Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationThu, 07 Mar 2013 09:42:40 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2013/Mar/07/t1362667455dhefxm45xguvv0m.htm/, Retrieved Tue, 30 Apr 2024 11:23:08 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=207601, Retrieved Tue, 30 Apr 2024 11:23:08 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact68
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [oef 2 centrummaten] [2013-03-07 14:42:40] [9bda411d6223d16f0472c7feaae49b5f] [Current]
Feedback Forum

Post a new message
Dataseries X:
6,3
6,2
6,2
6,3
6,5
6,5
6,2
6,2
6,2
6,1
6,1
6,2
6,1
6,1
6,2
6,2
6,4
6,2
5,7
5,7
5,7
5,9
6
6,3
6,4
6,5
6,8
7
7,3
7,4
6,9
6,9
7
7,1
7,2
7,1
6,8
6,5
6,4
6,5
6,7
6,6
6,2
6,2
6,5
6,8
6,8
6,5
5,9
5,5
5,6
6
6,3
6,2
5,6
5,4
5,7
5,9
6,2
6,3
6,1
5,9
5,9
5,7
5,9
6,1
6,1
6,5
6,8
6,8
6,9
6,9
6,8
6,6
6,5
6,5




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ jenkins.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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=207601&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]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=207601&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=207601&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'Gwilym Jenkins' @ jenkins.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean6.344736842105260.0510725228024903124.22994780661
Geometric Mean6.32937438623749
Harmonic Mean6.31406496557119
Quadratic Mean6.36013488767917
Winsorized Mean ( 1 / 25 )6.344736842105260.0504156316904215125.848603486024
Winsorized Mean ( 2 / 25 )6.344736842105260.0492182656452886128.910207601202
Winsorized Mean ( 3 / 25 )6.340789473684210.04834734091924131.150738657498
Winsorized Mean ( 4 / 25 )6.346052631578950.0473301502317528134.080551202677
Winsorized Mean ( 5 / 25 )6.339473684210530.0460007226246986137.812480380618
Winsorized Mean ( 6 / 25 )6.339473684210530.0460007226246986137.812480380618
Winsorized Mean ( 7 / 25 )6.330263157894740.0443281122176358142.804708822594
Winsorized Mean ( 8 / 25 )6.330263157894740.0443281122176358142.804708822594
Winsorized Mean ( 9 / 25 )6.353947368421050.0402815002365996157.738597894819
Winsorized Mean ( 10 / 25 )6.353947368421050.0402815002365996157.738597894819
Winsorized Mean ( 11 / 25 )6.339473684210530.0377934807043337167.739873810659
Winsorized Mean ( 12 / 25 )6.339473684210530.0377934807043337167.739873810659
Winsorized Mean ( 13 / 25 )6.339473684210530.0377934807043337167.739873810659
Winsorized Mean ( 14 / 25 )6.339473684210530.0377934807043337167.739873810659
Winsorized Mean ( 15 / 25 )6.359210526315790.0349022510498561182.200584060666
Winsorized Mean ( 16 / 25 )6.359210526315790.0349022510498561182.200584060666
Winsorized Mean ( 17 / 25 )6.381578947368420.0320476906859296199.127575522009
Winsorized Mean ( 18 / 25 )6.357894736842110.0280515288944269226.650560144879
Winsorized Mean ( 19 / 25 )6.33289473684210.0241623280723582262.097870614006
Winsorized Mean ( 20 / 25 )6.332894736842110.0241623280723582262.097870614006
Winsorized Mean ( 21 / 25 )6.305263157894740.0203387743806168310.011952534552
Winsorized Mean ( 22 / 25 )6.305263157894740.0203387743806168310.011952534552
Winsorized Mean ( 23 / 25 )6.305263157894740.0203387743806168310.011952534552
Winsorized Mean ( 24 / 25 )6.336842105263160.0164201529218212385.918580383132
Winsorized Mean ( 25 / 25 )6.336842105263160.0164201529218212385.918580383132
Trimmed Mean ( 1 / 25 )6.343243243243240.0487944665610681129.999233320943
Trimmed Mean ( 2 / 25 )6.341666666666670.0468803791905702135.273365449703
Trimmed Mean ( 3 / 25 )6.340.0453831172264813139.699526772493
Trimmed Mean ( 4 / 25 )6.339705882352940.0440059311332073144.064804881925
Trimmed Mean ( 5 / 25 )6.337878787878790.042736529606118148.301203824736
Trimmed Mean ( 6 / 25 )6.33750.0416368941250539152.208759398953
Trimmed Mean ( 7 / 25 )6.337096774193550.0403077709450702157.217743021054
