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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationMon, 01 Jun 2009 08:54:34 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Jun/01/t1243868136xbp0pdhyac4mk27.htm/, Retrieved Mon, 13 May 2024 05:03:10 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=40957, Retrieved Mon, 13 May 2024 05:03:10 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact116
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Robuustheid-finan...] [2009-06-01 14:54:34] [267e4485b61217b9c165d444603a8c11] [Current]
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Dataseries X:
1
-1
3
4
3
2
1
4
3
5
6
6
6
6
6
5
6
5
6
5
7
4
5
6
6
5
3
2
3
3
2
0
4
4
5
6
6
5
5
3
5
5
5
3
6
6
4
6
5
4
5
5
4
3
2
3
2
-1
0
-2
1
-2
-2
-2
-6
-4
-2
0
-5
-4
-5
-1




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=40957&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]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=40957&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=40957&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'Sir Ronald Aylmer Fisher' @ 193.190.124.24







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean2.833333333333330.3784078332472937.48751237261446
Geometric MeanNaN
Harmonic Mean0
Quadratic Mean4.26549463068991
Winsorized Mean ( 1 / 24 )2.833333333333330.3721527274952587.61336173028434
Winsorized Mean ( 2 / 24 )2.833333333333330.3721527274952587.61336173028434
Winsorized Mean ( 3 / 24 )2.8750.3603692572417157.97792803416529
Winsorized Mean ( 4 / 24 )2.8750.3603692572417157.97792803416529
Winsorized Mean ( 5 / 24 )3.013888888888890.3265106072778169.23060023689976
Winsorized Mean ( 6 / 24 )3.013888888888890.3265106072778169.23060023689976
Winsorized Mean ( 7 / 24 )3.013888888888890.3265106072778169.23060023689976
Winsorized Mean ( 8 / 24 )3.013888888888890.3265106072778169.23060023689976
Winsorized Mean ( 9 / 24 )3.013888888888890.3265106072778169.23060023689976
Winsorized Mean ( 10 / 24 )3.152777777777780.29778769720474210.5873338871018
Winsorized Mean ( 11 / 24 )3.152777777777780.29778769720474210.5873338871018
Winsorized Mean ( 12 / 24 )3.152777777777780.29778769720474210.5873338871018
Winsorized Mean ( 13 / 24 )3.333333333333330.2638940366848212.6313325424419
Winsorized Mean ( 14 / 24 )3.333333333333330.2638940366848212.6313325424419
Winsorized Mean ( 15 / 24 )3.1250.23730481642782513.1687171252610
Winsorized Mean ( 16 / 24 )3.347222222222220.19795484284364316.9090191183960
Winsorized Mean ( 17 / 24 )3.347222222222220.19795484284364316.9090191183960
Winsorized Mean ( 18 / 24 )3.347222222222220.19795484284364316.9090191183960
Winsorized Mean ( 19 / 24 )3.611111111111110.15644169687443623.0827917572991
Winsorized Mean ( 20 / 24 )3.611111111111110.15644169687443623.0827917572991
Winsorized Mean ( 21 / 24 )3.611111111111110.15644169687443623.0827917572991
Winsorized Mean ( 22 / 24 )3.611111111111110.15644169687443623.0827917572991
Winsorized Mean ( 23 / 24 )3.611111111111110.15644169687443623.0827917572991
Winsorized Mean ( 24 / 24 )3.944444444444440.11169642391137135.3139725187108
Trimmed Mean ( 1 / 24 )2.90.3629588550163547.9898863463996
Trimmed Mean ( 2 / 24 )2.970588235294120.3518236624787148.44340091955539
Trimmed Mean ( 3 / 24 )3.045454545454550.3382608875657849.00327131336542
Trimmed Mean ( 4 / 24 )3.1093750.3274156164007699.49672173300987
Trimmed Mean ( 5 / 24 )3.177419354838710.31406664922036110.1170224941946
Trimmed Mean ( 6 / 24 )3.216666666666670.30908253762694710.4071446137442
Trimmed Mean ( 7 / 24 )3.258620689655170.30280034494285410.7616148530813
Trimmed Mean ( 8 / 24 )3.303571428571430.29489117831853311.2026797390426
Trimmed Mean ( 9 / 24 )3.351851851851850.28490734012658711.7647086605863
Trimmed Mean ( 10 / 24 )3.403846153846150.27221732870211112.5041494238267
Trimmed Mean ( 11 / 24 )3.440.26366335988707013.0469398610159
Trimmed Mean ( 12 / 24 )3.479166666666670.25262729979254613.7719346623414
Trimmed Mean ( 13 / 24 )3.521739130434780.23822842615602214.7830348680904
Trimmed Mean ( 14 / 24 )3.545454545454550.22864280481345915.5065213985069
Trimmed Mean ( 15 / 24 )3.571428571428570.21592481899903116.5401485016162
Trimmed Mean ( 16 / 24 )3.6250.20471211806351717.7077939219761
Trimmed Mean ( 17 / 24 )3.657894736842110.20055511790854018.2388501225396
Trimmed Mean ( 18 / 24 )3.694444444444440.19444444444444419
Trimmed Mean ( 19 / 24 )3.735294117647060.185522452189320.1339194990572
