Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationWed, 16 Jan 2008 03:00:18 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/Jan/16/t12004773615198yrnh6xuwp79.htm/, Retrieved Wed, 15 May 2024 10:50:46 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=7975, Retrieved Wed, 15 May 2024 10:50:46 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact264
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2008-01-16 10:00:18] [d41d8cd98f00b204e9800998ecf8427e] [Current]
Feedback Forum

Post a new message
Dataseries X:
0,8833
0,87
0,8758
0,8858
0,917
0,9554
0,9922
0,9778
0,9808
0,9811
1,0014
1,0183
1,0622
1,0773
1,0807
1,0848
1,1582
1,1663
1,1372
1,1139
1,1222
1,1692
1,1702
1,2286
1,2613
1,2646
1,2262
1,1985
1,2007
1,2138
1,2266
1,2176
1,2218
1,249
1,2991
1,3408
1,3119
1,3014
1,3201
1,2938
1,2694
1,2165
1,2037
1,2292
1,2256
1,2015
1,1786
1,1856
1,2103
1,1938
1,202
1,2271
1,277
1,265
1,2684
1,2811
1,2727
1,2611
1,2881
1,3213




Summary of compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time5 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\begin{tabular}{lllllllll}
\hline
Summary of compuational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 5 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=7975&T=0

[TABLE]
[ROW][C]Summary of compuational 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]5 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=7975&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=7975&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 compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time5 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean1.1639150.016550966282577170.3230844730334
Geometric Mean1.15640302060152
Harmonic Mean1.14829989439360
Quadratic Mean1.17083741904388
Winsorized Mean ( 1 / 20 )1.163686666666670.016466289046197470.670851422677
Winsorized Mean ( 2 / 20 )1.163896666666670.01638649108891771.0278155555748
Winsorized Mean ( 3 / 20 )1.163611666666670.016285516960317371.4507049117336
Winsorized Mean ( 4 / 20 )1.164991666666670.015598189321918474.687621917092
Winsorized Mean ( 5 / 20 )1.1680.014746295905679379.2063313709964
Winsorized Mean ( 6 / 20 )1.169710.014135175640772282.7517131535337
Winsorized Mean ( 7 / 20 )1.1693950.013957412712704683.7830781442444
Winsorized Mean ( 8 / 20 )1.168501666666670.013816490902427984.5729697155831
Winsorized Mean ( 9 / 20 )1.169551666666670.013353211275395587.5857980935024
Winsorized Mean ( 10 / 20 )1.170368333333330.012913545967101590.631057984767
Winsorized Mean ( 11 / 20 )1.172861666666670.012154444234196296.4965278598963
Winsorized Mean ( 12 / 20 )1.181441666666670.0103132363230823114.555860998012
Winsorized Mean ( 13 / 20 )1.183976666666670.00957798658019107123.614358482746
Winsorized Mean ( 14 / 20 )1.184676666666670.00941545050893755125.822621609250
Winsorized Mean ( 15 / 20 )1.184876666666670.00910601507500067130.120217999593
Winsorized Mean ( 16 / 20 )1.192583333333330.00769915622593393154.897926257974
Winsorized Mean ( 17 / 20 )1.191506666666670.00678647203166232175.570850525529
Winsorized Mean ( 18 / 20 )1.190066666666670.00519708776918407228.987217364910
Winsorized Mean ( 19 / 20 )1.196526666666670.00406224581415428294.548070551898
Winsorized Mean ( 20 / 20 )1.198726666666670.00357095460077956335.688016421429
Trimmed Mean ( 1 / 20 )1.165932758620690.016051731326304872.6359502859367
Trimmed Mean ( 2 / 20 )1.168339285714290.015533554940245775.2139024330642
Trimmed Mean ( 3 / 20 )1.170807407407410.014937204184382278.3819644529973
Trimmed Mean ( 4 / 20 )1.1735750.014230315682613982.4700608317376
Trimmed Mean ( 5 / 20 )1.176150.013620715091060386.3500919105156
Trimmed Mean ( 6 / 20 )1.17818750.013156298758774989.5531122850323
Trimmed Mean ( 7 / 20 )1.180030434782610.012755776135802892.5094970482044
Trimmed Mean ( 8 / 20 )1.182102272727270.012278667749314696.2728446490668
Trimmed Mean ( 9 / 20 )1.184530952380950.0116769940128649101.441428425493
Trimmed Mean ( 10 / 20 )1.18702750.0110072074217014107.840931357367
Trimmed Mean ( 11 / 20 )1.189657894736840.0102232258868289116.368151100871
Trimmed Mean ( 12 / 20 )1.192202777777780.0093855549988631127.025282779995
Trimmed Mean ( 13 / 20 )1.193785294117650.00886619702998767134.644570843618
Trimmed Mean ( 14 / 20 )1.19520.00836993708304869142.796772322291
Trimmed Mean ( 15 / 20 )1.196703333333330.0076939287653801155.538655194998
Trimmed Mean ( 16 / 20 )1.198392857142860.00677745041215288176.820601297794
Trimmed Mean ( 17 / 20 )1.199230769230770.00603024369766716198.869370684754
Trimmed Mean ( 18 / 20 )1.200366666666670.00524660230518688228.789337716709
Trimmed Mean ( 19 / 20 )1.201927272727270.00472623781545459254.309520523284
Trimmed Mean ( 20 / 20 )1.202780.00449613635305505267.514128921542
Median1.20285
Midrange1.1054
Midmean - Weighted Average at Xnp1.19296129032258
Midmean - Weighted Average at X(n+1)p1.19670333333333
Midmean - Empirical Distribution Function1.19296129032258
Midmean - Empirical Distribution Function - Averaging1.19670333333333
