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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationSun, 29 Nov 2015 13:58:50 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2015/Nov/29/t14488055401vyu3treojgbmay.htm/, Retrieved Wed, 15 May 2024 09:15:06 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=284440, Retrieved Wed, 15 May 2024 09:15:06 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact113
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Central Tendency] [2015-11-29 13:58:50] [60e7016130b28a0c8bd4011f80276a66] [Current]
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Dataseries X:
2.3
1.9
0.6
0.6
-0.4
-1.1
-1.7
-0.8
-1.2
-1
-0.1
0.3
0.6
0.7
1.7
1.8
2.3
2.5
2.6
2.3
2.9
3
2.9
3.1
3.2
3.4
3.5
3.4
3.4
3.7
3.8
3.6
3.6
3.6
3.9
3.5
3.7
3.7
3.4
3.2
2.8
2.3
2.3
2.9
2.8
2.8
2.3
2.2
1.5
1.2
1.1
1
1.2
1.6
1.5
1
0.9
0.6
0.8
1
1.1
1
0.9
0.6
0.4
0.3
0.3
0
-0.1
0.1
-0.1
-0.4
-0.7
-0.4
-0.4
0.3
0.6
0.6
0.5
0.9




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284440&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=284440&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284440&T=0

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean1.521250.165895095627229.16995161459367
Geometric MeanNaN
Harmonic Mean0
Quadratic Mean2.11857853288473
Winsorized Mean ( 1 / 26 )1.526250.1642468787634779.29241402631383
Winsorized Mean ( 2 / 26 )1.526250.163300063077969.34629155208201
Winsorized Mean ( 3 / 26 )1.530.1625489215551259.41255091305625
Winsorized Mean ( 4 / 26 )1.540.1606415145674739.58656300114231
Winsorized Mean ( 5 / 26 )1.540.1584597541045879.71855603779095
Winsorized Mean ( 6 / 26 )1.56250.1546369267475410.1043135870835
Winsorized Mean ( 7 / 26 )1.56250.1546369267475410.1043135870835
Winsorized Mean ( 8 / 26 )1.55250.15299721806025510.1472433269249
Winsorized Mean ( 9 / 26 )1.55250.15299721806025510.1472433269249
Winsorized Mean ( 10 / 26 )1.57750.14521889849813910.8629112072505
Winsorized Mean ( 11 / 26 )1.57750.14521889849813910.8629112072505
Winsorized Mean ( 12 / 26 )1.57750.14521889849813910.8629112072505
Winsorized Mean ( 13 / 26 )1.593750.14288332575385111.1542056540985
Winsorized Mean ( 14 / 26 )1.576250.13496651893776211.6788223657666
Winsorized Mean ( 15 / 26 )1.613750.12996766576948912.4165498429598
Winsorized Mean ( 16 / 26 )1.593750.12691998563332912.5571240183112
Winsorized Mean ( 17 / 26 )1.57250.12377213393668412.7047983256426
Winsorized Mean ( 18 / 26 )1.550.12053414874075412.8594262803793
Winsorized Mean ( 19 / 26 )1.573750.11747264359701313.3967360554063
Winsorized Mean ( 20 / 26 )1.598750.1143707848362113.978657244414
Winsorized Mean ( 21 / 26 )1.598750.10748113979388414.874702697291
Winsorized Mean ( 22 / 26 )1.598750.10748113979388414.874702697291
Winsorized Mean ( 23 / 26 )1.598750.10748113979388414.874702697291
Winsorized Mean ( 24 / 26 )1.538750.099165724829764915.516954095193
Winsorized Mean ( 25 / 26 )1.50750.094981260643443415.8715518175644
Winsorized Mean ( 26 / 26 )1.44250.086598429400789616.6573459816911
Trimmed Mean ( 1 / 26 )1.532051282051280.1621378732515519.44906486884997
Trimmed Mean ( 2 / 26 )1.538157894736840.1596483757453129.63466046902146
Trimmed Mean ( 3 / 26 )1.544594594594590.157287987118739.82016886914983
Trimmed Mean ( 4 / 26 )1.550.15481322989407210.0120642212591
Trimmed Mean ( 5 / 26 )1.552857142857140.15253172535725610.1805518767986
Trimmed Mean ( 6 / 26 )1.555882352941180.15043662459632310.3424439169397
Trimmed Mean ( 7 / 26 )1.554545454545450.14889150346827510.4407935868327
Trimmed Mean ( 8 / 26 )1.5531250.14697628220145610.5671811583258
Trimmed Mean ( 9 / 26 )1.553225806451610.14497976193008610.7133974133619
Trimmed Mean ( 10 / 26 )1.553333333333330.14250516229457310.90018991819
Trimmed Mean ( 11 / 26 )1.550.14101974993935510.9913682350633