Trimmed Mean ( 20 / 24 )3.750.18513290779433920.25571814691
Trimmed Mean ( 21 / 24 )3.766666666666670.1837247649938120.5016817781401
Trimmed Mean ( 22 / 24 )3.785714285714290.18080612301419920.9379761183032
Trimmed Mean ( 23 / 24 )3.807692307692310.17558018785405121.686343739747
Trimmed Mean ( 24 / 24 )3.833333333333330.16666666666666723
Median4
Midrange0.5
Midmean - Weighted Average at Xnp3.65853658536585
Midmean - Weighted Average at X(n+1)p3.65853658536585
Midmean - Empirical Distribution Function3.65853658536585
Midmean - Empirical Distribution Function - Averaging3.65853658536585
Midmean - Empirical Distribution Function - Interpolation3.65853658536585
Midmean - Closest Observation3.65853658536585
Midmean - True Basic - Statistics Graphics Toolkit3.65853658536585
Midmean - MS Excel (old versions)3.65853658536585
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 2.83333333333333 & 0.378407833247293 & 7.48751237261446 \tabularnewline
Geometric Mean & NaN &  &  \tabularnewline
Harmonic Mean & 0 &  &  \tabularnewline
Quadratic Mean & 4.26549463068991 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 2.83333333333333 & 0.372152727495258 & 7.61336173028434 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 2.83333333333333 & 0.372152727495258 & 7.61336173028434 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 2.875 & 0.360369257241715 & 7.97792803416529 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 2.875 & 0.360369257241715 & 7.97792803416529 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 3.01388888888889 & 0.326510607277816 & 9.23060023689976 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 3.01388888888889 & 0.326510607277816 & 9.23060023689976 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 3.01388888888889 & 0.326510607277816 & 9.23060023689976 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 3.01388888888889 & 0.326510607277816 & 9.23060023689976 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 3.01388888888889 & 0.326510607277816 & 9.23060023689976 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 3.15277777777778 & 0.297787697204742 & 10.5873338871018 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 3.15277777777778 & 0.297787697204742 & 10.5873338871018 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 3.15277777777778 & 0.297787697204742 & 10.5873338871018 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 3.33333333333333 & 0.26389403668482 & 12.6313325424419 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 3.33333333333333 & 0.26389403668482 & 12.6313325424419 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 3.125 & 0.237304816427825 & 13.1687171252610 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 3.34722222222222 & 0.197954842843643 & 16.9090191183960 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 3.34722222222222 & 0.197954842843643 & 16.9090191183960 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 3.34722222222222 & 0.197954842843643 & 16.9090191183960 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 3.61111111111111 & 0.156441696874436 & 23.0827917572991 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 3.61111111111111 & 0.156441696874436 & 23.0827917572991 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 3.61111111111111 & 0.156441696874436 & 23.0827917572991 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 3.61111111111111 & 0.156441696874436 & 23.0827917572991 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 3.61111111111111 & 0.156441696874436 & 23.0827917572991 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 3.94444444444444 & 0.111696423911371 & 35.3139725187108 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 2.9 & 0.362958855016354 & 7.9898863463996 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 2.97058823529412 & 0.351823662478714 & 8.44340091955539 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 3.04545454545455 & 0.338260887565784 & 9.00327131336542 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 3.109375 & 0.327415616400769 & 9.49672173300987 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 3.17741935483871 & 0.314066649220361 & 10.1170224941946 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 3.21666666666667 & 0.309082537626947 & 10.4071446137442 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 3.25862068965517 & 0.302800344942854 & 10.7616148530813 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 3.30357142857143 & 0.294891178318533 & 11.2026797390426 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 3.35185185185185 & 0.284907340126587 & 11.7647086605863 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 3.40384615384615 & 0.272217328702111 & 12.5041494238267 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 3.44 & 0.263663359887070 & 13.0469398610159 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 3.47916666666667 & 0.252627299792546 & 13.7719346623414 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 3.52173913043478 & 0.238228426156022 & 14.7830348680904 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 3.54545454545455 & 0.228642804813459 & 15.5065213985069 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 3.57142857142857 & 0.215924818999031 & 16.5401485016162 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 3.625 & 0.204712118063517 & 17.7077939219761 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 3.65789473684211 & 0.200555117908540 & 18.2388501225396 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 3.69444444444444 & 0.194444444444444 & 19 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 3.73529411764706 & 0.1855224521893 & 20.1339194990572 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 3.75 & 0.185132907794339 & 20.25571814691 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 3.76666666666667 & 0.18372476499381 & 20.5016817781401 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 3.78571428571429 & 0.180806123014199 & 20.9379761183032 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 3.80769230769231 & 0.175580187854051 & 21.686343739747 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 3.83333333333333 & 0.166666666666667 & 23 \tabularnewline
Median & 4 &  &  \tabularnewline
Midrange & 0.5 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 3.65853658536585 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 3.65853658536585 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 3.65853658536585 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 3.65853658536585 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 3.65853658536585 &  &  \tabularnewline
Midmean - Closest Observation & 3.65853658536585 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 3.65853658536585 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 3.65853658536585 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=40957&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]2.83333333333333[/C][C]0.378407833247293[/C][C]7.48751237261446[/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]4.26549463068991[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]2.83333333333333[/C][C]0.372152727495258[/C][C]7.61336173028434[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]2.83333333333333[/C][C]0.372152727495258[/C][C]7.61336173028434[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]2.875[/C][C]0.360369257241715[/C][C]7.97792803416529[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]2.875[/C][C]0.360369257241715[/C][C]7.97792803416529[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]3.01388888888889[/C][C]0.326510607277816[/C][C]9.23060023689976[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]3.01388888888889[/C][C]0.326510607277816[/C][C]9.23060023689976[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]3.01388888888889[/C][C]0.326510607277816[/C][C]9.23060023689976[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]3.01388888888889[/C][C]0.326510607277816[/C][C]9.23060023689976[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]3.01388888888889[/C][C]0.326510607277816[/C][C]9.23060023689976[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]3.15277777777778[/C][C]0.297787697204742[/C][C]10.5873338871018[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]3.15277777777778[/C][C]0.297787697204742[/C][C]10.5873338871018[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]3.15277777777778[/C][C]0.297787697204742[/C][C]10.5873338871018[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]3.33333333333333[/C][C]0.26389403668482[/C][C]12.6313325424419[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]3.33333333333333[/C][C]0.26389403668482[/C][C]12.6313325424419[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]3.125[