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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, 21 Apr 2008 10:51:37 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/Apr/21/t12087967441lc1rgyrfo2s08w.htm/, Retrieved Thu, 16 May 2024 16:25:47 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=10537, Retrieved Thu, 16 May 2024 16:25:47 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact208
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [werkloosheid voor...] [2008-04-21 16:51:37] [2fa459907c4dcce485bca7190e4cae85] [Current]
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Dataseries X:
18,3
15,3
18,6
18,2
16,1
13,1
16,5
16,5
14,7
12,1
15,7
15,7
14
11,7
15,2
15,6
14,3
12,5
16,6
18,1
18,5
17,6
22,6
23,9
23,2
20,6
24,2
24,5
22,9
20,4
23,9
24,1
22,3
19,5
23,3
23,4
21,8
19,8
23,3
23,2
21,2
19
23,8
24,3
23,1
21,6
22,2
17,4
15,6
14,5
20,3
16,1
14,1
15,3
17,8
19,6
17,8
15,7
18,9
18,4
20,8
19
24,5
22,6
19,6
17,5
25
22,3
20,5
19,9
23,4
22,1
20
18,9
23
20
18,6
19,2
20,3
17,8




Summary of compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'George Udny Yule' @ 72.249.76.132

\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 & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=10537&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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=10537&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=10537&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'George Udny Yule' @ 72.249.76.132







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean19.293750.38568262576431450.0249394479859
Geometric Mean18.9721696575043
Harmonic Mean18.6341715550277
Quadratic Mean19.5959211317049
Winsorized Mean ( 1 / 26 )19.29250.38334295300716550.3269979235524
Winsorized Mean ( 2 / 26 )19.30250.38102532807270450.6593619317530
Winsorized Mean ( 3 / 26 )19.31750.37484078898728151.5352132626513
Winsorized Mean ( 4 / 26 )19.35750.36508961532093753.021228727592
Winsorized Mean ( 5 / 26 )19.35750.36289437299215253.3419679131223
Winsorized Mean ( 6 / 26 )19.35750.35773007556260254.112028376581
Winsorized Mean ( 7 / 26 )19.3750.35464146630118354.6326412477259
Winsorized Mean ( 8 / 26 )19.3850.34959787025391955.4494224633587
Winsorized Mean ( 9 / 26 )19.396250.33331592451902858.1917891501541
Winsorized Mean ( 10 / 26 )19.408750.33133883451761858.5767437380419
Winsorized Mean ( 11 / 26 )19.3950.32925837263366158.9051080003339
Winsorized Mean ( 12 / 26 )19.440.32232148429868360.3124549463345
Winsorized Mean ( 13 / 26 )19.423750.31987558771172960.7228270808356
Winsorized Mean ( 14 / 26 )19.441250.31724533168304261.2814376081147
Winsorized Mean ( 15 / 26 )19.42250.31445137576661861.7663063252588
Winsorized Mean ( 16 / 26 )19.40250.31150906177769662.2855074882102
Winsorized Mean ( 17 / 26 )19.466250.29587321817659965.7925381687677
Winsorized Mean ( 18 / 26 )19.398750.28613251416879767.7963846798486
Winsorized Mean ( 19 / 26 )19.493750.27258922444735471.5132817136169
Winsorized Mean ( 20 / 26 )19.418750.26195524396692774.1300296414441
Winsorized Mean ( 21 / 26 )19.4450.25827384642436375.2883045232944
Winsorized Mean ( 22 / 26 )19.63750.22509052328093787.2426778069652
Winsorized Mean ( 23 / 26 )19.63750.21735882221556390.3459993012142
Winsorized Mean ( 24 / 26 )19.57750.20086029372411297.4682434094729
Winsorized Mean ( 25 / 26 )19.57750.184433575226655106.149327615326
Winsorized Mean ( 26 / 26 )19.44750.166744470236438116.630554359159
Trimmed Mean ( 1 / 26 )19.31794871794870.37616173071099951.3554334233711
Trimmed Mean ( 2 / 26 )19.34473684210530.36774034860063952.6043359552948
Trimmed Mean ( 3 / 26 )19.36756756756760.35929560085971353.9042713610336
Trimmed Mean ( 4 / 26 )19.38611111111110.35209136824765455.0598874593123
Trimmed Mean ( 5 / 26 )19.39428571428570.34698873624647955.8931276100825
Trimmed Mean ( 6 / 26 )19.40294117647060.34150913968101756.8152910771105
Trimmed Mean ( 7 / 26 )19.41212121212120.33626576202614857.7285094240778
