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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 computationSun, 18 Oct 2009 14:42:18 -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/18/t12558986766zjejyeozqye1cw.htm/, Retrieved Mon, 29 Apr 2024 16:07:38 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=47499, Retrieved Mon, 29 Apr 2024 16:07:38 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordspart 2 vraag 1
Estimated Impact162
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Data Series] [tijdreeks 2: werk...] [2009-10-12 19:58:30] [616e2df490b611f6cb7080068870ecbd]
- RMP     [Central Tendency] [ws3 part 2 vraag 1] [2009-10-18 20:42:18] [88e98f4c87ea17c4967db8279bda8533] [Current]
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Dataseries X:
9.9
9.8
9.3
8.3
8.0
8.5
10.4
11.1
10.9
10.0
9.2
9.2
9.5
9.6
9.5
9.1
8.9
9.0
10.1
10.3
10.2
9.6
9.2
9.3
9.4
9.4
9.2
9.0
9.0
9.0
9.8
10.0
9.8
9.3
9.0
9.0
9.1
9.1
9.1
9.2
8.8
8.3
8.4
8.1
7.7
7.9
7.9
8.0
7.9
7.6
7.1
6.8
6.5
6.9
8.2
8.7
8.3
7.9
7.5
7.8
8.3
8.4
8.2
7.7
7.2
7.3
8.1
8.5




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'RServer@AstonUniversity' @ vre.aston.ac.uk

\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 & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=47499&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]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=47499&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=47499&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'RServer@AstonUniversity' @ vre.aston.ac.uk







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean8.783823529411760.11967563518258473.396924244527
Geometric Mean8.72812697378904
Harmonic Mean8.67128076832911
Quadratic Mean8.83827738073566
Winsorized Mean ( 1 / 22 )8.785294117647060.11767174894562674.6593315419027
Winsorized Mean ( 2 / 22 )8.77352941176470.11338470582377877.378420202461
Winsorized Mean ( 3 / 22 )8.777941176470590.11036784190972879.533503823063
Winsorized Mean ( 4 / 22 )8.777941176470590.10787364548382881.3724347323236
Winsorized Mean ( 5 / 22 )8.777941176470590.10488183886616383.6936239044389
Winsorized Mean ( 6 / 22 )8.786764705882350.099690134750046788.1407646595466
Winsorized Mean ( 7 / 22 )8.797058823529410.097757350155236789.9887201275389
Winsorized Mean ( 8 / 22 )8.797058823529410.093534878167818994.0511068795734
Winsorized Mean ( 9 / 22 )8.783823529411770.091269706499390396.2402955625857
Winsorized Mean ( 10 / 22 )8.79852941176470.08873050236701199.160144223819
Winsorized Mean ( 11 / 22 )8.814705882352940.0860881570812755102.391620185701
Winsorized Mean ( 12 / 22 )8.779411764705880.0803733284160451109.232900238498
Winsorized Mean ( 13 / 22 )8.779411764705880.0803733284160451109.232900238498
Winsorized Mean ( 14 / 22 )8.758823529411770.0773302126130634113.265219807919
Winsorized Mean ( 15 / 22 )8.780882352941180.0737571101300572119.051333999633
Winsorized Mean ( 16 / 22 )8.757352941176470.0704406105578453124.32250191791
Winsorized Mean ( 17 / 22 )8.782352941176470.0665182375617161132.029248866195
Winsorized Mean ( 18 / 22 )8.755882352941180.0629736609287486139.040389645569
Winsorized Mean ( 19 / 22 )8.783823529411770.0587254999675092149.574265596232
Winsorized Mean ( 20 / 22 )8.783823529411760.0587254999675092149.574265596232
Winsorized Mean ( 21 / 22 )8.783823529411760.0502675150033076174.741550857125
Winsorized Mean ( 22 / 22 )8.783823529411760.0502675150033076174.741550857125
Trimmed Mean ( 1 / 22 )8.783333333333330.11288922997336077.8048830291962
Trimmed Mean ( 2 / 22 )8.781250.10711019674163581.9833243438216
Trimmed Mean ( 3 / 22 )8.785483870967740.10296623399014385.3239312589482