Midmean - Empirical Distribution Function - Interpolation1.19670333333333
Midmean - Closest Observation1.19296129032258
Midmean - True Basic - Statistics Graphics Toolkit1.19670333333333
Midmean - MS Excel (old versions)1.1952
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 1.163915 & 0.0165509662825771 & 70.3230844730334 \tabularnewline
Geometric Mean & 1.15640302060152 &  &  \tabularnewline
Harmonic Mean & 1.14829989439360 &  &  \tabularnewline
Quadratic Mean & 1.17083741904388 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 1.16368666666667 & 0.0164662890461974 & 70.670851422677 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 1.16389666666667 & 0.016386491088917 & 71.0278155555748 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 1.16361166666667 & 0.0162855169603173 & 71.4507049117336 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 1.16499166666667 & 0.0155981893219184 & 74.687621917092 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 1.168 & 0.0147462959056793 & 79.2063313709964 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 1.16971 & 0.0141351756407722 & 82.7517131535337 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 1.169395 & 0.0139574127127046 & 83.7830781442444 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 1.16850166666667 & 0.0138164909024279 & 84.5729697155831 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 1.16955166666667 & 0.0133532112753955 & 87.5857980935024 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 1.17036833333333 & 0.0129135459671015 & 90.631057984767 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 1.17286166666667 & 0.0121544442341962 & 96.4965278598963 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 1.18144166666667 & 0.0103132363230823 & 114.555860998012 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 1.18397666666667 & 0.00957798658019107 & 123.614358482746 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 1.18467666666667 & 0.00941545050893755 & 125.822621609250 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 1.18487666666667 & 0.00910601507500067 & 130.120217999593 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 1.19258333333333 & 0.00769915622593393 & 154.897926257974 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 1.19150666666667 & 0.00678647203166232 & 175.570850525529 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 1.19006666666667 & 0.00519708776918407 & 228.987217364910 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 1.19652666666667 & 0.00406224581415428 & 294.548070551898 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 1.19872666666667 & 0.00357095460077956 & 335.688016421429 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 1.16593275862069 & 0.0160517313263048 & 72.6359502859367 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 1.16833928571429 & 0.0155335549402457 & 75.2139024330642 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 1.17080740740741 & 0.0149372041843822 & 78.3819644529973 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 1.173575 & 0.0142303156826139 & 82.4700608317376 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 1.17615 & 0.0136207150910603 & 86.3500919105156 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 1.1781875 & 0.0131562987587749 & 89.5531122850323 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 1.18003043478261 & 0.0127557761358028 & 92.5094970482044 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 1.18210227272727 & 0.0122786677493146 & 96.2728446490668 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 1.18453095238095 & 0.0116769940128649 & 101.441428425493 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 1.1870275 & 0.0110072074217014 & 107.840931357367 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 1.18965789473684 & 0.0102232258868289 & 116.368151100871 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 1.19220277777778 & 0.0093855549988631 & 127.025282779995 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 1.19378529411765 & 0.00886619702998767 & 134.644570843618 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 1.1952 & 0.00836993708304869 & 142.796772322291 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 1.19670333333333 & 0.0076939287653801 & 155.538655194998 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 1.19839285714286 & 0.00677745041215288 & 176.820601297794 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 1.19923076923077 & 0.00603024369766716 & 198.869370684754 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 1.20036666666667 & 0.00524660230518688 & 228.789337716709 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 1.20192727272727 & 0.00472623781545459 & 254.309520523284 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 1.20278 & 0.00449613635305505 & 267.514128921542 \tabularnewline
Median & 1.20285 &  &  \tabularnewline
