Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationMon, 22 Oct 2007 02:25:13 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2007/Oct/22/iqznocstn6c4cjk1193044876.htm/, Retrieved Mon, 06 May 2024 09:59:47 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=1495, Retrieved Mon, 06 May 2024 09:59:47 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsinvestigating associations, q8
Estimated Impact203
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [central tendancy ...] [2007-10-22 09:25:13] [e2f7a6e26aa7cf06a3d27eb5298a4843] [Current]
Feedback Forum

Post a new message
Dataseries X:
104,6
95,3
102,8
103,3
100,2
107,9
107,5
119,8
112
102,1
105,3
101,3
108,4
107,4
109,1
109,5
111,4
110,1
117
129,6
113,5
113,3
110,1
107,4
110,1
112,5
106
117,6
117,8
113,5
121,2
130,4
115,2
117,9
110,7
107,6
124,3
115,1
112,5
127,9
117,4
119,3
130,4
126
125,4
130,5
115,9
108,7
124
119,4
118,6
131,3
111,1
124,8
132,3
126,7
131,7
130,9
122,1
113,2
133,6




Summary of compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\begin{tabular}{lllllllll}
\hline
Summary of compuational 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' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=1495&T=0

[TABLE]
[ROW][C]Summary of compuational 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' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=1495&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=1495&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 compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean115.7786885245901.2182561996785395.0364041284101
Geometric Mean115.396232893287
Harmonic Mean115.016266338513
Quadratic Mean116.162617078634
Winsorized Mean ( 1 / 20 )115.8377049180331.1931548022596897.0852270792116
Winsorized Mean ( 2 / 20 )115.8540983606561.1810493013832198.0942101442935
Winsorized Mean ( 3 / 20 )115.8737704918031.1687808361014399.1407173292734
Winsorized Mean ( 4 / 20 )115.8934426229511.15420558834957100.4097049891
Winsorized Mean ( 5 / 20 )115.9016393442621.13950063793008101.712658585957
Winsorized Mean ( 6 / 20 )116.0196721311481.11468297748053104.083111050445
Winsorized Mean ( 7 / 20 )116.11.10125859442879105.424829905840
Winsorized Mean ( 8 / 20 )116.0868852459021.06403827997678109.100290309514
Winsorized Mean ( 9 / 20 )116.0426229508200.980633393551636118.334357889383
Winsorized Mean ( 10 / 20 )115.8459016393440.941901268045572122.991555027548
Winsorized Mean ( 11 / 20 )115.7377049180330.915280613109755126.450515022713
Winsorized Mean ( 12 / 20 )115.6393442622950.890512465858767129.857075218793
Winsorized Mean ( 13 / 20 )115.5754098360660.857791852348034134.735961317074
Winsorized Mean ( 14 / 20 )115.5754098360660.820411251457166140.874969267898
Winsorized Mean ( 15 / 20 )115.5754098360660.796689378478092145.069600471953
Winsorized Mean ( 16 / 20 )115.1819672131150.696146725460992165.456451923753
Winsorized Mean ( 17 / 20 )115.0426229508200.639032991342394180.026108995020
Winsorized Mean ( 18 / 20 )114.8065573770490.548947671132552209.139346816406
Winsorized Mean ( 19 / 20 )114.6819672131150.530261860234397216.274214333312
Winsorized Mean ( 20 / 20 )114.6491803278690.525412265665337218.208039324485
Trimmed Mean ( 1 / 20 )115.8237288135591.1713119096186898.8837626104781
Trimmed Mean ( 2 / 20 )115.8087719298251.14424921676229101.209395849543
Trimmed Mean ( 3 / 20 )115.7836363636361.11859629338959103.507974278
Trimmed Mean ( 4 / 20 )115.7490566037741.09228931849968105.969228704682
Trimmed Mean ( 5 / 20 )115.7058823529411.06473751442557108.670804574182
Trimmed Mean ( 6 / 20 )115.6571428571431.03467928581266111.780669085593
Trimmed Mean ( 7 / 20 )115.5787234042551.00370698744864115.151856915981
Trimmed Mean ( 8 / 20 )115.4777777777780.967209298528759119.392749794107
Trimmed Mean ( 9 / 20 )115.3697674418600.930149221073228124.033611842134
Trimmed Mean ( 10 / 20 )115.2585365853660.904419876116231127.439190169405
Trimmed Mean ( 11 / 20 )115.1666666666670.880316570875083130.824149489978
Trimmed Mean ( 12 / 20 )115.0810810810810.854275924349089134.711839349525
Trimmed Mean ( 13 / 20 )1150.82472302455242139.44075353348
Trimmed Mean ( 14 / 20 )114.9181818181820.79220222569189145.061675025989
Trimmed Mean ( 15 / 20 )114.8258064516130.756306357422826151.824462831294
Trimmed Mean ( 16 / 20 )114.7206896551720.710536107012233161.456523494023
Trimmed Mean ( 17 / 20 )114.6555555555560.679142523997161168.823997179177
Trimmed Mean ( 18 / 20 )114.60.651024833115706176.030151494439
Trimmed Mean ( 19 / 20 )114.5695652173910.639584684371474179.131189374836
Trimmed Mean ( 20 / 20 )114.5523809523810.624256473834847183.502111317610
Median113.5
Midrange114.45
Midmean - Weighted Average at Xnp114.52
Midmean - Weighted Average at X(n+1)p114.825806451613
Midmean - Empirical Distribution Function114.825806451613
Midmean - Empirical Distribution Function - Averaging114.825806451613
Midmean - Empirical Distribution Function - Interpolation114.825806451613
Midmean - Closest Observation114.625