Trimmed Mean ( 12 / 26 )1.546428571428570.13910577788037111.1169255151894
Trimmed Mean ( 13 / 26 )1.542592592592590.13666185633125311.2876601709077
Trimmed Mean ( 14 / 26 )1.536538461538460.13400177972506911.466552643487
Trimmed Mean ( 15 / 26 )1.5320.13215451686011611.5924906420082
Trimmed Mean ( 16 / 26 )1.522916666666670.13060957680956411.6600689158281
Trimmed Mean ( 17 / 26 )1.515217391304350.12909822464621811.736934380443
Trimmed Mean ( 18 / 26 )1.509090909090910.12762334670377111.824567746164
Trimmed Mean ( 19 / 26 )1.50476190476190.12618554545184711.9249942564629
Trimmed Mean ( 20 / 26 )1.49750.12467843253129812.0108985138555
Trimmed Mean ( 21 / 26 )1.486842105263160.12303482562363712.0847255866514
Trimmed Mean ( 22 / 26 )1.4750.12204442334593312.0857631963989
Trimmed Mean ( 23 / 26 )1.461764705882350.12030966475983212.150018943203
Trimmed Mean ( 24 / 26 )1.4468750.11751667477769512.3120825426438
Trimmed Mean ( 25 / 26 )1.436666666666670.11571698862284112.4153478565643
Trimmed Mean ( 26 / 26 )1.428571428571430.11395454663998512.536326725819
Median1.2
Midrange1.1
Midmean - Weighted Average at Xnp1.53720930232558
Midmean - Weighted Average at X(n+1)p1.56428571428571
Midmean - Empirical Distribution Function1.53720930232558
Midmean - Empirical Distribution Function - Averaging1.56428571428571
Midmean - Empirical Distribution Function - Interpolation1.56428571428571
Midmean - Closest Observation1.53720930232558
Midmean - True Basic - Statistics Graphics Toolkit1.56428571428571
Midmean - MS Excel (old versions)1.53720930232558
Number of observations80

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 1.52125 & 0.16589509562722 & 9.16995161459367 \tabularnewline
Geometric Mean & NaN &  &  \tabularnewline
Harmonic Mean & 0 &  &  \tabularnewline
Quadratic Mean & 2.11857853288473 &  &  \tabularnewline
Winsorized Mean ( 1 / 26 ) & 1.52625 & 0.164246878763477 & 9.29241402631383 \tabularnewline
Winsorized Mean ( 2 / 26 ) & 1.52625 & 0.16330006307796 & 9.34629155208201 \tabularnewline
Winsorized Mean ( 3 / 26 ) & 1.53 & 0.162548921555125 & 9.41255091305625 \tabularnewline
Winsorized Mean ( 4 / 26 ) & 1.54 & 0.160641514567473 & 9.58656300114231 \tabularnewline
Winsorized Mean ( 5 / 26 ) & 1.54 & 0.158459754104587 & 9.71855603779095 \tabularnewline
Winsorized Mean ( 6 / 26 ) & 1.5625 & 0.15463692674754 & 10.1043135870835 \tabularnewline
Winsorized Mean ( 7 / 26 ) & 1.5625 & 0.15463692674754 & 10.1043135870835 \tabularnewline
Winsorized Mean ( 8 / 26 ) & 1.5525 & 0.152997218060255 & 10.1472433269249 \tabularnewline
Winsorized Mean ( 9 / 26 ) & 1.5525 & 0.152997218060255 & 10.1472433269249 \tabularnewline
Winsorized Mean ( 10 / 26 ) & 1.5775 & 0.145218898498139 & 10.8629112072505 \tabularnewline
Winsorized Mean ( 11 / 26 ) & 1.5775 & 0.145218898498139 & 10.8629112072505 \tabularnewline
Winsorized Mean ( 12 / 26 ) & 1.5775 & 0.145218898498139 & 10.8629112072505 \tabularnewline
Winsorized Mean ( 13 / 26 ) & 1.59375 & 0.142883325753851 & 11.1542056540985 \tabularnewline
Winsorized Mean ( 14 / 26 ) & 1.57625 & 0.134966518937762 & 11.6788223657666 \tabularnewline
Winsorized Mean ( 15 / 26 ) & 1.61375 & 0.129967665769489 & 12.4165498429598 \tabularnewline
Winsorized Mean ( 16 / 26 ) & 1.59375 & 0.126919985633329 & 12.5571240183112 \tabularnewline
Winsorized Mean ( 17 / 26 ) & 1.5725 & 0.123772133936684 & 12.7047983256426 \tabularnewline
Winsorized Mean ( 18 / 26 ) & 1.55 & 0.120534148740754 & 12.8594262803793 \tabularnewline
Winsorized Mean ( 19 / 26 ) & 1.57375 & 0.117472643597013 & 13.3967360554063 \tabularnewline
Winsorized Mean ( 20 / 26 ) & 1.59875 & 0.11437078483621 & 13.978657244414 \tabularnewline
Winsorized Mean ( 21 / 26 ) & 1.59875 & 0.107481139793884 & 14.874702697291 \tabularnewline
Winsorized Mean ( 22 / 26 ) & 1.59875 & 0.107481139793884 & 14.874702697291 \tabularnewline
