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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, 08 Nov 2008 11:11:14 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/Nov/08/t1226167953vn5sfp2ddm3dxtp.htm/, Retrieved Sun, 19 May 2024 11:38:59 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=22653, Retrieved Sun, 19 May 2024 11:38:59 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact141
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Mean versus Median] [Mediaan vs Rek.ge...] [2008-11-08 17:46:16] [74be16979710d4c4e7c6647856088456]
- RM D    [Central Tendency] [Robuustheid eigen...] [2008-11-08 18:11:14] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataseries X:
18,33
18,22
18,21
18,06
18,26
18,21
18,05
18,25
18,27
18,28
18,13
18,01
18,02
17,97
18,06
18,08
18,23
18,06
18,23
18,17
18,27
18,33
18,18
18,29
18,33
18,31
18,44
18,63
18,37
18,59
18,72
18,75
18,87
18,83
18,89
18,78
19,27
19,19
19,43
19,36
19,39
19,07
19,31
19,19
19,06
19,05
19,49
19,25
19,76
20,35
19,61
19,33
18,95
18,97
19,28
19,41
18,99
19,37
19,63
19,53
19,86
20,13
19,47
19,49
18,95
19,33
19,65
19,44
19,73
18,89
19,56
19,56




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\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 & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=22653&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=22653&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=22653&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'Gwilym Jenkins' @ 72.249.127.135







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean18.86083333333330.0723995580745468260.510337838155
Geometric Mean18.8510050792795
Harmonic Mean18.8412177528031
Quadratic Mean18.8706967132760
Winsorized Mean ( 1 / 24 )18.85833333333330.071479173893306263.829760560501
Winsorized Mean ( 2 / 24 )18.85111111111110.0697265942677751270.357548781403
Winsorized Mean ( 3 / 24 )18.84819444444440.0687051394081909274.334563713838
Winsorized Mean ( 4 / 24 )18.84708333333330.0683071166644513275.916833467249
Winsorized Mean ( 5 / 24 )18.84152777777780.067331386727028279.832759930585
Winsorized Mean ( 6 / 24 )18.83986111111110.0670521405785389280.97329851899
Winsorized Mean ( 7 / 24 )18.83986111111110.0664160468381241283.664295121773
Winsorized Mean ( 8 / 24 )18.83986111111110.0646488931383993291.418154225457
Winsorized Mean ( 9 / 24 )18.84486111111110.0638902475700939294.956770834804
Winsorized Mean ( 10 / 24 )18.84208333333330.0630354799551558298.912348200376
Winsorized Mean ( 11 / 24 )18.84055555555560.0614403564904092306.647887996818
Winsorized Mean ( 12 / 24 )18.84055555555560.0614403564904092306.647887996818
Winsorized Mean ( 13 / 24 )18.838750.0606465998579879310.631594254475
Winsorized Mean ( 14 / 24 )18.83486111111110.0595224188953736316.433059352282
Winsorized Mean ( 15 / 24 )18.83277777777780.0592253138625822317.985276050620
Winsorized Mean ( 16 / 24 )18.83277777777780.0579647045425093324.900781025572
Winsorized Mean ( 17 / 24 )18.83041666666670.0569732240530447330.513446968258
Winsorized Mean ( 18 / 24 )18.82791666666670.0559342118244789336.608241227185
Winsorized Mean ( 19 / 24 )18.82527777777780.0555752996996567338.734615548894
Winsorized Mean ( 20 / 24 )18.81972222222220.0540658947855316348.088611071291
Winsorized Mean ( 21 / 24 )18.82263888888890.0536569528197241350.795896892038
Winsorized Mean ( 22 / 24 )18.82263888888890.0519950164096331362.008519058793
Winsorized Mean ( 23 / 24 )18.81944444444440.0498534192915417377.495560222033
Winsorized Mean ( 24 / 24 )18.81611111111110.0494209646911089380.731360237819
Trimmed Mean ( 1 / 24 )18.85228571428570.0701657816329026268.682045229941
Trimmed Mean ( 2 / 24 )18.84588235294120.0685905498851216274.759167035474
Trimmed Mean ( 3 / 24 )18.84303030303030.0678050715271391277.900013651462
Trimmed Mean ( 4 / 24 )18.841093750.0672840155562966280.023324919358
Trimmed Mean ( 5 / 24 )18.83935483870970.0667540340049617282.220469811748
Trimmed Mean ( 6 / 24 )18.83883333333330.066358933112027283.892950803318
Trimmed Mean ( 7 / 24 )18.83862068965520.0658966946542529285.881117232021
Trimmed Mean ( 8 / 24 )18.83839285714290.065429041957986287.920964351573
Trimmed Mean ( 9 / 24 )18.83814814814810.0651901878519956288.972140882878
Trimmed Mean ( 10 / 24 )18.83711538461540.0649726340689899289.923837236052
Trimmed Mean ( 11 / 24 )18.83640.064786468730841290.745897546243
Trimmed Mean ( 12 / 24 )18.83583333333330.0647682949682708290.818730716330
Trimmed Mean ( 13 / 24 )18.83521739130430.064621334125787291.470574634704
Trimmed Mean ( 14 / 24 )18.83477272727270.0644651836120529292.169690241156
