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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationWed, 21 Oct 2009 03:08:14 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Oct/21/t125611612070ehxgvq68kbsuy.htm/, Retrieved Thu, 02 May 2024 02:35:11 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=49300, Retrieved Thu, 02 May 2024 02:35:11 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact148
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Bivariate Data Series] [Bivariate dataset] [2008-01-05 23:51:08] [74be16979710d4c4e7c6647856088456]
F RMPD  [Univariate Explorative Data Analysis] [Colombia Coffee] [2008-01-07 14:21:11] [74be16979710d4c4e7c6647856088456]
F RMPD    [Univariate Data Series] [] [2009-10-14 08:30:28] [74be16979710d4c4e7c6647856088456]
- RMPD      [Central Tendency] [WS3 Part2 Vraag1] [2009-10-18 08:54:29] [42ad1186d39724f834063794eac7cea3]
- RMP         [Univariate Explorative Data Analysis] [WS3 Part2 Vraag1 TVD] [2009-10-20 17:08:04] [42ad1186d39724f834063794eac7cea3]
- RMPD          [Central Tendency] [WS3 Part2 Vraag4 C] [2009-10-20 17:41:57] [42ad1186d39724f834063794eac7cea3]
-                   [Central Tendency] [TG 15] [2009-10-21 09:08:14] [81cf732ffd29c90ba583bd04c2d9af10] [Current]
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Dataseries X:
-53.89500000000000
-47.89500000000000
-59.39500000000000
-51.59500000000000
-55.79500000000000
-54.29500000000000
-68.69500000000000
-81.09500000000000
-58.29500000000000
-42.29500000000000
-49.99500000000000
-60.89500000000000
-57.89500000000000
-57.09500000000000
-57.89500000000000
-59.19500000000000
-65.39500000000000
-58.49500000000000
-68.19500000000000
-85.59500000000000
-51.59500000000000
-45.49500000000000
-54.29500000000000
-61.69500000000000
-47.09500000000000
-32.79500000000000
-6.99500000000000
-19.59500000000000
-25.59500000000000
-9.59500000000003
-30.89500000000000
-39.49500000000000
-0.69499999999999
-5.79500000000002
-4.19499999999999
-10.89500000000000
-13.89500000000000
-10.89500000000000
12.20500000000000
6.20499999999998
-3.69499999999999
13.70500000000000
-5.29500000000002
-3.39500000000001
13.00500000000000
30.00500000000000
41.80499999999990
30.90500000000000
64.60500000000000
62.90500000000000
122.90500000000000
132.60500000000000
160.90500000000000
180.40500000000000
113.10500000000000
118.70500000000000
139.50500000000000
162.50500000000000
154.40500000000000
117.40500000000000




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=49300&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]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=49300&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=49300&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'Sir Ronald Aylmer Fisher' @ 193.190.124.24







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean-2.79914980083618e-159.2984751878579-3.01033206443498e-16
Geometric MeanNaN
Harmonic Mean-19.114994459725
Quadratic Mean71.4229431508765
Winsorized Mean ( 1 / 20 )-0.2233333333333369.19320281071949-0.0242933108223093
Winsorized Mean ( 2 / 20 )0.1366666666666659.119966142414930.0149854357497073
Winsorized Mean ( 3 / 20 )-0.1633333333333359.02101798521886-0.0181058649479428
Winsorized Mean ( 4 / 20 )-0.9700000000000038.71735609668345-0.111272269853590
Winsorized Mean ( 5 / 20 )-1.236666666666678.5244491485522-0.145072912644063
Winsorized Mean ( 6 / 20 )-2.126666666666678.26126605927152-0.257426240894389
Winsorized Mean ( 7 / 20 )-2.441666666666678.11546318761469-0.300865965407001