Trimmed Mean ( 4 / 22 )8.788333333333330.099379193523903188.4323269459771
Trimmed Mean ( 5 / 22 )8.791379310344830.09596469413917791.6105593750422
Trimmed Mean ( 6 / 22 )8.794642857142860.092771876436309794.7985876213316
Trimmed Mean ( 7 / 22 )8.79629629629630.090381711034194597.3238523108768
Trimmed Mean ( 8 / 22 )8.796153846153850.0879188547815832100.048548948984
Trimmed Mean ( 9 / 22 )8.7960.0859026501693775102.394978299931
Trimmed Mean ( 10 / 22 )8.797916666666670.0838718195924555104.897171772556
Trimmed Mean ( 11 / 22 )8.797826086956520.081855837127438107.479520040331
Trimmed Mean ( 12 / 22 )8.795454545454540.0798356229770698110.169548598384
Trimmed Mean ( 13 / 22 )8.797619047619050.078493961036131112.080202495699
Trimmed Mean ( 14 / 22 )8.80.0766276377803392114.841071118832
Trimmed Mean ( 15 / 22 )8.805263157894740.0747634837214382117.774917909154
Trimmed Mean ( 16 / 22 )8.808333333333330.073070416135983120.545821402483
Trimmed Mean ( 17 / 22 )8.814705882352940.071417073925983123.425749583196
Trimmed Mean ( 18 / 22 )8.818750.0700572202767368125.879245068026
Trimmed Mean ( 19 / 22 )8.826666666666670.0688047935601745128.285635490602
Trimmed Mean ( 20 / 22 )8.832142857142860.068051795444277129.785596389957
Trimmed Mean ( 21 / 22 )8.838461538461540.066581800025792132.745908567172
Trimmed Mean ( 22 / 22 )8.845833333333330.0667515311300988132.518807937046
Median9
Midrange8.8
Midmean - Weighted Average at Xnp8.78648648648648
Midmean - Weighted Average at X(n+1)p8.83142857142857
Midmean - Empirical Distribution Function8.78648648648648
Midmean - Empirical Distribution Function - Averaging8.83142857142857
Midmean - Empirical Distribution Function - Interpolation8.83142857142857
Midmean - Closest Observation8.78648648648648
Midmean - True Basic - Statistics Graphics Toolkit8.83142857142857
Midmean - MS Excel (old versions)8.78648648648648
Number of observations68

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 8.78382352941176 & 0.119675635182584 & 73.396924244527 \tabularnewline
Geometric Mean & 8.72812697378904 &  &  \tabularnewline
Harmonic Mean & 8.67128076832911 &  &  \tabularnewline
Quadratic Mean & 8.83827738073566 &  &  \tabularnewline
Winsorized Mean ( 1 / 22 ) & 8.78529411764706 & 0.117671748945626 & 74.6593315419027 \tabularnewline
Winsorized Mean ( 2 / 22 ) & 8.7735294117647 & 0.113384705823778 & 77.378420202461 \tabularnewline
Winsorized Mean ( 3 / 22 ) & 8.77794117647059 & 0.110367841909728 & 79.533503823063 \tabularnewline
Winsorized Mean ( 4 / 22 ) & 8.77794117647059 & 0.107873645483828 & 81.3724347323236 \tabularnewline
Winsorized Mean ( 5 / 22 ) & 8.77794117647059 & 0.104881838866163 & 83.6936239044389 \tabularnewline
Winsorized Mean ( 6 / 22 ) & 8.78676470588235 & 0.0996901347500467 & 88.1407646595466 \tabularnewline
Winsorized Mean ( 7 / 22 ) & 8.79705882352941 & 0.0977573501552367 & 89.9887201275389 \tabularnewline
Winsorized Mean ( 8 / 22 ) & 8.79705882352941 & 0.0935348781678189 & 94.0511068795734 \tabularnewline
Winsorized Mean ( 9 / 22 ) & 8.78382352941177 & 0.0912697064993903 & 96.2402955625857 \tabularnewline
Winsorized Mean ( 10 / 22 ) & 8.7985294117647 & 0.088730502367011 & 99.160144223819 \tabularnewline
Winsorized Mean ( 11 / 22 ) & 8.81470588235294 & 0.0860881570812755 & 102.391620185701 \tabularnewline
Winsorized Mean ( 12 / 22 ) & 8.77941176470588 & 0.0803733284160451 & 109.232900238498 \tabularnewline
Winsorized Mean ( 13 / 22 ) & 8.77941176470588 & 0.0803733284160451 & 109.232900238498 \tabularnewline
Winsorized Mean ( 14 / 22 ) & 8.75882352941177 & 0.0773302126130634 & 113.265219807919 \tabularnewline