Trimmed Mean ( 8 / 26 )19.418750.33065047573408258.72893410145
Trimmed Mean ( 9 / 26 )19.42419354838710.32495116570725759.7757312429093
Trimmed Mean ( 10 / 26 )19.42833333333330.32141188938266660.4468408765128
Trimmed Mean ( 11 / 26 )19.43103448275860.31731830520030761.235151468784
Trimmed Mean ( 12 / 26 )19.43571428571430.31253497021402162.187326661093
Trimmed Mean ( 13 / 26 )19.43518518518520.30783113850800163.1358649400572
Trimmed Mean ( 14 / 26 )19.43653846153850.30227928569825364.2999351299935
Trimmed Mean ( 15 / 26 )19.4360.29567991518684265.733243963217
Trimmed Mean ( 16 / 26 )19.43750.2877619836251167.5471434938492
Trimmed Mean ( 17 / 26 )19.44130434782610.27815083120158169.8948274353226
Trimmed Mean ( 18 / 26 )19.43863636363640.26911521910360472.2316501771416
Trimmed Mean ( 19 / 26 )19.44285714285710.25941376903950374.9492103477993
Trimmed Mean ( 20 / 26 )19.43750.24968409528021177.8483706708913
Trimmed Mean ( 21 / 26 )19.43947368421050.23917649951175081.2766878179664
Trimmed Mean ( 22 / 26 )19.43888888888890.22570094618229686.126749655663
Trimmed Mean ( 23 / 26 )19.41764705882350.21608535434105889.8610047776572
Trimmed Mean ( 24 / 26 )19.393750.20453219144846094.8200371914901
Trimmed Mean ( 25 / 26 )19.37333333333330.193214390681138100.268583851527
Trimmed Mean ( 26 / 26 )19.350.181957318095386106.343620594893
Median19.35
Midrange18.35
Midmean - Weighted Average at Xnp19.3658536585366
Midmean - Weighted Average at X(n+1)p19.3658536585366
Midmean - Empirical Distribution Function19.3658536585366
Midmean - Empirical Distribution Function - Averaging19.3658536585366
Midmean - Empirical Distribution Function - Interpolation19.3658536585366
Midmean - Closest Observation19.3658536585366
Midmean - True Basic - Statistics Graphics Toolkit19.3658536585366
Midmean - MS Excel (old versions)19.5162790697674
Number of observations80

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 19.29375 & 0.385682625764314 & 50.0249394479859 \tabularnewline
Geometric Mean & 18.9721696575043 &  &  \tabularnewline
Harmonic Mean & 18.6341715550277 &  &  \tabularnewline
Quadratic Mean & 19.5959211317049 &  &  \tabularnewline
Winsorized Mean ( 1 / 26 ) & 19.2925 & 0.383342953007165 & 50.3269979235524 \tabularnewline
Winsorized Mean ( 2 / 26 ) & 19.3025 & 0.381025328072704 & 50.6593619317530 \tabularnewline
Winsorized Mean ( 3 / 26 ) & 19.3175 & 0.374840788987281 & 51.5352132626513 \tabularnewline
Winsorized Mean ( 4 / 26 ) & 19.3575 & 0.365089615320937 & 53.021228727592 \tabularnewline
Winsorized Mean ( 5 / 26 ) & 19.3575 & 0.362894372992152 & 53.3419679131223 \tabularnewline
Winsorized Mean ( 6 / 26 ) & 19.3575 & 0.357730075562602 & 54.112028376581 \tabularnewline
Winsorized Mean ( 7 / 26 ) & 19.375 & 0.354641466301183 & 54.6326412477259 \tabularnewline
Winsorized Mean ( 8 / 26 ) & 19.385 & 0.349597870253919 & 55.4494224633587 \tabularnewline
Winsorized Mean ( 9 / 26 ) & 19.39625 & 0.333315924519028 & 58.1917891501541 \tabularnewline
Winsorized Mean ( 10 / 26 ) & 19.40875 & 0.331338834517618 & 58.5767437380419 \tabularnewline
Winsorized Mean ( 11 / 26 ) & 19.395 & 0.329258372633661 & 58.9051080003339 \tabularnewline
Winsorized Mean ( 12 / 26 ) & 19.44 & 0.322321484298683 & 60.3124549463345 \tabularnewline
Winsorized Mean ( 13 / 26 ) & 19.42375 & 0.319875587711729 & 60.7228270808356 \tabularnewline
Winsorized Mean ( 14 / 26 ) & 19.44125 & 0.317245331683042 & 61.2814376081147 \tabularnewline
Winsorized Mean ( 15 / 26 ) & 19.4225 & 0.314451375766618 & 61.7663063252588 \tabularnewline
Winsorized Mean ( 16 / 26 ) & 19.4025 & 0.311509061777696 & 62.2855074882102 \tabularnewline
Winsorized Mean ( 17 / 26 ) & 19.46625 & 0.295873218176599 & 65.7925381687677 \tabularnewline
Winsorized Mean ( 18 / 26 ) & 19.39875 & 0.286132514168797 & 67.7963846798486 \tabularnewline
Winsorized Mean ( 19 / 26 ) & 19.49375 & 0.272589224447354 & 71.5132817136169 \tabularnewline
