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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 computationMon, 20 Oct 2008 08:30:44 -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/2008/Oct/20/t1224513084g4fcm5wqjrxf51e.htm/, Retrieved Sun, 19 May 2024 14:55:59 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=17367, Retrieved Sun, 19 May 2024 14:55:59 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact141
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
F     [Univariate Data Series] [werkloosheid mannen] [2008-10-13 15:39:35] [e43247bc0ab243a5af99ac7f55ba0b41]
F   PD  [Univariate Data Series] [werkloosheid bove...] [2008-10-13 15:53:52] [e43247bc0ab243a5af99ac7f55ba0b41]
- RMP       [Central Tendency] [central tendancy ...] [2008-10-20 14:30:44] [f24298b2e4c2a19d76cf4460ec5d2246] [Current]
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Dataseries X:
7.0
6.9
6.7
6.6
6.5
6.4
6.5
6.5
6.6
6.7
6.8
7.2
7.6
7.6
7.3
6.4
6.1
6.3
7.1
7.5
7.4
7.1
6.8
6.9
7.2
7.4
7.3
6.9
6.9
6.8
7.1
7.2
7.1
7.0
6.9
7.0
7.4
7.5
7.5
7.4
7.3
7.0
6.7
6.5
6.5
6.5
6.6
6.8
6.9
6.9
6.8
6.8
6.5
6.1
6.0
5.9
5.8
5.9
5.9
6.2
6.3
6.2
6.0
5.8
5.5
5.5
5.7
5.8




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

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=17367&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=17367&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=17367&T=0

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

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







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean6.69852941176470.0661061962251853101.329826767626
Geometric Mean6.67611141293208
Harmonic Mean6.65313709259323
Quadratic Mean6.72034881797769
Winsorized Mean ( 1 / 22 )6.69852941176470.0661061962251853101.329826767626
Winsorized Mean ( 2 / 22 )6.70147058823530.0640488128388836104.630676060976
Winsorized Mean ( 3 / 22 )6.705882352941180.0630607366737684106.340057326521
Winsorized Mean ( 4 / 22 )6.705882352941180.0630607366737684106.340057326521
Winsorized Mean ( 5 / 22 )6.69852941176470.0617456281419119108.485889824771
Winsorized Mean ( 6 / 22 )6.707352941176470.0598988090388971111.978068492495
Winsorized Mean ( 7 / 22 )6.707352941176470.0598988090388971111.978068492495
Winsorized Mean ( 8 / 22 )6.707352941176470.0598988090388971111.978068492495
Winsorized Mean ( 9 / 22 )6.707352941176470.0550885700956429121.755800332653
Winsorized Mean ( 10 / 22 )6.707352941176470.0550885700956429121.755800332653
Winsorized Mean ( 11 / 22 )6.72352941176470.0520905222362278129.073949024236
Winsorized Mean ( 12 / 22 )6.705882352941180.0493096482331054135.995339517328
Winsorized Mean ( 13 / 22 )6.7250.0459212116801958146.446484183262
Winsorized Mean ( 14 / 22 )6.7250.0459212116801958146.446484183262
Winsorized Mean ( 15 / 22 )6.7250.0389375470777495172.712471758216
Winsorized Mean ( 16 / 22 )6.7250.0389375470777495172.712471758216
Winsorized Mean ( 17 / 22 )6.750.0350278955684515192.703554994023
Winsorized Mean ( 18 / 22 )6.750.0350278955684515192.703554994023
Winsorized Mean ( 19 / 22 )6.750.0269539326702352250.427278370919
Winsorized Mean ( 20 / 22 )6.750.0269539326702352250.427278370919
Winsorized Mean ( 21 / 22 )6.750.0269539326702352250.427278370919
Winsorized Mean ( 22 / 22 )6.750.0269539326702352250.427278370919
Trimmed Mean ( 1 / 22 )6.70303030303030.0641592459718907104.474892145195
Trimmed Mean ( 2 / 22 )6.70781250.0618138802468397108.516282640952
Trimmed Mean ( 3 / 22 )6.711290322580640.0603228068782043111.256267237882