/C][C]0.237304816427825[/C][C]13.1687171252610[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]3.34722222222222[/C][C]0.197954842843643[/C][C]16.9090191183960[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]3.34722222222222[/C][C]0.197954842843643[/C][C]16.9090191183960[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]3.34722222222222[/C][C]0.197954842843643[/C][C]16.9090191183960[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]3.61111111111111[/C][C]0.156441696874436[/C][C]23.0827917572991[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]3.61111111111111[/C][C]0.156441696874436[/C][C]23.0827917572991[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]3.61111111111111[/C][C]0.156441696874436[/C][C]23.0827917572991[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]3.61111111111111[/C][C]0.156441696874436[/C][C]23.0827917572991[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]3.61111111111111[/C][C]0.156441696874436[/C][C]23.0827917572991[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]3.94444444444444[/C][C]0.111696423911371[/C][C]35.3139725187108[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]2.9[/C][C]0.362958855016354[/C][C]7.9898863463996[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]2.97058823529412[/C][C]0.351823662478714[/C][C]8.44340091955539[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]3.04545454545455[/C][C]0.338260887565784[/C][C]9.00327131336542[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]3.109375[/C][C]0.327415616400769[/C][C]9.49672173300987[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]3.17741935483871[/C][C]0.314066649220361[/C][C]10.1170224941946[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]3.21666666666667[/C][C]0.309082537626947[/C][C]10.4071446137442[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]3.25862068965517[/C][C]0.302800344942854[/C][C]10.7616148530813[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]3.30357142857143[/C][C]0.294891178318533[/C][C]11.2026797390426[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]3.35185185185185[/C][C]0.284907340126587[/C][C]11.7647086605863[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]3.40384615384615[/C][C]0.272217328702111[/C][C]12.5041494238267[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]3.44[/C][C]0.263663359887070[/C][C]13.0469398610159[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]3.47916666666667[/C][C]0.252627299792546[/C][C]13.7719346623414[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]3.52173913043478[/C][C]0.238228426156022[/C][C]14.7830348680904[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]3.54545454545455[/C][C]0.228642804813459[/C][C]15.5065213985069[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]3.57142857142857[/C][C]0.215924818999031[/C][C]16.5401485016162[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]3.625[/C][C]0.204712118063517[/C][C]17.7077939219761[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]3.65789473684211[/C][C]0.200555117908540[/C][C]18.2388501225396[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]3.69444444444444[/C][C]0.194444444444444[/C][C]19[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]3.73529411764706[/C][C]0.1855224521893[/C][C]20.1339194990572[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]3.75[/C][C]0.185132907794339[/C][C]20.25571814691[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]3.76666666666667[/C][C]0.18372476499381[/C][C]20.5016817781401[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]3.78571428571429[/C][C]0.180806123014199[/C][C]20.9379761183032[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]3.80769230769231[/C][C]0.175580187854051[/C][C]21.686343739747[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]3.83333333333333[/C][C]0.166666666666667[/C][C]23[/C][/ROW]
[ROW][C]Median[/C][C]4[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]0.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]3.65853658536585[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]3.65853658536585[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]3.65853658536585[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]3.65853658536585[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]3.65853658536585[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]3.65853658536585[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]3.65853658536585[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]3.65853658536585[/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=40957&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=40957&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 Mean2.833333333333330.3784078332472937.48751237261446