Winsorized Mean ( 20 / 26 ) & 19.41875 & 0.261955243966927 & 74.1300296414441 \tabularnewline
Winsorized Mean ( 21 / 26 ) & 19.445 & 0.258273846424363 & 75.2883045232944 \tabularnewline
Winsorized Mean ( 22 / 26 ) & 19.6375 & 0.225090523280937 & 87.2426778069652 \tabularnewline
Winsorized Mean ( 23 / 26 ) & 19.6375 & 0.217358822215563 & 90.3459993012142 \tabularnewline
Winsorized Mean ( 24 / 26 ) & 19.5775 & 0.200860293724112 & 97.4682434094729 \tabularnewline
Winsorized Mean ( 25 / 26 ) & 19.5775 & 0.184433575226655 & 106.149327615326 \tabularnewline
Winsorized Mean ( 26 / 26 ) & 19.4475 & 0.166744470236438 & 116.630554359159 \tabularnewline
Trimmed Mean ( 1 / 26 ) & 19.3179487179487 & 0.376161730710999 & 51.3554334233711 \tabularnewline
Trimmed Mean ( 2 / 26 ) & 19.3447368421053 & 0.367740348600639 & 52.6043359552948 \tabularnewline
Trimmed Mean ( 3 / 26 ) & 19.3675675675676 & 0.359295600859713 & 53.9042713610336 \tabularnewline
Trimmed Mean ( 4 / 26 ) & 19.3861111111111 & 0.352091368247654 & 55.0598874593123 \tabularnewline
Trimmed Mean ( 5 / 26 ) & 19.3942857142857 & 0.346988736246479 & 55.8931276100825 \tabularnewline
Trimmed Mean ( 6 / 26 ) & 19.4029411764706 & 0.341509139681017 & 56.8152910771105 \tabularnewline
Trimmed Mean ( 7 / 26 ) & 19.4121212121212 & 0.336265762026148 & 57.7285094240778 \tabularnewline
Trimmed Mean ( 8 / 26 ) & 19.41875 & 0.330650475734082 & 58.72893410145 \tabularnewline
Trimmed Mean ( 9 / 26 ) & 19.4241935483871 & 0.324951165707257 & 59.7757312429093 \tabularnewline
Trimmed Mean ( 10 / 26 ) & 19.4283333333333 & 0.321411889382666 & 60.4468408765128 \tabularnewline
Trimmed Mean ( 11 / 26 ) & 19.4310344827586 & 0.317318305200307 & 61.235151468784 \tabularnewline
Trimmed Mean ( 12 / 26 ) & 19.4357142857143 & 0.312534970214021 & 62.187326661093 \tabularnewline
Trimmed Mean ( 13 / 26 ) & 19.4351851851852 & 0.307831138508001 & 63.1358649400572 \tabularnewline
Trimmed Mean ( 14 / 26 ) & 19.4365384615385 & 0.302279285698253 & 64.2999351299935 \tabularnewline
Trimmed Mean ( 15 / 26 ) & 19.436 & 0.295679915186842 & 65.733243963217 \tabularnewline
Trimmed Mean ( 16 / 26 ) & 19.4375 & 0.28776198362511 & 67.5471434938492 \tabularnewline
Trimmed Mean ( 17 / 26 ) & 19.4413043478261 & 0.278150831201581 & 69.8948274353226 \tabularnewline
Trimmed Mean ( 18 / 26 ) & 19.4386363636364 & 0.269115219103604 & 72.2316501771416 \tabularnewline
Trimmed Mean ( 19 / 26 ) & 19.4428571428571 & 0.259413769039503 & 74.9492103477993 \tabularnewline
Trimmed Mean ( 20 / 26 ) & 19.4375 & 0.249684095280211 & 77.8483706708913 \tabularnewline
Trimmed Mean ( 21 / 26 ) & 19.4394736842105 & 0.239176499511750 & 81.2766878179664 \tabularnewline
Trimmed Mean ( 22 / 26 ) & 19.4388888888889 & 0.225700946182296 & 86.126749655663 \tabularnewline
Trimmed Mean ( 23 / 26 ) & 19.4176470588235 & 0.216085354341058 & 89.8610047776572 \tabularnewline
Trimmed Mean ( 24 / 26 ) & 19.39375 & 0.204532191448460 & 94.8200371914901 \tabularnewline
Trimmed Mean ( 25 / 26 ) & 19.3733333333333 & 0.193214390681138 & 100.268583851527 \tabularnewline
Trimmed Mean ( 26 / 26 ) & 19.35 & 0.181957318095386 & 106.343620594893 \tabularnewline
Median & 19.35 &  &  \tabularnewline
Midrange & 18.35 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 19.3658536585366 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 19.3658536585366 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 19.3658536585366 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 19.3658536585366 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 19.3658536585366 &  &  \tabularnewline
Midmean - Closest Observation & 19.3658536585366 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 19.3658536585366 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 19.5162790697674 &  &  \tabularnewline
