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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 computationTue, 14 Mar 2017 17:53:09 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2017/Mar/14/t1489514500wp89377xel849wa.htm/, Retrieved Tue, 14 May 2024 12:38:09 +0200
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Tue, 14 May 2024 12:38:09 +0200
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact0
Dataseries X:
92,49
92,46
92,55
92,24
92,41
92,83
92,85
93,04
93,04
92,83
92,96
92,83
93,01
93,21
93,58
94,07
94,57
95,03
95,21
95,89
96,43
96,35
96,71
96,32
97,23
97,88
98,2
98,56
99,31
99,69
99,77
101,06
101,77
101,91
102,52
102,09
102,22
102,74
103,56
104,4
104,76
104,86
104,84
104,96
104,83
104,58
104,8
104,17
104,63
105,32
106,16
107,22
107,51
107,87
107,79
108,04
107,74
107,71
111,19
110,82
113,65
114,72
114,32
116,76
116,47
117,34
116,92
116,48
115,07
116,45
116,84
114,31




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Sir Maurice George Kendall' @ kendall.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 & 'Sir Maurice George Kendall' @ kendall.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]'Sir Maurice George Kendall' @ kendall.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'Sir Maurice George Kendall' @ kendall.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean102.568750.937115261429578109.451584262464
Geometric Mean102.269268368244
Harmonic Mean101.974738950269
Quadratic Mean102.872248991164
Winsorized Mean ( 1 / 24 )102.5652777777780.935473589236452109.63995024327
Winsorized Mean ( 2 / 24 )102.5644444444440.934782553796859109.720109802919
Winsorized Mean ( 3 / 24 )102.5623611111110.933877094558394109.824260289423
Winsorized Mean ( 4 / 24 )102.5501388888890.930065340332062110.261219767931
Winsorized Mean ( 5 / 24 )102.5688888888890.927007814470314110.645117859655
Winsorized Mean ( 6 / 24 )102.5672222222220.926655968590555110.68533058523
Winsorized Mean ( 7 / 24 )102.4330555555560.899209499797555113.914561154677
Winsorized Mean ( 8 / 24 )102.3963888888890.891238858048328114.892195245078
Winsorized Mean ( 9 / 24 )102.3601388888890.879509205972445116.383248968625
Winsorized Mean ( 10 / 24 )102.3656944444440.878199489726243116.563144982417
Winsorized Mean ( 11 / 24 )102.2694444444440.858433990380579119.134896323367
Winsorized Mean ( 12 / 24 )101.8594444444440.785690487290519129.643219680195
Winsorized Mean ( 13 / 24 )101.8233333333330.769758767569679132.279536944821
Winsorized Mean ( 14 / 24 )101.3547222222220.675669058440977150.006457978238
Winsorized Mean ( 15 / 24 )101.4213888888890.654392026477639154.985673396426
Winsorized Mean ( 16 / 24 )101.5147222222220.634563112070961159.975769614024
Winsorized Mean ( 17 / 24 )101.6115277777780.616373539637061164.853812247699
Winsorized Mean ( 18 / 24 )101.6490277777780.6085854567808167.025068780751
Winsorized Mean ( 19 / 24 )101.7756944444440.574855558723665177.045681997777
Winsorized Mean ( 20 / 24 )101.8145833333330.546511412222433186.299098346905
Winsorized Mean ( 21 / 24 )101.5141666666670.503580557930416201.584761500451
Winsorized Mean ( 22 / 24 )101.2819444444440.467709835030636216.54867368314
Winsorized Mean ( 23 / 24 )101.2563888888890.440877907859221229.669908797566
Winsorized Mean ( 24 / 24 )101.3963888888890.411992482190722246.112230858499
Trimmed Mean ( 1 / 24 )102.5052857142860.928513911421389110.397145862218
Trimmed Mean ( 2 / 24 )102.4417647058820.919756069056427111.379275606169
Trimmed Mean ( 3 / 24 )102.3748484848480.909277928703963112.589171311755
Trimmed Mean ( 4 / 24 )102.304531250.8966917517758114.091080962211
Trimmed Mean ( 5 / 24 )102.2332258064520.882514818441946115.84306990668
Trimmed Mean ( 6 / 24 )102.1526666666670.865870185944591117.976884208372
Trimmed Mean ( 7 / 24 )102.0668965517240.84530943824982120.745009972975
Trimmed Mean ( 8 / 24 )101.9996428571430.827223801918267123.303563824703
Trimmed Mean ( 9 / 24 )101.9335185185190.806568516188982126.3792430185
Trimmed Mean ( 10 / 24 )101.8678846153850.783432585888448130.027632817777
Trimmed Mean ( 11 / 24 )101.79620.754357079416178134.94431586535
Trimmed Mean ( 12 / 24 )101.7316666666670.722240488948847140.855668192637
Trimmed Mean ( 13 / 24 )101.7150.699130705920826145.487816710941
Trimmed Mean ( 14 / 24 )101.7013636363640.672841517212084151.152033628607
Trimmed Mean ( 15 / 24 )101.743809523810.660098710844206154.1342345506
Trimmed Mean ( 16 / 24 )101.78250.647406141103451157.215839544741
Trimmed Mean ( 17 / 24 )101.8142105263160.634309318666098160.511926169433