Trimmed Mean ( 4 / 22 )6.713333333333330.0589678964015706113.847258305021
Trimmed Mean ( 5 / 22 )6.715517241379310.0573039002872427117.191276819151
Trimmed Mean ( 6 / 22 )6.719642857142860.0556787890584952120.685865672892
Trimmed Mean ( 7 / 22 )6.722222222222220.0542187165928649123.983425736545
Trimmed Mean ( 8 / 22 )6.7250.0523846862589581128.377212507405
Trimmed Mean ( 9 / 22 )6.7280.050064448260136134.386780116724
Trimmed Mean ( 10 / 22 )6.731250.0483922589568864139.097660350946
Trimmed Mean ( 11 / 22 )6.734782608695650.0462316568982652145.674696961777
Trimmed Mean ( 12 / 22 )6.736363636363640.0442330591418404152.292510783900
Trimmed Mean ( 13 / 22 )6.740476190476190.0423002271816926159.348463106918
Trimmed Mean ( 14 / 22 )6.74250.0406497705547503165.868094899052
Trimmed Mean ( 15 / 22 )6.744736842105260.0384066303140169175.613866328796
Trimmed Mean ( 16 / 22 )6.747222222222220.0372648417457407181.061341096220
Trimmed Mean ( 17 / 22 )6.750.0356378096399853189.405579865564
Trimmed Mean ( 18 / 22 )6.750.0344893625489405195.712518328564
Trimmed Mean ( 19 / 22 )6.750.0327828101857995205.900591247174
Trimmed Mean ( 20 / 22 )6.750.0327326835353989206.215906273013
Trimmed Mean ( 21 / 22 )6.750.032462996686168207.929048117609
Trimmed Mean ( 22 / 22 )6.750.0318511028635303211.923587981275
Median6.8
Midrange6.55
Midmean - Weighted Average at Xnp6.74473684210527
Midmean - Weighted Average at X(n+1)p6.76944444444444
Midmean - Empirical Distribution Function6.74473684210527
Midmean - Empirical Distribution Function - Averaging6.76944444444444
Midmean - Empirical Distribution Function - Interpolation6.76944444444444
Midmean - Closest Observation6.74473684210527
Midmean - True Basic - Statistics Graphics Toolkit6.76944444444444
Midmean - MS Excel (old versions)6.74473684210527
Number of observations68

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 6.6985294117647 & 0.0661061962251853 & 101.329826767626 \tabularnewline
Geometric Mean & 6.67611141293208 &  &  \tabularnewline
Harmonic Mean & 6.65313709259323 &  &  \tabularnewline
Quadratic Mean & 6.72034881797769 &  &  \tabularnewline
Winsorized Mean ( 1 / 22 ) & 6.6985294117647 & 0.0661061962251853 & 101.329826767626 \tabularnewline
Winsorized Mean ( 2 / 22 ) & 6.7014705882353 & 0.0640488128388836 & 104.630676060976 \tabularnewline
Winsorized Mean ( 3 / 22 ) & 6.70588235294118 & 0.0630607366737684 & 106.340057326521 \tabularnewline
Winsorized Mean ( 4 / 22 ) & 6.70588235294118 & 0.0630607366737684 & 106.340057326521 \tabularnewline
Winsorized Mean ( 5 / 22 ) & 6.6985294117647 & 0.0617456281419119 & 108.485889824771 \tabularnewline
Winsorized Mean ( 6 / 22 ) & 6.70735294117647 & 0.0598988090388971 & 111.978068492495 \tabularnewline
Winsorized Mean ( 7 / 22 ) & 6.70735294117647 & 0.0598988090388971 & 111.978068492495 \tabularnewline
Winsorized Mean ( 8 / 22 ) & 6.70735294117647 & 0.0598988090388971 & 111.978068492495 \tabularnewline
Winsorized Mean ( 9 / 22 ) & 6.70735294117647 & 0.0550885700956429 & 121.755800332653 \tabularnewline
Winsorized Mean ( 10 / 22 ) & 6.70735294117647 & 0.0550885700956429 & 121.755800332653 \tabularnewline
Winsorized Mean ( 11 / 22 ) & 6.7235294117647 & 0.0520905222362278 & 129.073949024236 \tabularnewline
Winsorized Mean ( 12 / 22 ) & 6.70588235294118 & 0.0493096482331054 & 135.995339517328 \tabularnewline
Winsorized Mean ( 13 / 22 ) & 6.725 & 0.0459212116801958 & 146.446484183262 \tabularnewline
Winsorized Mean ( 14 / 22 ) & 6.725 & 0.0459212116801958 & 146.446484183262 \tabularnewline