Number of observations & 80 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=10537&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]19.29375[/C][C]0.385682625764314[/C][C]50.0249394479859[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]18.9721696575043[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]18.6341715550277[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]19.5959211317049[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 26 )[/C][C]19.2925[/C][C]0.383342953007165[/C][C]50.3269979235524[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 26 )[/C][C]19.3025[/C][C]0.381025328072704[/C][C]50.6593619317530[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 26 )[/C][C]19.3175[/C][C]0.374840788987281[/C][C]51.5352132626513[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 26 )[/C][C]19.3575[/C][C]0.365089615320937[/C][C]53.021228727592[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 26 )[/C][C]19.3575[/C][C]0.362894372992152[/C][C]53.3419679131223[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 26 )[/C][C]19.3575[/C][C]0.357730075562602[/C][C]54.112028376581[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 26 )[/C][C]19.375[/C][C]0.354641466301183[/C][C]54.6326412477259[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 26 )[/C][C]19.385[/C][C]0.349597870253919[/C][C]55.4494224633587[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 26 )[/C][C]19.39625[/C][C]0.333315924519028[/C][C]58.1917891501541[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 26 )[/C][C]19.40875[/C][C]0.331338834517618[/C][C]58.5767437380419[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 26 )[/C][C]19.395[/C][C]0.329258372633661[/C][C]58.9051080003339[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 26 )[/C][C]19.44[/C][C]0.322321484298683[/C][C]60.3124549463345[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 26 )[/C][C]19.42375[/C][C]0.319875587711729[/C][C]60.7228270808356[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 26 )[/C][C]19.44125[/C][C]0.317245331683042[/C][C]61.2814376081147[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 26 )[/C][C]19.4225[/C][C]0.314451375766618[/C][C]61.7663063252588[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 26 )[/C][C]19.4025[/C][C]0.311509061777696[/C][C]62.2855074882102[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 26 )[/C][C]19.46625[/C][C]0.295873218176599[/C][C]65.7925381687677[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 26 )[/C][C]19.39875[/C][C]0.286132514168797[/C][C]67.7963846798486[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 26 )[/C][C]19.49375[/C][C]0.272589224447354[/C][C]71.5132817136169[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 26 )[/C][C]19.41875[/C][C]0.261955243966927[/C][C]74.1300296414441[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 26 )[/C][C]19.445[/C][C]0.258273846424363[/C][C]75.2883045232944[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 26 )[/C][C]19.6375[/C][C]0.225090523280937[/C][C]87.2426778069652[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 26 )[/C][C]19.6375[/C][C]0.217358822215563[/C][C]90.3459993012142[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 26 )[/C][C]19.5775[/C][C]0.200860293724112[/C][C]97.4682434094729[/C][/ROW]
[ROW][C]Winsorized Mean ( 25 / 26 )[/C][C]19.5775[/C][C]0.184433575226655[/C][C]106.149327615326[/C][/ROW]
[ROW][C]Winsorized Mean ( 26 / 26 )[/C][C]19.4475[/C][C]0.166744470236438[/C][C]116.630554359159[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 26 )[/C][C]19.3179487179487[/C][C]0.376161730710999[/C][C]51.3554334233711[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 26 )[/C][C]19.3447368421053[/C][C]0.367740348600639[/C][C]52.6043359552948[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 26 )[/C][C]19.3675675675676[/C][C]0.359295600859713[/C][C]53.9042713610336[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 26 )[/C][C]19.3861111111111[/C][C]0.352091368247654[/C][C]55.0598874593123[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 26 )[/C][C]19.3942857142857[/C][C]0.346988736246479[/C][C]55.8931276100825[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 26 )[/C][C]19.4029411764706[/C][C]0.341509139681017[/C][C]56.8152910771105[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 26 )[/C][C]19.4121212121212[/C][C]0.336265762026148[/C][C]57.7285094240778[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 26 )[/C][C]19.41875[/C][C]0.330650475734082[/C][C]58.72893410145[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 26 )[/C][C]19.4241935483871[/C][C]0.324951165707257[/C][C]59.7757312429093[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 26 )[/C][C]19.4283333333333[/C][C]0.321411889382666[/C][C]60.4468408765128[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 26 )[/C][C]19.4310344827586[/C][C]0.317318305200307[/C][C]61.235151468784[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 26 )[/C][C]19.4357142857143[/C][C]0.312534970214021[/C][C]62.187326661093[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 26 )[/C][C]19.4351851851852[/C][C]0.307831138508001[/C][C]63.1358649400572[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 26 )[/C][C]19.4365384615385[/C][C]0.302279285698253[/C][C]64.2999351299935[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 26 )[/C][C]19.436[/C][C]0.295679915186842[/C][C]65.733243963217[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 26 )[/C][C]19.4375[/C][C]0.28776198362511[/C][C]67.5471434938492[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 26 )[/C][C]19.4413043478261[/C][C]0.278150831201581[/C][C]69.8948274353226[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 26 )[/C][C]19.4386363636364[/C][C]0.269115219103604[/C][C]72.2316501771416[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 26 )[/C][C]19.4428571428571[/C][C]0.259413769039503[/C][C]74.9492103477993[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 26 )[/C][C]19.4375[/C][C]0.249684095280211[/C][C]77.8483706708913[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 26 )[/C][C]19.4394736842105[/C][C]0.239176499511750[/C][C]81.2766878179664[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 26 )[/C][C]19.4388888888889[/C][C]0.225700946182296[/C][C]86.126749655663[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 26 )[/C][C]19.4176470588235[/C][C]0.216085354341058[/C][C]89.8610047776572[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 26 )[/C][C]19.39375[/C][C]0.204532191448460[/C][C]94.8200371914901[/C][/ROW]
[ROW][C]Trimmed Mean ( 25 / 26 )[/C][C]19.3733333333333[/C][C]0.193214390681138[/C][C]100.268583851527[/C][/ROW]
[ROW][C]Trimmed Mean ( 26 / 26 )[/C][C]19.35[/C][C]0.181957318095386[/C][C]106.343620594893[/C][/ROW]
[ROW][C]Median[/C][C]19.35[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]18.35[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]19.3658536585366[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]19.3658536585366[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]19.3658536585366[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]19.3658536585366[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]19.3658536585366[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]19.3658536585366[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]19.3658536585366[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]19.5162790697674[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]80[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=10537&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=10537&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 Mean19.293750.38568262576431450.0249394479859
Geometric Mean18.9721696575043
Harmonic Mean18.6341715550277
Quadratic Mean19.5959211317049
Winsorized Mean ( 1 / 26 )19.29250.38334295300716550.3269979235524
Winsorized Mean ( 2 / 26 )19.30250.38102532807270450.6593619317530
Winsorized Mean ( 3 / 26 )19.31750.37484078898728151.5352132626513
Winsorized Mean ( 4 / 26 )19.35750.36508961532093753.021228727592
