Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationTue, 11 Oct 2016 13:32:05 +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/2016/Oct/11/t1476189144dkmgux39bfsxj3i.htm/, Retrieved Mon, 29 Apr 2024 05:03:20 +0200
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Mon, 29 Apr 2024 05:03:20 +0200
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact0
Dataseries X:
92,64
91,48
92,65
93,91
90,49
94,56
95,11
93,07
93,26
92,92
90,9
91,77
86,16
92,79
97,45
97,74
99,92
99,46
98,52
97,92
97,85
104,94
104,55
105,35
95,75
105,99
106,11
107,33
106,11
108,17
104,62
106,71
97,86
104,41
96,09
102,41
96,3
103,04
105,11
99,4
104,45
104,31
104,06
101,16
100,82
102,6
92,78
99,68
95,14
101,28
100,03
101,17
98,93
97,77
100,24
98,05
95,82
99,19
97,42
98,02
97,34
101,23
100,16
100,72
99,8
100,39
101,82
102,95
98,8
100,24
98,4
98,15




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ jenkins.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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.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]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.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 time1 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean99.07972222222220.551574888902823179.63058909246
Geometric Mean98.9696415894822
Harmonic Mean98.8584577874551
Quadratic Mean99.1886688616979
Winsorized Mean ( 1 / 24 )99.12819444444440.532102722206174186.295221406582
Winsorized Mean ( 2 / 24 )99.12236111111110.525926579794121188.471860748916
Winsorized Mean ( 3 / 24 )99.12152777777780.515816491936585192.164324575268
Winsorized Mean ( 4 / 24 )99.13763888888890.51250445599252193.437613526497
Winsorized Mean ( 5 / 24 )99.18972222222220.499200846965626198.697023102311
Winsorized Mean ( 6 / 24 )99.13722222222220.489155808127924202.670029824722
Winsorized Mean ( 7 / 24 )99.12652777777780.482680721777202205.366660207186
Winsorized Mean ( 8 / 24 )99.108750.479206925742908206.818275521275
Winsorized Mean ( 9 / 24 )99.0850.469444949115859211.068412146332
Winsorized Mean ( 10 / 24 )99.09611111111110.464000665925688213.568898470033
Winsorized Mean ( 11 / 24 )99.10986111111110.456200135785888217.250836500468
Winsorized Mean ( 12 / 24 )99.21152777777780.436020633625152227.538607411571
Winsorized Mean ( 13 / 24 )99.31083333333330.413405867386227240.225988956639
Winsorized Mean ( 14 / 24 )99.36916666666670.388199202590653255.974680018725
Winsorized Mean ( 15 / 24 )99.16291666666670.352599137409436281.234144233085
Winsorized Mean ( 16 / 24 )99.27847222222220.328302330446992302.399535474062
Winsorized Mean ( 17 / 24 )99.21236111111110.312977615798988316.995069624503
Winsorized Mean ( 18 / 24 )99.23236111111110.295550565320074335.754259186224
Winsorized Mean ( 19 / 24 )99.13208333333330.264243312254454375.154559211223
Winsorized Mean ( 20 / 24 )99.27097222222220.20129881086767493.15230325668
Winsorized Mean ( 21 / 24 )99.27972222222220.19611783571619506.224851297533
Winsorized Mean ( 22 / 24 )99.27055555555550.192335624685183516.131921572214
Winsorized Mean ( 23 / 24 )99.360.179826033129031552.534014520056
Winsorized Mean ( 24 / 24 )99.25666666666670.162883831026949609.370899744155
Trimmed Mean ( 1 / 24 )99.13442857142860.519891437772267190.682941416037
Trimmed Mean ( 2 / 24 )99.14102941176470.505368507472812196.175717215815
Trimmed Mean ( 3 / 24 )99.15121212121210.491982219397071201.534137235128
Trimmed Mean ( 4 / 24 )99.162343750.480549079457278206.352166696463
Trimmed Mean ( 5 / 24 )99.16951612903230.467952176988356211.922330968235
Trimmed Mean ( 6 / 24 )99.16466666666670.45690697211534217.034697911403
Trimmed Mean ( 7 / 24 )99.17034482758620.446239714695364222.235586752486
Trimmed Mean ( 8 / 24 )99.17839285714290.434772576524525228.115567108563
Trimmed Mean ( 9 / 24 )99.190.421383697862884235.391166063277
Trimmed Mean ( 10 / 24 )99.20615384615380.407035335372485243.728603452495
Trimmed Mean ( 11 / 24 )99.2220.390267203074917254.241194797384
Trimmed Mean ( 12 / 24 )99.23729166666670.370850056151349267.594112554662
Trimmed Mean ( 13 / 24 )99.2406521739130.351071293828101282.679483964033
Trimmed Mean ( 14 / 24 )99.23181818181820.331183615188095299.627800504139
Trimmed Mean ( 15 / 24 )99.2150.311609334693395318.39546815124
Trimmed Mean ( 16 / 24 )99.221250.295228114215223336.083337671788
Trimmed Mean ( 17 / 24 )99.21447368421050.279725199780746354.685504781037
Trimmed Mean ( 18 / 24 )99.21472222222220.262814282339761377.508868007255
