.290038021024566 & 90.9558911396386 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 26.4035714285714 & 0.296067798562132 & 89.1808280292612 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 26.4292307692308 & 0.302676228680556 & 87.3184884205894 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 26.45875 & 0.309996676291205 & 85.3517215621536 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 26.4922727272727 & 0.317676856573903 & 83.3937763455226 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 26.533 & 0.325129205086224 & 81.6075565803554 \tabularnewline
Median & 27.35 &  &  \tabularnewline
Midrange & 25.79 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 26.308064516129 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 26.3806666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 26.308064516129 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 26.3806666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 26.3806666666667 &  &  \tabularnewline
Midmean - Closest Observation & 26.308064516129 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 26.3806666666667 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 26.4057575757576 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=163494&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]26.1358333333333[/C][C]0.254893385452172[/C][C]102.536334110708[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]26.0614560106331[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]25.9863032742793[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]26.2090643035318[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]26.1363333333333[/C][C]0.254794585112472[/C][C]102.57805644416[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]26.1403333333333[/C][C]0.253794810873598[/C][C]102.997903083024[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]26.1373333333333[/C][C]0.252511102476352[/C][C]103.509640079216[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]26.1406666666667[/C][C]0.251677857348382[/C][C]103.865580159012[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]26.1506666666667[/C][C]0.247246402253896[/C][C]105.767632727018[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]26.1526666666667[/C][C]0.245671323614915[/C][C]106.453884327421[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]26.1468333333333[/C][C]0.243816580553741[/C][C]107.239767180518[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]26.1468333333333[/C][C]0.243016296641079[/C][C]107.592921523081[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]26.1498333333333[/C][C]0.241181003326026[/C][C]108.424100458626[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]26.1465[/C][C]0.239763869832042[/C][C]109.051042670925[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]26.1483333333333[/C][C]0.238927472467717[/C][C]109.440463514996[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]26.1443333333333[/C][C]0.238412281973595[/C][C]109.66017822953[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]26.1421666666667[/C][C]0.236875982673652[/C][C]110.362251046292[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]26.2028333333333[/C][C]0.227249842804377[/C][C]115.304076825653[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]26.2203333333333[/C][C]0.222464110819333[/C][C]117.863206054964[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]26.2256666666667[/C][C]0.220175631828829[/C][C]119.11248510487[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]26.2285[/C][C]0.217402985052194[/C][C]120.644617615085[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]26.2375[/C][C]0.216060075475987[/C][C]121.436132715394[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]26.2343333333333[/C][C]0.215662475181721[/C][C]121.645331721375[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]26.2476666666667[/C][C]0.212770846558003[/C][C]123.361198638232[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]26.1477586206897[/C][C]0.255495798460682[/C][C]102.341247011596[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]26.16[/C][C]0.255958093160864[/C][C]102.204230688494[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]26.1709259259259[/C][C]0.256740204080372[/C][C]101.935441002194[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]26.1838461538462[/C][C]0.257806788915111[/C][C]101.563834932477[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]26.1968[/C][C]0.258910975165644[/C][C]101.180724313599[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]26.2083333333333[/C][C]0.261075641421668[/C][C]100.385976993556[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]26.2204347826087[/C][C]0.263524596936427[/C][C]99.4990034608958[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]26.2347727272727[/C][C]0.266296638043028[/C][C]98.5171007792961[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]26.2504761904762[/C][C]0.269144114339329[/C][C]97.5331608306334[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]26.26725[/C][C]0.272265892733838[/C][C]96.4764618008116[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]26.2863157894737[/C][C]0.275548443423666[/C][C]95.3963501403546[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]26.3072222222222[/C][C]0.27883989008632[/C][C]94.3452610531382[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]26.3311764