Midmean - True Basic - Statistics Graphics Toolkit114.825806451613
Midmean - MS Excel (old versions)114.825806451613
Number of observations61

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 115.778688524590 & 1.21825619967853 & 95.0364041284101 \tabularnewline
Geometric Mean & 115.396232893287 &  &  \tabularnewline
Harmonic Mean & 115.016266338513 &  &  \tabularnewline
Quadratic Mean & 116.162617078634 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 115.837704918033 & 1.19315480225968 & 97.0852270792116 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 115.854098360656 & 1.18104930138321 & 98.0942101442935 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 115.873770491803 & 1.16878083610143 & 99.1407173292734 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 115.893442622951 & 1.15420558834957 & 100.4097049891 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 115.901639344262 & 1.13950063793008 & 101.712658585957 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 116.019672131148 & 1.11468297748053 & 104.083111050445 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 116.1 & 1.10125859442879 & 105.424829905840 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 116.086885245902 & 1.06403827997678 & 109.100290309514 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 116.042622950820 & 0.980633393551636 & 118.334357889383 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 115.845901639344 & 0.941901268045572 & 122.991555027548 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 115.737704918033 & 0.915280613109755 & 126.450515022713 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 115.639344262295 & 0.890512465858767 & 129.857075218793 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 115.575409836066 & 0.857791852348034 & 134.735961317074 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 115.575409836066 & 0.820411251457166 & 140.874969267898 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 115.575409836066 & 0.796689378478092 & 145.069600471953 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 115.181967213115 & 0.696146725460992 & 165.456451923753 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 115.042622950820 & 0.639032991342394 & 180.026108995020 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 114.806557377049 & 0.548947671132552 & 209.139346816406 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 114.681967213115 & 0.530261860234397 & 216.274214333312 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 114.649180327869 & 0.525412265665337 & 218.208039324485 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 115.823728813559 & 1.17131190961868 & 98.8837626104781 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 115.808771929825 & 1.14424921676229 & 101.209395849543 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 115.783636363636 & 1.11859629338959 & 103.507974278 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 115.749056603774 & 1.09228931849968 & 105.969228704682 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 115.705882352941 & 1.06473751442557 & 108.670804574182 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 115.657142857143 & 1.03467928581266 & 111.780669085593 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 115.578723404255 & 1.00370698744864 & 115.151856915981 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 115.477777777778 & 0.967209298528759 & 119.392749794107 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 115.369767441860 & 0.930149221073228 & 124.033611842134 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 115.258536585366 & 0.904419876116231 & 127.439190169405 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 115.166666666667 & 0.880316570875083 & 130.824149489978 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 115.081081081081 & 0.854275924349089 & 134.711839349525 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 115 & 0.82472302455242 & 139.44075353348 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 114.918181818182 & 0.79220222569189 & 145.061675025989 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 114.825806451613 & 0.756306357422826 & 151.824462831294 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 114.720689655172 & 0.710536107012233 & 161.456523494023 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 114.655555555556 & 0.679142523997161 & 168.823997179177 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 114.6 & 0.651024833115706 & 176.030151494439 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 114.569565217391 & 0.639584684371474 & 179.131189374836 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 114.552380952381 & 0.624256473834847 & 183.502111317610 \tabularnewline
Median & 113.5 &  &  \tabularnewline
Midrange & 114.45 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 114.52 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 114.825806451613 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 114.825806451613 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 114.825806451613 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 114.825806451613 &  &  \tabularnewline