Trimmed Mean ( 8 / 25 )6.338333333333330.0391355508086933161.95845471339
Trimmed Mean ( 9 / 25 )6.339655172413790.0377000335514263168.160464997091
Trimmed Mean ( 10 / 25 )6.33750.03688896114755171.799362271304
Trimmed Mean ( 11 / 25 )6.335185185185190.0358735849600433176.597493454904
Trimmed Mean ( 12 / 25 )6.334615384615380.0351558280050346180.186778240815
Trimmed Mean ( 13 / 25 )6.3340.034239254235632184.992346983082
Trimmed Mean ( 14 / 25 )6.333333333333330.0330663063352593191.534345237102
Trimmed Mean ( 15 / 25 )6.332608695652170.0315546221954021200.687197471023
Trimmed Mean ( 16 / 25 )6.329545454545450.0302525566257593209.223489202761
Trimmed Mean ( 17 / 25 )6.326190476190480.0285254178501428221.773805713377
Trimmed Mean ( 18 / 25 )6.320.0268423698751213235.448659317434
Trimmed Mean ( 19 / 25 )6.315789473684210.0257259647081156245.502531988307
Trimmed Mean ( 20 / 25 )6.313888888888890.0252457061500039250.09753545309
Trimmed Mean ( 21 / 25 )6.311764705882350.0245329658829748257.276871291887
Trimmed Mean ( 22 / 25 )6.31250.0244907816759036257.750041772283
Trimmed Mean ( 23 / 25 )6.313333333333330.0243222301861086259.570495181775
Trimmed Mean ( 24 / 25 )6.314285714285710.0239677283659389263.449485820237
Trimmed Mean ( 25 / 25 )6.311538461538460.0243859499756113258.818642203839
Median6.3
Midrange6.4
Midmean - Weighted Average at Xnp6.305
Midmean - Weighted Average at X(n+1)p6.305
Midmean - Empirical Distribution Function6.305
Midmean - Empirical Distribution Function - Averaging6.305
Midmean - Empirical Distribution Function - Interpolation6.305
Midmean - Closest Observation6.305
Midmean - True Basic - Statistics Graphics Toolkit6.305
Midmean - MS Excel (old versions)6.31463414634147
Number of observations76

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 6.34473684210526 & 0.0510725228024903 & 124.22994780661 \tabularnewline
Geometric Mean & 6.32937438623749 &  &  \tabularnewline
Harmonic Mean & 6.31406496557119 &  &  \tabularnewline
Quadratic Mean & 6.36013488767917 &  &  \tabularnewline
Winsorized Mean ( 1 / 25 ) & 6.34473684210526 & 0.0504156316904215 & 125.848603486024 \tabularnewline
Winsorized Mean ( 2 / 25 ) & 6.34473684210526 & 0.0492182656452886 & 128.910207601202 \tabularnewline
Winsorized Mean ( 3 / 25 ) & 6.34078947368421 & 0.04834734091924 & 131.150738657498 \tabularnewline
Winsorized Mean ( 4 / 25 ) & 6.34605263157895 & 0.0473301502317528 & 134.080551202677 \tabularnewline
Winsorized Mean ( 5 / 25 ) & 6.33947368421053 & 0.0460007226246986 & 137.812480380618 \tabularnewline
Winsorized Mean ( 6 / 25 ) & 6.33947368421053 & 0.0460007226246986 & 137.812480380618 \tabularnewline
Winsorized Mean ( 7 / 25 ) & 6.33026315789474 & 0.0443281122176358 & 142.804708822594 \tabularnewline
Winsorized Mean ( 8 / 25 ) & 6.33026315789474 & 0.0443281122176358 & 142.804708822594 \tabularnewline
Winsorized Mean ( 9 / 25 ) & 6.35394736842105 & 0.0402815002365996 & 157.738597894819 \tabularnewline
Winsorized Mean ( 10 / 25 ) & 6.35394736842105 & 0.0402815002365996 & 157.738597894819 \tabularnewline
Winsorized Mean ( 11 / 25 ) & 6.33947368421053 & 0.0377934807043337 & 167.739873810659 \tabularnewline
Winsorized Mean ( 12 / 25 ) & 6.33947368421053 & 0.0377934807043337 & 167.739873810659 \tabularnewline
Winsorized Mean ( 13 / 25 ) & 6.33947368421053 & 0.0377934807043337 & 167.739873810659 \tabularnewline
Winsorized Mean ( 14 / 25 ) & 6.33947368421053 & 0.0377934807043337 & 167.739873810659 \tabularnewline
Winsorized Mean ( 15 / 25 ) & 6.35921052631579 & 0.0349022510498561 & 182.200584060666 \tabularnewline
Winsorized Mean ( 16 / 25 ) & 6.35921052631579 & 0.0349022510498561 & 182.200584060666 \tabularnewline
Winsorized Mean ( 17 / 25 ) & 6.38157894736842 & 0.0320476906859296 & 199.127575522009 \tabularnewline
Winsorized Mean ( 18 / 25 ) & 6.35789473684211 & 0.0280515288944269 & 226.650560144879 \tabularnewline
