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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationTue, 29 Nov 2011 08:20:32 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Nov/29/t1322572926lzvemunkencwbkt.htm/, Retrieved Fri, 29 Mar 2024 15:45:07 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=148324, Retrieved Fri, 29 Mar 2024 15:45:07 +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] [WS8] [2011-11-29 13:20:32] [84449ea5bbe6e767918d59f07903f9b5] [Current]
- R  D    [Central Tendency] [central tendency ...] [2011-12-14 15:27:55] [74be16979710d4c4e7c6647856088456]
- RMPD    [(Partial) Autocorrelation Function] [ACF paper] [2011-12-14 15:50:08] [d3c56829b3e69baec30b0d469b5d7237]
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Dataseries X:
37
30
47
35
30
43
82
40
47
19
52
136
80
42
54
66
81
63
137
72
107
58
36
52
79
77
54
84
48
96
83
66
61
53
30
74
69
59
42
65
70
100
63
105
82
81
75
102
121
98
76
77
63
37
35
23
40
29
37
51
20
28
13
22
25
13
16
13
16
17
9
17
25
14
8
7
10
7
10
3




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gertrude Mary Cox' @ cox.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 & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=148324&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=148324&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=148324&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'Gertrude Mary Cox' @ cox.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean51.83.5686486468349614.515298401803
Geometric Mean40.2405071216039
Harmonic Mean27.2206709184115
Quadratic Mean60.739813960861
Winsorized Mean ( 1 / 26 )51.83753.5565701258553314.5751378900573
Winsorized Mean ( 2 / 26 )51.46253.4524777265800914.9059614791424
Winsorized Mean ( 3 / 26 )50.9753.3232007123680515.3391276699854
Winsorized Mean ( 4 / 26 )50.9253.2940190814354415.459837584732
Winsorized Mean ( 5 / 26 )50.83.2458054723838515.650968744806
Winsorized Mean ( 6 / 26 )50.653.2162610968386815.7480995712023
Winsorized Mean ( 7 / 26 )50.73753.1416326356034416.1500423139876
Winsorized Mean ( 8 / 26 )50.53753.1040471616335916.2811637093179
Winsorized Mean ( 9 / 26 )49.18752.8745992428444717.1110808306371
Winsorized Mean ( 10 / 26 )49.18752.8358070843448217.3451502648193
Winsorized Mean ( 11 / 26 )49.3252.77264982017517.7898411985134
Winsorized Mean ( 12 / 26 )49.3252.77264982017517.7898411985134
Winsorized Mean ( 13 / 26 )49.3252.7240010943509818.1075551336194
Winsorized Mean ( 14 / 26 )49.3252.7240010943509818.1075551336194
Winsorized Mean ( 15 / 26 )49.51252.6409023288943318.748326834461
Winsorized Mean ( 16 / 26 )49.51252.5827442076994519.1705008387581
Winsorized Mean ( 17 / 26 )49.51252.4611534903708420.1175994076418
Winsorized Mean ( 18 / 26 )49.73752.4295610734232820.4718047815605
Winsorized Mean ( 19 / 26 )49.9752.3305874062621721.4430919285497
Winsorized Mean ( 20 / 26 )49.7252.2954946931055921.6619973678644
Winsorized Mean ( 21 / 26 )50.252.153632492184423.3326717452299
Winsorized Mean ( 22 / 26 )49.9752.0418078828282924.4758580962941
Winsorized Mean ( 23 / 26 )49.68751.9268747036114525.7865754876916
Winsorized Mean ( 24 / 26 )49.38751.8871227303403226.1707938789406
Winsorized Mean ( 25 / 26 )48.451.7664148773680927.4284374643566
Winsorized Mean ( 26 / 26 )50.0751.5590461827668932.1189972134952
Trimmed Mean ( 1 / 26 )51.33333333333333.4341077142535614.9480848024277
Trimmed Mean ( 2 / 26 )50.80263157894743.2893778933421115.4444497489251
Trimmed Mean ( 3 / 26 )50.44594594594593.1855573450539415.8358304314536
Trimmed Mean ( 4 / 26 )50.253.1216688035305516.0971592960689
Trimmed Mean ( 5 / 26 )50.05714285714293.0561945860056616.3789122218706
Trimmed Mean ( 6 / 26 )49.88235294117652.9928602053640816.6671175792884
Trimmed Mean ( 7 / 26 )49.72727272727272.9250581612806217.0004389606741