Trimmed Mean ( 18 / 24 )101.8380555555560.620125924161036164.221574341262
Trimmed Mean ( 19 / 24 )101.8602941176470.601626654961144169.308146967367
Trimmed Mean ( 20 / 24 )101.87031250.584188761400433174.379103520913
Trimmed Mean ( 21 / 24 )101.8770.5664162698975179.862418179541
Trimmed Mean ( 22 / 24 )101.9214285714290.551780119318906184.713847061464
Trimmed Mean ( 23 / 24 )102.0019230769230.538228152718434189.514284159498
Trimmed Mean ( 24 / 24 )102.0991666666670.523568758778713195.006224024568
Median102.37
Midrange104.79
Midmean - Weighted Average at Xnp101.654054054054
Midmean - Weighted Average at X(n+1)p101.838055555556
Midmean - Empirical Distribution Function101.654054054054
Midmean - Empirical Distribution Function - Averaging101.838055555556
Midmean - Empirical Distribution Function - Interpolation101.838055555556
Midmean - Closest Observation101.654054054054
Midmean - True Basic - Statistics Graphics Toolkit101.838055555556
Midmean - MS Excel (old versions)101.814210526316
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 102.56875 & 0.937115261429578 & 109.451584262464 \tabularnewline
Geometric Mean & 102.269268368244 &  &  \tabularnewline
Harmonic Mean & 101.974738950269 &  &  \tabularnewline
Quadratic Mean & 102.872248991164 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 102.565277777778 & 0.935473589236452 & 109.63995024327 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 102.564444444444 & 0.934782553796859 & 109.720109802919 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 102.562361111111 & 0.933877094558394 & 109.824260289423 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 102.550138888889 & 0.930065340332062 & 110.261219767931 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 102.568888888889 & 0.927007814470314 & 110.645117859655 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 102.567222222222 & 0.926655968590555 & 110.68533058523 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 102.433055555556 & 0.899209499797555 & 113.914561154677 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 102.396388888889 & 0.891238858048328 & 114.892195245078 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 102.360138888889 & 0.879509205972445 & 116.383248968625 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 102.365694444444 & 0.878199489726243 & 116.563144982417 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 102.269444444444 & 0.858433990380579 & 119.134896323367 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 101.859444444444 & 0.785690487290519 & 129.643219680195 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 101.823333333333 & 0.769758767569679 & 132.279536944821 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 101.354722222222 & 0.675669058440977 & 150.006457978238 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 101.421388888889 & 0.654392026477639 & 154.985673396426 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 101.514722222222 & 0.634563112070961 & 159.975769614024 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 101.611527777778 & 0.616373539637061 & 164.853812247699 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 101.649027777778 & 0.6085854567808 & 167.025068780751 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 101.775694444444 & 0.574855558723665 & 177.045681997777 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 101.814583333333 & 0.546511412222433 & 186.299098346905 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 101.514166666667 & 0.503580557930416 & 201.584761500451 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 101.281944444444 & 0.467709835030636 & 216.54867368314 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 101.256388888889 & 0.440877907859221 & 229.669908797566 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 101.396388888889 & 0.411992482190722 & 246.112230858499 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 102.505285714286 & 0.928513911421389 & 110.397145862218 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 102.441764705882 & 0.919756069056427 & 111.379275606169 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 102.374848484848 & 0.909277928703963 & 112.589171311755 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 102.30453125 & 0.8966917517758 & 114.091080962211 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 102.233225806452 & 0.882514818441946 & 115.84306990668 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 