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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, 17 Dec 2014 16:43:39 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2014/Dec/17/t1418834635wmqi8wbpakhf9g6.htm/, Retrieved Thu, 16 May 2024 15:28:23 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=270517, Retrieved Thu, 16 May 2024 15:28:23 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact67
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2014-12-17 16:43:39] [4897fbbb7461c8caec7645a3718e7cbe] [Current]
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Dataseries X:
7.5
6.5
1.0
1.0
5.5
8.5
6.5
4.5
2.0
5.0
0.5
5.0
2.5
5.0
5.5
3.5
4.0
6.5
4.5
5.5
4.0
7.5
4.0
5.5
2.5
5.5
3.5
4.5
4.5
6.0
5.0
6.5
5.0
6.0
4.5
5.0
5.0
6.5
7.0
4.5
8.5
3.5
6.0
1.5
3.5
7.5
5.0
6.5
6.5
6.5
7.0
1.5
4.0
4.5
0.0
3.5
4.5
0.0
3.0
3.5
3.0
1.0




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'George Udny Yule' @ yule.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=270517&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]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=270517&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=270517&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'George Udny Yule' @ yule.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean4.572580645161290.25911382717914617.6469958972892
Geometric Mean0
Harmonic Mean0
Quadratic Mean5.00040320954866
Winsorized Mean ( 1 / 20 )4.572580645161290.25911382717914617.6469958972892
Winsorized Mean ( 2 / 20 )4.556451612903230.24743657711001318.4146243296818
Winsorized Mean ( 3 / 20 )4.580645161290320.24123819841562118.9880590693124
Winsorized Mean ( 4 / 20 )4.580645161290320.24123819841562118.9880590693124
Winsorized Mean ( 5 / 20 )4.540322580645160.23375240890649519.4236397472223
Winsorized Mean ( 6 / 20 )4.588709677419350.22222023795099220.6493779312365
Winsorized Mean ( 7 / 20 )4.532258064516130.21290683137180621.2875182788349
Winsorized Mean ( 8 / 20 )4.596774193548390.19843341692249423.1653229825894
Winsorized Mean ( 9 / 20 )4.669354838709680.18358882952734525.4337633217177
Winsorized Mean ( 10 / 20 )4.669354838709680.18358882952734525.4337633217177
Winsorized Mean ( 11 / 20 )4.758064516129030.16731222672450228.4382355628062
Winsorized Mean ( 12 / 20 )4.758064516129030.16731222672450228.4382355628062
Winsorized Mean ( 13 / 20 )4.862903225806450.15043096684236332.3264772399043
Winsorized Mean ( 14 / 20 )4.862903225806450.15043096684236332.3264772399043
Winsorized Mean ( 15 / 20 )4.741935483870970.12995439925714936.4892263053581
Winsorized Mean ( 16 / 20 )4.741935483870970.12995439925714936.4892263053581
Winsorized Mean ( 17 / 20 )4.741935483870970.12995439925714936.4892263053581
Winsorized Mean ( 18 / 20 )4.596774193548390.10837406433698742.4158143525448
Winsorized Mean ( 19 / 20 )4.750.084297263041687256.3482114199959
Winsorized Mean ( 20 / 20 )4.750.084297263041687256.3482114199959
Trimmed Mean ( 1 / 20 )4.583333333333330.2479197823001318.4871626249848
Trimmed Mean ( 2 / 20 )4.59482758620690.23413253176500319.6249002715209
Trimmed Mean ( 3 / 20 )4.616071428571430.22505088581460220.5112342120447
Trimmed Mean ( 4 / 20 )4.629629629629630.2168581580761421.3486532888661
Trimmed Mean ( 5 / 20 )4.644230769230770.20657396101413322.4821693229431
Trimmed Mean ( 6 / 20 )4.670.19619336567451523.8030474880967
Trimmed Mean ( 7 / 20 )4.68750.18690804903568625.0791767619651
Trimmed Mean ( 8 / 20 )4.717391304347830.17764711119030826.5548438853825
Trimmed Mean ( 9 / 20 )4.738636363636360.17010181968502727.8576465108413
Trimmed Mean ( 10 / 20 )4.750.16454809124438928.8669407470988
Trimmed Mean ( 11 / 20 )4.76250.15708431102191830.3181136869581
Trimmed Mean ( 12 / 20 )4.763157894736840.15172882585403431.3925707124307
Trimmed Mean ( 13 / 20 )4.763888888888890.14431847376371733.0095570210124
Trimmed Mean ( 14 / 20 )4.750.13882945846730234.2146404116295
Trimmed Mean ( 15 / 20 )4.7343750.13087865093345536.1737759843442
Trimmed Mean ( 16 / 20 )4.733333333333330.126248553726437.4921786715371
Trimmed Mean ( 17 / 20 )4.732142857142860.11919633568155239.7004054703943
Trimmed Mean ( 18 / 20 )4.730769230769230.10824036368823343.7061468529001
Trimmed Mean ( 19 / 20 )4.750.099818676188086347.5862852663931
Trimmed Mean ( 20 / 20 )4.750.097312368020190448.8118837989275
Median4.75
Midrange4.25
Midmean - Weighted Average at Xnp4.66176470588235
Midmean - Weighted Average at X(n+1)p4.66176470588235
Midmean - Empirical Distribution Function4.66176470588235
Midmean - Empirical Distribution Function - Averaging4.66176470588235
Midmean - Empirical Distribution Function - Interpolation4.66176470588235
Midmean - Closest Observation4.66176470588235
Midmean - True Basic - Statistics Graphics Toolkit4.66176470588235
Midmean - MS Excel (old versions)4.66176470588235
Number of observations62

