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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 01:56:59 -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/i0r1d6dfvwmbq1f1193043176.htm/, Retrieved Mon, 06 May 2024 03:02:13 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=1485, Retrieved Mon, 06 May 2024 03:02:13 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsvraag 8, deel 1, ws1
Estimated Impact172
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [vraag 8, deel 1, ...] [2007-10-22 08:56:59] [234bcf6fb77cd83fa17f2489a043102b] [Current]
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Dataseries X:
19,1
20,8
20,8
20,8
19,0
19,0
19,0
15,2
15,2
15,2
19,9
19,9
19,9
19,0
19,0
19,0
19,9
19,9
19,9
17,5
17,5
17,5
26,6
26,6
26,6
20,8
20,8
20,8
18,9
18,9
18,9
19,5
19,5
19,5
27,1
27,1
27,1
24,1
24,1
24,1
21,3
21,3
21,3
19,1
19,1
19,1
26,2
26,2
26,2
21,7
21,7
21,7
19,4
19,4
19,4
19,5
19,5
19,5
28,7
28,7
28,7
21,8
21,8
21,8
20,0
20,0
20,0
22,6
22,6
22,6
24,6
24,6
24,6




Summary of compuational 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 compuational 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=1485&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]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=1485&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=1485&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 time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean21.35205479452050.37918697365983956.3100957515357
Geometric Mean21.1196020350804
Harmonic Mean20.8962949280357
Quadratic Mean21.5931147067700
Winsorized Mean ( 1 / 24 )21.35205479452050.37918697365983956.3100957515357
Winsorized Mean ( 2 / 24 )21.35205479452060.37918697365983956.3100957515357
Winsorized Mean ( 3 / 24 )21.38082191780820.34449717142475962.0638533239103
Winsorized Mean ( 4 / 24 )21.38082191780820.34449717142475962.0638533239103
Winsorized Mean ( 5 / 24 )21.38082191780820.34449717142475962.0638533239103
Winsorized Mean ( 6 / 24 )21.45479452054790.31967473656667767.1144512418265
Winsorized Mean ( 7 / 24 )21.45479452054790.31967473656667767.1144512418264
Winsorized Mean ( 8 / 24 )21.45479452054790.31967473656667767.1144512418264
Winsorized Mean ( 9 / 24 )21.41780821917810.30747500217502669.6570715267002
Winsorized Mean ( 10 / 24 )21.41780821917810.30747500217502669.6570715267002
Winsorized Mean ( 11 / 24 )21.41780821917810.30747500217502669.6570715267002
Winsorized Mean ( 12 / 24 )21.15479452054790.25394183929970983.3056678603499
Winsorized Mean ( 13 / 24 )21.15479452054790.25394183929970983.3056678603499
Winsorized Mean ( 14 / 24 )21.15479452054790.25394183929970983.30566786035
Winsorized Mean ( 15 / 24 )21.07260273972600.2325350031258590.6212073729019
Winsorized Mean ( 16 / 24 )21.07260273972600.2325350031258590.6212073729019
Winsorized Mean ( 17 / 24 )21.07260273972600.2325350031258590.6212073729019
Winsorized Mean ( 18 / 24 )20.70273972602740.169630862128259122.04583214565
Winsorized Mean ( 19 / 24 )20.78082191780820.159809360530812130.035073344791
Winsorized Mean ( 20 / 24 )20.78082191780820.159809360530812130.035073344791
Winsorized Mean ( 21 / 24 )20.55068493150690.125423533431629163.85031077688
Winsorized Mean ( 22 / 24 )20.58082191780820.121643012873107169.190333515310
Winsorized Mean ( 23 / 24 )20.58082191780820.121643012873107169.190333515310
Winsorized Mean ( 24 / 24 )20.54794520547950.117107932449609175.461600044226
Trimmed Mean ( 1 / 24 )21.33521126760560.36547754704022658.3762571473574
Trimmed Mean ( 2 / 24 )21.31739130434780.34914312672608161.0563109296787
Trimmed Mean ( 3 / 24 )21.29850746268660.32946987103116564.644780404433
Trimmed Mean ( 4 / 24 )21.26769230769230.32220027584016666.0076787713321
Trimmed Mean ( 5 / 24 )21.23492063492060.31337450076128967.7621203490841
Trimmed Mean ( 6 / 24 )21.20.30261158353870670.0568026910588
Trimmed Mean ( 7 / 24 )21.14745762711860.2963577451402971.3578705935553
Trimmed Mean ( 8 / 24 )21.09122807017540.28845019183368173.1191334493429
Trimmed Mean ( 9 / 24 )21.03090909090910.27842598382062575.5350086307252
Trimmed Mean ( 10 / 24 )20.97169811320750.26885200981595778.004617215113
Trimmed Mean ( 11 / 24 )20.90784313725490.25650506454129281.5104496070842
Trimmed Mean ( 12 / 24 )20.83877551020410.24037273222158286.6935917298403
Trimmed Mean ( 13 / 24 )20.79787234042550.23390837967140288.9146099410491
Trimmed Mean ( 14 / 24 )20.75333333333330.22530787017686892.1110004592465
Trimmed Mean ( 15 / 24 )20.70465116279070.21378188987430496.8494158928254
Trimmed Mean ( 16 / 24 )20.66097560975610.204160328220921101.199757023308