Midrange & 1.1054 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 1.19296129032258 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 1.19670333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 1.19296129032258 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 1.19670333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 1.19670333333333 &  &  \tabularnewline
Midmean - Closest Observation & 1.19296129032258 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 1.19670333333333 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 1.1952 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=7975&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]1.163915[/C][C]0.0165509662825771[/C][C]70.3230844730334[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]1.15640302060152[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]1.14829989439360[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]1.17083741904388[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]1.16368666666667[/C][C]0.0164662890461974[/C][C]70.670851422677[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]1.16389666666667[/C][C]0.016386491088917[/C][C]71.0278155555748[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]1.16361166666667[/C][C]0.0162855169603173[/C][C]71.4507049117336[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]1.16499166666667[/C][C]0.0155981893219184[/C][C]74.687621917092[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]1.168[/C][C]0.0147462959056793[/C][C]79.2063313709964[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]1.16971[/C][C]0.0141351756407722[/C][C]82.7517131535337[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]1.169395[/C][C]0.0139574127127046[/C][C]83.7830781442444[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]1.16850166666667[/C][C]0.0138164909024279[/C][C]84.5729697155831[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]1.16955166666667[/C][C]0.0133532112753955[/C][C]87.5857980935024[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]1.17036833333333[/C][C]0.0129135459671015[/C][C]90.631057984767[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]1.17286166666667[/C][C]0.0121544442341962[/C][C]96.4965278598963[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]1.18144166666667[/C][C]0.0103132363230823[/C][C]114.555860998012[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]1.18397666666667[/C][C]0.00957798658019107[/C][C]123.614358482746[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]1.18467666666667[/C][C]0.00941545050893755[/C][C]125.822621609250[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]1.18487666666667[/C][C]0.00910601507500067[/C][C]130.120217999593[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]1.19258333333333[/C][C]0.00769915622593393[/C][C]154.897926257974[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]1.19150666666667[/C][C]0.00678647203166232[/C][C]175.570850525529[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]1.19006666666667[/C][C]0.00519708776918407[/C][C]228.987217364910[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]1.19652666666667[/C][C]0.00406224581415428[/C][C]294.548070551898[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]1.19872666666667[/C][C]0.00357095460077956[/C][C]335.688016421429[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]1.16593275862069[/C][C]0.0160517313263048[/C][C]72.6359502859367[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]1.16833928571429[/C][C]0.0155335549402457[/C][C]75.2139024330642[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]1.17080740740741[/C][C]0.0149372041843822[/C][C]78.3819644529973[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]1.173575[/C][C]0.0142303156826139[/C][C]82.4700608317376[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]1.17615[/C][C]0.0136207150910603[/C][C]86.3500919105156[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]1.1781875[/C][C]0.0131562987587749[/C][C]89.5531122850323[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]1.18003043478261[/C][C]0.0127557761358028[/C][C]92.5094970482044[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]1.18210227272727[/C][C]0.0122786677493146[/C][C]96.2728446490668[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]1.18453095238095[/C][C]0.0116769940128649[/C][C]101.441428425493[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]1.1870275[/C][C]0.0110072074217014[/C][C]107.840931357367[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]1.18965789473684[/C][C]0.0102232258868289[/C][C]116.368151100871[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]1.19220277777778[/C][C]0.0093855549988631[/C][C]127.025282779995[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]1.19378529411765[/C][C]0.00886619702998767[/C][C]134.644570843618[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]1.1952[/C][C]0.00836993708304869[/C][C]142.796772322291[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]1.19670333333333[/C][C]0.0076939287653801[/C][C]155.538655194998[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]1.19839285714286[/C][C]0.00677745041215288[/C][C]176.820601297794[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]1.19923076923077[/C][C]0.00603024369766716[/C][C]198.869370684754[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]1.20036666666667[/C][C]0.00524660230518688[/C][C]228.789337716709[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]1.20192727272727[/C][C]0.00472623781545459[/C][C]254.309520523284[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]1.20278[/C][C]0.00449613635305505[/C][C]267.514128921542[/C][/ROW]