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 4.57258064516129 & 0.259113827179146 & 17.6469958972892 \tabularnewline
Geometric Mean & 0 &  &  \tabularnewline
Harmonic Mean & 0 &  &  \tabularnewline
Quadratic Mean & 5.00040320954866 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 4.57258064516129 & 0.259113827179146 & 17.6469958972892 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 4.55645161290323 & 0.247436577110013 & 18.4146243296818 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 4.58064516129032 & 0.241238198415621 & 18.9880590693124 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 4.58064516129032 & 0.241238198415621 & 18.9880590693124 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 4.54032258064516 & 0.233752408906495 & 19.4236397472223 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 4.58870967741935 & 0.222220237950992 & 20.6493779312365 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 4.53225806451613 & 0.212906831371806 & 21.2875182788349 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 4.59677419354839 & 0.198433416922494 & 23.1653229825894 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 4.66935483870968 & 0.183588829527345 & 25.4337633217177 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 4.66935483870968 & 0.183588829527345 & 25.4337633217177 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 4.75806451612903 & 0.167312226724502 & 28.4382355628062 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 4.75806451612903 & 0.167312226724502 & 28.4382355628062 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 4.86290322580645 & 0.150430966842363 & 32.3264772399043 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 4.86290322580645 & 0.150430966842363 & 32.3264772399043 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 4.74193548387097 & 0.129954399257149 & 36.4892263053581 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 4.74193548387097 & 0.129954399257149 & 36.4892263053581 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 4.74193548387097 & 0.129954399257149 & 36.4892263053581 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 4.59677419354839 & 0.108374064336987 & 42.4158143525448 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 4.75 & 0.0842972630416872 & 56.3482114199959 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 4.75 & 0.0842972630416872 & 56.3482114199959 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 4.58333333333333 & 0.24791978230013 & 18.4871626249848 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 4.5948275862069 & 0.234132531765003 & 19.6249002715209 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 4.61607142857143 & 0.225050885814602 & 20.5112342120447 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 4.62962962962963 & 0.21685815807614 & 21.3486532888661 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 4.64423076923077 & 0.206573961014133 & 22.4821693229431 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 4.67 & 0.196193365674515 & 23.8030474880967 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 4.6875 & 0.186908049035686 & 25.0791767619651 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 4.71739130434783 & 0.177647111190308 & 26.5548438853825 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 4.73863636363636 & 0.170101819685027 & 27.8576465108413 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 4.75 & 0.164548091244389 & 28.8669407470988 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 4.7625 & 0.157084311021918 & 30.3181136869581 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 4.76315789473684 & 0.151728825854034 & 31.3925707124307 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 4.76388888888889 & 0.144318473763717 & 33.0095570210124 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 4.75 & 0.138829458467302 & 34.2146404116295 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 4.734375 & 0.130878650933455 & 36.1737759843442 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 4.73333333333333 & 0.1262485537264 & 37.4921786715371 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 4.73214285714286 & 0.119196335681552 & 39.7004054703943 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 4.73076923076923 & 0.108240363688233 & 43.7061468529001 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 4.75 & 0.0998186761880863 & 47.5862852663931 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 4.75 & 0.0973123680201904 & 48.8118837989275 \tabularnewline
Median & 4.75 &  &  \tabularnewline
Midrange & 4.25 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 4.66176470588235 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 4.66176470588235 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 4.66176470588235 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 4.66176470588235 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 4.66176470588235 &  &  \tabularnewline