Trimmed Mean ( 17 / 24 )20.61282051282050.190891773507152107.981712014679
Trimmed Mean ( 18 / 24 )20.55945945945950.172094475217225119.466121347059
Trimmed Mean ( 19 / 24 )20.54285714285710.166893802810550123.089394554551
Trimmed Mean ( 20 / 24 )20.51515151515150.161615964330688126.937654953287
Trimmed Mean ( 21 / 24 )20.48387096774190.153671677257910133.296332370756
Trimmed Mean ( 22 / 24 )20.47586206896550.153180981566382133.671046232931
Trimmed Mean ( 23 / 24 )20.46296296296300.152579730047326134.113246606322
Trimmed Mean ( 24 / 24 )20.4480.150678465614699135.706186790405
Median20
Midrange21.95
Midmean - Weighted Average at Xnp20.45
Midmean - Weighted Average at X(n+1)p20.45
Midmean - Empirical Distribution Function20.45
Midmean - Empirical Distribution Function - Averaging20.45
Midmean - Empirical Distribution Function - Interpolation20.45
Midmean - Closest Observation20.45
Midmean - True Basic - Statistics Graphics Toolkit20.45
Midmean - MS Excel (old versions)20.45
Number of observations73

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 21.3520547945205 & 0.379186973659839 & 56.3100957515357 \tabularnewline
Geometric Mean & 21.1196020350804 &  &  \tabularnewline
Harmonic Mean & 20.8962949280357 &  &  \tabularnewline
Quadratic Mean & 21.5931147067700 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 21.3520547945205 & 0.379186973659839 & 56.3100957515357 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 21.3520547945206 & 0.379186973659839 & 56.3100957515357 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 21.3808219178082 & 0.344497171424759 & 62.0638533239103 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 21.3808219178082 & 0.344497171424759 & 62.0638533239103 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 21.3808219178082 & 0.344497171424759 & 62.0638533239103 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 21.4547945205479 & 0.319674736566677 & 67.1144512418265 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 21.4547945205479 & 0.319674736566677 & 67.1144512418264 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 21.4547945205479 & 0.319674736566677 & 67.1144512418264 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 21.4178082191781 & 0.307475002175026 & 69.6570715267002 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 21.4178082191781 & 0.307475002175026 & 69.6570715267002 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 21.4178082191781 & 0.307475002175026 & 69.6570715267002 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 21.1547945205479 & 0.253941839299709 & 83.3056678603499 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 21.1547945205479 & 0.253941839299709 & 83.3056678603499 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 21.1547945205479 & 0.253941839299709 & 83.30566786035 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 21.0726027397260 & 0.23253500312585 & 90.6212073729019 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 21.0726027397260 & 0.23253500312585 & 90.6212073729019 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 21.0726027397260 & 0.23253500312585 & 90.6212073729019 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 20.7027397260274 & 0.169630862128259 & 122.04583214565 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 20.7808219178082 & 0.159809360530812 & 130.035073344791 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 20.7808219178082 & 0.159809360530812 & 130.035073344791 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 20.5506849315069 & 0.125423533431629 & 163.85031077688 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 20.5808219178082 & 0.121643012873107 & 169.190333515310 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 20.5808219178082 & 0.121643012873107 & 169.190333515310 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 20.5479452054795 & 0.117107932449609 & 175.461600044226 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 21.3352112676056 & 0.365477547040226 & 58.3762571473574 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 21.3173913043478 & 0.349143126726081 & 61.0563109296787 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 21.2985074626866 & 0.329469871031165 & 64.644780404433 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 21.2676923076923 & 0.322200275840166 & 66.0076787713321 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 21.2349206349206 & 0.313374500761289 & 67.7621203490841 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 