Winsorized Mean ( 19 / 25 ) & 6.3328947368421 & 0.0241623280723582 & 262.097870614006 \tabularnewline
Winsorized Mean ( 20 / 25 ) & 6.33289473684211 & 0.0241623280723582 & 262.097870614006 \tabularnewline
Winsorized Mean ( 21 / 25 ) & 6.30526315789474 & 0.0203387743806168 & 310.011952534552 \tabularnewline
Winsorized Mean ( 22 / 25 ) & 6.30526315789474 & 0.0203387743806168 & 310.011952534552 \tabularnewline
Winsorized Mean ( 23 / 25 ) & 6.30526315789474 & 0.0203387743806168 & 310.011952534552 \tabularnewline
Winsorized Mean ( 24 / 25 ) & 6.33684210526316 & 0.0164201529218212 & 385.918580383132 \tabularnewline
Winsorized Mean ( 25 / 25 ) & 6.33684210526316 & 0.0164201529218212 & 385.918580383132 \tabularnewline
Trimmed Mean ( 1 / 25 ) & 6.34324324324324 & 0.0487944665610681 & 129.999233320943 \tabularnewline
Trimmed Mean ( 2 / 25 ) & 6.34166666666667 & 0.0468803791905702 & 135.273365449703 \tabularnewline
Trimmed Mean ( 3 / 25 ) & 6.34 & 0.0453831172264813 & 139.699526772493 \tabularnewline
Trimmed Mean ( 4 / 25 ) & 6.33970588235294 & 0.0440059311332073 & 144.064804881925 \tabularnewline
Trimmed Mean ( 5 / 25 ) & 6.33787878787879 & 0.042736529606118 & 148.301203824736 \tabularnewline
Trimmed Mean ( 6 / 25 ) & 6.3375 & 0.0416368941250539 & 152.208759398953 \tabularnewline
Trimmed Mean ( 7 / 25 ) & 6.33709677419355 & 0.0403077709450702 & 157.217743021054 \tabularnewline
Trimmed Mean ( 8 / 25 ) & 6.33833333333333 & 0.0391355508086933 & 161.95845471339 \tabularnewline
Trimmed Mean ( 9 / 25 ) & 6.33965517241379 & 0.0377000335514263 & 168.160464997091 \tabularnewline
Trimmed Mean ( 10 / 25 ) & 6.3375 & 0.03688896114755 & 171.799362271304 \tabularnewline
Trimmed Mean ( 11 / 25 ) & 6.33518518518519 & 0.0358735849600433 & 176.597493454904 \tabularnewline
Trimmed Mean ( 12 / 25 ) & 6.33461538461538 & 0.0351558280050346 & 180.186778240815 \tabularnewline
Trimmed Mean ( 13 / 25 ) & 6.334 & 0.034239254235632 & 184.992346983082 \tabularnewline
Trimmed Mean ( 14 / 25 ) & 6.33333333333333 & 0.0330663063352593 & 191.534345237102 \tabularnewline
Trimmed Mean ( 15 / 25 ) & 6.33260869565217 & 0.0315546221954021 & 200.687197471023 \tabularnewline
Trimmed Mean ( 16 / 25 ) & 6.32954545454545 & 0.0302525566257593 & 209.223489202761 \tabularnewline
Trimmed Mean ( 17 / 25 ) & 6.32619047619048 & 0.0285254178501428 & 221.773805713377 \tabularnewline
Trimmed Mean ( 18 / 25 ) & 6.32 & 0.0268423698751213 & 235.448659317434 \tabularnewline
Trimmed Mean ( 19 / 25 ) & 6.31578947368421 & 0.0257259647081156 & 245.502531988307 \tabularnewline
Trimmed Mean ( 20 / 25 ) & 6.31388888888889 & 0.0252457061500039 & 250.09753545309 \tabularnewline
Trimmed Mean ( 21 / 25 ) & 6.31176470588235 & 0.0245329658829748 & 257.276871291887 \tabularnewline
Trimmed Mean ( 22 / 25 ) & 6.3125 & 0.0244907816759036 & 257.750041772283 \tabularnewline
Trimmed Mean ( 23 / 25 ) & 6.31333333333333 & 0.0243222301861086 & 259.570495181775 \tabularnewline
Trimmed Mean ( 24 / 25 ) & 6.31428571428571 & 0.0239677283659389 & 263.449485820237 \tabularnewline
Trimmed Mean ( 25 / 25 ) & 6.31153846153846 & 0.0243859499756113 & 258.818642203839 \tabularnewline
Median & 6.3 &  &  \tabularnewline
Midrange & 6.4 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 6.305 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 6.305 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 6.305 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 6.305 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 6.305 &  &  \tabularnewline
Midmean - Closest Observation & 6.305 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 6.305 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 6.31463414634147 &  &  \tabularnewline