Trimmed Mean ( 19 / 24 )99.21264705882350.244468322960482405.830276321163
Trimmed Mean ( 20 / 24 )99.22218750.228448807694186434.330073776635
Trimmed Mean ( 21 / 24 )99.21633333333330.224870580062795441.215268380716
Trimmed Mean ( 22 / 24 )99.20857142857140.220358482755138450.214442340355
Trimmed Mean ( 23 / 24 )99.20076923076920.21400353920648463.547330098387
Trimmed Mean ( 24 / 24 )99.180.207580960284087477.789484470378
Median99.295
Midrange97.165
Midmean - Weighted Average at Xnp99.122972972973
Midmean - Weighted Average at X(n+1)p99.2147222222222
Midmean - Empirical Distribution Function99.122972972973
Midmean - Empirical Distribution Function - Averaging99.2147222222222
Midmean - Empirical Distribution Function - Interpolation99.2147222222222
Midmean - Closest Observation99.122972972973
Midmean - True Basic - Statistics Graphics Toolkit99.2147222222222
Midmean - MS Excel (old versions)99.2144736842105
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 99.0797222222222 & 0.551574888902823 & 179.63058909246 \tabularnewline
Geometric Mean & 98.9696415894822 &  &  \tabularnewline
Harmonic Mean & 98.8584577874551 &  &  \tabularnewline
Quadratic Mean & 99.1886688616979 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 99.1281944444444 & 0.532102722206174 & 186.295221406582 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 99.1223611111111 & 0.525926579794121 & 188.471860748916 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 99.1215277777778 & 0.515816491936585 & 192.164324575268 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 99.1376388888889 & 0.51250445599252 & 193.437613526497 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 99.1897222222222 & 0.499200846965626 & 198.697023102311 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 99.1372222222222 & 0.489155808127924 & 202.670029824722 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 99.1265277777778 & 0.482680721777202 & 205.366660207186 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 99.10875 & 0.479206925742908 & 206.818275521275 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 99.085 & 0.469444949115859 & 211.068412146332 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 99.0961111111111 & 0.464000665925688 & 213.568898470033 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 99.1098611111111 & 0.456200135785888 & 217.250836500468 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 99.2115277777778 & 0.436020633625152 & 227.538607411571 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 99.3108333333333 & 0.413405867386227 & 240.225988956639 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 99.3691666666667 & 0.388199202590653 & 255.974680018725 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 99.1629166666667 & 0.352599137409436 & 281.234144233085 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 99.2784722222222 & 0.328302330446992 & 302.399535474062 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 99.2123611111111 & 0.312977615798988 & 316.995069624503 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 99.2323611111111 & 0.295550565320074 & 335.754259186224 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 99.1320833333333 & 0.264243312254454 & 375.154559211223 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 99.2709722222222 & 0.20129881086767 & 493.15230325668 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 99.2797222222222 & 0.19611783571619 & 506.224851297533 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 99.2705555555555 & 0.192335624685183 & 516.131921572214 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 99.36 & 0.179826033129031 & 552.534014520056 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 99.2566666666667 & 0.162883831026949 & 609.370899744155 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 99.1344285714286 & 0.519891437772267 & 190.682941416037 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 99.1410294117647 & 0.505368507472812 & 196.175717215815 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 99.1512121212121 & 0.491982219397071 & 201.534137235128 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 99.16234375 & 0.480549079457278 & 206.352166696463 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 99.1695161290323 & 0.467952176988356 & 211.922330968235 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 99.1646666666667 & 0.45690697211534 & 217.034697911403 