705882[/C][C]0.28197633454823[/C][C]93.3808027286222[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]26.3584375[/C][C]0.285053443409825[/C][C]92.4684058704884[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]26.3806666666667[/C][C]0.290038021024566[/C][C]90.9558911396386[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]26.4035714285714[/C][C]0.296067798562132[/C][C]89.1808280292612[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]26.4292307692308[/C][C]0.302676228680556[/C][C]87.3184884205894[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]26.45875[/C][C]0.309996676291205[/C][C]85.3517215621536[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]26.4922727272727[/C][C]0.317676856573903[/C][C]83.3937763455226[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]26.533[/C][C]0.325129205086224[/C][C]81.6075565803554[/C][/ROW]
[ROW][C]Median[/C][C]27.35[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]25.79[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]26.308064516129[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]26.3806666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]26.308064516129[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]26.3806666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]26.3806666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]26.308064516129[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]26.3806666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]26.4057575757576[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]60[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=163494&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=163494&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 Mean26.13583333333330.254893385452172102.536334110708
Geometric Mean26.0614560106331
Harmonic Mean25.9863032742793
Quadratic Mean26.2090643035318
Winsorized Mean ( 1 / 20 )26.13633333333330.254794585112472102.57805644416
Winsorized Mean ( 2 / 20 )26.14033333333330.253794810873598102.997903083024
Winsorized Mean ( 3 / 20 )26.13733333333330.252511102476352103.509640079216
Winsorized Mean ( 4 / 20 )26.14066666666670.251677857348382103.865580159012
Winsorized Mean ( 5 / 20 )26.15066666666670.247246402253896105.767632727018
Winsorized Mean ( 6 / 20 )26.15266666666670.245671323614915106.453884327421
Winsorized Mean ( 7 / 20 )26.14683333333330.243816580553741107.239767180518
Winsorized Mean ( 8 / 20 )26.14683333333330.243016296641079107.592921523081
Winsorized Mean ( 9 / 20 )26.14983333333330.241181003326026108.424100458626
Winsorized Mean ( 10 / 20 )26.14650.239763869832042109.051042670925
Winsorized Mean ( 11 / 20 )26.14833333333330.238927472467717109.440463514996
Winsorized Mean ( 12 / 20 )26.14433333333330.238412281973595109.66017822953
Winsorized Mean ( 13 / 20 )26.14216666666670.236875982673652110.362251046292
Winsorized Mean ( 14 / 20 )26.20283333333330.227249842804377115.304076825653
Winsorized Mean ( 15 / 20 )26.22033333333330.222464110819333117.863206054964
Winsorized Mean ( 16 / 20 )26.22566666666670.220175631828829119.11248510487
Winsorized Mean ( 17 / 20 )26.22850.217402985052194120.644617615085
Winsorized Mean ( 18 / 20 )26.23750.216060075475987121.436132715394
Winsorized Mean ( 19 / 20 )26.23433333333330.215662475181721121.645331721375
Winsorized Mean ( 20 / 20 )26.24766666666670.212770846558003123.361198638232
Trimmed Mean ( 1 / 20 )26.14775862068970.255495798460682102.341247011596
Trimmed Mean ( 2 / 20 )26.160.255958093160864102.204230688494
Trimmed Mean ( 3 / 20 )26.17092592592590.256740204080372101.935441002194
Trimmed Mean ( 4 / 20 )26.18384615384620.257806788915111101.563834932477
Trimmed Mean ( 5 / 20 )26.19680.258910975165644101.180724313599
Trimmed Mean ( 6 / 20 )26.20833333333330.261075641421668100.385976993556
Trimmed Mean ( 7 / 20 )26.22043478260870.26352459693642799.4990034608958
Trimmed Mean ( 8 / 20 )26.23477272727270.26629663804302898.5171007792961
Trimmed Mean ( 9 / 20 )26.25047619047620.26914411433932997.5331608306334
Trimmed Mean ( 10 / 20 )26.267250.27226589273383896.4764618008116
Trimmed Mean ( 11 / 20 )26.28631578947370.27554844342366695.3963501403546
Trimmed Mean ( 12 / 20 )26.30722222222220.2788398900863294.3452610531382
Trimmed Mean ( 13 / 20 )26.33117647058820.2819763345482393.3808027286222
Trimmed Mean ( 14 / 20 )26.35843750.28505344340982592.4684058704884
Trimmed Mean ( 15 / 20 )26.38066666666670.29003802102456690.9558911396386
Trimmed Mean ( 16 / 20 )26.40357142857140.29606779856213289.1808280292612
Trimmed Mean ( 17 / 20 )26.42923076923080.30267622868055687.3184884205894
Trimmed Mean ( 18 / 20 )26.458750.30999667629120585.3517215621536
Trimmed Mean ( 19 / 20 )26.49227272727270.31767685657390383.3937763455226
Trimmed Mean ( 20 / 20 )26.5330.32512920508622481.6075565803554
Median27.35
Midrange25.79
Midmean - Weighted Average at Xnp26.308064516129
Midmean - Weighted Average at X(n+1)p26.3806666666667
Midmean - Empirical Distribution Function26.308064516129
Midmean - Empirical Distribution Function - Averaging26.3806666666667
Midmean - Empirical Distribution Function - Interpolation26.3806666666667
Midmean - Closest Observation26.308064516129
Midmean - True Basic - Statistics Graphics Toolkit26.3806666666667
Midmean - MS Excel (old versions)26.4057575757576
Number of observations60



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')