Winsorized Mean ( 15 / 22 ) & 6.725 & 0.0389375470777495 & 172.712471758216 \tabularnewline
Winsorized Mean ( 16 / 22 ) & 6.725 & 0.0389375470777495 & 172.712471758216 \tabularnewline
Winsorized Mean ( 17 / 22 ) & 6.75 & 0.0350278955684515 & 192.703554994023 \tabularnewline
Winsorized Mean ( 18 / 22 ) & 6.75 & 0.0350278955684515 & 192.703554994023 \tabularnewline
Winsorized Mean ( 19 / 22 ) & 6.75 & 0.0269539326702352 & 250.427278370919 \tabularnewline
Winsorized Mean ( 20 / 22 ) & 6.75 & 0.0269539326702352 & 250.427278370919 \tabularnewline
Winsorized Mean ( 21 / 22 ) & 6.75 & 0.0269539326702352 & 250.427278370919 \tabularnewline
Winsorized Mean ( 22 / 22 ) & 6.75 & 0.0269539326702352 & 250.427278370919 \tabularnewline
Trimmed Mean ( 1 / 22 ) & 6.7030303030303 & 0.0641592459718907 & 104.474892145195 \tabularnewline
Trimmed Mean ( 2 / 22 ) & 6.7078125 & 0.0618138802468397 & 108.516282640952 \tabularnewline
Trimmed Mean ( 3 / 22 ) & 6.71129032258064 & 0.0603228068782043 & 111.256267237882 \tabularnewline
Trimmed Mean ( 4 / 22 ) & 6.71333333333333 & 0.0589678964015706 & 113.847258305021 \tabularnewline
Trimmed Mean ( 5 / 22 ) & 6.71551724137931 & 0.0573039002872427 & 117.191276819151 \tabularnewline
Trimmed Mean ( 6 / 22 ) & 6.71964285714286 & 0.0556787890584952 & 120.685865672892 \tabularnewline
Trimmed Mean ( 7 / 22 ) & 6.72222222222222 & 0.0542187165928649 & 123.983425736545 \tabularnewline
Trimmed Mean ( 8 / 22 ) & 6.725 & 0.0523846862589581 & 128.377212507405 \tabularnewline
Trimmed Mean ( 9 / 22 ) & 6.728 & 0.050064448260136 & 134.386780116724 \tabularnewline
Trimmed Mean ( 10 / 22 ) & 6.73125 & 0.0483922589568864 & 139.097660350946 \tabularnewline
Trimmed Mean ( 11 / 22 ) & 6.73478260869565 & 0.0462316568982652 & 145.674696961777 \tabularnewline
Trimmed Mean ( 12 / 22 ) & 6.73636363636364 & 0.0442330591418404 & 152.292510783900 \tabularnewline
Trimmed Mean ( 13 / 22 ) & 6.74047619047619 & 0.0423002271816926 & 159.348463106918 \tabularnewline
Trimmed Mean ( 14 / 22 ) & 6.7425 & 0.0406497705547503 & 165.868094899052 \tabularnewline
Trimmed Mean ( 15 / 22 ) & 6.74473684210526 & 0.0384066303140169 & 175.613866328796 \tabularnewline
Trimmed Mean ( 16 / 22 ) & 6.74722222222222 & 0.0372648417457407 & 181.061341096220 \tabularnewline
Trimmed Mean ( 17 / 22 ) & 6.75 & 0.0356378096399853 & 189.405579865564 \tabularnewline
Trimmed Mean ( 18 / 22 ) & 6.75 & 0.0344893625489405 & 195.712518328564 \tabularnewline
Trimmed Mean ( 19 / 22 ) & 6.75 & 0.0327828101857995 & 205.900591247174 \tabularnewline
Trimmed Mean ( 20 / 22 ) & 6.75 & 0.0327326835353989 & 206.215906273013 \tabularnewline
Trimmed Mean ( 21 / 22 ) & 6.75 & 0.032462996686168 & 207.929048117609 \tabularnewline
Trimmed Mean ( 22 / 22 ) & 6.75 & 0.0318511028635303 & 211.923587981275 \tabularnewline
Median & 6.8 &  &  \tabularnewline
Midrange & 6.55 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 6.74473684210527 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 6.76944444444444 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 6.74473684210527 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 6.76944444444444 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 6.76944444444444 &  &  \tabularnewline
Midmean - Closest Observation & 6.74473684210527 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 6.76944444444444 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 6.74473684210527 &  &  \tabularnewline