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 99.1703448275862 & 0.446239714695364 & 222.235586752486 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 99.1783928571429 & 0.434772576524525 & 228.115567108563 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 99.19 & 0.421383697862884 & 235.391166063277 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 99.2061538461538 & 0.407035335372485 & 243.728603452495 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 99.222 & 0.390267203074917 & 254.241194797384 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 99.2372916666667 & 0.370850056151349 & 267.594112554662 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 99.240652173913 & 0.351071293828101 & 282.679483964033 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 99.2318181818182 & 0.331183615188095 & 299.627800504139 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 99.215 & 0.311609334693395 & 318.39546815124 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 99.22125 & 0.295228114215223 & 336.083337671788 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 99.2144736842105 & 0.279725199780746 & 354.685504781037 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 99.2147222222222 & 0.262814282339761 & 377.508868007255 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 99.2126470588235 & 0.244468322960482 & 405.830276321163 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 99.2221875 & 0.228448807694186 & 434.330073776635 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 99.2163333333333 & 0.224870580062795 & 441.215268380716 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 99.2085714285714 & 0.220358482755138 & 450.214442340355 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 99.2007692307692 & 0.21400353920648 & 463.547330098387 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 99.18 & 0.207580960284087 & 477.789484470378 \tabularnewline
Median & 99.295 &  &  \tabularnewline
Midrange & 97.165 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 99.122972972973 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 99.2147222222222 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 99.122972972973 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 99.2147222222222 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 99.2147222222222 &  &  \tabularnewline
Midmean - Closest Observation & 99.122972972973 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 99.2147222222222 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 99.2144736842105 &  &  \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]99.0797222222222[/C][C]0.551574888902823[/C][C]179.63058909246[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]98.9696415894822[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]98.8584577874551[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]99.1886688616979[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]99.1281944444444[/C][C]0.532102722206174[/C][C]186.295221406582[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]99.1223611111111[/C][C]0.525926579794121[/C][C]188.471860748916[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]99.1215277777778[/C][C]0.515816491936585[/C][C]192.164324575268[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]99.1376388888889[/C][C]0.51250445599252[/C][C]193.437613526497[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]99.1897222222222[/C][C]0.499200846965626[/C][C]198.697023102311[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]99.1372222222222[/C][C]0.489155808127924[/C][C]202.670029824722[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]99.1265277777778[/C][C]0.482680721777202[/C][C]205.366660207186[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]99.10875[/C][C]0.479206925742908[/C][C]206.818275521275[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]99.085[/C][C]0.469444949115859[/C][C]211.068412146332[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]99.0961111111111[/C][C]0.464000665925688[/C][C]213.568898470033[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]99.1098611111111[/C][C]0.456200135785888[/C][C]217.250836500468[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]99.2115277777778[/C][C]0.436020633625152[/C][C]227.538607411571[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]99.3108333333333[/C][C]0.413405867386227[/C][C]240.225988956639[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]99