21.2 & 0.302611583538706 & 70.0568026910588 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 21.1474576271186 & 0.29635774514029 & 71.3578705935553 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 21.0912280701754 & 0.288450191833681 & 73.1191334493429 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 21.0309090909091 & 0.278425983820625 & 75.5350086307252 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 20.9716981132075 & 0.268852009815957 & 78.004617215113 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 20.9078431372549 & 0.256505064541292 & 81.5104496070842 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 20.8387755102041 & 0.240372732221582 & 86.6935917298403 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 20.7978723404255 & 0.233908379671402 & 88.9146099410491 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 20.7533333333333 & 0.225307870176868 & 92.1110004592465 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 20.7046511627907 & 0.213781889874304 & 96.8494158928254 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 20.6609756097561 & 0.204160328220921 & 101.199757023308 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 20.6128205128205 & 0.190891773507152 & 107.981712014679 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 20.5594594594595 & 0.172094475217225 & 119.466121347059 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 20.5428571428571 & 0.166893802810550 & 123.089394554551 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 20.5151515151515 & 0.161615964330688 & 126.937654953287 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 20.4838709677419 & 0.153671677257910 & 133.296332370756 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 20.4758620689655 & 0.153180981566382 & 133.671046232931 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 20.4629629629630 & 0.152579730047326 & 134.113246606322 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 20.448 & 0.150678465614699 & 135.706186790405 \tabularnewline
Median & 20 &  &  \tabularnewline
Midrange & 21.95 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 20.45 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 20.45 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 20.45 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 20.45 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 20.45 &  &  \tabularnewline
Midmean - Closest Observation & 20.45 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 20.45 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 20.45 &  &  \tabularnewline
Number of observations & 73 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=1485&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]21.3520547945205[/C][C]0.379186973659839[/C][C]56.3100957515357[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]21.1196020350804[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]20.8962949280357[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]21.5931147067700[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]21.3520547945205[/C][C]0.379186973659839[/C][C]56.3100957515357[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]21.3520547945206[/C][C]0.379186973659839[/C][C]56.3100957515357[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]21.3808219178082[/C][C]0.344497171424759[/C][C]62.0638533239103[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]21.3808219178082[/C][C]0.344497171424759[/C][C]62.0638533239103[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]21.3808219178082[/C][C]0.344497171424759[/C][C]62.0638533239103[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]21.4547945205479[/C][C]0.319674736566677[/C][C]67.1144512418265[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]21.4547945205479[/C][C]0.319674736566677[/C][C]67.1144512418264[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]21.4547945205479[/C][C]0.319674736566677[/C][C]67.1144512418264[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]21.4178082191781[/C][C]0.307475002175026[/C][C]69.6570715267002[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]21.4178082191781[/C][C]0.307475002175026[/C][C]69.6570715267002[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]21.4178082191781[/C][C]0.307475002175026[/C][C]69.6570715267002[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]21.1547945205479[/C][C]0.253941839299709[/C][C]83.3056678603499[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]21.1547945205479[/C][C]0.253941839299709[/C][C]83.3056678603499[