Number of observations & 76 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=207601&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]6.34473684210526[/C][C]0.0510725228024903[/C][C]124.22994780661[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]6.32937438623749[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]6.31406496557119[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]6.36013488767917[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 25 )[/C][C]6.34473684210526[/C][C]0.0504156316904215[/C][C]125.848603486024[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 25 )[/C][C]6.34473684210526[/C][C]0.0492182656452886[/C][C]128.910207601202[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 25 )[/C][C]6.34078947368421[/C][C]0.04834734091924[/C][C]131.150738657498[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 25 )[/C][C]6.34605263157895[/C][C]0.0473301502317528[/C][C]134.080551202677[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 25 )[/C][C]6.33947368421053[/C][C]0.0460007226246986[/C][C]137.812480380618[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 25 )[/C][C]6.33947368421053[/C][C]0.0460007226246986[/C][C]137.812480380618[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 25 )[/C][C]6.33026315789474[/C][C]0.0443281122176358[/C][C]142.804708822594[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 25 )[/C][C]6.33026315789474[/C][C]0.0443281122176358[/C][C]142.804708822594[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 25 )[/C][C]6.35394736842105[/C][C]0.0402815002365996[/C][C]157.738597894819[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 25 )[/C][C]6.35394736842105[/C][C]0.0402815002365996[/C][C]157.738597894819[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 25 )[/C][C]6.33947368421053[/C][C]0.0377934807043337[/C][C]167.739873810659[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 25 )[/C][C]6.33947368421053[/C][C]0.0377934807043337[/C][C]167.739873810659[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 25 )[/C][C]6.33947368421053[/C][C]0.0377934807043337[/C][C]167.739873810659[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 25 )[/C][C]6.33947368421053[/C][C]0.0377934807043337[/C][C]167.739873810659[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 25 )[/C][C]6.35921052631579[/C][C]0.0349022510498561[/C][C]182.200584060666[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 25 )[/C][C]6.35921052631579[/C][C]0.0349022510498561[/C][C]182.200584060666[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 25 )[/C][C]6.38157894736842[/C][C]0.0320476906859296[/C][C]199.127575522009[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 25 )[/C][C]6.35789473684211[/C][C]0.0280515288944269[/C][C]226.650560144879[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 25 )[/C][C]6.3328947368421[/C][C]0.0241623280723582[/C][C]262.097870614006[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 25 )[/C][C]6.33289473684211[/C][C]0.0241623280723582[/C][C]262.097870614006[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 25 )[/C][C]6.30526315789474[/C][C]0.0203387743806168[/C][C]310.011952534552[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 25 )[/C][C]6.30526315789474[/C][C]0.0203387743806168[/C][C]310.011952534552[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 25 )[/C][C]6.30526315789474[/C][C]0.0203387743806168[/C][C]310.011952534552[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 25 )[/C][C]6.33684210526316[/C][C]0.0164201529218212[/C][C]385.918580383132[/C][/ROW]
[ROW][C]Winsorized Mean ( 25 / 25 )[/C][C]6.33684210526316[/C][C]0.0164201529218212[/C][C]385.918580383132[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 25 )[/C][C]6.34324324324324[/C][C]0.0487944665610681[/C][C]129.999233320943[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 25 )[/C][C]6.34166666666667[/C][C]0.0468803791905702[/C][C]135.273365449703[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 25 )[/C][C]6.34[/C][C]0.0453831172264813[/C][C]139.699526772493[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 25 )[/C][C]6.33970588235294[/C][C]0.0440059311332073[/C][C]144.064804881925[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 