Trimmed Mean ( 8 / 26 )49.5468752.8618947068758617.312612822883
Trimmed Mean ( 9 / 26 )49.38709677419362.7942256352034617.6746989047638
Trimmed Mean ( 10 / 26 )49.41666666666672.7620605248164917.8912323689757
Trimmed Mean ( 11 / 26 )49.4482758620692.7291720659632418.1184163793706
Trimmed Mean ( 12 / 26 )49.46428571428572.69956276951818.3230730075291
Trimmed Mean ( 13 / 26 )49.48148148148152.661123791333818.5942050657781
Trimmed Mean ( 14 / 26 )49.52.6210512208391618.8855523335221
Trimmed Mean ( 15 / 26 )49.522.5690846460105919.2753477690575
Trimmed Mean ( 16 / 26 )49.52083333333332.5185463807024519.6624662991203
Trimmed Mean ( 17 / 26 )49.52173913043482.4641858128450520.0965929080076
Trimmed Mean ( 18 / 26 )49.52272727272732.4174507908054320.4855161731038
Trimmed Mean ( 19 / 26 )49.52.3609408742801420.9662175530307
Trimmed Mean ( 20 / 26 )49.452.3060539055678221.4435577072184
Trimmed Mean ( 21 / 26 )49.42105263157892.2384940766232422.0778125560781
Trimmed Mean ( 22 / 26 )49.33333333333332.1789031753657722.6413609797286
Trimmed Mean ( 23 / 26 )49.26470588235292.1225001332297823.2106962497041
Trimmed Mean ( 24 / 26 )49.218752.0706933421776223.769212464961
Trimmed Mean ( 25 / 26 )49.22.0036747849085124.5548830431814
Trimmed Mean ( 26 / 26 )49.28571428571431.9387834665866925.4209483086236
Median49.5
Midrange70
Midmean - Weighted Average at Xnp48.8536585365854
Midmean - Weighted Average at X(n+1)p48.8536585365854
Midmean - Empirical Distribution Function48.8536585365854
Midmean - Empirical Distribution Function - Averaging48.8536585365854
Midmean - Empirical Distribution Function - Interpolation48.8536585365854
Midmean - Closest Observation48.8536585365854
Midmean - True Basic - Statistics Graphics Toolkit48.8536585365854
Midmean - MS Excel (old versions)49.5
Number of observations80

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 51.8 & 3.56864864683496 & 14.515298401803 \tabularnewline
Geometric Mean & 40.2405071216039 &  &  \tabularnewline
Harmonic Mean & 27.2206709184115 &  &  \tabularnewline
Quadratic Mean & 60.739813960861 &  &  \tabularnewline
Winsorized Mean ( 1 / 26 ) & 51.8375 & 3.55657012585533 & 14.5751378900573 \tabularnewline
Winsorized Mean ( 2 / 26 ) & 51.4625 & 3.45247772658009 & 14.9059614791424 \tabularnewline
Winsorized Mean ( 3 / 26 ) & 50.975 & 3.32320071236805 & 15.3391276699854 \tabularnewline
Winsorized Mean ( 4 / 26 ) & 50.925 & 3.29401908143544 & 15.459837584732 \tabularnewline
Winsorized Mean ( 5 / 26 ) & 50.8 & 3.24580547238385 & 15.650968744806 \tabularnewline
Winsorized Mean ( 6 / 26 ) & 50.65 & 3.21626109683868 & 15.7480995712023 \tabularnewline
Winsorized Mean ( 7 / 26 ) & 50.7375 & 3.14163263560344 & 16.1500423139876 \tabularnewline
Winsorized Mean ( 8 / 26 ) & 50.5375 & 3.10404716163359 & 16.2811637093179 \tabularnewline
Winsorized Mean ( 9 / 26 ) & 49.1875 & 2.87459924284447 & 17.1110808306371 \tabularnewline
Winsorized Mean ( 10 / 26 ) & 49.1875 & 2.83580708434482 & 17.3451502648193 \tabularnewline
Winsorized Mean ( 11 / 26 ) & 49.325 & 2.772649820175 & 17.7898411985134 \tabularnewline
Winsorized Mean ( 12 / 26 ) & 49.325 & 2.772649820175 & 17.7898411985134 \tabularnewline
Winsorized Mean ( 13 / 26 ) & 49.325 & 2.72400109435098 & 18.1075551336194 \tabularnewline
Winsorized Mean ( 14 / 26 ) & 49.325 & 2.72400109435098 & 18.1075551336194 \tabularnewline
Winsorized Mean ( 15 / 26 ) & 49.5125 & 2.64090232889433 & 18.748326834461 \tabularnewline
Winsorized Mean ( 16 / 26 ) & 49.5125 & 2.58274420769945 & 19.1705008387581 \tabularnewline
Winsorized Mean ( 17 / 26 ) & 49.5125 & 2.46115349037084 & 20.1175994076418 \tabularnewline
Winsorized Mean ( 18 / 26 ) & 49.7375 & 2.42956107342328 & 20.4718047815605 \tabularnewline
Winsorized Mean ( 19 / 26 ) & 49.975 & 2.33058740626217 & 21.4430919285497 \tabularnewline
Winsorized Mean ( 20 / 26 ) & 49.725 & 2.29549469310559 & 21.6619973678644 \tabularnewline