Number of observations & 68 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=17367&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]6.6985294117647[/C][C]0.0661061962251853[/C][C]101.329826767626[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]6.67611141293208[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]6.65313709259323[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]6.72034881797769[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 22 )[/C][C]6.6985294117647[/C][C]0.0661061962251853[/C][C]101.329826767626[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 22 )[/C][C]6.7014705882353[/C][C]0.0640488128388836[/C][C]104.630676060976[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 22 )[/C][C]6.70588235294118[/C][C]0.0630607366737684[/C][C]106.340057326521[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 22 )[/C][C]6.70588235294118[/C][C]0.0630607366737684[/C][C]106.340057326521[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 22 )[/C][C]6.6985294117647[/C][C]0.0617456281419119[/C][C]108.485889824771[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 22 )[/C][C]6.70735294117647[/C][C]0.0598988090388971[/C][C]111.978068492495[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 22 )[/C][C]6.70735294117647[/C][C]0.0598988090388971[/C][C]111.978068492495[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 22 )[/C][C]6.70735294117647[/C][C]0.0598988090388971[/C][C]111.978068492495[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 22 )[/C][C]6.70735294117647[/C][C]0.0550885700956429[/C][C]121.755800332653[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 22 )[/C][C]6.70735294117647[/C][C]0.0550885700956429[/C][C]121.755800332653[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 22 )[/C][C]6.7235294117647[/C][C]0.0520905222362278[/C][C]129.073949024236[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 22 )[/C][C]6.70588235294118[/C][C]0.0493096482331054[/C][C]135.995339517328[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 22 )[/C][C]6.725[/C][C]0.0459212116801958[/C][C]146.446484183262[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 22 )[/C][C]6.725[/C][C]0.0459212116801958[/C][C]146.446484183262[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 22 )[/C][C]6.725[/C][C]0.0389375470777495[/C][C]172.712471758216[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 22 )[/C][C]6.725[/C][C]0.0389375470777495[/C][C]172.712471758216[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 22 )[/C][C]6.75[/C][C]0.0350278955684515[/C][C]192.703554994023[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 22 )[/C][C]6.75[/C][C]0.0350278955684515[/C][C]192.703554994023[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 22 )[/C][C]6.75[/C][C]0.0269539326702352[/C][C]250.427278370919[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 22 )[/C][C]6.75[/C][C]0.0269539326702352[/C][C]250.427278370919[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 22 )[/C][C]6.75[/C][C]0.0269539326702352[/C][C]250.427278370919[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 22 )[/C][C]6.75[/C][C]0.0269539326702352[/C][C]250.427278370919[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 22 )[/C][C]6.7030303030303[/C][C]0.0641592459718907[/C][C]104.474892145195[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 22 )[/C][C]6.7078125[/C][C]0.0618138802468397[/C][C]108.516282640952[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 22 )[/C][C]6.71129032258064[/C][C]0.0603228068782043[/C][C]111.256267237882[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 