Winsorized Mean ( 8 / 20 )-2.588333333333348.068517974049-0.320794146044945
Winsorized Mean ( 9 / 20 )-3.128333333333337.89425295738481-0.396279844365372
Winsorized Mean ( 10 / 20 )-11.17833333333335.99616222208814-1.86424798384466
Winsorized Mean ( 11 / 20 )-11.41666666666675.9198565086379-1.92853773567115
Winsorized Mean ( 12 / 20 )-15.63666666666675.06164724514411-3.0892446488972
Winsorized Mean ( 13 / 20 )-17.8254.59683463924525-3.87766830849645
Winsorized Mean ( 14 / 20 )-17.73166666666674.51552248521707-3.92682501852591
Winsorized Mean ( 15 / 20 )-21.43166666666673.77031294439622-5.68432036882252
Winsorized Mean ( 16 / 20 )-21.61833333333333.74092904158338-5.77886752008084
Winsorized Mean ( 17 / 20 )-21.73166666666673.68871309963923-5.89139520468319
Winsorized Mean ( 18 / 20 )-22.84166666666673.31250111750683-6.89559515797494
Winsorized Mean ( 19 / 20 )-25.02666666666672.99930923466094-8.34414350392776
Winsorized Mean ( 20 / 20 )-25.39333333333332.79760136532114-9.07682332733578
Trimmed Mean ( 1 / 20 )-1.634655172413808.97072537370983-0.182221069569738
Trimmed Mean ( 2 / 20 )-3.146785714285728.69137017543482-0.362058645618358
Trimmed Mean ( 3 / 20 )-4.970925925925938.38607416723707-0.592759594870561
Trimmed Mean ( 4 / 20 )-6.828.04629181851228-0.847595408397827
Trimmed Mean ( 5 / 20 )-8.5757.73810871793698-1.10815191574178
Trimmed Mean ( 6 / 20 )-10.40958333333337.4074316894518-1.40528914335540
Trimmed Mean ( 7 / 20 )-12.21021739130447.06478370277999-1.72832147522077
Trimmed Mean ( 8 / 20 )-14.11318181818186.65487094711073-2.12072960247399
Trimmed Mean ( 9 / 20 )-16.17119047619056.10992491416405-2.64670854443765
Trimmed Mean ( 10 / 20 )-18.3455.40605311261462-3.39341838081341
Trimmed Mean ( 11 / 20 )-19.47657894736845.1344842233543-3.79328830319097
Trimmed Mean ( 12 / 20 )-20.69777777777784.77675337393657-4.33302206697779
Trimmed Mean ( 13 / 20 )-21.44205882352944.57077680806323-4.69111919569204
Trimmed Mean ( 14 / 20 )-21.963754.42463420553864-4.96396967064675
Trimmed Mean ( 15 / 20 )-22.56833333333334.22968419063296-5.33570174891853
Trimmed Mean ( 16 / 20 )-22.73071428571434.18510591132889-5.43133549480391
Trimmed Mean ( 17 / 20 )-22.89115384615384.10766817912821-5.57278554350321
Trimmed Mean ( 18 / 20 )-23.06166666666673.98678372180439-5.78452915329682
Trimmed Mean ( 19 / 20 )-23.0953.92103330316157-5.89002903427988
Trimmed Mean ( 20 / 20 )-22.793.90247880064372-5.83987797608042
Median-16.745
Midrange47.405
Midmean - Weighted Average at Xnp-23.6401612903226
Midmean - Weighted Average at X(n+1)p-22.5683333333333
Midmean - Empirical Distribution Function-23.6401612903226
Midmean - Empirical Distribution Function - Averaging-22.5683333333333
Midmean - Empirical Distribution Function - Interpolation-22.5683333333333
Midmean - Closest Observation-23.6401612903226
Midmean - True Basic - Statistics Graphics Toolkit-22.5683333333333
Midmean - MS Excel (old versions)-21.96375
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & -2.79914980083618e-15 & 9.2984751878579 & -3.01033206443498e-16 \tabularnewline
Geometric Mean & NaN &  &  \tabularnewline
Harmonic Mean & -19.114994459725 &  &  \tabularnewline
Quadratic Mean & 71.4229431508765 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & -0.223333333333336 & 9.19320281071949 & -0.0242933108223093 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 0.136666666666665 & 9.11996614241493 & 0.0149854357497073 \tabularnewline
Winsorized Mean ( 3 / 20 ) & -0.163333333333335 & 9.02101798521886 & -0.0181058649479428 \tabularnewline