Winsorized Mean ( 21 / 26 ) & 50.25 & 2.1536324921844 & 23.3326717452299 \tabularnewline
Winsorized Mean ( 22 / 26 ) & 49.975 & 2.04180788282829 & 24.4758580962941 \tabularnewline
Winsorized Mean ( 23 / 26 ) & 49.6875 & 1.92687470361145 & 25.7865754876916 \tabularnewline
Winsorized Mean ( 24 / 26 ) & 49.3875 & 1.88712273034032 & 26.1707938789406 \tabularnewline
Winsorized Mean ( 25 / 26 ) & 48.45 & 1.76641487736809 & 27.4284374643566 \tabularnewline
Winsorized Mean ( 26 / 26 ) & 50.075 & 1.55904618276689 & 32.1189972134952 \tabularnewline
Trimmed Mean ( 1 / 26 ) & 51.3333333333333 & 3.43410771425356 & 14.9480848024277 \tabularnewline
Trimmed Mean ( 2 / 26 ) & 50.8026315789474 & 3.28937789334211 & 15.4444497489251 \tabularnewline
Trimmed Mean ( 3 / 26 ) & 50.4459459459459 & 3.18555734505394 & 15.8358304314536 \tabularnewline
Trimmed Mean ( 4 / 26 ) & 50.25 & 3.12166880353055 & 16.0971592960689 \tabularnewline
Trimmed Mean ( 5 / 26 ) & 50.0571428571429 & 3.05619458600566 & 16.3789122218706 \tabularnewline
Trimmed Mean ( 6 / 26 ) & 49.8823529411765 & 2.99286020536408 & 16.6671175792884 \tabularnewline
Trimmed Mean ( 7 / 26 ) & 49.7272727272727 & 2.92505816128062 & 17.0004389606741 \tabularnewline
Trimmed Mean ( 8 / 26 ) & 49.546875 & 2.86189470687586 & 17.312612822883 \tabularnewline
Trimmed Mean ( 9 / 26 ) & 49.3870967741936 & 2.79422563520346 & 17.6746989047638 \tabularnewline
Trimmed Mean ( 10 / 26 ) & 49.4166666666667 & 2.76206052481649 & 17.8912323689757 \tabularnewline
Trimmed Mean ( 11 / 26 ) & 49.448275862069 & 2.72917206596324 & 18.1184163793706 \tabularnewline
Trimmed Mean ( 12 / 26 ) & 49.4642857142857 & 2.699562769518 & 18.3230730075291 \tabularnewline
Trimmed Mean ( 13 / 26 ) & 49.4814814814815 & 2.6611237913338 & 18.5942050657781 \tabularnewline
Trimmed Mean ( 14 / 26 ) & 49.5 & 2.62105122083916 & 18.8855523335221 \tabularnewline
Trimmed Mean ( 15 / 26 ) & 49.52 & 2.56908464601059 & 19.2753477690575 \tabularnewline
Trimmed Mean ( 16 / 26 ) & 49.5208333333333 & 2.51854638070245 & 19.6624662991203 \tabularnewline
Trimmed Mean ( 17 / 26 ) & 49.5217391304348 & 2.46418581284505 & 20.0965929080076 \tabularnewline
Trimmed Mean ( 18 / 26 ) & 49.5227272727273 & 2.41745079080543 & 20.4855161731038 \tabularnewline
Trimmed Mean ( 19 / 26 ) & 49.5 & 2.36094087428014 & 20.9662175530307 \tabularnewline
Trimmed Mean ( 20 / 26 ) & 49.45 & 2.30605390556782 & 21.4435577072184 \tabularnewline
Trimmed Mean ( 21 / 26 ) & 49.4210526315789 & 2.23849407662324 & 22.0778125560781 \tabularnewline
Trimmed Mean ( 22 / 26 ) & 49.3333333333333 & 2.17890317536577 & 22.6413609797286 \tabularnewline
Trimmed Mean ( 23 / 26 ) & 49.2647058823529 & 2.12250013322978 & 23.2106962497041 \tabularnewline
Trimmed Mean ( 24 / 26 ) & 49.21875 & 2.07069334217762 & 23.769212464961 \tabularnewline
Trimmed Mean ( 25 / 26 ) & 49.2 & 2.00367478490851 & 24.5548830431814 \tabularnewline
Trimmed Mean ( 26 / 26 ) & 49.2857142857143 & 1.93878346658669 & 25.4209483086236 \tabularnewline
Median & 49.5 &  &  \tabularnewline
Midrange & 70 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 48.8536585365854 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 48.8536585365854 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 48.8536585365854 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 48.8536585365854 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 48.8536585365854 &  &  \tabularnewline
Midmean - Closest Observation & 48.8536585365854 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 48.8536585365854 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 49.5 &  &  \tabularnewline