[ROW][C]Median[/C][C]1.20285[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]1.1054[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]1.19296129032258[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]1.19670333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]1.19296129032258[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]1.19670333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]1.19670333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]1.19296129032258[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]1.19670333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]1.1952[/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=7975&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=7975&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 Mean1.1639150.016550966282577170.3230844730334
Geometric Mean1.15640302060152
Harmonic Mean1.14829989439360
Quadratic Mean1.17083741904388
Winsorized Mean ( 1 / 20 )1.163686666666670.016466289046197470.670851422677
Winsorized Mean ( 2 / 20 )1.163896666666670.01638649108891771.0278155555748
Winsorized Mean ( 3 / 20 )1.163611666666670.016285516960317371.4507049117336
Winsorized Mean ( 4 / 20 )1.164991666666670.015598189321918474.687621917092
Winsorized Mean ( 5 / 20 )1.1680.014746295905679379.2063313709964
Winsorized Mean ( 6 / 20 )1.169710.014135175640772282.7517131535337
Winsorized Mean ( 7 / 20 )1.1693950.013957412712704683.7830781442444
Winsorized Mean ( 8 / 20 )1.168501666666670.013816490902427984.5729697155831
Winsorized Mean ( 9 / 20 )1.169551666666670.013353211275395587.5857980935024
Winsorized Mean ( 10 / 20 )1.170368333333330.012913545967101590.631057984767
Winsorized Mean ( 11 / 20 )1.172861666666670.012154444234196296.4965278598963
Winsorized Mean ( 12 / 20 )1.181441666666670.0103132363230823114.555860998012
Winsorized Mean ( 13 / 20 )1.183976666666670.00957798658019107123.614358482746
Winsorized Mean ( 14 / 20 )1.184676666666670.00941545050893755125.822621609250
Winsorized Mean ( 15 / 20 )1.184876666666670.00910601507500067130.120217999593
Winsorized Mean ( 16 / 20 )1.192583333333330.00769915622593393154.897926257974
Winsorized Mean ( 17 / 20 )1.191506666666670.00678647203166232175.570850525529
Winsorized Mean ( 18 / 20 )1.190066666666670.00519708776918407228.987217364910
Winsorized Mean ( 19 / 20 )1.196526666666670.00406224581415428294.548070551898
Winsorized Mean ( 20 / 20 )1.198726666666670.00357095460077956335.688016421429
Trimmed Mean ( 1 / 20 )1.165932758620690.016051731326304872.6359502859367
Trimmed Mean ( 2 / 20 )1.168339285714290.015533554940245775.2139024330642
Trimmed Mean ( 3 / 20 )1.170807407407410.014937204184382278.3819644529973
Trimmed Mean ( 4 / 20 )1.1735750.014230315682613982.4700608317376
Trimmed Mean ( 5 / 20 )1.176150.013620715091060386.3500919105156
Trimmed Mean ( 6 / 20 )1.17818750.013156298758774989.5531122850323
Trimmed Mean ( 7 / 20 )1.180030434782610.012755776135802892.5094970482044
Trimmed Mean ( 8 / 20 )1.182102272727270.012278667749314696.2728446490668
Trimmed Mean ( 9 / 20 )1.184530952380950.0116769940128649101.441428425493
Trimmed Mean ( 10 / 20 )1.18702750.0110072074217014107.840931357367
Trimmed Mean ( 11 / 20 )1.189657894736840.0102232258868289116.368151100871
Trimmed Mean ( 12 / 20 )1.192202777777780.0093855549988631127.025282779995
Trimmed Mean ( 13 / 20 )1.193785294117650.00886619702998767134.644570843618
Trimmed Mean ( 14 / 20 )1.19520.00836993708304869142.796772322291
Trimmed Mean ( 15 / 20 )1.196703333333330.0076939287653801155.538655194998
Trimmed Mean ( 16 / 20 )1.198392857142860.00677745041215288176.820601297794
Trimmed Mean ( 17 / 20 )1.199230769230770.00603024369766716198.869370684754
Trimmed Mean ( 18 / 20 )1.200366666666670.00524660230518688228.789337716709
Trimmed Mean ( 19 / 20 )1.201927272727270.00472623781545459254.309520523284
Trimmed Mean ( 20 / 20 )1.202780.00449613635305505267.514128921542
Median1.20285
Midrange1.1054
Midmean - Weighted Average at Xnp1.19296129032258
Midmean - Weighted Average at X(n+1)p1.19670333333333
Midmean - Empirical Distribution Function1.19296129032258
Midmean - Empirical Distribution Function - Averaging1.19670333333333
Midmean - Empirical Distribution Function - Interpolation1.19670333333333
Midmean - Closest Observation1.19296129032258
Midmean - True Basic - Statistics Graphics Toolkit1.19670333333333
Midmean - MS Excel (old versions)1.1952
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')