Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationFri, 28 Apr 2017 13:33:59 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2017/Apr/28/t14933837698a066ovlpmb8loq.htm/, Retrieved Fri, 10 May 2024 10:21:12 +0200
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Fri, 10 May 2024 10:21:12 +0200
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact0
Dataseries X:
89,88
89,88
89,91
90,21
91,46
91,51
91,55
91,56
91,58
91,60
91,61
91,62
91,62
91,62
91,62
91,63
92,01
92,43
92,59
92,67
92,79
92,79
92,84
92,86
92,86
92,91
92,94
93,49
95,31
96,07
96,35
96,66
97,31
97,66
97,75
97,76
97,79
97,93
97,95
98,05
99,01
99,32
99,55
100,56
101,88
102,30
102,79
102,80
102,87
103,57
105,61
107,25
107,61
107,85
107,93
107,98
108,10
108,26
108,32
108,32
108,36
109,07
110,86
112,49
112,83
112,98
113,03
113,34
113,38
113,51
113,68
113,69




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'George Udny Yule' @ yule.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 & 3 seconds \tabularnewline
R Server & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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 time3 seconds
R Server'George Udny Yule' @ yule.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean99.69069444444440.93512404352352106.606920370492
Geometric Mean99.3857428839097
Harmonic Mean99.087943691709
Quadratic Mean100.001605007953
Winsorized Mean ( 1 / 24 )99.69055555555560.935094768298849106.610109408392
Winsorized Mean ( 2 / 24 )99.68666666666670.933982064114529106.73295612071
Winsorized Mean ( 3 / 24 )99.693750.931038582359895107.078000728291
Winsorized Mean ( 4 / 24 )99.76097222222220.921186406717053108.296183589761
Winsorized Mean ( 5 / 24 )99.74291666666670.91631315072934108.852433894762
Winsorized Mean ( 6 / 24 )99.74208333333330.915042093011883109.002726863668
Winsorized Mean ( 7 / 24 )99.72847222222220.911958280465694109.356397500219
Winsorized Mean ( 8 / 24 )99.69291666666670.904089678630965110.268836181858
Winsorized Mean ( 9 / 24 )99.49166666666670.864561545910218115.077598740435
Winsorized Mean ( 10 / 24 )99.24444444444450.82033601003604120.980236427856
Winsorized Mean ( 11 / 24 )99.13750.802199435228587123.5821114381
Winsorized Mean ( 12 / 24 )99.13083333333330.801121176158069123.740123571236
Winsorized Mean ( 13 / 24 )99.13083333333330.801121176158069123.740123571236
Winsorized Mean ( 14 / 24 )99.11916666666670.799239117572397124.0169111939
Winsorized Mean ( 15 / 24 )99.08791666666670.793613123264137124.85670128427
Winsorized Mean ( 16 / 24 )99.14569444444450.778307064590466127.386347824831
Winsorized Mean ( 17 / 24 )99.23305555555560.763792137136487129.921546361537
Winsorized Mean ( 18 / 24 )99.25305555555560.755592727124608131.357875734539
Winsorized Mean ( 19 / 24 )99.21083333333330.742854952226172133.553438711044
Winsorized Mean ( 20 / 24 )99.14416666666670.722864448263559137.15457566744
Winsorized Mean ( 21 / 24 )98.66583333333330.648952862752848152.038520817667
Winsorized Mean ( 22 / 24 )98.05777777777780.556231775464925176.289421250371
Winsorized Mean ( 23 / 24 )97.84055555555560.52466715318478186.481190906757
Winsorized Mean ( 24 / 24 )97.81722222222220.521522022508873187.561057827731
Trimmed Mean ( 1 / 24 )99.63085714285710.93003073799594107.126413216777
Trimmed Mean ( 2 / 24 )99.56764705882350.923430950221224107.82359746007
Trimmed Mean ( 3 / 24 )99.50272727272730.915685167581313108.664779987158
Trimmed Mean ( 4 / 24 )99.431093750.907122175196653109.611578758335
Trimmed Mean ( 5 / 24 )99.33532258064520.899534185751073110.429735916823
Trimmed Mean ( 6 / 24 )99.23750.8910882898992111.366630136309
Trimmed Mean ( 7 / 24 )99.13310344827590.880368268611776112.60413054709
Trimmed Mean ( 8 / 24 )99.023750.867277257698355114.177731655038
Trimmed Mean ( 9 / 24 )98.91222222222220.85235361517486116.045993659487
Trimmed Mean ( 10 / 24 )98.82307692307690.842550289795335117.290419479984
Trimmed Mean ( 11 / 24 )98.76240.839197603156049117.686704095168
Trimmed Mean ( 12 / 24 )98.711250.837445225529653117.871888203278
Trimmed Mean ( 13 / 24 )98.65652173913040.833887886056175118.309095729548
Trimmed Mean ( 14 / 24 )98.59681818181820.827756320216448119.113337794916
Trimmed Mean ( 15 / 24 )98.53285714285710.818675971781788120.356356530665
Trimmed Mean ( 16 / 24 )98.466250.806535618262232122.085432770045
Trimmed Mean ( 17 / 24 )98.38578947368420.792182162871627124.19591614767
Trimmed Mean ( 18 / 24 )98.28611111111110.774298379566719126.93570554301