Number of observations & 80 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=148324&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]51.8[/C][C]3.56864864683496[/C][C]14.515298401803[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]40.2405071216039[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]27.2206709184115[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]60.739813960861[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 26 )[/C][C]51.8375[/C][C]3.55657012585533[/C][C]14.5751378900573[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 26 )[/C][C]51.4625[/C][C]3.45247772658009[/C][C]14.9059614791424[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 26 )[/C][C]50.975[/C][C]3.32320071236805[/C][C]15.3391276699854[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 26 )[/C][C]50.925[/C][C]3.29401908143544[/C][C]15.459837584732[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 26 )[/C][C]50.8[/C][C]3.24580547238385[/C][C]15.650968744806[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 26 )[/C][C]50.65[/C][C]3.21626109683868[/C][C]15.7480995712023[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 26 )[/C][C]50.7375[/C][C]3.14163263560344[/C][C]16.1500423139876[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 26 )[/C][C]50.5375[/C][C]3.10404716163359[/C][C]16.2811637093179[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 26 )[/C][C]49.1875[/C][C]2.87459924284447[/C][C]17.1110808306371[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 26 )[/C][C]49.1875[/C][C]2.83580708434482[/C][C]17.3451502648193[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 26 )[/C][C]49.325[/C][C]2.772649820175[/C][C]17.7898411985134[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 26 )[/C][C]49.325[/C][C]2.772649820175[/C][C]17.7898411985134[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 26 )[/C][C]49.325[/C][C]2.72400109435098[/C][C]18.1075551336194[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 26 )[/C][C]49.325[/C][C]2.72400109435098[/C][C]18.1075551336194[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 26 )[/C][C]49.5125[/C][C]2.64090232889433[/C][C]18.748326834461[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 26 )[/C][C]49.5125[/C][C]2.58274420769945[/C][C]19.1705008387581[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 26 )[/C][C]49.5125[/C][C]2.46115349037084[/C][C]20.1175994076418[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 26 )[/C][C]49.7375[/C][C]2.42956107342328[/C][C]20.4718047815605[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 26 )[/C][C]49.975[/C][C]2.33058740626217[/C][C]21.4430919285497[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 26 )[/C][C]49.725[/C][C]2.29549469310559[/C][C]21.6619973678644[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 26 )[/C][C]50.25[/C][C]2.1536324921844[/C][C]23.3326717452299[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 26 )[/C][C]49.975[/C][C]2.04180788282829[/C][C]24.4758580962941[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 26 )[/C][C]49.6875[/C][C]1.92687470361145[/C][C]25.7865754876916[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 26 )[/C][C]49.3875[/C][C]1.88712273034032[/C][C]26.1707938789406[/C][/ROW]
[ROW][C]Winsorized Mean ( 25 / 26 )[/C][C]48.45[/C][C]1.76641487736809[/C][C]27.4284374643566[/C][/ROW]
[ROW][C]Winsorized Mean ( 26 / 26 )[/C][C]50.075[/C][C]1.55904618276689[/C][C]32.1189972134952[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 26 )[/C][C]51.3333333333333[/C][C]3.43410771425356[/C][C]14.9480848024277[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 26 )[/C][C]50.8026315789474[/C][C]3.28937789334211[/C][C]15.4444497489251[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 26 )[/C][C]50.4459459459459[/C][C]3.18555734505394[/C][C]15.8358304314536[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 26 )[/C][C]50.25[/C][C]3.12166880353055[/C][C]16.0971592960689[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 26 )[/C][C]50.0571428571429[/C][C]3.05619458600566[/C][C]16.3789122218706[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 26 )[/C][C]49.8823529411765[/C][C]2.99286020536408[/C][C]16.6671175792884[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 26 )[/C][C]49.7272727272727[/C][C]2.92505816128062[/C][C]17.0004389606741[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 26 )[/C][C]49.546875[/C][C]2.86189470687586[/C][C]17.312612822883[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 26 )[/C][C]49.3870967741936[/C][C]2.79422563520346[/C][C]17.6746989047638[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 26 )[/C][C]49.4166666666667[/C][C]2.76206052481649[/C][C]17.8912323689757[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 26 )[/C][C]49.448275862069[/C][C]2.72917206596324[/C][C]18.1184163793706[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 26 )[/C][C]49.4642857142857[/C][C]2.699562769518[/C][C]18.3230730075291[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 26 )[/C][C]49.4814814814815[/C][C]2.6611237913338[/C][C]18.5942050657781[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 26 )[/C][C]49.5[/C][C]2.62105122083916[/C][C]18.8855523335221[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 26 )[/C][C]49.52[/C][C]2.56908464601059[/C][C]19.2753477690575[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 26 )[/C][C]49.5208333333333[/C][C]2.51854638070245[/C][C]19.6624662991203[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 26 )[/C][C]49.5217391304348[/C][C]2.46418581284505[/C][C]20.0965929080076[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 26 )[/C][C]49.5227272727273[/C][C]2.41745079080543[/C][C]20.4855161731038[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 26 )[/C][C]49.5[/C][C]2.36094087428014[/C][C]20.9662175530307[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 26 )[/C][C]49.45[/C][C]2.30605390556782[/C][C]21.4435577072184[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 26 )[/C][C]49.4210526315789[/C][C]2.23849407662324[/C][C]22.0778125560781[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 26 )[/C][C]49.3333333333333[/C][C]2.17890317536577[/C][C]22.6413609797286[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 26 )[/C][C]49.2647058823529[/C][C]2.12250013322978[/C][C]23.2106962497041[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 26 )[/C][C]49.21875[/C][C]2.07069334217762[/C][C]23.769212464961[/C][/ROW]
[ROW][C]Trimmed Mean ( 25 / 26 )[/C][C]49.2[/C][C]2.00367478490851[/C][C]24.5548830431814[/C][/ROW]
[ROW][C]Trimmed Mean ( 26 / 26 )[/C][C]49.2857142857143[/C][C]1.93878346658669[/C][C]25.4209483086236[/C][/ROW]
[ROW][C]Median[/C][C]49.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]70[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]48.8536585365854[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]48.8536585365854[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]48.8536585365854[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]48.8536585365854[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]48.8536585365854[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]48.8536585365854[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]48.8536585365854[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]49.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]80[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=148324&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=148324&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 Mean51.83.5686486468349614.515298401803
Geometric Mean40.2405071216039
Harmonic Mean27.2206709184115
Quadratic Mean60.739813960861
Winsorized Mean ( 1 / 26 )51.83753.5565701258553314.5751378900573
Winsorized Mean ( 2 / 26 )51.46253.4524777265800914.9059614791424
Winsorized Mean ( 3 / 26 )50.9753.3232007123680515.3391276699854