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]21.1547945205479[/C][C]0.253941839299709[/C][C]83.30566786035[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]21.0726027397260[/C][C]0.23253500312585[/C][C]90.6212073729019[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]21.0726027397260[/C][C]0.23253500312585[/C][C]90.6212073729019[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]21.0726027397260[/C][C]0.23253500312585[/C][C]90.6212073729019[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]20.7027397260274[/C][C]0.169630862128259[/C][C]122.04583214565[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]20.7808219178082[/C][C]0.159809360530812[/C][C]130.035073344791[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]20.7808219178082[/C][C]0.159809360530812[/C][C]130.035073344791[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]20.5506849315069[/C][C]0.125423533431629[/C][C]163.85031077688[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]20.5808219178082[/C][C]0.121643012873107[/C][C]169.190333515310[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]20.5808219178082[/C][C]0.121643012873107[/C][C]169.190333515310[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]20.5479452054795[/C][C]0.117107932449609[/C][C]175.461600044226[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]21.3352112676056[/C][C]0.365477547040226[/C][C]58.3762571473574[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]21.3173913043478[/C][C]0.349143126726081[/C][C]61.0563109296787[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]21.2985074626866[/C][C]0.329469871031165[/C][C]64.644780404433[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]21.2676923076923[/C][C]0.322200275840166[/C][C]66.0076787713321[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]21.2349206349206[/C][C]0.313374500761289[/C][C]67.7621203490841[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]21.2[/C][C]0.302611583538706[/C][C]70.0568026910588[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]21.1474576271186[/C][C]0.29635774514029[/C][C]71.3578705935553[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]21.0912280701754[/C][C]0.288450191833681[/C][C]73.1191334493429[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]21.0309090909091[/C][C]0.278425983820625[/C][C]75.5350086307252[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]20.9716981132075[/C][C]0.268852009815957[/C][C]78.004617215113[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]20.9078431372549[/C][C]0.256505064541292[/C][C]81.5104496070842[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]20.8387755102041[/C][C]0.240372732221582[/C][C]86.6935917298403[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]20.7978723404255[/C][C]0.233908379671402[/C][C]88.9146099410491[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]20.7533333333333[/C][C]0.225307870176868[/C][C]92.1110004592465[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]20.7046511627907[/C][C]0.213781889874304[/C][C]96.8494158928254[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]20.6609756097561[/C][C]0.204160328220921[/C][C]101.199757023308[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]20.6128205128205[/C][C]0.190891773507152[/C][C]107.981712014679[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]20.5594594594595[/C][C]0.172094475217225[/C][C]119.466121347059[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]20.5428571428571[/C][C]0.166893802810550[/C][C]123.089394554551[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]20.5151515151515[/C][C]0.161615964330688[/C][C]126.937654953287[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]20.4838709677419[/C][C]0.153671677257910[/C][C]133.296332370756[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]20.4758620689655[/C][C]0.153180981566382[/C][C]133.671046232931[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]20.4629629629630[/C][C]0.152579730047326[/C][C]134.113246606322[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]20.448[/C][C]0.150678465614699[/C][C]135.706186790405[/C][/ROW]
[ROW][C]Median[/C][C]20[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]21.95[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]20.45[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]20.45[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]20.45[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]20.45[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]20.45[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]20.45[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]20.45[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]20.45[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]73[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=1485&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=1485&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 Mean21.35205479452050.37918697365983956.3100957515357
