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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 computationSun, 25 Oct 2009 11:54:25 -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/Oct/25/t12564933308rk3zjr6cusqi51.htm/, Retrieved Mon, 29 Apr 2024 16:05:06 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=50356, Retrieved Mon, 29 Apr 2024 16:05:06 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsWS 3 Part 2
Estimated Impact182
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Bivariate Data Series] [Bivariate dataset] [2008-01-05 23:51:08] [74be16979710d4c4e7c6647856088456]
F RMPD  [Univariate Explorative Data Analysis] [Colombia Coffee] [2008-01-07 14:21:11] [74be16979710d4c4e7c6647856088456]
F RMPD    [Univariate Data Series] [] [2009-10-14 08:30:28] [74be16979710d4c4e7c6647856088456]
-           [Univariate Data Series] [WS 3 Part 1/1] [2009-10-21 21:03:12] [9717cb857c153ca3061376906953b329]
- RMPD        [Central Tendency] [WS 3 Part 2] [2009-10-22 15:25:33] [9717cb857c153ca3061376906953b329]
-    D            [Central Tendency] [WS 3 Part 2] [2009-10-25 17:54:25] [52b85b290d6f50b0921ad6729b8a5af2] [Current]
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Dataseries X:
1,538869863
1,516743946
1,503330487
1,464730999
1,438632131
1,469782034
1,462748344
1,450720751
1,436743492
1,396151294
1,413492197
1,496284212
1,458544563
1,465595586
1,423659769
1,409434874
1,379530576
1,369324388
1,381151995
1,33598751
1,347405588
1,326935179
1,351613914
1,338554026
1,388818699
1,379165996
1,341199607
1,322806446
1,305177994
1,324812765
1,313209997
1,293617021
1,291789336
1,283838548
1,305183271
1,305244358
1,319678846
1,324443717
1,320926385
1,304987735
1,292925992
1,275542308
1,285096474
1,275983855
1,24232715
1,23546123
1,223636364
1,233880325
1,269562278
1,276994526
1,25485357
1,247605131
1,259110612
1,256353591
1,265801267
1,273322173
1,245863615
1,242902687
1,254183627
1,258955224




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'RServer@AstonUniversity' @ vre.aston.ac.uk

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 3 seconds \tabularnewline
R Server & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=50356&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=50356&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=50356&T=0

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'RServer@AstonUniversity' @ vre.aston.ac.uk







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean1.341187173966670.0108034603186944124.144221795851
Geometric Mean1.33867890262947
Harmonic Mean1.33623080646895
Quadratic Mean1.34375191391465
Winsorized Mean ( 1 / 20 )1.340989141366670.0106644530818778125.743826811468
Winsorized Mean ( 2 / 20 )1.34059472290.0105345068202556127.257473536618
Winsorized Mean ( 3 / 20 )1.340585705150.0103870533448693129.063138566838
Winsorized Mean ( 4 / 20 )1.338857262416670.00995898415201044134.437131536793
Winsorized Mean ( 5 / 20 )1.338755135750.00984212426182124136.022986515542
Winsorized Mean ( 6 / 20 )1.338842828650.00979558894427046136.678135053136
Winsorized Mean ( 7 / 20 )1.33937901010.00962711009252614139.125760194620
Winsorized Mean ( 8 / 20 )1.33890783170.0094929674439981141.042075578435
Winsorized Mean ( 9 / 20 )1.337959263050.00921205862201508145.239985756553
Winsorized Mean ( 10 / 20 )1.336378098550.0087378942376296152.940521160683
Winsorized Mean ( 11 / 20 )1.336060335866670.00866517686052801154.187312892914
Winsorized Mean ( 12 / 20 )1.334781722266670.00796041601089559167.677382744787
Winsorized Mean ( 13 / 20 )1.333393634050.00743132130779643179.428876618630
Winsorized Mean ( 14 / 20 )1.333324234183330.00713278760768332186.928913002695
Winsorized Mean ( 15 / 20 )1.330558372933330.006466735345436205.754264224281
Winsorized Mean ( 16 / 20 )1.328720760133330.00611866153042314217.158728837456
Winsorized Mean ( 17 / 20 )1.326834884116670.00572081139421249231.931240638167
Winsorized Mean ( 18 / 20 )1.328401665016670.0053453794466248248.514006962677
Winsorized Mean ( 19 / 20 )1.328684557916670.00527058743261204252.094206747309
Winsorized Mean ( 20 / 20 )1.327634975916670.00443289637336094299.496054970957
Trimmed Mean ( 1 / 20 )1.339805589844830.0104375376123209128.364144840375