Winsorized Mean ( 15 / 22 ) & 8.78088235294118 & 0.0737571101300572 & 119.051333999633 \tabularnewline
Winsorized Mean ( 16 / 22 ) & 8.75735294117647 & 0.0704406105578453 & 124.32250191791 \tabularnewline
Winsorized Mean ( 17 / 22 ) & 8.78235294117647 & 0.0665182375617161 & 132.029248866195 \tabularnewline
Winsorized Mean ( 18 / 22 ) & 8.75588235294118 & 0.0629736609287486 & 139.040389645569 \tabularnewline
Winsorized Mean ( 19 / 22 ) & 8.78382352941177 & 0.0587254999675092 & 149.574265596232 \tabularnewline
Winsorized Mean ( 20 / 22 ) & 8.78382352941176 & 0.0587254999675092 & 149.574265596232 \tabularnewline
Winsorized Mean ( 21 / 22 ) & 8.78382352941176 & 0.0502675150033076 & 174.741550857125 \tabularnewline
Winsorized Mean ( 22 / 22 ) & 8.78382352941176 & 0.0502675150033076 & 174.741550857125 \tabularnewline
Trimmed Mean ( 1 / 22 ) & 8.78333333333333 & 0.112889229973360 & 77.8048830291962 \tabularnewline
Trimmed Mean ( 2 / 22 ) & 8.78125 & 0.107110196741635 & 81.9833243438216 \tabularnewline
Trimmed Mean ( 3 / 22 ) & 8.78548387096774 & 0.102966233990143 & 85.3239312589482 \tabularnewline
Trimmed Mean ( 4 / 22 ) & 8.78833333333333 & 0.0993791935239031 & 88.4323269459771 \tabularnewline
Trimmed Mean ( 5 / 22 ) & 8.79137931034483 & 0.095964694139177 & 91.6105593750422 \tabularnewline
Trimmed Mean ( 6 / 22 ) & 8.79464285714286 & 0.0927718764363097 & 94.7985876213316 \tabularnewline
Trimmed Mean ( 7 / 22 ) & 8.7962962962963 & 0.0903817110341945 & 97.3238523108768 \tabularnewline
Trimmed Mean ( 8 / 22 ) & 8.79615384615385 & 0.0879188547815832 & 100.048548948984 \tabularnewline
Trimmed Mean ( 9 / 22 ) & 8.796 & 0.0859026501693775 & 102.394978299931 \tabularnewline
Trimmed Mean ( 10 / 22 ) & 8.79791666666667 & 0.0838718195924555 & 104.897171772556 \tabularnewline
Trimmed Mean ( 11 / 22 ) & 8.79782608695652 & 0.081855837127438 & 107.479520040331 \tabularnewline
Trimmed Mean ( 12 / 22 ) & 8.79545454545454 & 0.0798356229770698 & 110.169548598384 \tabularnewline
Trimmed Mean ( 13 / 22 ) & 8.79761904761905 & 0.078493961036131 & 112.080202495699 \tabularnewline
Trimmed Mean ( 14 / 22 ) & 8.8 & 0.0766276377803392 & 114.841071118832 \tabularnewline
Trimmed Mean ( 15 / 22 ) & 8.80526315789474 & 0.0747634837214382 & 117.774917909154 \tabularnewline
Trimmed Mean ( 16 / 22 ) & 8.80833333333333 & 0.073070416135983 & 120.545821402483 \tabularnewline
Trimmed Mean ( 17 / 22 ) & 8.81470588235294 & 0.071417073925983 & 123.425749583196 \tabularnewline
Trimmed Mean ( 18 / 22 ) & 8.81875 & 0.0700572202767368 & 125.879245068026 \tabularnewline
Trimmed Mean ( 19 / 22 ) & 8.82666666666667 & 0.0688047935601745 & 128.285635490602 \tabularnewline
Trimmed Mean ( 20 / 22 ) & 8.83214285714286 & 0.068051795444277 & 129.785596389957 \tabularnewline
Trimmed Mean ( 21 / 22 ) & 8.83846153846154 & 0.066581800025792 & 132.745908567172 \tabularnewline
Trimmed Mean ( 22 / 22 ) & 8.84583333333333 & 0.0667515311300988 & 132.518807937046 \tabularnewline
Median & 9 &  &  \tabularnewline
Midrange & 8.8 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 8.78648648648648 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 8.83142857142857 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 8.78648648648648 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 8.83142857142857 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 8.83142857142857 &  &  \tabularnewline
Midmean - Closest Observation & 8.78648648648648 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 8.83142857142857 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 8.78648648648648 &  &  \tabularnewline