.3691666666667[/C][C]0.388199202590653[/C][C]255.974680018725[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]99.1629166666667[/C][C]0.352599137409436[/C][C]281.234144233085[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]99.2784722222222[/C][C]0.328302330446992[/C][C]302.399535474062[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]99.2123611111111[/C][C]0.312977615798988[/C][C]316.995069624503[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]99.2323611111111[/C][C]0.295550565320074[/C][C]335.754259186224[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]99.1320833333333[/C][C]0.264243312254454[/C][C]375.154559211223[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]99.2709722222222[/C][C]0.20129881086767[/C][C]493.15230325668[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]99.2797222222222[/C][C]0.19611783571619[/C][C]506.224851297533[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]99.2705555555555[/C][C]0.192335624685183[/C][C]516.131921572214[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]99.36[/C][C]0.179826033129031[/C][C]552.534014520056[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]99.2566666666667[/C][C]0.162883831026949[/C][C]609.370899744155[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]99.1344285714286[/C][C]0.519891437772267[/C][C]190.682941416037[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]99.1410294117647[/C][C]0.505368507472812[/C][C]196.175717215815[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]99.1512121212121[/C][C]0.491982219397071[/C][C]201.534137235128[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]99.16234375[/C][C]0.480549079457278[/C][C]206.352166696463[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]99.1695161290323[/C][C]0.467952176988356[/C][C]211.922330968235[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]99.1646666666667[/C][C]0.45690697211534[/C][C]217.034697911403[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]99.1703448275862[/C][C]0.446239714695364[/C][C]222.235586752486[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]99.1783928571429[/C][C]0.434772576524525[/C][C]228.115567108563[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]99.19[/C][C]0.421383697862884[/C][C]235.391166063277[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]99.2061538461538[/C][C]0.407035335372485[/C][C]243.728603452495[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]99.222[/C][C]0.390267203074917[/C][C]254.241194797384[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]99.2372916666667[/C][C]0.370850056151349[/C][C]267.594112554662[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]99.240652173913[/C][C]0.351071293828101[/C][C]282.679483964033[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]99.2318181818182[/C][C]0.331183615188095[/C][C]299.627800504139[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]99.215[/C][C]0.311609334693395[/C][C]318.39546815124[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]99.22125[/C][C]0.295228114215223[/C][C]336.083337671788[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]99.2144736842105[/C][C]0.279725199780746[/C][C]354.685504781037[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]99.2147222222222[/C][C]0.262814282339761[/C][C]377.508868007255[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]99.2126470588235[/C][C]0.244468322960482[/C][C]405.830276321163[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]99.2221875[/C][C]0.228448807694186[/C][C]434.330073776635[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]99.2163333333333[/C][C]0.224870580062795[/C][C]441.215268380716[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]99.2085714285714[/C][C]0.220358482755138[/C][C]450.214442340355[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]99.2007692307692[/C][C]0.21400353920648[/C][C]463.547330098387[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]99.18[/C][C]0.207580960284087[/C][C]477.789484470378[/C][/ROW]
[ROW][C]Median[/C][C]99.295[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]97.165[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]99.122972972973[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]99.2147222222222[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]99.122972972973[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]99.2147222222222[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]99.2147222222222[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]99.122972972973[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]99.2147222222222[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]99.2144736842105[/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 Mean99.07972222222220.551574888902823179.63058909246