Trimmed Mean ( 2 / 20 )1.338537498928570.0101537768887731131.8265620361
Trimmed Mean ( 3 / 20 )1.337394596722220.00988567612913498135.286102766473
Trimmed Mean ( 4 / 20 )1.336167247326920.00961811243942379138.921982430783
Trimmed Mean ( 5 / 20 )1.33536024280.00944906202462815141.321989348731
Trimmed Mean ( 6 / 20 )1.33451151956250.00926707326264723144.005715908335
Trimmed Mean ( 7 / 20 )1.333569930630430.00904074542105831147.506634521994
Trimmed Mean ( 8 / 20 )1.332438291772730.00878886766457233151.605228639834
Trimmed Mean ( 9 / 20 )1.331283016785710.00849156786725734156.777056675130
Trimmed Mean ( 10 / 20 )1.3301703090750.00817432127822252162.725474544138
Trimmed Mean ( 11 / 20 )1.329190131789470.0078827828247776168.619402733193
Trimmed Mean ( 12 / 20 )1.328149191777780.00749859924864507177.119638980275
Trimmed Mean ( 13 / 20 )1.327173819647060.00717781839279197184.899331108714
Trimmed Mean ( 14 / 20 )1.326276731031250.00688404417457702192.659532303588
Trimmed Mean ( 15 / 20 )1.325269944866670.00654437313579213202.505254111898
Trimmed Mean ( 16 / 20 )1.324514455142860.00627290387835076211.148533570563
Trimmed Mean ( 17 / 20 )1.323907776538460.00598051499946716221.370195820329
Trimmed Mean ( 18 / 20 )1.323477319541670.005673173446312233.286948136943
Trimmed Mean ( 19 / 20 )1.322731206590910.00531285631120422248.967999341789
Trimmed Mean ( 20 / 20 )1.321791203750.00470768845644579280.772871012778
Median1.3218664155
Midrange1.3812531135
Midmean - Weighted Average at Xnp1.32359421029032
Midmean - Weighted Average at X(n+1)p1.32526994486667
Midmean - Empirical Distribution Function1.32359421029032
Midmean - Empirical Distribution Function - Averaging1.32526994486667
Midmean - Empirical Distribution Function - Interpolation1.32526994486667
Midmean - Closest Observation1.32359421029032
Midmean - True Basic - Statistics Graphics Toolkit1.32526994486667
Midmean - MS Excel (old versions)1.32627673103125
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 1.34118717396667 & 0.0108034603186944 & 124.144221795851 \tabularnewline
Geometric Mean & 1.33867890262947 &  &  \tabularnewline
Harmonic Mean & 1.33623080646895 &  &  \tabularnewline
Quadratic Mean & 1.34375191391465 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 1.34098914136667 & 0.0106644530818778 & 125.743826811468 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 1.3405947229 & 0.0105345068202556 & 127.257473536618 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 1.34058570515 & 0.0103870533448693 & 129.063138566838 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 1.33885726241667 & 0.00995898415201044 & 134.437131536793 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 1.33875513575 & 0.00984212426182124 & 136.022986515542 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 1.33884282865 & 0.00979558894427046 & 136.678135053136 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 1.3393790101 & 0.00962711009252614 & 139.125760194620 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 1.3389078317 & 0.0094929674439981 & 141.042075578435 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 1.33795926305 & 0.00921205862201508 & 145.239985756553 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 1.33637809855 & 0.0087378942376296 & 152.940521160683 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 1.33606033586667 & 0.00866517686052801 & 154.187312892914 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 1.33478172226667 & 0.00796041601089559 & 167.677382744787 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 1.33339363405 & 0.00743132130779643 & 179.428876618630 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 1.33332423418333 & 0.00713278760768332 & 186.928913002695 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 1.33055837293333 & 0.006466735345436 & 205.754264224281 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 1.32872076013333 & 0.00611866153042314 & 217.158728837456 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 1.32683488411667 & 0.00572081139421249 & 231.931240638167 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 1.32840166501667 & 0.0053453794466248 & 248.514006962677 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 1.32868455791667 & 0.00527058743261204 & 252.094206747309 