25 )[/C][C]6.33787878787879[/C][C]0.042736529606118[/C][C]148.301203824736[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 25 )[/C][C]6.3375[/C][C]0.0416368941250539[/C][C]152.208759398953[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 25 )[/C][C]6.33709677419355[/C][C]0.0403077709450702[/C][C]157.217743021054[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 25 )[/C][C]6.33833333333333[/C][C]0.0391355508086933[/C][C]161.95845471339[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 25 )[/C][C]6.33965517241379[/C][C]0.0377000335514263[/C][C]168.160464997091[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 25 )[/C][C]6.3375[/C][C]0.03688896114755[/C][C]171.799362271304[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 25 )[/C][C]6.33518518518519[/C][C]0.0358735849600433[/C][C]176.597493454904[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 25 )[/C][C]6.33461538461538[/C][C]0.0351558280050346[/C][C]180.186778240815[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 25 )[/C][C]6.334[/C][C]0.034239254235632[/C][C]184.992346983082[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 25 )[/C][C]6.33333333333333[/C][C]0.0330663063352593[/C][C]191.534345237102[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 25 )[/C][C]6.33260869565217[/C][C]0.0315546221954021[/C][C]200.687197471023[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 25 )[/C][C]6.32954545454545[/C][C]0.0302525566257593[/C][C]209.223489202761[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 25 )[/C][C]6.32619047619048[/C][C]0.0285254178501428[/C][C]221.773805713377[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 25 )[/C][C]6.32[/C][C]0.0268423698751213[/C][C]235.448659317434[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 25 )[/C][C]6.31578947368421[/C][C]0.0257259647081156[/C][C]245.502531988307[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 25 )[/C][C]6.31388888888889[/C][C]0.0252457061500039[/C][C]250.09753545309[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 25 )[/C][C]6.31176470588235[/C][C]0.0245329658829748[/C][C]257.276871291887[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 25 )[/C][C]6.3125[/C][C]0.0244907816759036[/C][C]257.750041772283[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 25 )[/C][C]6.31333333333333[/C][C]0.0243222301861086[/C][C]259.570495181775[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 25 )[/C][C]6.31428571428571[/C][C]0.0239677283659389[/C][C]263.449485820237[/C][/ROW]
[ROW][C]Trimmed Mean ( 25 / 25 )[/C][C]6.31153846153846[/C][C]0.0243859499756113[/C][C]258.818642203839[/C][/ROW]
[ROW][C]Median[/C][C]6.3[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]6.4[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]6.305[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]6.305[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]6.305[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]6.305[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]6.305[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]6.305[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]6.305[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]6.31463414634147[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]76[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=207601&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=207601&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 Mean6.344736842105260.0510725228024903124.22994780661
Geometric Mean6.32937438623749
Harmonic Mean6.31406496557119
Quadratic Mean6.36013488767917
Winsorized Mean ( 1 / 25 )6.344736842105260.0504156316904215125.848603486024
Winsorized Mean ( 2 / 25 )6.344736842105260.0492182656452886128.910207601202
Winsorized Mean ( 3 / 25 )6.340789473684210.04834734091924131.150738657498
Winsorized Mean ( 4 / 25 )6.346052631578950.0473301502317528134.080551202677