Winsorized Mean ( 23 / 26 ) & 1.59875 & 0.107481139793884 & 14.874702697291 \tabularnewline
Winsorized Mean ( 24 / 26 ) & 1.53875 & 0.0991657248297649 & 15.516954095193 \tabularnewline
Winsorized Mean ( 25 / 26 ) & 1.5075 & 0.0949812606434434 & 15.8715518175644 \tabularnewline
Winsorized Mean ( 26 / 26 ) & 1.4425 & 0.0865984294007896 & 16.6573459816911 \tabularnewline
Trimmed Mean ( 1 / 26 ) & 1.53205128205128 & 0.162137873251551 & 9.44906486884997 \tabularnewline
Trimmed Mean ( 2 / 26 ) & 1.53815789473684 & 0.159648375745312 & 9.63466046902146 \tabularnewline
Trimmed Mean ( 3 / 26 ) & 1.54459459459459 & 0.15728798711873 & 9.82016886914983 \tabularnewline
Trimmed Mean ( 4 / 26 ) & 1.55 & 0.154813229894072 & 10.0120642212591 \tabularnewline
Trimmed Mean ( 5 / 26 ) & 1.55285714285714 & 0.152531725357256 & 10.1805518767986 \tabularnewline
Trimmed Mean ( 6 / 26 ) & 1.55588235294118 & 0.150436624596323 & 10.3424439169397 \tabularnewline
Trimmed Mean ( 7 / 26 ) & 1.55454545454545 & 0.148891503468275 & 10.4407935868327 \tabularnewline
Trimmed Mean ( 8 / 26 ) & 1.553125 & 0.146976282201456 & 10.5671811583258 \tabularnewline
Trimmed Mean ( 9 / 26 ) & 1.55322580645161 & 0.144979761930086 & 10.7133974133619 \tabularnewline
Trimmed Mean ( 10 / 26 ) & 1.55333333333333 & 0.142505162294573 & 10.90018991819 \tabularnewline
Trimmed Mean ( 11 / 26 ) & 1.55 & 0.141019749939355 & 10.9913682350633 \tabularnewline
Trimmed Mean ( 12 / 26 ) & 1.54642857142857 & 0.139105777880371 & 11.1169255151894 \tabularnewline
Trimmed Mean ( 13 / 26 ) & 1.54259259259259 & 0.136661856331253 & 11.2876601709077 \tabularnewline
Trimmed Mean ( 14 / 26 ) & 1.53653846153846 & 0.134001779725069 & 11.466552643487 \tabularnewline
Trimmed Mean ( 15 / 26 ) & 1.532 & 0.132154516860116 & 11.5924906420082 \tabularnewline
Trimmed Mean ( 16 / 26 ) & 1.52291666666667 & 0.130609576809564 & 11.6600689158281 \tabularnewline
Trimmed Mean ( 17 / 26 ) & 1.51521739130435 & 0.129098224646218 & 11.736934380443 \tabularnewline
Trimmed Mean ( 18 / 26 ) & 1.50909090909091 & 0.127623346703771 & 11.824567746164 \tabularnewline
Trimmed Mean ( 19 / 26 ) & 1.5047619047619 & 0.126185545451847 & 11.9249942564629 \tabularnewline
Trimmed Mean ( 20 / 26 ) & 1.4975 & 0.124678432531298 & 12.0108985138555 \tabularnewline
Trimmed Mean ( 21 / 26 ) & 1.48684210526316 & 0.123034825623637 & 12.0847255866514 \tabularnewline
Trimmed Mean ( 22 / 26 ) & 1.475 & 0.122044423345933 & 12.0857631963989 \tabularnewline
Trimmed Mean ( 23 / 26 ) & 1.46176470588235 & 0.120309664759832 & 12.150018943203 \tabularnewline
Trimmed Mean ( 24 / 26 ) & 1.446875 & 0.117516674777695 & 12.3120825426438 \tabularnewline
Trimmed Mean ( 25 / 26 ) & 1.43666666666667 & 0.115716988622841 & 12.4153478565643 \tabularnewline
Trimmed Mean ( 26 / 26 ) & 1.42857142857143 & 0.113954546639985 & 12.536326725819 \tabularnewline
Median & 1.2 &  &  \tabularnewline
Midrange & 1.1 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 1.53720930232558 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 1.56428571428571 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 1.53720930232558 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 1.56428571428571 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 1.56428571428571 &  &  \tabularnewline
Midmean - Closest Observation & 1.53720930232558 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 1.56428571428571 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 1.53720930232558 &  &  \tabularnewline