Winsorized Mean ( 5 / 26 )19.35750.36289437299215253.3419679131223
Winsorized Mean ( 6 / 26 )19.35750.35773007556260254.112028376581
Winsorized Mean ( 7 / 26 )19.3750.35464146630118354.6326412477259
Winsorized Mean ( 8 / 26 )19.3850.34959787025391955.4494224633587
Winsorized Mean ( 9 / 26 )19.396250.33331592451902858.1917891501541
Winsorized Mean ( 10 / 26 )19.408750.33133883451761858.5767437380419
Winsorized Mean ( 11 / 26 )19.3950.32925837263366158.9051080003339
Winsorized Mean ( 12 / 26 )19.440.32232148429868360.3124549463345
Winsorized Mean ( 13 / 26 )19.423750.31987558771172960.7228270808356
Winsorized Mean ( 14 / 26 )19.441250.31724533168304261.2814376081147
Winsorized Mean ( 15 / 26 )19.42250.31445137576661861.7663063252588
Winsorized Mean ( 16 / 26 )19.40250.31150906177769662.2855074882102
Winsorized Mean ( 17 / 26 )19.466250.29587321817659965.7925381687677
Winsorized Mean ( 18 / 26 )19.398750.28613251416879767.7963846798486
Winsorized Mean ( 19 / 26 )19.493750.27258922444735471.5132817136169
Winsorized Mean ( 20 / 26 )19.418750.26195524396692774.1300296414441
Winsorized Mean ( 21 / 26 )19.4450.25827384642436375.2883045232944
Winsorized Mean ( 22 / 26 )19.63750.22509052328093787.2426778069652
Winsorized Mean ( 23 / 26 )19.63750.21735882221556390.3459993012142
Winsorized Mean ( 24 / 26 )19.57750.20086029372411297.4682434094729
Winsorized Mean ( 25 / 26 )19.57750.184433575226655106.149327615326
Winsorized Mean ( 26 / 26 )19.44750.166744470236438116.630554359159
Trimmed Mean ( 1 / 26 )19.31794871794870.37616173071099951.3554334233711
Trimmed Mean ( 2 / 26 )19.34473684210530.36774034860063952.6043359552948
Trimmed Mean ( 3 / 26 )19.36756756756760.35929560085971353.9042713610336
Trimmed Mean ( 4 / 26 )19.38611111111110.35209136824765455.0598874593123
Trimmed Mean ( 5 / 26 )19.39428571428570.34698873624647955.8931276100825
Trimmed Mean ( 6 / 26 )19.40294117647060.34150913968101756.8152910771105
Trimmed Mean ( 7 / 26 )19.41212121212120.33626576202614857.7285094240778
Trimmed Mean ( 8 / 26 )19.418750.33065047573408258.72893410145
Trimmed Mean ( 9 / 26 )19.42419354838710.32495116570725759.7757312429093
Trimmed Mean ( 10 / 26 )19.42833333333330.32141188938266660.4468408765128
Trimmed Mean ( 11 / 26 )19.43103448275860.31731830520030761.235151468784
Trimmed Mean ( 12 / 26 )19.43571428571430.31253497021402162.187326661093
Trimmed Mean ( 13 / 26 )19.43518518518520.30783113850800163.1358649400572
Trimmed Mean ( 14 / 26 )19.43653846153850.30227928569825364.2999351299935
Trimmed Mean ( 15 / 26 )19.4360.29567991518684265.733243963217
Trimmed Mean ( 16 / 26 )19.43750.2877619836251167.5471434938492
Trimmed Mean ( 17 / 26 )19.44130434782610.27815083120158169.8948274353226
Trimmed Mean ( 18 / 26 )19.43863636363640.26911521910360472.2316501771416
Trimmed Mean ( 19 / 26 )19.44285714285710.25941376903950374.9492103477993
Trimmed Mean ( 20 / 26 )19.43750.24968409528021177.8483706708913
Trimmed Mean ( 21 / 26 )19.43947368421050.23917649951175081.2766878179664
Trimmed Mean ( 22 / 26 )19.43888888888890.22570094618229686.126749655663
Trimmed Mean ( 23 / 26 )19.41764705882350.21608535434105889.8610047776572
Trimmed Mean ( 24 / 26 )19.393750.20453219144846094.8200371914901
Trimmed Mean ( 25 / 26 )19.37333333333330.193214390681138100.268583851527
Trimmed Mean ( 26 / 26 )19.350.181957318095386106.343620594893
Median19.35
Midrange18.35
Midmean - Weighted Average at Xnp19.3658536585366
Midmean - Weighted Average at X(n+1)p19.3658536585366
Midmean - Empirical Distribution Function19.3658536585366
Midmean - Empirical Distribution Function - Averaging19.3658536585366
Midmean - Empirical Distribution Function - Interpolation19.3658536585366
Midmean - Closest Observation19.3658536585366
Midmean - True Basic - Statistics Graphics Toolkit19.3658536585366
Midmean - MS Excel (old versions)19.5162790697674
Number of observations80



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')