Winsorized Mean ( 5 / 25 )6.339473684210530.0460007226246986137.812480380618
Winsorized Mean ( 6 / 25 )6.339473684210530.0460007226246986137.812480380618
Winsorized Mean ( 7 / 25 )6.330263157894740.0443281122176358142.804708822594
Winsorized Mean ( 8 / 25 )6.330263157894740.0443281122176358142.804708822594
Winsorized Mean ( 9 / 25 )6.353947368421050.0402815002365996157.738597894819
Winsorized Mean ( 10 / 25 )6.353947368421050.0402815002365996157.738597894819
Winsorized Mean ( 11 / 25 )6.339473684210530.0377934807043337167.739873810659
Winsorized Mean ( 12 / 25 )6.339473684210530.0377934807043337167.739873810659
Winsorized Mean ( 13 / 25 )6.339473684210530.0377934807043337167.739873810659
Winsorized Mean ( 14 / 25 )6.339473684210530.0377934807043337167.739873810659
Winsorized Mean ( 15 / 25 )6.359210526315790.0349022510498561182.200584060666
Winsorized Mean ( 16 / 25 )6.359210526315790.0349022510498561182.200584060666
Winsorized Mean ( 17 / 25 )6.381578947368420.0320476906859296199.127575522009
Winsorized Mean ( 18 / 25 )6.357894736842110.0280515288944269226.650560144879
Winsorized Mean ( 19 / 25 )6.33289473684210.0241623280723582262.097870614006
Winsorized Mean ( 20 / 25 )6.332894736842110.0241623280723582262.097870614006
Winsorized Mean ( 21 / 25 )6.305263157894740.0203387743806168310.011952534552
Winsorized Mean ( 22 / 25 )6.305263157894740.0203387743806168310.011952534552
Winsorized Mean ( 23 / 25 )6.305263157894740.0203387743806168310.011952534552
Winsorized Mean ( 24 / 25 )6.336842105263160.0164201529218212385.918580383132
Winsorized Mean ( 25 / 25 )6.336842105263160.0164201529218212385.918580383132
Trimmed Mean ( 1 / 25 )6.343243243243240.0487944665610681129.999233320943
Trimmed Mean ( 2 / 25 )6.341666666666670.0468803791905702135.273365449703
Trimmed Mean ( 3 / 25 )6.340.0453831172264813139.699526772493
Trimmed Mean ( 4 / 25 )6.339705882352940.0440059311332073144.064804881925
Trimmed Mean ( 5 / 25 )6.337878787878790.042736529606118148.301203824736
Trimmed Mean ( 6 / 25 )6.33750.0416368941250539152.208759398953
Trimmed Mean ( 7 / 25 )6.337096774193550.0403077709450702157.217743021054
Trimmed Mean ( 8 / 25 )6.338333333333330.0391355508086933161.95845471339
Trimmed Mean ( 9 / 25 )6.339655172413790.0377000335514263168.160464997091
Trimmed Mean ( 10 / 25 )6.33750.03688896114755171.799362271304
Trimmed Mean ( 11 / 25 )6.335185185185190.0358735849600433176.597493454904
Trimmed Mean ( 12 / 25 )6.334615384615380.0351558280050346180.186778240815
Trimmed Mean ( 13 / 25 )6.3340.034239254235632184.992346983082
Trimmed Mean ( 14 / 25 )6.333333333333330.0330663063352593191.534345237102
Trimmed Mean ( 15 / 25 )6.332608695652170.0315546221954021200.687197471023
Trimmed Mean ( 16 / 25 )6.329545454545450.0302525566257593209.223489202761
Trimmed Mean ( 17 / 25 )6.326190476190480.0285254178501428221.773805713377
Trimmed Mean ( 18 / 25 )6.320.0268423698751213235.448659317434
Trimmed Mean ( 19 / 25 )6.315789473684210.0257259647081156245.502531988307
Trimmed Mean ( 20 / 25 )6.313888888888890.0252457061500039250.09753545309
Trimmed Mean ( 21 / 25 )6.311764705882350.0245329658829748257.276871291887
Trimmed Mean ( 22 / 25 )6.31250.0244907816759036257.750041772283
Trimmed Mean ( 23 / 25 )6.313333333333330.0243222301861086259.570495181775
Trimmed Mean ( 24 / 25 )6.314285714285710.0239677283659389263.449485820237
Trimmed Mean ( 25 / 25 )6.311538461538460.0243859499756113258.818642203839
Median6.3
Midrange6.4
Midmean - Weighted Average at Xnp6.305
Midmean - Weighted Average at X(n+1)p6.305
Midmean - Empirical Distribution Function6.305
Midmean - Empirical Distribution Function - Averaging6.305
Midmean - Empirical Distribution Function - Interpolation6.305
Midmean - Closest Observation6.305
Midmean - True Basic - Statistics Graphics Toolkit6.305
Midmean - MS Excel (old versions)6.31463414634147
Number of observations76



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')