Winsorized Mean ( 4 / 20 ) & -0.970000000000003 & 8.71735609668345 & -0.111272269853590 \tabularnewline
Winsorized Mean ( 5 / 20 ) & -1.23666666666667 & 8.5244491485522 & -0.145072912644063 \tabularnewline
Winsorized Mean ( 6 / 20 ) & -2.12666666666667 & 8.26126605927152 & -0.257426240894389 \tabularnewline
Winsorized Mean ( 7 / 20 ) & -2.44166666666667 & 8.11546318761469 & -0.300865965407001 \tabularnewline
Winsorized Mean ( 8 / 20 ) & -2.58833333333334 & 8.068517974049 & -0.320794146044945 \tabularnewline
Winsorized Mean ( 9 / 20 ) & -3.12833333333333 & 7.89425295738481 & -0.396279844365372 \tabularnewline
Winsorized Mean ( 10 / 20 ) & -11.1783333333333 & 5.99616222208814 & -1.86424798384466 \tabularnewline
Winsorized Mean ( 11 / 20 ) & -11.4166666666667 & 5.9198565086379 & -1.92853773567115 \tabularnewline
Winsorized Mean ( 12 / 20 ) & -15.6366666666667 & 5.06164724514411 & -3.0892446488972 \tabularnewline
Winsorized Mean ( 13 / 20 ) & -17.825 & 4.59683463924525 & -3.87766830849645 \tabularnewline
Winsorized Mean ( 14 / 20 ) & -17.7316666666667 & 4.51552248521707 & -3.92682501852591 \tabularnewline
Winsorized Mean ( 15 / 20 ) & -21.4316666666667 & 3.77031294439622 & -5.68432036882252 \tabularnewline
Winsorized Mean ( 16 / 20 ) & -21.6183333333333 & 3.74092904158338 & -5.77886752008084 \tabularnewline
Winsorized Mean ( 17 / 20 ) & -21.7316666666667 & 3.68871309963923 & -5.89139520468319 \tabularnewline
Winsorized Mean ( 18 / 20 ) & -22.8416666666667 & 3.31250111750683 & -6.89559515797494 \tabularnewline
Winsorized Mean ( 19 / 20 ) & -25.0266666666667 & 2.99930923466094 & -8.34414350392776 \tabularnewline
Winsorized Mean ( 20 / 20 ) & -25.3933333333333 & 2.79760136532114 & -9.07682332733578 \tabularnewline
Trimmed Mean ( 1 / 20 ) & -1.63465517241380 & 8.97072537370983 & -0.182221069569738 \tabularnewline
Trimmed Mean ( 2 / 20 ) & -3.14678571428572 & 8.69137017543482 & -0.362058645618358 \tabularnewline
Trimmed Mean ( 3 / 20 ) & -4.97092592592593 & 8.38607416723707 & -0.592759594870561 \tabularnewline
Trimmed Mean ( 4 / 20 ) & -6.82 & 8.04629181851228 & -0.847595408397827 \tabularnewline
Trimmed Mean ( 5 / 20 ) & -8.575 & 7.73810871793698 & -1.10815191574178 \tabularnewline
Trimmed Mean ( 6 / 20 ) & -10.4095833333333 & 7.4074316894518 & -1.40528914335540 \tabularnewline
Trimmed Mean ( 7 / 20 ) & -12.2102173913044 & 7.06478370277999 & -1.72832147522077 \tabularnewline
Trimmed Mean ( 8 / 20 ) & -14.1131818181818 & 6.65487094711073 & -2.12072960247399 \tabularnewline
Trimmed Mean ( 9 / 20 ) & -16.1711904761905 & 6.10992491416405 & -2.64670854443765 \tabularnewline
Trimmed Mean ( 10 / 20 ) & -18.345 & 5.40605311261462 & -3.39341838081341 \tabularnewline
Trimmed Mean ( 11 / 20 ) & -19.4765789473684 & 5.1344842233543 & -3.79328830319097 \tabularnewline
Trimmed Mean ( 12 / 20 ) & -20.6977777777778 & 4.77675337393657 & -4.33302206697779 \tabularnewline
Trimmed Mean ( 13 / 20 ) & -21.4420588235294 & 4.57077680806323 & -4.69111919569204 \tabularnewline
Trimmed Mean ( 14 / 20 ) & -21.96375 & 4.42463420553864 & -4.96396967064675 \tabularnewline
Trimmed Mean ( 15 / 20 ) & -22.5683333333333 & 4.22968419063296 & -5.33570174891853 \tabularnewline
Trimmed Mean ( 16 / 20 ) & -22.7307142857143 & 4.18510591132889 & -5.43133549480391 \tabularnewline
Trimmed Mean ( 17 / 20 ) & -22.8911538461538 & 4.10766817912821 & -5.57278554350321 \tabularnewline
Trimmed Mean ( 18 / 20 ) & -23.0616666666667 & 3.98678372180439 & -5.78452915329682 \tabularnewline