Trimmed Mean ( 15 / 24 )18.83476190476190.064349905577856292.692922167135
Trimmed Mean ( 16 / 24 )18.8350.0641042820282622293.818125779742
Trimmed Mean ( 17 / 24 )18.83526315789470.0638819332833233294.844914513753
Trimmed Mean ( 18 / 24 )18.83583333333330.0636151312239071296.090457898084
Trimmed Mean ( 19 / 24 )18.83676470588240.0632846054054647297.651610295982
Trimmed Mean ( 20 / 24 )18.8381250.0626891291638557300.500664967944
Trimmed Mean ( 21 / 24 )18.84033333333330.0620057159644217303.848331404539
Trimmed Mean ( 22 / 24 )18.84250.0608811510261145309.496448119348
Trimmed Mean ( 23 / 24 )18.8450.0594830292539879316.813051324830
Trimmed Mean ( 24 / 24 )18.84833333333330.0578155070049684326.008268537948
Median18.89
Midrange19.16
Midmean - Weighted Average at Xnp18.8202702702703
Midmean - Weighted Average at X(n+1)p18.8358333333333
Midmean - Empirical Distribution Function18.8202702702703
Midmean - Empirical Distribution Function - Averaging18.8358333333333
Midmean - Empirical Distribution Function - Interpolation18.8358333333333
Midmean - Closest Observation18.8202702702703
Midmean - True Basic - Statistics Graphics Toolkit18.8358333333333
Midmean - MS Excel (old versions)18.8352631578947
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 18.8608333333333 & 0.0723995580745468 & 260.510337838155 \tabularnewline
Geometric Mean & 18.8510050792795 &  &  \tabularnewline
Harmonic Mean & 18.8412177528031 &  &  \tabularnewline
Quadratic Mean & 18.8706967132760 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 18.8583333333333 & 0.071479173893306 & 263.829760560501 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 18.8511111111111 & 0.0697265942677751 & 270.357548781403 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 18.8481944444444 & 0.0687051394081909 & 274.334563713838 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 18.8470833333333 & 0.0683071166644513 & 275.916833467249 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 18.8415277777778 & 0.067331386727028 & 279.832759930585 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 18.8398611111111 & 0.0670521405785389 & 280.97329851899 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 18.8398611111111 & 0.0664160468381241 & 283.664295121773 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 18.8398611111111 & 0.0646488931383993 & 291.418154225457 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 18.8448611111111 & 0.0638902475700939 & 294.956770834804 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 18.8420833333333 & 0.0630354799551558 & 298.912348200376 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 18.8405555555556 & 0.0614403564904092 & 306.647887996818 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 18.8405555555556 & 0.0614403564904092 & 306.647887996818 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 18.83875 & 0.0606465998579879 & 310.631594254475 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 18.8348611111111 & 0.0595224188953736 & 316.433059352282 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 18.8327777777778 & 0.0592253138625822 & 317.985276050620 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 18.8327777777778 & 0.0579647045425093 & 324.900781025572 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 18.8304166666667 & 0.0569732240530447 & 330.513446968258 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 18.8279166666667 & 0.0559342118244789 & 336.608241227185 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 18.8252777777778 & 0.0555752996996567 & 338.734615548894 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 18.8197222222222 & 0.0540658947855316 & 348.088611071291 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 18.8226388888889 & 0.0536569528197241 & 350.795896892038 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 18.8226388888889 & 0.0519950164096331 & 362.008519058793 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 18.8194444444444 & 0.0498534192915417 & 377.495560222033 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 18.8161111111111 & 0.0494209646911089 & 380.731360237819 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 18.8522857142857 & 0.0701657816329026 & 268.682045229941 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 18.8458823529412 & 0.0685905498851216 & 274.759167035474 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 18.8430303030303 & 0.0678050715271391 & 277.900013651462 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 18.84109375 & 0.0672840155562966 & 280.023324919358 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 18.8393548387097 & 0.0667540340049617 & 282.220469811748 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 18.8388333333333 & 0.066358933112027 & 283.892950803318 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 18.8386206896552 & 0.0658966946542529 & 285.881117232021 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 18.8383928571429 & 0.065429041957986 & 287.920964351573 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 18.8381481481481 & 0.0651901878519956 & 288.972140882878 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 18.8371153846154 & 0.0649726340689899 & 289.923837236052 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 18.8364 & 0.064786468730841 & 290.745897546243 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 18.8358333333333 & 0.0647682949682708 & 290.818730716330 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 18.8352173913043 & 0.064621334125787 & 291.470574634704 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 18.8347727272727 & 0.0644651836120529 & 292.169690241156 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 18.8347619047619 & 0.064349905577856 & 292.692922167135 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 18.835 & 0.0641042820282622 & 293.818125779742 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 18.8352631578947 & 0.0638819332833233 & 294.844914513753 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 18.8358333333333 & 0.0636151312239071 & 296.090457898084 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 18.8367647058824 & 0.0632846054054647 & 297.651610295982 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 18.838125 & 0.0626891291638557 & 300.500664967944 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 18.8403333333333 & 0.0620057159644217 & 303.848331404539 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 18.8425 & 0.0608811510261145 & 309.496448119348 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 18.845 & 0.0594830292539879 & 316.813051324830 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 18.8483333333333 & 0.0578155070049684 & 326.008268537948 \tabularnewline
Median & 18.89 &  &  \tabularnewline
Midrange & 19.16 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 18.8202702702703 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 18.8358333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 18.8202702702703 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 18.8358333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 18.8358333333333 &  &  \tabularnewline
Midmean - Closest Observation & 18.8202702702703 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 18.8358333333333 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 18.8352631578947 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=22653&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]18.8608333333333[/C][C]0.0723995580745468[/C][C]260.510337838155[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]18.8510050792795[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]18.8412177528031[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]18.8706967132760[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]18.8583333333333[/C][C]0.071479173893306[/C][C]263.829760560501[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]18.8511111111111[/C][C]0.0697265942677751[/C][C]270.357548781403[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]18.8481944444444[/C][C]0.0687051394081909[/C][C]274.334563713838[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]18.8470833333333[/C][C]0.0683071166644513[/C][C]275.916833467249[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]18.8415277777778[/C][C]0.067331386727028[/C][C]279.832759930585[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]18.8398611111111[/C][C]0.0670521405785389[/C][C]280.97329851899[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]18.8398611111111[/C][C]0.0664160468381241[/C][C]283.664295121773[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]18.8398611111111[/C][C]0.0646488931383993[/C][C]291.418154225457[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]18.8448611111111[/C][C]0.0638902475700939[/C][C]294.956770834804[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]18.8420833333333[/C][C]0.0630354799551558[/C][C]298.912348200376[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]18.8405555555556[/C][C]0.0614403564904092[/C][C]306.647887996818[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]18.8405555555556[/C][C]0.0614403564904092[/C][C]306.647887996818[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]18.83875[/C][C]0.0606465