Winsorized Mean ( 4 / 26 )50.9253.2940190814354415.459837584732
Winsorized Mean ( 5 / 26 )50.83.2458054723838515.650968744806
Winsorized Mean ( 6 / 26 )50.653.2162610968386815.7480995712023
Winsorized Mean ( 7 / 26 )50.73753.1416326356034416.1500423139876
Winsorized Mean ( 8 / 26 )50.53753.1040471616335916.2811637093179
Winsorized Mean ( 9 / 26 )49.18752.8745992428444717.1110808306371
Winsorized Mean ( 10 / 26 )49.18752.8358070843448217.3451502648193
Winsorized Mean ( 11 / 26 )49.3252.77264982017517.7898411985134
Winsorized Mean ( 12 / 26 )49.3252.77264982017517.7898411985134
Winsorized Mean ( 13 / 26 )49.3252.7240010943509818.1075551336194
Winsorized Mean ( 14 / 26 )49.3252.7240010943509818.1075551336194
Winsorized Mean ( 15 / 26 )49.51252.6409023288943318.748326834461
Winsorized Mean ( 16 / 26 )49.51252.5827442076994519.1705008387581
Winsorized Mean ( 17 / 26 )49.51252.4611534903708420.1175994076418
Winsorized Mean ( 18 / 26 )49.73752.4295610734232820.4718047815605
Winsorized Mean ( 19 / 26 )49.9752.3305874062621721.4430919285497
Winsorized Mean ( 20 / 26 )49.7252.2954946931055921.6619973678644
Winsorized Mean ( 21 / 26 )50.252.153632492184423.3326717452299
Winsorized Mean ( 22 / 26 )49.9752.0418078828282924.4758580962941
Winsorized Mean ( 23 / 26 )49.68751.9268747036114525.7865754876916
Winsorized Mean ( 24 / 26 )49.38751.8871227303403226.1707938789406
Winsorized Mean ( 25 / 26 )48.451.7664148773680927.4284374643566
Winsorized Mean ( 26 / 26 )50.0751.5590461827668932.1189972134952
Trimmed Mean ( 1 / 26 )51.33333333333333.4341077142535614.9480848024277
Trimmed Mean ( 2 / 26 )50.80263157894743.2893778933421115.4444497489251
Trimmed Mean ( 3 / 26 )50.44594594594593.1855573450539415.8358304314536
Trimmed Mean ( 4 / 26 )50.253.1216688035305516.0971592960689
Trimmed Mean ( 5 / 26 )50.05714285714293.0561945860056616.3789122218706
Trimmed Mean ( 6 / 26 )49.88235294117652.9928602053640816.6671175792884
Trimmed Mean ( 7 / 26 )49.72727272727272.9250581612806217.0004389606741
Trimmed Mean ( 8 / 26 )49.5468752.8618947068758617.312612822883
Trimmed Mean ( 9 / 26 )49.38709677419362.7942256352034617.6746989047638
Trimmed Mean ( 10 / 26 )49.41666666666672.7620605248164917.8912323689757
Trimmed Mean ( 11 / 26 )49.4482758620692.7291720659632418.1184163793706
Trimmed Mean ( 12 / 26 )49.46428571428572.69956276951818.3230730075291
Trimmed Mean ( 13 / 26 )49.48148148148152.661123791333818.5942050657781
Trimmed Mean ( 14 / 26 )49.52.6210512208391618.8855523335221
Trimmed Mean ( 15 / 26 )49.522.5690846460105919.2753477690575
Trimmed Mean ( 16 / 26 )49.52083333333332.5185463807024519.6624662991203
Trimmed Mean ( 17 / 26 )49.52173913043482.4641858128450520.0965929080076
Trimmed Mean ( 18 / 26 )49.52272727272732.4174507908054320.4855161731038
Trimmed Mean ( 19 / 26 )49.52.3609408742801420.9662175530307
Trimmed Mean ( 20 / 26 )49.452.3060539055678221.4435577072184
Trimmed Mean ( 21 / 26 )49.42105263157892.2384940766232422.0778125560781
Trimmed Mean ( 22 / 26 )49.33333333333332.1789031753657722.6413609797286
Trimmed Mean ( 23 / 26 )49.26470588235292.1225001332297823.2106962497041
Trimmed Mean ( 24 / 26 )49.218752.0706933421776223.769212464961
Trimmed Mean ( 25 / 26 )49.22.0036747849085124.5548830431814
Trimmed Mean ( 26 / 26 )49.28571428571431.9387834665866925.4209483086236
Median49.5
Midrange70
Midmean - Weighted Average at Xnp48.8536585365854
Midmean - Weighted Average at X(n+1)p48.8536585365854
Midmean - Empirical Distribution Function48.8536585365854
Midmean - Empirical Distribution Function - Averaging48.8536585365854
Midmean - Empirical Distribution Function - Interpolation48.8536585365854
Midmean - Closest Observation48.8536585365854
Midmean - True Basic - Statistics Graphics Toolkit48.8536585365854
Midmean - MS Excel (old versions)49.5
Number of observations80



Parameters (Session):
Parameters (R input):