Trimmed Mean ( 19 / 20 ) & -23.095 & 3.92103330316157 & -5.89002903427988 \tabularnewline
Trimmed Mean ( 20 / 20 ) & -22.79 & 3.90247880064372 & -5.83987797608042 \tabularnewline
Median & -16.745 &  &  \tabularnewline
Midrange & 47.405 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & -23.6401612903226 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & -22.5683333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function & -23.6401612903226 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & -22.5683333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & -22.5683333333333 &  &  \tabularnewline
Midmean - Closest Observation & -23.6401612903226 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & -22.5683333333333 &  &  \tabularnewline
Midmean - MS Excel (old versions) & -21.96375 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=49300&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]-2.79914980083618e-15[/C][C]9.2984751878579[/C][C]-3.01033206443498e-16[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]NaN[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]-19.114994459725[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]71.4229431508765[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]-0.223333333333336[/C][C]9.19320281071949[/C][C]-0.0242933108223093[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]0.136666666666665[/C][C]9.11996614241493[/C][C]0.0149854357497073[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]-0.163333333333335[/C][C]9.02101798521886[/C][C]-0.0181058649479428[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]-0.970000000000003[/C][C]8.71735609668345[/C][C]-0.111272269853590[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]-1.23666666666667[/C][C]8.5244491485522[/C][C]-0.145072912644063[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]-2.12666666666667[/C][C]8.26126605927152[/C][C]-0.257426240894389[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]-2.44166666666667[/C][C]8.11546318761469[/C][C]-0.300865965407001[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]-2.58833333333334[/C][C]8.068517974049[/C][C]-0.320794146044945[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]-3.12833333333333[/C][C]7.89425295738481[/C][C]-0.396279844365372[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]-11.1783333333333[/C][C]5.99616222208814[/C][C]-1.86424798384466[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]-11.4166666666667[/C][C]5.9198565086379[/C][C]-1.92853773567115[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]-15.6366666666667[/C][C]5.06164724514411[/C][C]-3.0892446488972[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]-17.825[/C][C]4.59683463924525[/C][C]-3.87766830849645[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]-17.7316666666667[/C][C]4.51552248521707[/C][C]-3.92682501852591[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]-21.4316666666667[/C][C]3.77031294439622[/C][C]-5.68432036882252[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]-21.6183333333333[/C][C]3.74092904158338[/C][C]-5.77886752008084[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]-21.7316666666667[/C][C]3.68871309963923[/C][C]-5.89139520468319[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]-22.8416666666667[/C][C]3.31250111750683[/C][C]-6.89559515797494[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]-25.0266666666667[/C][C]2.99930923466094[/C][C]-8.34414350392776[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]-25.3933333333333[/C][C]2.79760136532114[/C][C]-9.07682332733578[