102.152666666667 & 0.865870185944591 & 117.976884208372 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 102.066896551724 & 0.84530943824982 & 120.745009972975 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 101.999642857143 & 0.827223801918267 & 123.303563824703 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 101.933518518519 & 0.806568516188982 & 126.3792430185 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 101.867884615385 & 0.783432585888448 & 130.027632817777 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 101.7962 & 0.754357079416178 & 134.94431586535 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 101.731666666667 & 0.722240488948847 & 140.855668192637 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 101.715 & 0.699130705920826 & 145.487816710941 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 101.701363636364 & 0.672841517212084 & 151.152033628607 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 101.74380952381 & 0.660098710844206 & 154.1342345506 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 101.7825 & 0.647406141103451 & 157.215839544741 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 101.814210526316 & 0.634309318666098 & 160.511926169433 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 101.838055555556 & 0.620125924161036 & 164.221574341262 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 101.860294117647 & 0.601626654961144 & 169.308146967367 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 101.8703125 & 0.584188761400433 & 174.379103520913 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 101.877 & 0.5664162698975 & 179.862418179541 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 101.921428571429 & 0.551780119318906 & 184.713847061464 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 102.001923076923 & 0.538228152718434 & 189.514284159498 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 102.099166666667 & 0.523568758778713 & 195.006224024568 \tabularnewline
Median & 102.37 &  &  \tabularnewline
Midrange & 104.79 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 101.654054054054 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 101.838055555556 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 101.654054054054 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 101.838055555556 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 101.838055555556 &  &  \tabularnewline
Midmean - Closest Observation & 101.654054054054 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 101.838055555556 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 101.814210526316 &  &  \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]102.56875[/C][C]0.937115261429578[/C][C]109.451584262464[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]102.269268368244[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]101.974738950269[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]102.872248991164[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]102.565277777778[/C][C]0.935473589236452[/C][C]109.63995024327[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]102.564444444444[/C][C]0.934782553796859[/C][C]109.720109802919[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]102.562361111111[/C][C]0.933877094558394[/C][C]109.824260289423[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]102.550138888889[/C][C]0.930065340332062[/C][C]110.261219767931[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]102.568888888889[/C][C]0.927007814470314[/C][C]110.645117859655[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]102.567222222222[/C][C]0.926655968590555[/C][C]110.68533058523[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]102.433055555556[/C][C]0.899209499797555[/C][C]113.914561154677[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]102.396388888889[/C][C]0.891238858048328[/C][C]114.892195245078[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]102.360138888889[/C][C]0.879509205972445[/C][C]116.383248968625[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]102.365694444444[/C][C]0.878199489726243[/C][C]116.563144982417[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]102.269444444444[/C][C]0.858433990380579[/C][C]119.134896323367[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]101.859444444444[/C][C]0.785690487290519[/C][C]129.643219680195[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]101.823333333333[/C][C]0.769758767569679[/C][C]132.279536944821[