Trimmed Mean ( 19 / 24 )98.17235294117650.749963880155018130.902774838815
Trimmed Mean ( 20 / 24 )98.0493750.717884427965479136.581002708022
Trimmed Mean ( 21 / 24 )97.9180.676710162239463144.697102930974
Trimmed Mean ( 22 / 24 )97.82642857142860.643143366616399152.106720910607
Trimmed Mean ( 23 / 24 )97.79730769230770.626137993562321156.191300796018
Trimmed Mean ( 24 / 24 )97.79166666666670.608993189874903160.579245043372
Median97.775
Midrange101.785
Midmean - Weighted Average at Xnp98.1278378378379
Midmean - Weighted Average at X(n+1)p98.2861111111111
Midmean - Empirical Distribution Function98.1278378378379
Midmean - Empirical Distribution Function - Averaging98.2861111111111
Midmean - Empirical Distribution Function - Interpolation98.2861111111111
Midmean - Closest Observation98.1278378378379
Midmean - True Basic - Statistics Graphics Toolkit98.2861111111111
Midmean - MS Excel (old versions)98.3857894736842
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 99.6906944444444 & 0.93512404352352 & 106.606920370492 \tabularnewline
Geometric Mean & 99.3857428839097 &  &  \tabularnewline
Harmonic Mean & 99.087943691709 &  &  \tabularnewline
Quadratic Mean & 100.001605007953 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 99.6905555555556 & 0.935094768298849 & 106.610109408392 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 99.6866666666667 & 0.933982064114529 & 106.73295612071 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 99.69375 & 0.931038582359895 & 107.078000728291 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 99.7609722222222 & 0.921186406717053 & 108.296183589761 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 99.7429166666667 & 0.91631315072934 & 108.852433894762 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 99.7420833333333 & 0.915042093011883 & 109.002726863668 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 99.7284722222222 & 0.911958280465694 & 109.356397500219 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 99.6929166666667 & 0.904089678630965 & 110.268836181858 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 99.4916666666667 & 0.864561545910218 & 115.077598740435 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 99.2444444444445 & 0.82033601003604 & 120.980236427856 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 99.1375 & 0.802199435228587 & 123.5821114381 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 99.1308333333333 & 0.801121176158069 & 123.740123571236 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 99.1308333333333 & 0.801121176158069 & 123.740123571236 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 99.1191666666667 & 0.799239117572397 & 124.0169111939 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 99.0879166666667 & 0.793613123264137 & 124.85670128427 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 99.1456944444445 & 0.778307064590466 & 127.386347824831 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 99.2330555555556 & 0.763792137136487 & 129.921546361537 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 99.2530555555556 & 0.755592727124608 & 131.357875734539 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 99.2108333333333 & 0.742854952226172 & 133.553438711044 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 99.1441666666667 & 0.722864448263559 & 137.15457566744 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 98.6658333333333 & 0.648952862752848 & 152.038520817667 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 98.0577777777778 & 0.556231775464925 & 176.289421250371 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 97.8405555555556 & 0.52466715318478 & 186.481190906757 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 97.8172222222222 & 0.521522022508873 & 187.561057827731 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 99.6308571428571 & 0.93003073799594 & 107.126413216777 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 99.5676470588235 & 0.923430950221224 & 107.82359746007 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 99.5027272727273 & 0.915685167581313 & 108.664779987158 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 99.43109375 & 0.907122175196653 & 109.611578758335 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 99.3353225806452 & 0.899534185751073 & 110.429735916823 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 99.2375 & 0.8910882898992 & 111.366630136309 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 99.1331034482759 & 0.880368268611776 & 112.60413054709 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 99.02375 & 0.867277257698355 & 114.177731655038 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 98.9122222222222 & 0.85235361517486 & 116.045993659487 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 98.8230769230769 & 0.842550289795335 & 117.290419479984 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 98.7624 & 0.839197603156049 & 117.686704095168 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 98.71125 & 0.837445225529653 & 117.871888203278 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 98.6565217391304 & 0.833887886056175 & 118.309095729548 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 98.5968181818182 & 0.827756320216448 & 119.113337794916 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 98.5328571428571 & 0.818675971781788 & 120.356356530665 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 98.46625 & 0.806535618262232 & 122.085432770045 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 98.3857894736842 & 0.792182162871627 & 124.19591614767 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 98.2861111111111 & 0.774298379566719 & 126.93570554301 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 98.1723529411765 & 0.749963880155018 & 130.902774838815 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 98.049375 & 0.717884427965479 & 136.581002708022 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 97.918 & 0.676710162239463 & 144.697102930974 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 97.8264285714286 & 0.643143366616399 & 152.106720910607 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 97.7973076923077 & 0.626137993562321 & 156.191300796018 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 97.7916666666667 & 0.608993189874903 & 160.579245043372 \tabularnewline
Median & 97.775 &  &  \tabularnewline
Midrange & 101.785 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 98.1278378378379 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 98.2861111111111 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 98.1278378378379 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 98.2861111111111 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 98.2861111111111 &  &  \tabularnewline
Midmean - Closest Observation & 98.1278378378379 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 98.2861111111111 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 98.3857894736842 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]99.6906944444444[/C][C]0.93512404352352[/C][C]106.606920370492[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]99.3857428839097[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]99.087943691709[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]100.001605007953[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]99.6905555555556[/C][C]0.935094768298849[/C][C]106.610109408392[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]99.6866666666667[/C][C]0.933982064114529[/C][C]106.73295612071[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]99.69375[/C][C]0.931038582359895[/C][C]107.078000728291[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]99.7609722222222[/C][C]0.921186406717053[/C][C]108.296183589761[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]99.7429166666667[/C][C]0.91631315072934[/C][C]108.852433894762[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]99.7420833333333[/C][C]0.915042093011883[/C][C]109.002726863668[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]99.7284722222222[/C][C]0.911958280465694[/C][C]109.356397500219[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]99.6929166666667[/C][C]0.904089678630965[/C][C]110.268836181858[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]99.4916666666667[/C][C]0.864561545910218[/C][C]115.077598740435[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]99.2444444444445[/C][C]0.82033601003604[/C][C]120.980236427856[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]99.1375[/C][C]0.802199435228587[/C][C]123.5821114381[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]99.1308333333333[/C][C]0.801121176158069[/C][C]123.740123571236[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]99.1308333333333[/C][C]0.801121176158069[/C][C]123.740123571236[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]99.1191666666667[/C][C]0.799239117572397[/C][C]124.0169111939[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