Geometric MeanNaN
Harmonic Mean0
Quadratic Mean4.26549463068991
Winsorized Mean ( 1 / 24 )2.833333333333330.3721527274952587.61336173028434
Winsorized Mean ( 2 / 24 )2.833333333333330.3721527274952587.61336173028434
Winsorized Mean ( 3 / 24 )2.8750.3603692572417157.97792803416529
Winsorized Mean ( 4 / 24 )2.8750.3603692572417157.97792803416529
Winsorized Mean ( 5 / 24 )3.013888888888890.3265106072778169.23060023689976
Winsorized Mean ( 6 / 24 )3.013888888888890.3265106072778169.23060023689976
Winsorized Mean ( 7 / 24 )3.013888888888890.3265106072778169.23060023689976
Winsorized Mean ( 8 / 24 )3.013888888888890.3265106072778169.23060023689976
Winsorized Mean ( 9 / 24 )3.013888888888890.3265106072778169.23060023689976
Winsorized Mean ( 10 / 24 )3.152777777777780.29778769720474210.5873338871018
Winsorized Mean ( 11 / 24 )3.152777777777780.29778769720474210.5873338871018
Winsorized Mean ( 12 / 24 )3.152777777777780.29778769720474210.5873338871018
Winsorized Mean ( 13 / 24 )3.333333333333330.2638940366848212.6313325424419
Winsorized Mean ( 14 / 24 )3.333333333333330.2638940366848212.6313325424419
Winsorized Mean ( 15 / 24 )3.1250.23730481642782513.1687171252610
Winsorized Mean ( 16 / 24 )3.347222222222220.19795484284364316.9090191183960
Winsorized Mean ( 17 / 24 )3.347222222222220.19795484284364316.9090191183960
Winsorized Mean ( 18 / 24 )3.347222222222220.19795484284364316.9090191183960
Winsorized Mean ( 19 / 24 )3.611111111111110.15644169687443623.0827917572991
Winsorized Mean ( 20 / 24 )3.611111111111110.15644169687443623.0827917572991
Winsorized Mean ( 21 / 24 )3.611111111111110.15644169687443623.0827917572991
Winsorized Mean ( 22 / 24 )3.611111111111110.15644169687443623.0827917572991
Winsorized Mean ( 23 / 24 )3.611111111111110.15644169687443623.0827917572991
Winsorized Mean ( 24 / 24 )3.944444444444440.11169642391137135.3139725187108
Trimmed Mean ( 1 / 24 )2.90.3629588550163547.9898863463996
Trimmed Mean ( 2 / 24 )2.970588235294120.3518236624787148.44340091955539
Trimmed Mean ( 3 / 24 )3.045454545454550.3382608875657849.00327131336542
Trimmed Mean ( 4 / 24 )3.1093750.3274156164007699.49672173300987
Trimmed Mean ( 5 / 24 )3.177419354838710.31406664922036110.1170224941946
Trimmed Mean ( 6 / 24 )3.216666666666670.30908253762694710.4071446137442
Trimmed Mean ( 7 / 24 )3.258620689655170.30280034494285410.7616148530813
Trimmed Mean ( 8 / 24 )3.303571428571430.29489117831853311.2026797390426
Trimmed Mean ( 9 / 24 )3.351851851851850.28490734012658711.7647086605863
Trimmed Mean ( 10 / 24 )3.403846153846150.27221732870211112.5041494238267
Trimmed Mean ( 11 / 24 )3.440.26366335988707013.0469398610159
Trimmed Mean ( 12 / 24 )3.479166666666670.25262729979254613.7719346623414
Trimmed Mean ( 13 / 24 )3.521739130434780.23822842615602214.7830348680904
Trimmed Mean ( 14 / 24 )3.545454545454550.22864280481345915.5065213985069
Trimmed Mean ( 15 / 24 )3.571428571428570.21592481899903116.5401485016162
Trimmed Mean ( 16 / 24 )3.6250.20471211806351717.7077939219761
Trimmed Mean ( 17 / 24 )3.657894736842110.20055511790854018.2388501225396
Trimmed Mean ( 18 / 24 )3.694444444444440.19444444444444419
Trimmed Mean ( 19 / 24 )3.735294117647060.185522452189320.1339194990572
Trimmed Mean ( 20 / 24 )3.750.18513290779433920.25571814691
Trimmed Mean ( 21 / 24 )3.766666666666670.1837247649938120.5016817781401
Trimmed Mean ( 22 / 24 )3.785714285714290.18080612301419920.9379761183032
Trimmed Mean ( 23 / 24 )3.807692307692310.17558018785405121.686343739747
Trimmed Mean ( 24 / 24 )3.833333333333330.16666666666666723
Median4
Midrange0.5
Midmean - Weighted Average at Xnp3.65853658536585
Midmean - Weighted Average at X(n+1)p3.65853658536585
Midmean - Empirical Distribution Function3.65853658536585
Midmean - Empirical Distribution Function - Averaging3.65853658536585
Midmean - Empirical Distribution Function - Interpolation3.65853658536585
Midmean - Closest Observation3.65853658536585
Midmean - True Basic - Statistics Graphics Toolkit3.65853658536585
Midmean - MS Excel (old versions)3.65853658536585
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')