R code (references can be found in the software module):
geomean <- function(x) {
return(exp(mean(log(x))))
}
harmean <- function(x) {
return(1/mean(1/x))
}
quamean <- function(x) {
return(sqrt(mean(x*x)))
}
winmean <- function(x) {
x <-sort(x[!is.na(x)])
n<-length(x)
denom <- 3
nodenom <- n/denom
if (nodenom>40) denom <- n/40
sqrtn = sqrt(n)
roundnodenom = floor(nodenom)
win <- array(NA,dim=c(roundnodenom,2))
for (j in 1:roundnodenom) {
win[j,1] <- (j*x[j+1]+sum(x[(j+1):(n-j)])+j*x[n-j])/n
win[j,2] <- sd(c(rep(x[j+1],j),x[(j+1):(n-j)],rep(x[n-j],j)))/sqrtn
}
return(win)
}
trimean <- function(x) {
x <-sort(x[!is.na(x)])
n<-length(x)
denom <- 3
nodenom <- n/denom
if (nodenom>40) denom <- n/40
sqrtn = sqrt(n)
roundnodenom = floor(nodenom)
tri <- array(NA,dim=c(roundnodenom,2))
for (j in 1:roundnodenom) {
tri[j,1] <- mean(x,trim=j/n)
tri[j,2] <- sd(x[(j+1):(n-j)]) / sqrt(n-j*2)
}
return(tri)
}
midrange <- function(x) {
return((max(x)+min(x))/2)
}
q1 <- function(data,n,p,i,f) {
np <- n*p;
i <<- floor(np)
f <<- np - i
qvalue <- (1-f)*data[i] + f*data[i+1]
}
q2 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
qvalue <- (1-f)*data[i] + f*data[i+1]
}
q3 <- function(data,n,p,i,f) {
np <- n*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
qvalue <- data[i+1]
}
}
q4 <- function(data,n,p,i,f) {
np <- n*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- (data[i]+data[i+1])/2
} else {
qvalue <- data[i+1]
}
}
q5 <- function(data,n,p,i,f) {
np <- (n-1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i+1]
} else {
qvalue <- data[i+1] + f*(data[i+2]-data[i+1])
}
}
q6 <- function(data,n,p,i,f) {
np <- n*p+0.5
i <<- floor(np)
f <<- np - i
qvalue <- data[i]
}
q7 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
qvalue <- f*data[i] + (1-f)*data[i+1]
}
}
q8 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
if (f == 0.5) {
qvalue <- (data[i]+data[i+1])/2
} else {
if (f < 0.5) {
qvalue <- data[i]
} else {
qvalue <- data[i+1]
}
}
}
}
midmean <- function(x,def) {
x <-sort(x[!is.na(x)])
n<-length(x)
if (def==1) {
qvalue1 <- q1(x,n,0.25,i,f)
qvalue3 <- q1(x,n,0.75,i,f)
}
if (def==2) {
qvalue1 <- q2(x,n,0.25,i,f)
qvalue3 <- q2(x,n,0.75,i,f)
}
if (def==3) {
qvalue1 <- q3(x,n,0.25,i,f)
qvalue3 <- q3(x,n,0.75,i,f)
}
if (def==4) {
qvalue1 <- q4(x,n,0.25,i,f)
qvalue3 <- q4(x,n,0.75,i,f)
}
if (def==5) {
qvalue1 <- q5(x,n,0.25,i,f)
qvalue3 <- q5(x,n,0.75,i,f)
}
if (def==6) {
qvalue1 <- q6(x,n,0.25,i,f)
qvalue3 <- q6(x,n,0.75,i,f)
}
if (def==7) {
qvalue1 <- q7(x,n,0.25,i,f)
qvalue3 <- q7(x,n,0.75,i,f)
}
if (def==8) {
qvalue1 <- q8(x,n,0.25,i,f)
qvalue3 <- q8(x,n,0.75,i,f)
}
midm <- 0
myn <- 0
roundno4 <- round(n/4)
round3no4 <- round(3*n/4)
for (i in 1:n) {
if ((x[i]>=qvalue1) & (x[i]<=qvalue3)){
midm = midm + x[i]
myn = myn + 1
}
}
midm = midm / myn
return(midm)
}
(arm <- mean(x))
sqrtn <- sqrt(length(x))
(armse <- sd(x) / sqrtn)
(armose <- arm / armse)
(geo <- geomean(x))
(har <- harmean(x))
(qua <- quamean(x))
(win <- winmean(x))
(tri <- trimean(x))
(midr <- midrange(x))
midm <- array(NA,dim=8)
for (j in 1:8) midm[j] <- midmean(x,j)
midm
bitmap(file='test1.png')
lb <- win[,1] - 2*win[,2]
ub <- win[,1] + 2*win[,2]
if ((ylimmin == '') | (ylimmax == '')) plot(win[,1],type='b',main=main, xlab='j', pch=19, ylab='Winsorized Mean(j/n)', ylim=c(min(lb),max(ub))) else plot(win[,1],type='l',main=main, xlab='j', pch=19, ylab='Winsorized Mean(j/n)', ylim=c(ylimmin,ylimmax))
lines(ub,lty=3)
lines(lb,lty=3)
grid()
dev.off()
bitmap(file='test2.png')
lb <- tri[,1] - 2*tri[,2]
ub <- tri[,1] + 2*tri[,2]
if ((ylimmin == '') | (ylimmax == '')) plot(tri[,1],type='b',main=main, xlab='j', pch=19, ylab='Trimmed Mean(j/n)', ylim=c(min(lb),max(ub))) else plot(tri[,1],type='l',main=main, xlab='j', pch=19, ylab='Trimmed Mean(j/n)', ylim=c(ylimmin,ylimmax))
lines(ub,lty=3)
lines(lb,lty=3)
grid()