Midmean - Closest Observation & 4.66176470588235 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 4.66176470588235 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 4.66176470588235 &  &  \tabularnewline
Number of observations & 62 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=270517&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]4.57258064516129[/C][C]0.259113827179146[/C][C]17.6469958972892[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]0[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]0[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]5.00040320954866[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]4.57258064516129[/C][C]0.259113827179146[/C][C]17.6469958972892[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]4.55645161290323[/C][C]0.247436577110013[/C][C]18.4146243296818[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]4.58064516129032[/C][C]0.241238198415621[/C][C]18.9880590693124[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]4.58064516129032[/C][C]0.241238198415621[/C][C]18.9880590693124[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]4.54032258064516[/C][C]0.233752408906495[/C][C]19.4236397472223[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]4.58870967741935[/C][C]0.222220237950992[/C][C]20.6493779312365[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]4.53225806451613[/C][C]0.212906831371806[/C][C]21.2875182788349[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]4.59677419354839[/C][C]0.198433416922494[/C][C]23.1653229825894[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]4.66935483870968[/C][C]0.183588829527345[/C][C]25.4337633217177[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]4.66935483870968[/C][C]0.183588829527345[/C][C]25.4337633217177[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]4.75806451612903[/C][C]0.167312226724502[/C][C]28.4382355628062[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]4.75806451612903[/C][C]0.167312226724502[/C][C]28.4382355628062[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]4.86290322580645[/C][C]0.150430966842363[/C][C]32.3264772399043[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]4.86290322580645[/C][C]0.150430966842363[/C][C]32.3264772399043[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]4.74193548387097[/C][C]0.129954399257149[/C][C]36.4892263053581[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]4.74193548387097[/C][C]0.129954399257149[/C][C]36.4892263053581[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]4.74193548387097[/C][C]0.129954399257149[/C][C]36.4892263053581[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]4.59677419354839[/C][C]0.108374064336987[/C][C]42.4158143525448[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]4.75[/C][C]0.0842972630416872[/C][C]56.3482114199959[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]4.75[/C][C]0.0842972630416872[/C][C]56.3482114199959[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]4.58333333333333[/C][C]0.24791978230013[/C][C]18.4871626249848[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]4.5948275862069[/C][C]0.234132531765003[/C][C]19.6249002715209[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]4.61607142857143[/C][C]0.225050885814602[/C][C]20.5112342120447[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]4.62962962962963[/C][C]0.21685815807614[/C][C]21.3486532888661[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]4.64423076923077[/C][C]0.206573961014133[/C][C]22.4821693229431[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]4.67[/C][C]0.196193365674515[/C][C]23.8030474880967[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]4.6875[/C][C]0.186908049035686[/C][C]25.0791767619651[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]4.71739130434783[/C][C]0.177647111190308[/C][C]26.5548438853825[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]4.73863636363636[/C][C]0.170101819685027[/C][C]27.8576465108413[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]4.75[/C][C]0.164548091244389[/C][C]28.8669407470988[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]4.7625[/C][C]0.157084311021918[/C][C]30.3181136869581[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]4.76315789473684[/C][C]0.151728825854034[/C][C]31.3925707124307[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]4.76388888888889[/C][C]0.144318473763717[/C][C]33.0095570210124[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]4.75[/C][C]0.138829458467302[/C][C]34.2146404116295[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]4.734375[/C][C]0.130878650933455[/C][C]36.1737759843442[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]4.73333333333333[/C][C]0.1262485537264[/C][C]37.4921786715371[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]4.73214285714286[/C][C]0.119196335681552[/C][C]39.7004054703943[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]4.73076923076923[/C][C]0.108240363688233[/C][C]43.7061468529001[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]4.75[/C][C]0.0998186761880863[/C][C]47.5862852663931[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]4.75[/C][C]0.0973123680201904[/C][C]48.8118837989275[/C][/ROW]