]99.0879166666667[/C][C]0.793613123264137[/C][C]124.85670128427[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]99.1456944444445[/C][C]0.778307064590466[/C][C]127.386347824831[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]99.2330555555556[/C][C]0.763792137136487[/C][C]129.921546361537[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]99.2530555555556[/C][C]0.755592727124608[/C][C]131.357875734539[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]99.2108333333333[/C][C]0.742854952226172[/C][C]133.553438711044[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]99.1441666666667[/C][C]0.722864448263559[/C][C]137.15457566744[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]98.6658333333333[/C][C]0.648952862752848[/C][C]152.038520817667[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]98.0577777777778[/C][C]0.556231775464925[/C][C]176.289421250371[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]97.8405555555556[/C][C]0.52466715318478[/C][C]186.481190906757[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]97.8172222222222[/C][C]0.521522022508873[/C][C]187.561057827731[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]99.6308571428571[/C][C]0.93003073799594[/C][C]107.126413216777[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]99.5676470588235[/C][C]0.923430950221224[/C][C]107.82359746007[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]99.5027272727273[/C][C]0.915685167581313[/C][C]108.664779987158[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]99.43109375[/C][C]0.907122175196653[/C][C]109.611578758335[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]99.3353225806452[/C][C]0.899534185751073[/C][C]110.429735916823[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]99.2375[/C][C]0.8910882898992[/C][C]111.366630136309[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]99.1331034482759[/C][C]0.880368268611776[/C][C]112.60413054709[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]99.02375[/C][C]0.867277257698355[/C][C]114.177731655038[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]98.9122222222222[/C][C]0.85235361517486[/C][C]116.045993659487[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]98.8230769230769[/C][C]0.842550289795335[/C][C]117.290419479984[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]98.7624[/C][C]0.839197603156049[/C][C]117.686704095168[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]98.71125[/C][C]0.837445225529653[/C][C]117.871888203278[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]98.6565217391304[/C][C]0.833887886056175[/C][C]118.309095729548[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]98.5968181818182[/C][C]0.827756320216448[/C][C]119.113337794916[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]98.5328571428571[/C][C]0.818675971781788[/C][C]120.356356530665[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]98.46625[/C][C]0.806535618262232[/C][C]122.085432770045[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]98.3857894736842[/C][C]0.792182162871627[/C][C]124.19591614767[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]98.2861111111111[/C][C]0.774298379566719[/C][C]126.93570554301[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]98.1723529411765[/C][C]0.749963880155018[/C][C]130.902774838815[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]98.049375[/C][C]0.717884427965479[/C][C]136.581002708022[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]97.918[/C][C]0.676710162239463[/C][C]144.697102930974[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]97.8264285714286[/C][C]0.643143366616399[/C][C]152.106720910607[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]97.7973076923077[/C][C]0.626137993562321[/C][C]156.191300796018[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]97.7916666666667[/C][C]0.608993189874903[/C][C]160.579245043372[/C][/ROW]
[ROW][C]Median[/C][C]97.775[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]101.785[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]98.1278378378379[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]98.2861111111111[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]98.1278378378379[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]98.2861111111111[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]98.2861111111111[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]98.1278378378379[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]98.2861111111111[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]98.3857894736842[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]72[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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 Mean99.69069444444440.93512404352352106.606920370492