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 1.32763497591667 & 0.00443289637336094 & 299.496054970957 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 1.33980558984483 & 0.0104375376123209 & 128.364144840375 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 1.33853749892857 & 0.0101537768887731 & 131.8265620361 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 1.33739459672222 & 0.00988567612913498 & 135.286102766473 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 1.33616724732692 & 0.00961811243942379 & 138.921982430783 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 1.3353602428 & 0.00944906202462815 & 141.321989348731 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 1.3345115195625 & 0.00926707326264723 & 144.005715908335 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 1.33356993063043 & 0.00904074542105831 & 147.506634521994 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 1.33243829177273 & 0.00878886766457233 & 151.605228639834 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 1.33128301678571 & 0.00849156786725734 & 156.777056675130 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 1.330170309075 & 0.00817432127822252 & 162.725474544138 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 1.32919013178947 & 0.0078827828247776 & 168.619402733193 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 1.32814919177778 & 0.00749859924864507 & 177.119638980275 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 1.32717381964706 & 0.00717781839279197 & 184.899331108714 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 1.32627673103125 & 0.00688404417457702 & 192.659532303588 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 1.32526994486667 & 0.00654437313579213 & 202.505254111898 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 1.32451445514286 & 0.00627290387835076 & 211.148533570563 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 1.32390777653846 & 0.00598051499946716 & 221.370195820329 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 1.32347731954167 & 0.005673173446312 & 233.286948136943 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 1.32273120659091 & 0.00531285631120422 & 248.967999341789 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 1.32179120375 & 0.00470768845644579 & 280.772871012778 \tabularnewline
Median & 1.3218664155 &  &  \tabularnewline
Midrange & 1.3812531135 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 1.32359421029032 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 1.32526994486667 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 1.32359421029032 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 1.32526994486667 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 1.32526994486667 &  &  \tabularnewline
Midmean - Closest Observation & 1.32359421029032 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 1.32526994486667 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 1.32627673103125 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=50356&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]1.34118717396667[/C][C]0.0108034603186944[/C][C]124.144221795851[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]1.33867890262947[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]1.33623080646895[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]1.34375191391465[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]1.34098914136667[/C][C]0.0106644530818778[/C][C]125.743826811468[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]1.3405947229[/C][C]0.0105345068202556[/C][C]127.257473536618[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]1.34058570515[/C][C]0.0103870533448693[/C][C]129.063138566838[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]1.33885726241667[/C][C]0.00995898415201044[/C][C]134.437131536793[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]1.33875513575[/C][C]0.00984212426182124[/C][C]136.022986515542[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]1.33884282865[/C][C]0.00979558894427046[/C][C]136.678135053136[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]1.3393790101[/C][C]0.00962711009252614[/C][C]139.125760194620[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]1.3389078317[/C][