Midmean - Closest Observation & 114.625 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 114.825806451613 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 114.825806451613 &  &  \tabularnewline
Number of observations & 61 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=1495&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]115.778688524590[/C][C]1.21825619967853[/C][C]95.0364041284101[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]115.396232893287[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]115.016266338513[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]116.162617078634[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]115.837704918033[/C][C]1.19315480225968[/C][C]97.0852270792116[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]115.854098360656[/C][C]1.18104930138321[/C][C]98.0942101442935[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]115.873770491803[/C][C]1.16878083610143[/C][C]99.1407173292734[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]115.893442622951[/C][C]1.15420558834957[/C][C]100.4097049891[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]115.901639344262[/C][C]1.13950063793008[/C][C]101.712658585957[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]116.019672131148[/C][C]1.11468297748053[/C][C]104.083111050445[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]116.1[/C][C]1.10125859442879[/C][C]105.424829905840[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]116.086885245902[/C][C]1.06403827997678[/C][C]109.100290309514[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]116.042622950820[/C][C]0.980633393551636[/C][C]118.334357889383[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]115.845901639344[/C][C]0.941901268045572[/C][C]122.991555027548[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]115.737704918033[/C][C]0.915280613109755[/C][C]126.450515022713[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]115.639344262295[/C][C]0.890512465858767[/C][C]129.857075218793[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]115.575409836066[/C][C]0.857791852348034[/C][C]134.735961317074[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]115.575409836066[/C][C]0.820411251457166[/C][C]140.874969267898[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]115.575409836066[/C][C]0.796689378478092[/C][C]145.069600471953[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]115.181967213115[/C][C]0.696146725460992[/C][C]165.456451923753[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]115.042622950820[/C][C]0.639032991342394[/C][C]180.026108995020[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]114.806557377049[/C][C]0.548947671132552[/C][C]209.139346816406[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]114.681967213115[/C][C]0.530261860234397[/C][C]216.274214333312[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]114.649180327869[/C][C]0.525412265665337[/C][C]218.208039324485[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]115.823728813559[/C][C]1.17131190961868[/C][C]98.8837626104781[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]115.808771929825[/C][C]1.14424921676229[/C][C]101.209395849543[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]115.783636363636[/C][C]1.11859629338959[/C][C]103.507974278[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]115.749056603774[/C][C]1.09228931849968[/C][C]105.969228704682[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]115.705882352941[/C][C]1.06473751442557[/C][C]108.670804574182[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]115.657142857143[/C][C]1.03467928581266[/C][C]111.780669085593[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]115.578723404255[/C][C]1.00370698744864[/C][C]115.151856915981[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]115.477777777778[/C][C]0.967209298528759[/C][C]119.392749794107[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]115.369767441860[/C][C]0.930149221073228[/C][C]124.033611842134[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]115.258536585366[/C][C]0.904419876116231[/C][C]127.439190169405[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]115.166666666667[/C][C]0.880316570875083[/C][C]130.824149489978[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]115.081081081081[/C][C]0.854275924349089[/C][C]134.711839349525[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]115[/C][C]0.82472302455242[/C][C]139.44075353348[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]114.918181818182[/C][C]0.79220222569189[/C][C]145.061675025989[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]114.825806451613[/C][C]0.756306357422826[/C][C]151.824462831294[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]114.720689655172[/C][C]0.710536107012233[/C][C]161.456523494023[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]114.655555555556[/C][C]0.679142523997161[/C][C]168.823997179177[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]114.6[/C][C]0.651024833115706[/C][C]176.030151494439[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]114.569565217391[/C][C]0.639584684371474[/C][C]179.131189374836[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]114.552380952381[/C][C]0.624256473834847[/C][C]183.502111317610[/C][/ROW]