Number of observations & 80 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284440&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]1.52125[/C][C]0.16589509562722[/C][C]9.16995161459367[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]NaN[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]0[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]2.11857853288473[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 26 )[/C][C]1.52625[/C][C]0.164246878763477[/C][C]9.29241402631383[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 26 )[/C][C]1.52625[/C][C]0.16330006307796[/C][C]9.34629155208201[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 26 )[/C][C]1.53[/C][C]0.162548921555125[/C][C]9.41255091305625[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 26 )[/C][C]1.54[/C][C]0.160641514567473[/C][C]9.58656300114231[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 26 )[/C][C]1.54[/C][C]0.158459754104587[/C][C]9.71855603779095[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 26 )[/C][C]1.5625[/C][C]0.15463692674754[/C][C]10.1043135870835[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 26 )[/C][C]1.5625[/C][C]0.15463692674754[/C][C]10.1043135870835[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 26 )[/C][C]1.5525[/C][C]0.152997218060255[/C][C]10.1472433269249[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 26 )[/C][C]1.5525[/C][C]0.152997218060255[/C][C]10.1472433269249[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 26 )[/C][C]1.5775[/C][C]0.145218898498139[/C][C]10.8629112072505[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 26 )[/C][C]1.5775[/C][C]0.145218898498139[/C][C]10.8629112072505[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 26 )[/C][C]1.5775[/C][C]0.145218898498139[/C][C]10.8629112072505[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 26 )[/C][C]1.59375[/C][C]0.142883325753851[/C][C]11.1542056540985[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 26 )[/C][C]1.57625[/C][C]0.134966518937762[/C][C]11.6788223657666[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 26 )[/C][C]1.61375[/C][C]0.129967665769489[/C][C]12.4165498429598[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 26 )[/C][C]1.59375[/C][C]0.126919985633329[/C][C]12.5571240183112[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 26 )[/C][C]1.5725[/C][C]0.123772133936684[/C][C]12.7047983256426[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 26 )[/C][C]1.55[/C][C]0.120534148740754[/C][C]12.8594262803793[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 26 )[/C][C]1.57375[/C][C]0.117472643597013[/C][C]13.3967360554063[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 26 )[/C][C]1.59875[/C][C]0.11437078483621[/C][C]13.978657244414[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 26 )[/C][C]1.59875[/C][C]0.107481139793884[/C][C]14.874702697291[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 26 )[/C][C]1.59875[/C][C]0.107481139793884[/C][C]14.874702697291[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 26 )[/C][C]1.59875[/C][C]0.107481139793884[/C][C]14.874702697291[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 26 )[/C][C]1.53875[/C][C]0.0991657248297649[/C][C]15.516954095193[/C][/ROW]
[ROW][C]Winsorized Mean ( 25 / 26 )[/C][C]1.5075[/C][C]0.0949812606434434[/C][C]15.8715518175644[/C][/ROW]
[ROW][C]Winsorized Mean ( 26 / 26 )[/C][C]1.4425[/C][C]0.0865984294007896[/C][C]16.6573459816911[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 26 )[/C][C]1.53205128205128[/C][C]0.162137873251551[/C][C]9.44906486884997[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 26 )[/C][C]1.53815789473684[/C][C]0.159648375745312[/C][C]9.63466046902146[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 26 )[/C][C]1.54459459459459[/C][C]0.15728798711873[/C][C]9.82016886914983[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 26 )[/C][C]1.55[/C][C]0.154813229894072[/C][C]10.0120642212591[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 26 )[/C][C]1.55285714285714[/C][C]0.152531725357256[/C][C]10.1805518767986[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 