998579879[/C][C]310.631594254475[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]18.8348611111111[/C][C]0.0595224188953736[/C][C]316.433059352282[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]18.8327777777778[/C][C]0.0592253138625822[/C][C]317.985276050620[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]18.8327777777778[/C][C]0.0579647045425093[/C][C]324.900781025572[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]18.8304166666667[/C][C]0.0569732240530447[/C][C]330.513446968258[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]18.8279166666667[/C][C]0.0559342118244789[/C][C]336.608241227185[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]18.8252777777778[/C][C]0.0555752996996567[/C][C]338.734615548894[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]18.8197222222222[/C][C]0.0540658947855316[/C][C]348.088611071291[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]18.8226388888889[/C][C]0.0536569528197241[/C][C]350.795896892038[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]18.8226388888889[/C][C]0.0519950164096331[/C][C]362.008519058793[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]18.8194444444444[/C][C]0.0498534192915417[/C][C]377.495560222033[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]18.8161111111111[/C][C]0.0494209646911089[/C][C]380.731360237819[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]18.8522857142857[/C][C]0.0701657816329026[/C][C]268.682045229941[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]18.8458823529412[/C][C]0.0685905498851216[/C][C]274.759167035474[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]18.8430303030303[/C][C]0.0678050715271391[/C][C]277.900013651462[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]18.84109375[/C][C]0.0672840155562966[/C][C]280.023324919358[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]18.8393548387097[/C][C]0.0667540340049617[/C][C]282.220469811748[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]18.8388333333333[/C][C]0.066358933112027[/C][C]283.892950803318[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]18.8386206896552[/C][C]0.0658966946542529[/C][C]285.881117232021[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]18.8383928571429[/C][C]0.065429041957986[/C][C]287.920964351573[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]18.8381481481481[/C][C]0.0651901878519956[/C][C]288.972140882878[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]18.8371153846154[/C][C]0.0649726340689899[/C][C]289.923837236052[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]18.8364[/C][C]0.064786468730841[/C][C]290.745897546243[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]18.8358333333333[/C][C]0.0647682949682708[/C][C]290.818730716330[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]18.8352173913043[/C][C]0.064621334125787[/C][C]291.470574634704[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]18.8347727272727[/C][C]0.0644651836120529[/C][C]292.169690241156[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]18.8347619047619[/C][C]0.064349905577856[/C][C]292.692922167135[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]18.835[/C][C]0.0641042820282622[/C][C]293.818125779742[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]18.8352631578947[/C][C]0.0638819332833233[/C][C]294.844914513753[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]18.8358333333333[/C][C]0.0636151312239071[/C][C]296.090457898084[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]18.8367647058824[/C][C]0.0632846054054647[/C][C]297.651610295982[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]18.838125[/C][C]0.0626891291638557[/C][C]300.500664967944[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]18.8403333333333[/C][C]0.0620057159644217[/C][C]303.848331404539[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]18.8425[/C][C]0.0608811510261145[/C][C]309.496448119348[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]18.845[/C][C]0.0594830292539879[/C][C]316.813051324830[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]18.8483333333333[/C][C]0.0578155070049684[/C][C]326.008268537948[/C][/ROW]
[ROW][C]Median[/C][C]18.89[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]19.16[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]18.8202702702703[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]18.8358333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]18.8202702702703[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]18.8358333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]18.8358333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]18.8202702702703[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]18.8358333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]18.8352631578947[/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=22653&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=22653&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 Mean18.86083333333330.0723995580745468260.510337838155