[ROW][C]Median[/C][C]4.75[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]4.25[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]4.66176470588235[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]4.66176470588235[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]4.66176470588235[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]4.66176470588235[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]4.66176470588235[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]4.66176470588235[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]4.66176470588235[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]4.66176470588235[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]62[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=270517&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=270517&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 Mean4.572580645161290.25911382717914617.6469958972892
Geometric Mean0
Harmonic Mean0
Quadratic Mean5.00040320954866
Winsorized Mean ( 1 / 20 )4.572580645161290.25911382717914617.6469958972892
Winsorized Mean ( 2 / 20 )4.556451612903230.24743657711001318.4146243296818
Winsorized Mean ( 3 / 20 )4.580645161290320.24123819841562118.9880590693124
Winsorized Mean ( 4 / 20 )4.580645161290320.24123819841562118.9880590693124
Winsorized Mean ( 5 / 20 )4.540322580645160.23375240890649519.4236397472223
Winsorized Mean ( 6 / 20 )4.588709677419350.22222023795099220.6493779312365
Winsorized Mean ( 7 / 20 )4.532258064516130.21290683137180621.2875182788349
Winsorized Mean ( 8 / 20 )4.596774193548390.19843341692249423.1653229825894
Winsorized Mean ( 9 / 20 )4.669354838709680.18358882952734525.4337633217177
Winsorized Mean ( 10 / 20 )4.669354838709680.18358882952734525.4337633217177
Winsorized Mean ( 11 / 20 )4.758064516129030.16731222672450228.4382355628062
Winsorized Mean ( 12 / 20 )4.758064516129030.16731222672450228.4382355628062
Winsorized Mean ( 13 / 20 )4.862903225806450.15043096684236332.3264772399043
Winsorized Mean ( 14 / 20 )4.862903225806450.15043096684236332.3264772399043
Winsorized Mean ( 15 / 20 )4.741935483870970.12995439925714936.4892263053581
Winsorized Mean ( 16 / 20 )4.741935483870970.12995439925714936.4892263053581
Winsorized Mean ( 17 / 20 )4.741935483870970.12995439925714936.4892263053581
Winsorized Mean ( 18 / 20 )4.596774193548390.10837406433698742.4158143525448
Winsorized Mean ( 19 / 20 )4.750.084297263041687256.3482114199959
Winsorized Mean ( 20 / 20 )4.750.084297263041687256.3482114199959
Trimmed Mean ( 1 / 20 )4.583333333333330.2479197823001318.4871626249848
Trimmed Mean ( 2 / 20 )4.59482758620690.23413253176500319.6249002715209
Trimmed Mean ( 3 / 20 )4.616071428571430.22505088581460220.5112342120447
Trimmed Mean ( 4 / 20 )4.629629629629630.2168581580761421.3486532888661
Trimmed Mean ( 5 / 20 )4.644230769230770.20657396101413322.4821693229431
Trimmed Mean ( 6 / 20 )4.670.19619336567451523.8030474880967
Trimmed Mean ( 7 / 20 )4.68750.18690804903568625.0791767619651
Trimmed Mean ( 8 / 20 )4.717391304347830.17764711119030826.5548438853825
Trimmed Mean ( 9 / 20 )4.738636363636360.17010181968502727.8576465108413
Trimmed Mean ( 10 / 20 )4.750.16454809124438928.8669407470988
Trimmed Mean ( 11 / 20 )4.76250.15708431102191830.3181136869581
Trimmed Mean ( 12 / 20 )4.763157894736840.15172882585403431.3925707124307
Trimmed Mean ( 13 / 20 )4.763888888888890.14431847376371733.0095570210124
Trimmed Mean ( 14 / 20 )4.750.13882945846730234.2146404116295
Trimmed Mean ( 15 / 20 )4.7343750.13087865093345536.1737759843442
Trimmed Mean ( 16 / 20 )4.733333333333330.126248553726437.4921786715371
Trimmed Mean ( 17 / 20 )4.732142857142860.11919633568155239.7004054703943
Trimmed Mean ( 18 / 20 )4.730769230769230.10824036368823343.7061468529001
Trimmed Mean ( 19 / 20 )4.750.099818676188086347.5862852663931
Trimmed Mean ( 20 / 20 )4.750.097312368020190448.8118837989275
Median4.75
Midrange4.25
Midmean - Weighted Average at Xnp4.66176470588235
Midmean - Weighted Average at X(n+1)p4.66176470588235
Midmean - Empirical Distribution Function4.66176470588235
Midmean - Empirical Distribution Function - Averaging4.66176470588235
Midmean - Empirical Distribution Function - Interpolation4.66176470588235
Midmean - Closest Observation4.66176470588235
Midmean - True Basic - Statistics Graphics Toolkit4.66176470588235
Midmean - MS Excel (old versions)4.66176470588235
Number of observations62



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')