26 )[/C][C]1.55588235294118[/C][C]0.150436624596323[/C][C]10.3424439169397[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 26 )[/C][C]1.55454545454545[/C][C]0.148891503468275[/C][C]10.4407935868327[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 26 )[/C][C]1.553125[/C][C]0.146976282201456[/C][C]10.5671811583258[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 26 )[/C][C]1.55322580645161[/C][C]0.144979761930086[/C][C]10.7133974133619[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 26 )[/C][C]1.55333333333333[/C][C]0.142505162294573[/C][C]10.90018991819[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 26 )[/C][C]1.55[/C][C]0.141019749939355[/C][C]10.9913682350633[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 26 )[/C][C]1.54642857142857[/C][C]0.139105777880371[/C][C]11.1169255151894[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 26 )[/C][C]1.54259259259259[/C][C]0.136661856331253[/C][C]11.2876601709077[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 26 )[/C][C]1.53653846153846[/C][C]0.134001779725069[/C][C]11.466552643487[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 26 )[/C][C]1.532[/C][C]0.132154516860116[/C][C]11.5924906420082[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 26 )[/C][C]1.52291666666667[/C][C]0.130609576809564[/C][C]11.6600689158281[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 26 )[/C][C]1.51521739130435[/C][C]0.129098224646218[/C][C]11.736934380443[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 26 )[/C][C]1.50909090909091[/C][C]0.127623346703771[/C][C]11.824567746164[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 26 )[/C][C]1.5047619047619[/C][C]0.126185545451847[/C][C]11.9249942564629[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 26 )[/C][C]1.4975[/C][C]0.124678432531298[/C][C]12.0108985138555[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 26 )[/C][C]1.48684210526316[/C][C]0.123034825623637[/C][C]12.0847255866514[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 26 )[/C][C]1.475[/C][C]0.122044423345933[/C][C]12.0857631963989[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 26 )[/C][C]1.46176470588235[/C][C]0.120309664759832[/C][C]12.150018943203[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 26 )[/C][C]1.446875[/C][C]0.117516674777695[/C][C]12.3120825426438[/C][/ROW]
[ROW][C]Trimmed Mean ( 25 / 26 )[/C][C]1.43666666666667[/C][C]0.115716988622841[/C][C]12.4153478565643[/C][/ROW]
[ROW][C]Trimmed Mean ( 26 / 26 )[/C][C]1.42857142857143[/C][C]0.113954546639985[/C][C]12.536326725819[/C][/ROW]
[ROW][C]Median[/C][C]1.2[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]1.1[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]1.53720930232558[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]1.56428571428571[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]1.53720930232558[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]1.56428571428571[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]1.56428571428571[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]1.53720930232558[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]1.56428571428571[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]1.53720930232558[/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=284440&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284440&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 Mean1.521250.165895095627229.16995161459367
Geometric MeanNaN
Harmonic Mean0
Quadratic Mean2.11857853288473
Winsorized Mean ( 1 / 26 )1.526250.1642468787634779.29241402631383
Winsorized Mean ( 2 / 26 )1.526250.163300063077969.34629155208201
Winsorized Mean ( 3 / 26 )1.530.1625489215551259.41255091305625
Winsorized Mean ( 4 / 26 )1.540.1606415145674739.58656300114231
Winsorized Mean ( 5 / 26 )1.540.1584597541045879.71855603779095