Geometric Mean21.1196020350804
Harmonic Mean20.8962949280357
Quadratic Mean21.5931147067700
Winsorized Mean ( 1 / 24 )21.35205479452050.37918697365983956.3100957515357
Winsorized Mean ( 2 / 24 )21.35205479452060.37918697365983956.3100957515357
Winsorized Mean ( 3 / 24 )21.38082191780820.34449717142475962.0638533239103
Winsorized Mean ( 4 / 24 )21.38082191780820.34449717142475962.0638533239103
Winsorized Mean ( 5 / 24 )21.38082191780820.34449717142475962.0638533239103
Winsorized Mean ( 6 / 24 )21.45479452054790.31967473656667767.1144512418265
Winsorized Mean ( 7 / 24 )21.45479452054790.31967473656667767.1144512418264
Winsorized Mean ( 8 / 24 )21.45479452054790.31967473656667767.1144512418264
Winsorized Mean ( 9 / 24 )21.41780821917810.30747500217502669.6570715267002
Winsorized Mean ( 10 / 24 )21.41780821917810.30747500217502669.6570715267002
Winsorized Mean ( 11 / 24 )21.41780821917810.30747500217502669.6570715267002
Winsorized Mean ( 12 / 24 )21.15479452054790.25394183929970983.3056678603499
Winsorized Mean ( 13 / 24 )21.15479452054790.25394183929970983.3056678603499
Winsorized Mean ( 14 / 24 )21.15479452054790.25394183929970983.30566786035
Winsorized Mean ( 15 / 24 )21.07260273972600.2325350031258590.6212073729019
Winsorized Mean ( 16 / 24 )21.07260273972600.2325350031258590.6212073729019
Winsorized Mean ( 17 / 24 )21.07260273972600.2325350031258590.6212073729019
Winsorized Mean ( 18 / 24 )20.70273972602740.169630862128259122.04583214565
Winsorized Mean ( 19 / 24 )20.78082191780820.159809360530812130.035073344791
Winsorized Mean ( 20 / 24 )20.78082191780820.159809360530812130.035073344791
Winsorized Mean ( 21 / 24 )20.55068493150690.125423533431629163.85031077688
Winsorized Mean ( 22 / 24 )20.58082191780820.121643012873107169.190333515310
Winsorized Mean ( 23 / 24 )20.58082191780820.121643012873107169.190333515310
Winsorized Mean ( 24 / 24 )20.54794520547950.117107932449609175.461600044226
Trimmed Mean ( 1 / 24 )21.33521126760560.36547754704022658.3762571473574
Trimmed Mean ( 2 / 24 )21.31739130434780.34914312672608161.0563109296787
Trimmed Mean ( 3 / 24 )21.29850746268660.32946987103116564.644780404433
Trimmed Mean ( 4 / 24 )21.26769230769230.32220027584016666.0076787713321
Trimmed Mean ( 5 / 24 )21.23492063492060.31337450076128967.7621203490841
Trimmed Mean ( 6 / 24 )21.20.30261158353870670.0568026910588
Trimmed Mean ( 7 / 24 )21.14745762711860.2963577451402971.3578705935553
Trimmed Mean ( 8 / 24 )21.09122807017540.28845019183368173.1191334493429
Trimmed Mean ( 9 / 24 )21.03090909090910.27842598382062575.5350086307252
Trimmed Mean ( 10 / 24 )20.97169811320750.26885200981595778.004617215113
Trimmed Mean ( 11 / 24 )20.90784313725490.25650506454129281.5104496070842
Trimmed Mean ( 12 / 24 )20.83877551020410.24037273222158286.6935917298403
Trimmed Mean ( 13 / 24 )20.79787234042550.23390837967140288.9146099410491
Trimmed Mean ( 14 / 24 )20.75333333333330.22530787017686892.1110004592465
Trimmed Mean ( 15 / 24 )20.70465116279070.21378188987430496.8494158928254
Trimmed Mean ( 16 / 24 )20.66097560975610.204160328220921101.199757023308
Trimmed Mean ( 17 / 24 )20.61282051282050.190891773507152107.981712014679
Trimmed Mean ( 18 / 24 )20.55945945945950.172094475217225119.466121347059
Trimmed Mean ( 19 / 24 )20.54285714285710.166893802810550123.089394554551
Trimmed Mean ( 20 / 24 )20.51515151515150.161615964330688126.937654953287
Trimmed Mean ( 21 / 24 )20.48387096774190.153671677257910133.296332370756
Trimmed Mean ( 22 / 24 )20.47586206896550.153180981566382133.671046232931
Trimmed Mean ( 23 / 24 )20.46296296296300.152579730047326134.113246606322
Trimmed Mean ( 24 / 24 )20.4480.150678465614699135.706186790405
Median20
Midrange21.95
Midmean - Weighted Average at Xnp20.45
Midmean - Weighted Average at X(n+1)p20.45
Midmean - Empirical Distribution Function20.45
Midmean - Empirical Distribution Function - Averaging20.45
Midmean - Empirical Distribution Function - Interpolation20.45
Midmean - Closest Observation20.45
Midmean - True Basic - Statistics Graphics Toolkit20.45
Midmean - MS Excel (old versions)20.45
Number of observations73



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')