22 )[/C][C]6.71333333333333[/C][C]0.0589678964015706[/C][C]113.847258305021[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 22 )[/C][C]6.71551724137931[/C][C]0.0573039002872427[/C][C]117.191276819151[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 22 )[/C][C]6.71964285714286[/C][C]0.0556787890584952[/C][C]120.685865672892[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 22 )[/C][C]6.72222222222222[/C][C]0.0542187165928649[/C][C]123.983425736545[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 22 )[/C][C]6.725[/C][C]0.0523846862589581[/C][C]128.377212507405[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 22 )[/C][C]6.728[/C][C]0.050064448260136[/C][C]134.386780116724[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 22 )[/C][C]6.73125[/C][C]0.0483922589568864[/C][C]139.097660350946[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 22 )[/C][C]6.73478260869565[/C][C]0.0462316568982652[/C][C]145.674696961777[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 22 )[/C][C]6.73636363636364[/C][C]0.0442330591418404[/C][C]152.292510783900[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 22 )[/C][C]6.74047619047619[/C][C]0.0423002271816926[/C][C]159.348463106918[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 22 )[/C][C]6.7425[/C][C]0.0406497705547503[/C][C]165.868094899052[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 22 )[/C][C]6.74473684210526[/C][C]0.0384066303140169[/C][C]175.613866328796[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 22 )[/C][C]6.74722222222222[/C][C]0.0372648417457407[/C][C]181.061341096220[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 22 )[/C][C]6.75[/C][C]0.0356378096399853[/C][C]189.405579865564[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 22 )[/C][C]6.75[/C][C]0.0344893625489405[/C][C]195.712518328564[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 22 )[/C][C]6.75[/C][C]0.0327828101857995[/C][C]205.900591247174[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 22 )[/C][C]6.75[/C][C]0.0327326835353989[/C][C]206.215906273013[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 22 )[/C][C]6.75[/C][C]0.032462996686168[/C][C]207.929048117609[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 22 )[/C][C]6.75[/C][C]0.0318511028635303[/C][C]211.923587981275[/C][/ROW]
[ROW][C]Median[/C][C]6.8[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]6.55[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]6.74473684210527[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]6.76944444444444[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]6.74473684210527[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]6.76944444444444[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]6.76944444444444[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]6.74473684210527[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]6.76944444444444[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]6.74473684210527[/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=17367&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=17367&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 Mean6.69852941176470.0661061962251853101.329826767626
Geometric Mean6.67611141293208
Harmonic Mean6.65313709259323
Quadratic Mean6.72034881797769
Winsorized Mean ( 1 / 22 )6.69852941176470.0661061962251853101.329826767626
Winsorized Mean ( 2 / 22 )6.70147058823530.0640488128388836104.630676060976