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Central Tendency - Ungrouped Data',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Measure',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.element(a,'S.E.',header=TRUE)
a<-table.element(a,'Value/S.E.',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('arithmetic_mean.htm', 'Arithmetic Mean', 'click to view the definition of the Arithmetic Mean'),header=TRUE)
a<-table.element(a,arm)
a<-table.element(a,hyperlink('arithmetic_mean_standard_error.htm', armse, 'click to view the definition of the Standard Error of the Arithmetic Mean'))
a<-table.element(a,armose)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('geometric_mean.htm', 'Geometric Mean', 'click to view the definition of the Geometric Mean'),header=TRUE)
a<-table.element(a,geo)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('harmonic_mean.htm', 'Harmonic Mean', 'click to view the definition of the Harmonic Mean'),header=TRUE)
a<-table.element(a,har)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('quadratic_mean.htm', 'Quadratic Mean', 'click to view the definition of the Quadratic Mean'),header=TRUE)
a<-table.element(a,qua)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
for (j in 1:length(win[,1])) {
a<-table.row.start(a)
mylabel <- paste('Winsorized Mean (',j)
mylabel <- paste(mylabel,'/')
mylabel <- paste(mylabel,length(win[,1]))
mylabel <- paste(mylabel,')')
a<-table.element(a,hyperlink('winsorized_mean.htm', mylabel, 'click to view the definition of the Winsorized Mean'),header=TRUE)
a<-table.element(a,win[j,1])
a<-table.element(a,win[j,2])
a<-table.element(a,win[j,1]/win[j,2])
a<-table.row.end(a)
}
for (j in 1:length(tri[,1])) {
a<-table.row.start(a)
mylabel <- paste('Trimmed Mean (',j)
mylabel <- paste(mylabel,'/')
mylabel <- paste(mylabel,length(tri[,1]))
mylabel <- paste(mylabel,')')
a<-table.element(a,hyperlink('arithmetic_mean.htm', mylabel, 'click to view the definition of the Trimmed Mean'),header=TRUE)
a<-table.element(a,tri[j,1])
a<-table.element(a,tri[j,2])
a<-table.element(a,tri[j,1]/tri[j,2])
a<-table.row.end(a)
}
a<-table.row.start(a)
a<-table.element(a,hyperlink('median_1.htm', 'Median', 'click to view the definition of the Median'),header=TRUE)
a<-table.element(a,median(x))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('midrange.htm', 'Midrange', 'click to view the definition of the Midrange'),header=TRUE)
a<-table.element(a,midr)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_1.htm','Weighted Average at Xnp',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[1])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_2.htm','Weighted Average at X(n+1)p',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[2])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_3.htm','Empirical Distribution Function',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[3])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_4.htm','Empirical Distribution Function - Averaging',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[4])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_5.htm','Empirical Distribution Function - Interpolation',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[5])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_6.htm','Closest Observation',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[6])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_7.htm','True Basic - Statistics Graphics Toolkit',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[7])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_8.htm','MS Excel (old versions)',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[8])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Number of observations',header=TRUE)
a<-table.element(a,length(x))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')