Number of observations & 68 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=47499&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]8.78382352941176[/C][C]0.119675635182584[/C][C]73.396924244527[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]8.72812697378904[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]8.67128076832911[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]8.83827738073566[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 22 )[/C][C]8.78529411764706[/C][C]0.117671748945626[/C][C]74.6593315419027[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 22 )[/C][C]8.7735294117647[/C][C]0.113384705823778[/C][C]77.378420202461[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 22 )[/C][C]8.77794117647059[/C][C]0.110367841909728[/C][C]79.533503823063[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 22 )[/C][C]8.77794117647059[/C][C]0.107873645483828[/C][C]81.3724347323236[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 22 )[/C][C]8.77794117647059[/C][C]0.104881838866163[/C][C]83.6936239044389[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 22 )[/C][C]8.78676470588235[/C][C]0.0996901347500467[/C][C]88.1407646595466[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 22 )[/C][C]8.79705882352941[/C][C]0.0977573501552367[/C][C]89.9887201275389[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 22 )[/C][C]8.79705882352941[/C][C]0.0935348781678189[/C][C]94.0511068795734[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 22 )[/C][C]8.78382352941177[/C][C]0.0912697064993903[/C][C]96.2402955625857[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 22 )[/C][C]8.7985294117647[/C][C]0.088730502367011[/C][C]99.160144223819[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 22 )[/C][C]8.81470588235294[/C][C]0.0860881570812755[/C][C]102.391620185701[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 22 )[/C][C]8.77941176470588[/C][C]0.0803733284160451[/C][C]109.232900238498[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 22 )[/C][C]8.77941176470588[/C][C]0.0803733284160451[/C][C]109.232900238498[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 22 )[/C][C]8.75882352941177[/C][C]0.0773302126130634[/C][C]113.265219807919[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 22 )[/C][C]8.78088235294118[/C][C]0.0737571101300572[/C][C]119.051333999633[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 22 )[/C][C]8.75735294117647[/C][C]0.0704406105578453[/C][C]124.32250191791[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 22 )[/C][C]8.78235294117647[/C][C]0.0665182375617161[/C][C]132.029248866195[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 22 )[/C][C]8.75588235294118[/C][C]0.0629736609287486[/C][C]139.040389645569[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 22 )[/C][C]8.78382352941177[/C][C]0.0587254999675092[/C][C]149.574265596232[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 22 )[/C][C]8.78382352941176[/C][C]0.0587254999675092[/C][C]149.574265596232[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 22 )[/C][C]8.78382352941176[/C][C]0.0502675150033076[/C][C]174.741550857125[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 22 )[/C][C]8.78382352941176[/C][C]0.0502675150033076[/C][C]174.741550857125[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 22 )[/C][C]8.78333333333333[/C][C]0.112889229973360[/C][C]77.8048830291962[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 22 )[/C][C]8.78125[/C][C]0.107110196741635[/C][C]81.9833243438216[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 22 )[/C][C]8.78548387096774[/C][C]0.102966233990143[/C][C]85.3239312589482[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 22 )[/C][C]8.78833333333333[/C][C]0.0993791935239031[/C][C]88.4323269459771[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 22 )[/C][C]8.79137931034483[/C][C]0.095964694139177[/C][C]91.6105593750422[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 22 )[/C][C]8.79464285714286[/C][C]0.0927718764363097[/C][C]94.7985876213316[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 22 )[/C][C]8.7962962962963[/C][C]0.0903817110341945[/C][C]97.3238523108768[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 22 )[/C][C]8.79615384615385[/C][C]0.0879188547815832[/C][C]100.048548948984[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 22 )[/C][C]8.796[/C][C]0.0859026501693775[/C][C]102.394978299931[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 22 )[/C][C]8.79791666666667[/C][C]0.0838718195924555[/C][C]104.897171772556[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 22 )[/C][C]8.79782608695652[/C][C]0.081855837127438[/C][C]107.479520040331[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 22 )[/C][C]8.79545454545454[/C][C]0.0798356229770698[/C][C]110.169548598384[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 22 )[/C][C]8.79761904761905[/C][C]0.078493961036131[/C][C]112.080202495699[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 22 )[/C][C]8.8[/C][C]0.0766276377803392[/C][C]114.841071118832[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 22 )[/C][C]8.80526315789474[/C][C]0.0747634837214382[/C][C]117.774917909154[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 22 )[/C][C]8.80833333333333[/C][C]0.073070416135983[/C][C]120.545821402483[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 22 )[/C][C]8.81470588235294[/C][C]0.071417073925983[/C][C]123.425749583196[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 22 )[/C][C]8.81875[/C][C]0.0700572202767368[/C][C]125.879245068026[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 22 )[/C][C]8.82666666666667[/C][C]0.0688047935601745[/C][C]128.285635490602[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 22 )[/C][C]8.83214285714286[/C][C]0.068051795444277[/C][C]129.785596389957[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 22 )[/C][C]8.83846153846154[/C][C]0.066581800025792[/C][C]132.745908567172[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 22 )[/C][C]8.84583333333333[/C][C]0.0667515311300988[/C][C]132.518807937046[/C][/ROW]
[ROW][C]Median[/C][C]9[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]8.8[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]8.78648648648648[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]8.83142857142857[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]8.78648648648648[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]8.83142857142857[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]8.83142857142857[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]8.78648648648648[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]8.83142857142857[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]8.78648648648648[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]68[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=47499&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=47499&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 Mean8.783823529411760.11967563518258473.396924244527
Geometric Mean8.72812697378904
Harmonic Mean8.67128076832911
Quadratic Mean8.83827738073566
Winsorized Mean ( 1 / 22 )8.785294117647060.11767174894562674.6593315419027
Winsorized Mean ( 2 / 22 )8.77352941176470.11338470582377877.378420202461
Winsorized Mean ( 3 / 22 )8.777941176470590.11036784190972879.533503823063
Winsorized Mean ( 4 / 22 )8.777941176470590.10787364548382881.3724347323236