Winsorized Mean ( 3 / 22 )6.705882352941180.0630607366737684106.340057326521
Winsorized Mean ( 4 / 22 )6.705882352941180.0630607366737684106.340057326521
Winsorized Mean ( 5 / 22 )6.69852941176470.0617456281419119108.485889824771
Winsorized Mean ( 6 / 22 )6.707352941176470.0598988090388971111.978068492495
Winsorized Mean ( 7 / 22 )6.707352941176470.0598988090388971111.978068492495
Winsorized Mean ( 8 / 22 )6.707352941176470.0598988090388971111.978068492495
Winsorized Mean ( 9 / 22 )6.707352941176470.0550885700956429121.755800332653
Winsorized Mean ( 10 / 22 )6.707352941176470.0550885700956429121.755800332653
Winsorized Mean ( 11 / 22 )6.72352941176470.0520905222362278129.073949024236
Winsorized Mean ( 12 / 22 )6.705882352941180.0493096482331054135.995339517328
Winsorized Mean ( 13 / 22 )6.7250.0459212116801958146.446484183262
Winsorized Mean ( 14 / 22 )6.7250.0459212116801958146.446484183262
Winsorized Mean ( 15 / 22 )6.7250.0389375470777495172.712471758216
Winsorized Mean ( 16 / 22 )6.7250.0389375470777495172.712471758216
Winsorized Mean ( 17 / 22 )6.750.0350278955684515192.703554994023
Winsorized Mean ( 18 / 22 )6.750.0350278955684515192.703554994023
Winsorized Mean ( 19 / 22 )6.750.0269539326702352250.427278370919
Winsorized Mean ( 20 / 22 )6.750.0269539326702352250.427278370919
Winsorized Mean ( 21 / 22 )6.750.0269539326702352250.427278370919
Winsorized Mean ( 22 / 22 )6.750.0269539326702352250.427278370919
Trimmed Mean ( 1 / 22 )6.70303030303030.0641592459718907104.474892145195
Trimmed Mean ( 2 / 22 )6.70781250.0618138802468397108.516282640952
Trimmed Mean ( 3 / 22 )6.711290322580640.0603228068782043111.256267237882
Trimmed Mean ( 4 / 22 )6.713333333333330.0589678964015706113.847258305021
Trimmed Mean ( 5 / 22 )6.715517241379310.0573039002872427117.191276819151
Trimmed Mean ( 6 / 22 )6.719642857142860.0556787890584952120.685865672892
Trimmed Mean ( 7 / 22 )6.722222222222220.0542187165928649123.983425736545
Trimmed Mean ( 8 / 22 )6.7250.0523846862589581128.377212507405
Trimmed Mean ( 9 / 22 )6.7280.050064448260136134.386780116724
Trimmed Mean ( 10 / 22 )6.731250.0483922589568864139.097660350946
Trimmed Mean ( 11 / 22 )6.734782608695650.0462316568982652145.674696961777
Trimmed Mean ( 12 / 22 )6.736363636363640.0442330591418404152.292510783900
Trimmed Mean ( 13 / 22 )6.740476190476190.0423002271816926159.348463106918
Trimmed Mean ( 14 / 22 )6.74250.0406497705547503165.868094899052
Trimmed Mean ( 15 / 22 )6.744736842105260.0384066303140169175.613866328796
Trimmed Mean ( 16 / 22 )6.747222222222220.0372648417457407181.061341096220
Trimmed Mean ( 17 / 22 )6.750.0356378096399853189.405579865564
Trimmed Mean ( 18 / 22 )6.750.0344893625489405195.712518328564
Trimmed Mean ( 19 / 22 )6.750.0327828101857995205.900591247174
Trimmed Mean ( 20 / 22 )6.750.0327326835353989206.215906273013
Trimmed Mean ( 21 / 22 )6.750.032462996686168207.929048117609
Trimmed Mean ( 22 / 22 )6.750.0318511028635303211.923587981275
Median6.8
Midrange6.55
Midmean - Weighted Average at Xnp6.74473684210527
Midmean - Weighted Average at X(n+1)p6.76944444444444
Midmean - Empirical Distribution Function6.74473684210527
Midmean - Empirical Distribution Function - Averaging6.76944444444444
Midmean - Empirical Distribution Function - Interpolation6.76944444444444
Midmean - Closest Observation6.74473684210527
Midmean - True Basic - Statistics Graphics Toolkit6.76944444444444
Midmean - MS Excel (old versions)6.74473684210527
Number of observations68



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')