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]101.354722222222[/C][C]0.675669058440977[/C][C]150.006457978238[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]101.421388888889[/C][C]0.654392026477639[/C][C]154.985673396426[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]101.514722222222[/C][C]0.634563112070961[/C][C]159.975769614024[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]101.611527777778[/C][C]0.616373539637061[/C][C]164.853812247699[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]101.649027777778[/C][C]0.6085854567808[/C][C]167.025068780751[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]101.775694444444[/C][C]0.574855558723665[/C][C]177.045681997777[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]101.814583333333[/C][C]0.546511412222433[/C][C]186.299098346905[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]101.514166666667[/C][C]0.503580557930416[/C][C]201.584761500451[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]101.281944444444[/C][C]0.467709835030636[/C][C]216.54867368314[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]101.256388888889[/C][C]0.440877907859221[/C][C]229.669908797566[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]101.396388888889[/C][C]0.411992482190722[/C][C]246.112230858499[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]102.505285714286[/C][C]0.928513911421389[/C][C]110.397145862218[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]102.441764705882[/C][C]0.919756069056427[/C][C]111.379275606169[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]102.374848484848[/C][C]0.909277928703963[/C][C]112.589171311755[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]102.30453125[/C][C]0.8966917517758[/C][C]114.091080962211[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]102.233225806452[/C][C]0.882514818441946[/C][C]115.84306990668[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]102.152666666667[/C][C]0.865870185944591[/C][C]117.976884208372[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]102.066896551724[/C][C]0.84530943824982[/C][C]120.745009972975[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]101.999642857143[/C][C]0.827223801918267[/C][C]123.303563824703[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]101.933518518519[/C][C]0.806568516188982[/C][C]126.3792430185[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]101.867884615385[/C][C]0.783432585888448[/C][C]130.027632817777[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]101.7962[/C][C]0.754357079416178[/C][C]134.94431586535[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]101.731666666667[/C][C]0.722240488948847[/C][C]140.855668192637[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]101.715[/C][C]0.699130705920826[/C][C]145.487816710941[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]101.701363636364[/C][C]0.672841517212084[/C][C]151.152033628607[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]101.74380952381[/C][C]0.660098710844206[/C][C]154.1342345506[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]101.7825[/C][C]0.647406141103451[/C][C]157.215839544741[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]101.814210526316[/C][C]0.634309318666098[/C][C]160.511926169433[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]101.838055555556[/C][C]0.620125924161036[/C][C]164.221574341262[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]101.860294117647[/C][C]0.601626654961144[/C][C]169.308146967367[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]101.8703125[/C][C]0.584188761400433[/C][C]174.379103520913[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]101.877[/C][C]0.5664162698975[/C][C]179.862418179541[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]101.921428571429[/C][C]0.551780119318906[/C][C]184.713847061464[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]102.001923076923[/C][C]0.538228152718434[/C][C]189.514284159498[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]102.099166666667[/C][C]0.523568758778713[/C][C]195.006224024568[/C][/ROW]
[ROW][C]Median[/C][C]102.37[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]104.79[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]101.654054054054[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]101.838055555556[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]101.654054054054[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]101.838055555556[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]101.838055555556[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]101.654054054054[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]101.838055555556[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]101.814210526316[/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 Mean102.568750.937115261429578109.451584262464