Winsorized Mean ( 5 / 22 )8.777941176470590.10488183886616383.6936239044389
Winsorized Mean ( 6 / 22 )8.786764705882350.099690134750046788.1407646595466
Winsorized Mean ( 7 / 22 )8.797058823529410.097757350155236789.9887201275389
Winsorized Mean ( 8 / 22 )8.797058823529410.093534878167818994.0511068795734
Winsorized Mean ( 9 / 22 )8.783823529411770.091269706499390396.2402955625857
Winsorized Mean ( 10 / 22 )8.79852941176470.08873050236701199.160144223819
Winsorized Mean ( 11 / 22 )8.814705882352940.0860881570812755102.391620185701
Winsorized Mean ( 12 / 22 )8.779411764705880.0803733284160451109.232900238498
Winsorized Mean ( 13 / 22 )8.779411764705880.0803733284160451109.232900238498
Winsorized Mean ( 14 / 22 )8.758823529411770.0773302126130634113.265219807919
Winsorized Mean ( 15 / 22 )8.780882352941180.0737571101300572119.051333999633
Winsorized Mean ( 16 / 22 )8.757352941176470.0704406105578453124.32250191791
Winsorized Mean ( 17 / 22 )8.782352941176470.0665182375617161132.029248866195
Winsorized Mean ( 18 / 22 )8.755882352941180.0629736609287486139.040389645569
Winsorized Mean ( 19 / 22 )8.783823529411770.0587254999675092149.574265596232
Winsorized Mean ( 20 / 22 )8.783823529411760.0587254999675092149.574265596232
Winsorized Mean ( 21 / 22 )8.783823529411760.0502675150033076174.741550857125
Winsorized Mean ( 22 / 22 )8.783823529411760.0502675150033076174.741550857125
Trimmed Mean ( 1 / 22 )8.783333333333330.11288922997336077.8048830291962
Trimmed Mean ( 2 / 22 )8.781250.10711019674163581.9833243438216
Trimmed Mean ( 3 / 22 )8.785483870967740.10296623399014385.3239312589482
Trimmed Mean ( 4 / 22 )8.788333333333330.099379193523903188.4323269459771
Trimmed Mean ( 5 / 22 )8.791379310344830.09596469413917791.6105593750422
Trimmed Mean ( 6 / 22 )8.794642857142860.092771876436309794.7985876213316
Trimmed Mean ( 7 / 22 )8.79629629629630.090381711034194597.3238523108768
Trimmed Mean ( 8 / 22 )8.796153846153850.0879188547815832100.048548948984
Trimmed Mean ( 9 / 22 )8.7960.0859026501693775102.394978299931
Trimmed Mean ( 10 / 22 )8.797916666666670.0838718195924555104.897171772556
Trimmed Mean ( 11 / 22 )8.797826086956520.081855837127438107.479520040331
Trimmed Mean ( 12 / 22 )8.795454545454540.0798356229770698110.169548598384
Trimmed Mean ( 13 / 22 )8.797619047619050.078493961036131112.080202495699
Trimmed Mean ( 14 / 22 )8.80.0766276377803392114.841071118832
Trimmed Mean ( 15 / 22 )8.805263157894740.0747634837214382117.774917909154
Trimmed Mean ( 16 / 22 )8.808333333333330.073070416135983120.545821402483
Trimmed Mean ( 17 / 22 )8.814705882352940.071417073925983123.425749583196
Trimmed Mean ( 18 / 22 )8.818750.0700572202767368125.879245068026
Trimmed Mean ( 19 / 22 )8.826666666666670.0688047935601745128.285635490602
Trimmed Mean ( 20 / 22 )8.832142857142860.068051795444277129.785596389957
Trimmed Mean ( 21 / 22 )8.838461538461540.066581800025792132.745908567172
Trimmed Mean ( 22 / 22 )8.845833333333330.0667515311300988132.518807937046
Median9
Midrange8.8
Midmean - Weighted Average at Xnp8.78648648648648
Midmean - Weighted Average at X(n+1)p8.83142857142857
Midmean - Empirical Distribution Function8.78648648648648
Midmean - Empirical Distribution Function - Averaging8.83142857142857
Midmean - Empirical Distribution Function - Interpolation8.83142857142857
Midmean - Closest Observation8.78648648648648
Midmean - True Basic - Statistics Graphics Toolkit8.83142857142857
Midmean - MS Excel (old versions)8.78648648648648
Number of observations68



Parameters (Session):
par1 = 0.01 ; par2 = 0.99 ; par3 = 0.05 ;
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')