C]0.0094929674439981[/C][C]141.042075578435[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]1.33795926305[/C][C]0.00921205862201508[/C][C]145.239985756553[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]1.33637809855[/C][C]0.0087378942376296[/C][C]152.940521160683[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]1.33606033586667[/C][C]0.00866517686052801[/C][C]154.187312892914[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]1.33478172226667[/C][C]0.00796041601089559[/C][C]167.677382744787[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]1.33339363405[/C][C]0.00743132130779643[/C][C]179.428876618630[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]1.33332423418333[/C][C]0.00713278760768332[/C][C]186.928913002695[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]1.33055837293333[/C][C]0.006466735345436[/C][C]205.754264224281[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]1.32872076013333[/C][C]0.00611866153042314[/C][C]217.158728837456[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]1.32683488411667[/C][C]0.00572081139421249[/C][C]231.931240638167[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]1.32840166501667[/C][C]0.0053453794466248[/C][C]248.514006962677[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]1.32868455791667[/C][C]0.00527058743261204[/C][C]252.094206747309[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]1.32763497591667[/C][C]0.00443289637336094[/C][C]299.496054970957[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]1.33980558984483[/C][C]0.0104375376123209[/C][C]128.364144840375[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]1.33853749892857[/C][C]0.0101537768887731[/C][C]131.8265620361[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]1.33739459672222[/C][C]0.00988567612913498[/C][C]135.286102766473[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]1.33616724732692[/C][C]0.00961811243942379[/C][C]138.921982430783[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]1.3353602428[/C][C]0.00944906202462815[/C][C]141.321989348731[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]1.3345115195625[/C][C]0.00926707326264723[/C][C]144.005715908335[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]1.33356993063043[/C][C]0.00904074542105831[/C][C]147.506634521994[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]1.33243829177273[/C][C]0.00878886766457233[/C][C]151.605228639834[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]1.33128301678571[/C][C]0.00849156786725734[/C][C]156.777056675130[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]1.330170309075[/C][C]0.00817432127822252[/C][C]162.725474544138[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]1.32919013178947[/C][C]0.0078827828247776[/C][C]168.619402733193[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]1.32814919177778[/C][C]0.00749859924864507[/C][C]177.119638980275[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]1.32717381964706[/C][C]0.00717781839279197[/C][C]184.899331108714[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]1.32627673103125[/C][C]0.00688404417457702[/C][C]192.659532303588[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]1.32526994486667[/C][C]0.00654437313579213[/C][C]202.505254111898[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]1.32451445514286[/C][C]0.00627290387835076[/C][C]211.148533570563[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]1.32390777653846[/C][C]0.00598051499946716[/C][C]221.370195820329[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]1.32347731954167[/C][C]0.005673173446312[/C][C]233.286948136943[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]1.32273120659091[/C][C]0.00531285631120422[/C][C]248.967999341789[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]1.32179120375[/C][C]0.00470768845644579[/C][C]280.772871012778[/C][/ROW]