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]-1.63465517241380[/C][C]8.97072537370983[/C][C]-0.182221069569738[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]-3.14678571428572[/C][C]8.69137017543482[/C][C]-0.362058645618358[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]-4.97092592592593[/C][C]8.38607416723707[/C][C]-0.592759594870561[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]-6.82[/C][C]8.04629181851228[/C][C]-0.847595408397827[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]-8.575[/C][C]7.73810871793698[/C][C]-1.10815191574178[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]-10.4095833333333[/C][C]7.4074316894518[/C][C]-1.40528914335540[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]-12.2102173913044[/C][C]7.06478370277999[/C][C]-1.72832147522077[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]-14.1131818181818[/C][C]6.65487094711073[/C][C]-2.12072960247399[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]-16.1711904761905[/C][C]6.10992491416405[/C][C]-2.64670854443765[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]-18.345[/C][C]5.40605311261462[/C][C]-3.39341838081341[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]-19.4765789473684[/C][C]5.1344842233543[/C][C]-3.79328830319097[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]-20.6977777777778[/C][C]4.77675337393657[/C][C]-4.33302206697779[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]-21.4420588235294[/C][C]4.57077680806323[/C][C]-4.69111919569204[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]-21.96375[/C][C]4.42463420553864[/C][C]-4.96396967064675[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]-22.5683333333333[/C][C]4.22968419063296[/C][C]-5.33570174891853[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]-22.7307142857143[/C][C]4.18510591132889[/C][C]-5.43133549480391[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]-22.8911538461538[/C][C]4.10766817912821[/C][C]-5.57278554350321[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]-23.0616666666667[/C][C]3.98678372180439[/C][C]-5.78452915329682[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]-23.095[/C][C]3.92103330316157[/C][C]-5.89002903427988[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]-22.79[/C][C]3.90247880064372[/C][C]-5.83987797608042[/C][/ROW]
[ROW][C]Median[/C][C]-16.745[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]47.405[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]-23.6401612903226[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]-22.5683333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]-23.6401612903226[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]-22.5683333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]-22.5683333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]-23.6401612903226[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]-22.5683333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]-21.96375[/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=49300&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=49300&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 Mean-2.79914980083618e-159.2984751878579-3.01033206443498e-16
Geometric MeanNaN
Harmonic Mean-19.114994459725
Quadratic Mean71.4229431508765
Winsorized Mean ( 1 / 20 )-0.2233333333333369.19320281071949-0.0242933108223093
Winsorized Mean ( 2 / 20 )0.1366666666666659.119966142414930.0149854357497073
Winsorized Mean ( 3 / 20 )-0.1633333333333359.02101798521886-0.0181058649479428