[ROW][C]Median[/C][C]113.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]114.45[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]114.52[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]114.825806451613[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]114.825806451613[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]114.825806451613[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]114.825806451613[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]114.625[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]114.825806451613[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]114.825806451613[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]61[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=1495&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=1495&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 Mean115.7786885245901.2182561996785395.0364041284101
Geometric Mean115.396232893287
Harmonic Mean115.016266338513
Quadratic Mean116.162617078634
Winsorized Mean ( 1 / 20 )115.8377049180331.1931548022596897.0852270792116
Winsorized Mean ( 2 / 20 )115.8540983606561.1810493013832198.0942101442935
Winsorized Mean ( 3 / 20 )115.8737704918031.1687808361014399.1407173292734
Winsorized Mean ( 4 / 20 )115.8934426229511.15420558834957100.4097049891
Winsorized Mean ( 5 / 20 )115.9016393442621.13950063793008101.712658585957
Winsorized Mean ( 6 / 20 )116.0196721311481.11468297748053104.083111050445
Winsorized Mean ( 7 / 20 )116.11.10125859442879105.424829905840
Winsorized Mean ( 8 / 20 )116.0868852459021.06403827997678109.100290309514
Winsorized Mean ( 9 / 20 )116.0426229508200.980633393551636118.334357889383
Winsorized Mean ( 10 / 20 )115.8459016393440.941901268045572122.991555027548
Winsorized Mean ( 11 / 20 )115.7377049180330.915280613109755126.450515022713
Winsorized Mean ( 12 / 20 )115.6393442622950.890512465858767129.857075218793
Winsorized Mean ( 13 / 20 )115.5754098360660.857791852348034134.735961317074
Winsorized Mean ( 14 / 20 )115.5754098360660.820411251457166140.874969267898
Winsorized Mean ( 15 / 20 )115.5754098360660.796689378478092145.069600471953
Winsorized Mean ( 16 / 20 )115.1819672131150.696146725460992165.456451923753
Winsorized Mean ( 17 / 20 )115.0426229508200.639032991342394180.026108995020
Winsorized Mean ( 18 / 20 )114.8065573770490.548947671132552209.139346816406
Winsorized Mean ( 19 / 20 )114.6819672131150.530261860234397216.274214333312
Winsorized Mean ( 20 / 20 )114.6491803278690.525412265665337218.208039324485
Trimmed Mean ( 1 / 20 )115.8237288135591.1713119096186898.8837626104781
Trimmed Mean ( 2 / 20 )115.8087719298251.14424921676229101.209395849543
Trimmed Mean ( 3 / 20 )115.7836363636361.11859629338959103.507974278
Trimmed Mean ( 4 / 20 )115.7490566037741.09228931849968105.969228704682
Trimmed Mean ( 5 / 20 )115.7058823529411.06473751442557108.670804574182
Trimmed Mean ( 6 / 20 )115.6571428571431.03467928581266111.780669085593
Trimmed Mean ( 7 / 20 )115.5787234042551.00370698744864115.151856915981
Trimmed Mean ( 8 / 20 )115.4777777777780.967209298528759119.392749794107
Trimmed Mean ( 9 / 20 )115.3697674418600.930149221073228124.033611842134
Trimmed Mean ( 10 / 20 )115.2585365853660.904419876116231127.439190169405
Trimmed Mean ( 11 / 20 )115.1666666666670.880316570875083130.824149489978
Trimmed Mean ( 12 / 20 )115.0810810810810.854275924349089134.711839349525
Trimmed Mean ( 13 / 20 )1150.82472302455242139.44075353348
Trimmed Mean ( 14 / 20 )114.9181818181820.79220222569189145.061675025989
Trimmed Mean ( 15 / 20 )114.8258064516130.756306357422826151.824462831294
Trimmed Mean ( 16 / 20 )114.7206896551720.710536107012233161.456523494023
Trimmed Mean ( 17 / 20 )114.6555555555560.679142523997161168.823997179177
Trimmed Mean ( 18 / 20 )114.60.651024833115706176.030151494439
Trimmed Mean ( 19 / 20 )114.5695652173910.639584684371474179.131189374836
Trimmed Mean ( 20 / 20 )114.5523809523810.624256473834847183.502111317610
Median113.5
Midrange114.45
Midmean - Weighted Average at Xnp114.52
Midmean - Weighted Average at X(n+1)p114.825806451613
Midmean - Empirical Distribution Function114.825806451613
Midmean - Empirical Distribution Function - Averaging114.825806451613
Midmean - Empirical Distribution Function - Interpolation114.825806451613
Midmean - Closest Observation114.625
Midmean - True Basic - Statistics Graphics Toolkit114.825806451613
Midmean - MS Excel (old versions)114.825806451613
Number of observations61



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')