Geometric Mean18.8510050792795
Harmonic Mean18.8412177528031
Quadratic Mean18.8706967132760
Winsorized Mean ( 1 / 24 )18.85833333333330.071479173893306263.829760560501
Winsorized Mean ( 2 / 24 )18.85111111111110.0697265942677751270.357548781403
Winsorized Mean ( 3 / 24 )18.84819444444440.0687051394081909274.334563713838
Winsorized Mean ( 4 / 24 )18.84708333333330.0683071166644513275.916833467249
Winsorized Mean ( 5 / 24 )18.84152777777780.067331386727028279.832759930585
Winsorized Mean ( 6 / 24 )18.83986111111110.0670521405785389280.97329851899
Winsorized Mean ( 7 / 24 )18.83986111111110.0664160468381241283.664295121773
Winsorized Mean ( 8 / 24 )18.83986111111110.0646488931383993291.418154225457
Winsorized Mean ( 9 / 24 )18.84486111111110.0638902475700939294.956770834804
Winsorized Mean ( 10 / 24 )18.84208333333330.0630354799551558298.912348200376
Winsorized Mean ( 11 / 24 )18.84055555555560.0614403564904092306.647887996818
Winsorized Mean ( 12 / 24 )18.84055555555560.0614403564904092306.647887996818
Winsorized Mean ( 13 / 24 )18.838750.0606465998579879310.631594254475
Winsorized Mean ( 14 / 24 )18.83486111111110.0595224188953736316.433059352282
Winsorized Mean ( 15 / 24 )18.83277777777780.0592253138625822317.985276050620
Winsorized Mean ( 16 / 24 )18.83277777777780.0579647045425093324.900781025572
Winsorized Mean ( 17 / 24 )18.83041666666670.0569732240530447330.513446968258
Winsorized Mean ( 18 / 24 )18.82791666666670.0559342118244789336.608241227185
Winsorized Mean ( 19 / 24 )18.82527777777780.0555752996996567338.734615548894
Winsorized Mean ( 20 / 24 )18.81972222222220.0540658947855316348.088611071291
Winsorized Mean ( 21 / 24 )18.82263888888890.0536569528197241350.795896892038
Winsorized Mean ( 22 / 24 )18.82263888888890.0519950164096331362.008519058793
Winsorized Mean ( 23 / 24 )18.81944444444440.0498534192915417377.495560222033
Winsorized Mean ( 24 / 24 )18.81611111111110.0494209646911089380.731360237819
Trimmed Mean ( 1 / 24 )18.85228571428570.0701657816329026268.682045229941
Trimmed Mean ( 2 / 24 )18.84588235294120.0685905498851216274.759167035474
Trimmed Mean ( 3 / 24 )18.84303030303030.0678050715271391277.900013651462
Trimmed Mean ( 4 / 24 )18.841093750.0672840155562966280.023324919358
Trimmed Mean ( 5 / 24 )18.83935483870970.0667540340049617282.220469811748
Trimmed Mean ( 6 / 24 )18.83883333333330.066358933112027283.892950803318
Trimmed Mean ( 7 / 24 )18.83862068965520.0658966946542529285.881117232021
Trimmed Mean ( 8 / 24 )18.83839285714290.065429041957986287.920964351573
Trimmed Mean ( 9 / 24 )18.83814814814810.0651901878519956288.972140882878
Trimmed Mean ( 10 / 24 )18.83711538461540.0649726340689899289.923837236052
Trimmed Mean ( 11 / 24 )18.83640.064786468730841290.745897546243
Trimmed Mean ( 12 / 24 )18.83583333333330.0647682949682708290.818730716330
Trimmed Mean ( 13 / 24 )18.83521739130430.064621334125787291.470574634704
Trimmed Mean ( 14 / 24 )18.83477272727270.0644651836120529292.169690241156
Trimmed Mean ( 15 / 24 )18.83476190476190.064349905577856292.692922167135
Trimmed Mean ( 16 / 24 )18.8350.0641042820282622293.818125779742
Trimmed Mean ( 17 / 24 )18.83526315789470.0638819332833233294.844914513753
Trimmed Mean ( 18 / 24 )18.83583333333330.0636151312239071296.090457898084
Trimmed Mean ( 19 / 24 )18.83676470588240.0632846054054647297.651610295982
Trimmed Mean ( 20 / 24 )18.8381250.0626891291638557300.500664967944
Trimmed Mean ( 21 / 24 )18.84033333333330.0620057159644217303.848331404539
Trimmed Mean ( 22 / 24 )18.84250.0608811510261145309.496448119348
Trimmed Mean ( 23 / 24 )18.8450.0594830292539879316.813051324830
Trimmed Mean ( 24 / 24 )18.84833333333330.0578155070049684326.008268537948
Median18.89
Midrange19.16
Midmean - Weighted Average at Xnp18.8202702702703
Midmean - Weighted Average at X(n+1)p18.8358333333333
Midmean - Empirical Distribution Function18.8202702702703
Midmean - Empirical Distribution Function - Averaging18.8358333333333
Midmean - Empirical Distribution Function - Interpolation18.8358333333333
Midmean - Closest Observation18.8202702702703
Midmean - True Basic - Statistics Graphics Toolkit18.8358333333333
Midmean - MS Excel (old versions)18.8352631578947
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')