Winsorized Mean ( 4 / 20 )-0.9700000000000038.71735609668345-0.111272269853590
Winsorized Mean ( 5 / 20 )-1.236666666666678.5244491485522-0.145072912644063
Winsorized Mean ( 6 / 20 )-2.126666666666678.26126605927152-0.257426240894389
Winsorized Mean ( 7 / 20 )-2.441666666666678.11546318761469-0.300865965407001
Winsorized Mean ( 8 / 20 )-2.588333333333348.068517974049-0.320794146044945
Winsorized Mean ( 9 / 20 )-3.128333333333337.89425295738481-0.396279844365372
Winsorized Mean ( 10 / 20 )-11.17833333333335.99616222208814-1.86424798384466
Winsorized Mean ( 11 / 20 )-11.41666666666675.9198565086379-1.92853773567115
Winsorized Mean ( 12 / 20 )-15.63666666666675.06164724514411-3.0892446488972
Winsorized Mean ( 13 / 20 )-17.8254.59683463924525-3.87766830849645
Winsorized Mean ( 14 / 20 )-17.73166666666674.51552248521707-3.92682501852591
Winsorized Mean ( 15 / 20 )-21.43166666666673.77031294439622-5.68432036882252
Winsorized Mean ( 16 / 20 )-21.61833333333333.74092904158338-5.77886752008084
Winsorized Mean ( 17 / 20 )-21.73166666666673.68871309963923-5.89139520468319
Winsorized Mean ( 18 / 20 )-22.84166666666673.31250111750683-6.89559515797494
Winsorized Mean ( 19 / 20 )-25.02666666666672.99930923466094-8.34414350392776
Winsorized Mean ( 20 / 20 )-25.39333333333332.79760136532114-9.07682332733578
Trimmed Mean ( 1 / 20 )-1.634655172413808.97072537370983-0.182221069569738
Trimmed Mean ( 2 / 20 )-3.146785714285728.69137017543482-0.362058645618358
Trimmed Mean ( 3 / 20 )-4.970925925925938.38607416723707-0.592759594870561
Trimmed Mean ( 4 / 20 )-6.828.04629181851228-0.847595408397827
Trimmed Mean ( 5 / 20 )-8.5757.73810871793698-1.10815191574178
Trimmed Mean ( 6 / 20 )-10.40958333333337.4074316894518-1.40528914335540
Trimmed Mean ( 7 / 20 )-12.21021739130447.06478370277999-1.72832147522077
Trimmed Mean ( 8 / 20 )-14.11318181818186.65487094711073-2.12072960247399
Trimmed Mean ( 9 / 20 )-16.17119047619056.10992491416405-2.64670854443765
Trimmed Mean ( 10 / 20 )-18.3455.40605311261462-3.39341838081341
Trimmed Mean ( 11 / 20 )-19.47657894736845.1344842233543-3.79328830319097
Trimmed Mean ( 12 / 20 )-20.69777777777784.77675337393657-4.33302206697779
Trimmed Mean ( 13 / 20 )-21.44205882352944.57077680806323-4.69111919569204
Trimmed Mean ( 14 / 20 )-21.963754.42463420553864-4.96396967064675
Trimmed Mean ( 15 / 20 )-22.56833333333334.22968419063296-5.33570174891853
Trimmed Mean ( 16 / 20 )-22.73071428571434.18510591132889-5.43133549480391
Trimmed Mean ( 17 / 20 )-22.89115384615384.10766817912821-5.57278554350321
Trimmed Mean ( 18 / 20 )-23.06166666666673.98678372180439-5.78452915329682
Trimmed Mean ( 19 / 20 )-23.0953.92103330316157-5.89002903427988
Trimmed Mean ( 20 / 20 )-22.793.90247880064372-5.83987797608042
Median-16.745
Midrange47.405
Midmean - Weighted Average at Xnp-23.6401612903226
Midmean - Weighted Average at X(n+1)p-22.5683333333333
Midmean - Empirical Distribution Function-23.6401612903226
Midmean - Empirical Distribution Function - Averaging-22.5683333333333
Midmean - Empirical Distribution Function - Interpolation-22.5683333333333
Midmean - Closest Observation-23.6401612903226
Midmean - True Basic - Statistics Graphics Toolkit-22.5683333333333
Midmean - MS Excel (old versions)-21.96375
Number of observations60



Parameters (Session):
Parameters (R input):
par1 = ; par2 = ; par3 = ; par4 = ; par5 = ; par6 = ; par7 = ; par8 = ; par9 = ; par10 = ; par11 = ; par12 = ; par13 = ; par14 = ; par15 = ; par16 = ; par17 = ; par18 = ; par19 = ; par20 = ;
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')