[ROW][C]Median[/C][C]1.3218664155[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]1.3812531135[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]1.32359421029032[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]1.32526994486667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]1.32359421029032[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]1.32526994486667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]1.32526994486667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]1.32359421029032[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]1.32526994486667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]1.32627673103125[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]60[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=50356&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=50356&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 Mean1.341187173966670.0108034603186944124.144221795851
Geometric Mean1.33867890262947
Harmonic Mean1.33623080646895
Quadratic Mean1.34375191391465
Winsorized Mean ( 1 / 20 )1.340989141366670.0106644530818778125.743826811468
Winsorized Mean ( 2 / 20 )1.34059472290.0105345068202556127.257473536618
Winsorized Mean ( 3 / 20 )1.340585705150.0103870533448693129.063138566838
Winsorized Mean ( 4 / 20 )1.338857262416670.00995898415201044134.437131536793
Winsorized Mean ( 5 / 20 )1.338755135750.00984212426182124136.022986515542
Winsorized Mean ( 6 / 20 )1.338842828650.00979558894427046136.678135053136
Winsorized Mean ( 7 / 20 )1.33937901010.00962711009252614139.125760194620
Winsorized Mean ( 8 / 20 )1.33890783170.0094929674439981141.042075578435
Winsorized Mean ( 9 / 20 )1.337959263050.00921205862201508145.239985756553
Winsorized Mean ( 10 / 20 )1.336378098550.0087378942376296152.940521160683
Winsorized Mean ( 11 / 20 )1.336060335866670.00866517686052801154.187312892914
Winsorized Mean ( 12 / 20 )1.334781722266670.00796041601089559167.677382744787
Winsorized Mean ( 13 / 20 )1.333393634050.00743132130779643179.428876618630
Winsorized Mean ( 14 / 20 )1.333324234183330.00713278760768332186.928913002695
Winsorized Mean ( 15 / 20 )1.330558372933330.006466735345436205.754264224281
Winsorized Mean ( 16 / 20 )1.328720760133330.00611866153042314217.158728837456
Winsorized Mean ( 17 / 20 )1.326834884116670.00572081139421249231.931240638167
Winsorized Mean ( 18 / 20 )1.328401665016670.0053453794466248248.514006962677
Winsorized Mean ( 19 / 20 )1.328684557916670.00527058743261204252.094206747309
Winsorized Mean ( 20 / 20 )1.327634975916670.00443289637336094299.496054970957
Trimmed Mean ( 1 / 20 )1.339805589844830.0104375376123209128.364144840375
Trimmed Mean ( 2 / 20 )1.338537498928570.0101537768887731131.8265620361
Trimmed Mean ( 3 / 20 )1.337394596722220.00988567612913498135.286102766473
Trimmed Mean ( 4 / 20 )1.336167247326920.00961811243942379138.921982430783
Trimmed Mean ( 5 / 20 )1.33536024280.00944906202462815141.321989348731
Trimmed Mean ( 6 / 20 )1.33451151956250.00926707326264723144.005715908335
Trimmed Mean ( 7 / 20 )1.333569930630430.00904074542105831147.506634521994
Trimmed Mean ( 8 / 20 )1.332438291772730.00878886766457233151.605228639834
Trimmed Mean ( 9 / 20 )1.331283016785710.00849156786725734156.777056675130
Trimmed Mean ( 10 / 20 )1.3301703090750.00817432127822252162.725474544138
Trimmed Mean ( 11 / 20 )1.329190131789470.0078827828247776168.619402733193
Trimmed Mean ( 12 / 20 )1.328149191777780.00749859924864507177.119638980275
Trimmed Mean ( 13 / 20 )1.327173819647060.00717781839279197184.899331108714
Trimmed Mean ( 14 / 20 )1.326276731031250.00688404417457702192.659532303588
Trimmed Mean ( 15 / 20 )1.325269944866670.00654437313579213202.505254111898
Trimmed Mean ( 16 / 20 )1.324514455142860.00627290387835076211.148533570563
Trimmed Mean ( 17 / 20 )1.323907776538460.00598051499946716221.370195820329
Trimmed Mean ( 18 / 20 )1.323477319541670.005673173446312233.286948136943
Trimmed Mean ( 19 / 20 )1.322731206590910.00531285631120422248.967999341789
Trimmed Mean ( 20 / 20 )1.321791203750.00470768845644579280.772871012778
Median1.3218664155
Midrange1.3812531135
Midmean - Weighted Average at Xnp1.32359421029032
Midmean - Weighted Average at X(n+1)p1.32526994486667
Midmean - Empirical Distribution Function1.32359421029032
Midmean - Empirical Distribution Function - Averaging1.32526994486667
Midmean - Empirical Distribution Function - Interpolation1.32526994486667
Midmean - Closest Observation1.32359421029032
Midmean - True Basic - Statistics Graphics Toolkit1.32526994486667
Midmean - MS Excel (old versions)1.32627673103125
Number of observations60



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')