Geometric Mean98.9696415894822
Harmonic Mean98.8584577874551
Quadratic Mean99.1886688616979
Winsorized Mean ( 1 / 24 )99.12819444444440.532102722206174186.295221406582
Winsorized Mean ( 2 / 24 )99.12236111111110.525926579794121188.471860748916
Winsorized Mean ( 3 / 24 )99.12152777777780.515816491936585192.164324575268
Winsorized Mean ( 4 / 24 )99.13763888888890.51250445599252193.437613526497
Winsorized Mean ( 5 / 24 )99.18972222222220.499200846965626198.697023102311
Winsorized Mean ( 6 / 24 )99.13722222222220.489155808127924202.670029824722
Winsorized Mean ( 7 / 24 )99.12652777777780.482680721777202205.366660207186
Winsorized Mean ( 8 / 24 )99.108750.479206925742908206.818275521275
Winsorized Mean ( 9 / 24 )99.0850.469444949115859211.068412146332
Winsorized Mean ( 10 / 24 )99.09611111111110.464000665925688213.568898470033
Winsorized Mean ( 11 / 24 )99.10986111111110.456200135785888217.250836500468
Winsorized Mean ( 12 / 24 )99.21152777777780.436020633625152227.538607411571
Winsorized Mean ( 13 / 24 )99.31083333333330.413405867386227240.225988956639
Winsorized Mean ( 14 / 24 )99.36916666666670.388199202590653255.974680018725
Winsorized Mean ( 15 / 24 )99.16291666666670.352599137409436281.234144233085
Winsorized Mean ( 16 / 24 )99.27847222222220.328302330446992302.399535474062
Winsorized Mean ( 17 / 24 )99.21236111111110.312977615798988316.995069624503
Winsorized Mean ( 18 / 24 )99.23236111111110.295550565320074335.754259186224
Winsorized Mean ( 19 / 24 )99.13208333333330.264243312254454375.154559211223
Winsorized Mean ( 20 / 24 )99.27097222222220.20129881086767493.15230325668
Winsorized Mean ( 21 / 24 )99.27972222222220.19611783571619506.224851297533
Winsorized Mean ( 22 / 24 )99.27055555555550.192335624685183516.131921572214
Winsorized Mean ( 23 / 24 )99.360.179826033129031552.534014520056
Winsorized Mean ( 24 / 24 )99.25666666666670.162883831026949609.370899744155
Trimmed Mean ( 1 / 24 )99.13442857142860.519891437772267190.682941416037
Trimmed Mean ( 2 / 24 )99.14102941176470.505368507472812196.175717215815
Trimmed Mean ( 3 / 24 )99.15121212121210.491982219397071201.534137235128
Trimmed Mean ( 4 / 24 )99.162343750.480549079457278206.352166696463
Trimmed Mean ( 5 / 24 )99.16951612903230.467952176988356211.922330968235
Trimmed Mean ( 6 / 24 )99.16466666666670.45690697211534217.034697911403
Trimmed Mean ( 7 / 24 )99.17034482758620.446239714695364222.235586752486
Trimmed Mean ( 8 / 24 )99.17839285714290.434772576524525228.115567108563
Trimmed Mean ( 9 / 24 )99.190.421383697862884235.391166063277
Trimmed Mean ( 10 / 24 )99.20615384615380.407035335372485243.728603452495
Trimmed Mean ( 11 / 24 )99.2220.390267203074917254.241194797384
Trimmed Mean ( 12 / 24 )99.23729166666670.370850056151349267.594112554662
Trimmed Mean ( 13 / 24 )99.2406521739130.351071293828101282.679483964033
Trimmed Mean ( 14 / 24 )99.23181818181820.331183615188095299.627800504139
Trimmed Mean ( 15 / 24 )99.2150.311609334693395318.39546815124
Trimmed Mean ( 16 / 24 )99.221250.295228114215223336.083337671788
Trimmed Mean ( 17 / 24 )99.21447368421050.279725199780746354.685504781037
Trimmed Mean ( 18 / 24 )99.21472222222220.262814282339761377.508868007255
Trimmed Mean ( 19 / 24 )99.21264705882350.244468322960482405.830276321163
Trimmed Mean ( 20 / 24 )99.22218750.228448807694186434.330073776635
Trimmed Mean ( 21 / 24 )99.21633333333330.224870580062795441.215268380716
Trimmed Mean ( 22 / 24 )99.20857142857140.220358482755138450.214442340355
Trimmed Mean ( 23 / 24 )99.20076923076920.21400353920648463.547330098387
Trimmed Mean ( 24 / 24 )99.180.207580960284087477.789484470378
Median99.295
Midrange97.165
Midmean - Weighted Average at Xnp99.122972972973
Midmean - Weighted Average at X(n+1)p99.2147222222222
Midmean - Empirical Distribution Function99.122972972973
Midmean - Empirical Distribution Function - Averaging99.2147222222222
Midmean - Empirical Distribution Function - Interpolation99.2147222222222
Midmean - Closest Observation99.122972972973
Midmean - True Basic - Statistics Graphics Toolkit99.2147222222222
Midmean - MS Excel (old versions)99.2144736842105
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')