Winsorized Mean ( 6 / 26 )1.56250.1546369267475410.1043135870835
Winsorized Mean ( 7 / 26 )1.56250.1546369267475410.1043135870835
Winsorized Mean ( 8 / 26 )1.55250.15299721806025510.1472433269249
Winsorized Mean ( 9 / 26 )1.55250.15299721806025510.1472433269249
Winsorized Mean ( 10 / 26 )1.57750.14521889849813910.8629112072505
Winsorized Mean ( 11 / 26 )1.57750.14521889849813910.8629112072505
Winsorized Mean ( 12 / 26 )1.57750.14521889849813910.8629112072505
Winsorized Mean ( 13 / 26 )1.593750.14288332575385111.1542056540985
Winsorized Mean ( 14 / 26 )1.576250.13496651893776211.6788223657666
Winsorized Mean ( 15 / 26 )1.613750.12996766576948912.4165498429598
Winsorized Mean ( 16 / 26 )1.593750.12691998563332912.5571240183112
Winsorized Mean ( 17 / 26 )1.57250.12377213393668412.7047983256426
Winsorized Mean ( 18 / 26 )1.550.12053414874075412.8594262803793
Winsorized Mean ( 19 / 26 )1.573750.11747264359701313.3967360554063
Winsorized Mean ( 20 / 26 )1.598750.1143707848362113.978657244414
Winsorized Mean ( 21 / 26 )1.598750.10748113979388414.874702697291
Winsorized Mean ( 22 / 26 )1.598750.10748113979388414.874702697291
Winsorized Mean ( 23 / 26 )1.598750.10748113979388414.874702697291
Winsorized Mean ( 24 / 26 )1.538750.099165724829764915.516954095193
Winsorized Mean ( 25 / 26 )1.50750.094981260643443415.8715518175644
Winsorized Mean ( 26 / 26 )1.44250.086598429400789616.6573459816911
Trimmed Mean ( 1 / 26 )1.532051282051280.1621378732515519.44906486884997
Trimmed Mean ( 2 / 26 )1.538157894736840.1596483757453129.63466046902146
Trimmed Mean ( 3 / 26 )1.544594594594590.157287987118739.82016886914983
Trimmed Mean ( 4 / 26 )1.550.15481322989407210.0120642212591
Trimmed Mean ( 5 / 26 )1.552857142857140.15253172535725610.1805518767986
Trimmed Mean ( 6 / 26 )1.555882352941180.15043662459632310.3424439169397
Trimmed Mean ( 7 / 26 )1.554545454545450.14889150346827510.4407935868327
Trimmed Mean ( 8 / 26 )1.5531250.14697628220145610.5671811583258
Trimmed Mean ( 9 / 26 )1.553225806451610.14497976193008610.7133974133619
Trimmed Mean ( 10 / 26 )1.553333333333330.14250516229457310.90018991819
Trimmed Mean ( 11 / 26 )1.550.14101974993935510.9913682350633
Trimmed Mean ( 12 / 26 )1.546428571428570.13910577788037111.1169255151894
Trimmed Mean ( 13 / 26 )1.542592592592590.13666185633125311.2876601709077
Trimmed Mean ( 14 / 26 )1.536538461538460.13400177972506911.466552643487
Trimmed Mean ( 15 / 26 )1.5320.13215451686011611.5924906420082
Trimmed Mean ( 16 / 26 )1.522916666666670.13060957680956411.6600689158281
Trimmed Mean ( 17 / 26 )1.515217391304350.12909822464621811.736934380443
Trimmed Mean ( 18 / 26 )1.509090909090910.12762334670377111.824567746164
Trimmed Mean ( 19 / 26 )1.50476190476190.12618554545184711.9249942564629
Trimmed Mean ( 20 / 26 )1.49750.12467843253129812.0108985138555
Trimmed Mean ( 21 / 26 )1.486842105263160.12303482562363712.0847255866514
Trimmed Mean ( 22 / 26 )1.4750.12204442334593312.0857631963989
Trimmed Mean ( 23 / 26 )1.461764705882350.12030966475983212.150018943203
Trimmed Mean ( 24 / 26 )1.4468750.11751667477769512.3120825426438
Trimmed Mean ( 25 / 26 )1.436666666666670.11571698862284112.4153478565643
Trimmed Mean ( 26 / 26 )1.428571428571430.11395454663998512.536326725819
Median1.2
Midrange1.1
Midmean - Weighted Average at Xnp1.53720930232558
Midmean - Weighted Average at X(n+1)p1.56428571428571
Midmean - Empirical Distribution Function1.53720930232558
Midmean - Empirical Distribution Function - Averaging1.56428571428571
Midmean - Empirical Distribution Function - Interpolation1.56428571428571
Midmean - Closest Observation1.53720930232558
Midmean - True Basic - Statistics Graphics Toolkit1.56428571428571
Midmean - MS Excel (old versions)1.53720930232558
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')