Geometric Mean99.3857428839097
Harmonic Mean99.087943691709
Quadratic Mean100.001605007953
Winsorized Mean ( 1 / 24 )99.69055555555560.935094768298849106.610109408392
Winsorized Mean ( 2 / 24 )99.68666666666670.933982064114529106.73295612071
Winsorized Mean ( 3 / 24 )99.693750.931038582359895107.078000728291
Winsorized Mean ( 4 / 24 )99.76097222222220.921186406717053108.296183589761
Winsorized Mean ( 5 / 24 )99.74291666666670.91631315072934108.852433894762
Winsorized Mean ( 6 / 24 )99.74208333333330.915042093011883109.002726863668
Winsorized Mean ( 7 / 24 )99.72847222222220.911958280465694109.356397500219
Winsorized Mean ( 8 / 24 )99.69291666666670.904089678630965110.268836181858
Winsorized Mean ( 9 / 24 )99.49166666666670.864561545910218115.077598740435
Winsorized Mean ( 10 / 24 )99.24444444444450.82033601003604120.980236427856
Winsorized Mean ( 11 / 24 )99.13750.802199435228587123.5821114381
Winsorized Mean ( 12 / 24 )99.13083333333330.801121176158069123.740123571236
Winsorized Mean ( 13 / 24 )99.13083333333330.801121176158069123.740123571236
Winsorized Mean ( 14 / 24 )99.11916666666670.799239117572397124.0169111939
Winsorized Mean ( 15 / 24 )99.08791666666670.793613123264137124.85670128427
Winsorized Mean ( 16 / 24 )99.14569444444450.778307064590466127.386347824831
Winsorized Mean ( 17 / 24 )99.23305555555560.763792137136487129.921546361537
Winsorized Mean ( 18 / 24 )99.25305555555560.755592727124608131.357875734539
Winsorized Mean ( 19 / 24 )99.21083333333330.742854952226172133.553438711044
Winsorized Mean ( 20 / 24 )99.14416666666670.722864448263559137.15457566744
Winsorized Mean ( 21 / 24 )98.66583333333330.648952862752848152.038520817667
Winsorized Mean ( 22 / 24 )98.05777777777780.556231775464925176.289421250371
Winsorized Mean ( 23 / 24 )97.84055555555560.52466715318478186.481190906757
Winsorized Mean ( 24 / 24 )97.81722222222220.521522022508873187.561057827731
Trimmed Mean ( 1 / 24 )99.63085714285710.93003073799594107.126413216777
Trimmed Mean ( 2 / 24 )99.56764705882350.923430950221224107.82359746007
Trimmed Mean ( 3 / 24 )99.50272727272730.915685167581313108.664779987158
Trimmed Mean ( 4 / 24 )99.431093750.907122175196653109.611578758335
Trimmed Mean ( 5 / 24 )99.33532258064520.899534185751073110.429735916823
Trimmed Mean ( 6 / 24 )99.23750.8910882898992111.366630136309
Trimmed Mean ( 7 / 24 )99.13310344827590.880368268611776112.60413054709
Trimmed Mean ( 8 / 24 )99.023750.867277257698355114.177731655038
Trimmed Mean ( 9 / 24 )98.91222222222220.85235361517486116.045993659487
Trimmed Mean ( 10 / 24 )98.82307692307690.842550289795335117.290419479984
Trimmed Mean ( 11 / 24 )98.76240.839197603156049117.686704095168
Trimmed Mean ( 12 / 24 )98.711250.837445225529653117.871888203278
Trimmed Mean ( 13 / 24 )98.65652173913040.833887886056175118.309095729548
Trimmed Mean ( 14 / 24 )98.59681818181820.827756320216448119.113337794916
Trimmed Mean ( 15 / 24 )98.53285714285710.818675971781788120.356356530665
Trimmed Mean ( 16 / 24 )98.466250.806535618262232122.085432770045
Trimmed Mean ( 17 / 24 )98.38578947368420.792182162871627124.19591614767
Trimmed Mean ( 18 / 24 )98.28611111111110.774298379566719126.93570554301
Trimmed Mean ( 19 / 24 )98.17235294117650.749963880155018130.902774838815
Trimmed Mean ( 20 / 24 )98.0493750.717884427965479136.581002708022
Trimmed Mean ( 21 / 24 )97.9180.676710162239463144.697102930974
Trimmed Mean ( 22 / 24 )97.82642857142860.643143366616399152.106720910607
Trimmed Mean ( 23 / 24 )97.79730769230770.626137993562321156.191300796018
Trimmed Mean ( 24 / 24 )97.79166666666670.608993189874903160.579245043372
Median97.775
Midrange101.785
Midmean - Weighted Average at Xnp98.1278378378379
Midmean - Weighted Average at X(n+1)p98.2861111111111
Midmean - Empirical Distribution Function98.1278378378379
Midmean - Empirical Distribution Function - Averaging98.2861111111111
Midmean - Empirical Distribution Function - Interpolation98.2861111111111
Midmean - Closest Observation98.1278378378379
Midmean - True Basic - Statistics Graphics Toolkit98.2861111111111
Midmean - MS Excel (old versions)98.3857894736842
Number of observations72



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')