Geometric Mean102.269268368244
Harmonic Mean101.974738950269
Quadratic Mean102.872248991164
Winsorized Mean ( 1 / 24 )102.5652777777780.935473589236452109.63995024327
Winsorized Mean ( 2 / 24 )102.5644444444440.934782553796859109.720109802919
Winsorized Mean ( 3 / 24 )102.5623611111110.933877094558394109.824260289423
Winsorized Mean ( 4 / 24 )102.5501388888890.930065340332062110.261219767931
Winsorized Mean ( 5 / 24 )102.5688888888890.927007814470314110.645117859655
Winsorized Mean ( 6 / 24 )102.5672222222220.926655968590555110.68533058523
Winsorized Mean ( 7 / 24 )102.4330555555560.899209499797555113.914561154677
Winsorized Mean ( 8 / 24 )102.3963888888890.891238858048328114.892195245078
Winsorized Mean ( 9 / 24 )102.3601388888890.879509205972445116.383248968625
Winsorized Mean ( 10 / 24 )102.3656944444440.878199489726243116.563144982417
Winsorized Mean ( 11 / 24 )102.2694444444440.858433990380579119.134896323367
Winsorized Mean ( 12 / 24 )101.8594444444440.785690487290519129.643219680195
Winsorized Mean ( 13 / 24 )101.8233333333330.769758767569679132.279536944821
Winsorized Mean ( 14 / 24 )101.3547222222220.675669058440977150.006457978238
Winsorized Mean ( 15 / 24 )101.4213888888890.654392026477639154.985673396426
Winsorized Mean ( 16 / 24 )101.5147222222220.634563112070961159.975769614024
Winsorized Mean ( 17 / 24 )101.6115277777780.616373539637061164.853812247699
Winsorized Mean ( 18 / 24 )101.6490277777780.6085854567808167.025068780751
Winsorized Mean ( 19 / 24 )101.7756944444440.574855558723665177.045681997777
Winsorized Mean ( 20 / 24 )101.8145833333330.546511412222433186.299098346905
Winsorized Mean ( 21 / 24 )101.5141666666670.503580557930416201.584761500451
Winsorized Mean ( 22 / 24 )101.2819444444440.467709835030636216.54867368314
Winsorized Mean ( 23 / 24 )101.2563888888890.440877907859221229.669908797566
Winsorized Mean ( 24 / 24 )101.3963888888890.411992482190722246.112230858499
Trimmed Mean ( 1 / 24 )102.5052857142860.928513911421389110.397145862218
Trimmed Mean ( 2 / 24 )102.4417647058820.919756069056427111.379275606169
Trimmed Mean ( 3 / 24 )102.3748484848480.909277928703963112.589171311755
Trimmed Mean ( 4 / 24 )102.304531250.8966917517758114.091080962211
Trimmed Mean ( 5 / 24 )102.2332258064520.882514818441946115.84306990668
Trimmed Mean ( 6 / 24 )102.1526666666670.865870185944591117.976884208372
Trimmed Mean ( 7 / 24 )102.0668965517240.84530943824982120.745009972975
Trimmed Mean ( 8 / 24 )101.9996428571430.827223801918267123.303563824703
Trimmed Mean ( 9 / 24 )101.9335185185190.806568516188982126.3792430185
Trimmed Mean ( 10 / 24 )101.8678846153850.783432585888448130.027632817777
Trimmed Mean ( 11 / 24 )101.79620.754357079416178134.94431586535
Trimmed Mean ( 12 / 24 )101.7316666666670.722240488948847140.855668192637
Trimmed Mean ( 13 / 24 )101.7150.699130705920826145.487816710941
Trimmed Mean ( 14 / 24 )101.7013636363640.672841517212084151.152033628607
Trimmed Mean ( 15 / 24 )101.743809523810.660098710844206154.1342345506
Trimmed Mean ( 16 / 24 )101.78250.647406141103451157.215839544741
Trimmed Mean ( 17 / 24 )101.8142105263160.634309318666098160.511926169433
Trimmed Mean ( 18 / 24 )101.8380555555560.620125924161036164.221574341262
Trimmed Mean ( 19 / 24 )101.8602941176470.601626654961144169.308146967367
Trimmed Mean ( 20 / 24 )101.87031250.584188761400433174.379103520913
Trimmed Mean ( 21 / 24 )101.8770.5664162698975179.862418179541
Trimmed Mean ( 22 / 24 )101.9214285714290.551780119318906184.713847061464
Trimmed Mean ( 23 / 24 )102.0019230769230.538228152718434189.514284159498
Trimmed Mean ( 24 / 24 )102.0991666666670.523568758778713195.006224024568
Median102.37
Midrange104.79
Midmean - Weighted Average at Xnp101.654054054054
Midmean - Weighted Average at X(n+1)p101.838055555556
Midmean - Empirical Distribution Function101.654054054054
Midmean - Empirical Distribution Function - Averaging101.838055555556
Midmean - Empirical Distribution Function - Interpolation101.838055555556
Midmean - Closest Observation101.654054054054
Midmean - True Basic - Statistics Graphics Toolkit101.838055555556
Midmean - MS Excel (old versions)101.814210526316
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')