Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationMon, 27 Oct 2008 17:30:58 -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/2008/Oct/28/t1225150361fwytceoja02d9lz.htm/, Retrieved Sun, 19 May 2024 16:59:56 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=19711, Retrieved Sun, 19 May 2024 16:59:56 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact182
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
F     [Harrell-Davis Quantiles] [Q5 Distributions] [2007-10-22 09:17:45] [b731da8b544846036771bbf9bf2f34ce]
F RMPD    [Central Tendency] [] [2008-10-27 23:30:58] [e0f4dc76ea1a8276fe566258b977cec4] [Current]
Feedback Forum
2008-10-31 14:50:48 [Stijn Van de Velde] [reply
Ook met deze berekening ga ik volledig akkoord.
2008-11-03 09:48:23 [256f97d8b7c07ed49f142eff724c6520] [reply
Duidelijk omschreven in word document. Goed gewerkt.
2008-11-03 09:48:29 [Bas van Keken] [reply
Duidelijk en logisch verloop van de berekenening. Goed dat deze tussenstap ook is meegenomen.
2008-11-03 09:50:57 [256f97d8b7c07ed49f142eff724c6520] [reply
goed uitgewerkt

Post a new message
Dataseries X:
8,7800
8,8300
8,8300
8,8500
8,7400
8,7100
8,6800
8,5900
8,6400
8,6100
8,5900
8,5800
8,5700
8,5600
8,5500
8,5700
8,5300
8,5900
8,5500
8,5400
8,5600
8,5300
8,5500
8,5600
8,4800
8,5000
8,5400
8,4900
8,5100
8,5000
8,5900
8,5600
8,4500
8,4800
8,4800
8,4900
8,5200
8,4900
8,5700
8,5900
8,5700
8,5300
8,5700
8,5300
8,5400
8,4800
8,4800
8,5300
8,5700
8,4900
8,5400
8,5400
8,5600
8,6100
8,6700
8,6900
8,6900
8,7200
8,6600
8,6000
8,1100
8,1400
8,1800
8,1900
8,2200
8,2800
8,2800
8,3400
8,4100
8,3800
8,3800
8,3800
8,3900
8,4200
8,4400
8,4400
8,4400
8,4300
8,4000
8,4200




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001

\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 & 4 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=19711&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]4 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ 193.190.124.10:1001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=19711&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=19711&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 time4 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean8.5196250.016174917828915526.718286306837
Geometric Mean8.51840503330904
Harmonic Mean8.5171778322452
Quadratic Mean8.5208379136092
Winsorized Mean ( 1 / 26 )8.519750.0159954255723474532.63665674071
Winsorized Mean ( 2 / 26 )8.520750.015707749236474542.455183853743
Winsorized Mean ( 3 / 26 )8.519250.015166559442288561.712762371556
Winsorized Mean ( 4 / 26 )8.518750.0143491443312127593.676515014887
Winsorized Mean ( 5 / 26 )8.521250.0131764738084708646.701850879248
Winsorized Mean ( 6 / 26 )8.52050.0130358561016835653.620286503443
Winsorized Mean ( 7 / 26 )8.5240.0115692740163686736.779160726933
Winsorized Mean ( 8 / 26 )8.5280.0108184090643469788.285962314442
Winsorized Mean ( 9 / 26 )8.5268750.0106089789860562803.741341292807
Winsorized Mean ( 10 / 26 )8.5256250.0103847559742908820.974996534014
Winsorized Mean ( 11 / 26 )8.5256250.00990435869718638860.795257993024
Winsorized Mean ( 12 / 26 )8.5241250.00914664936576522931.939627193402
Winsorized Mean ( 13 / 26 )8.5208750.00813492577747721047.44348419150
Winsorized Mean ( 14 / 26 )8.5226250.007838851129171691087.22883743559
Winsorized Mean ( 15 / 26 )8.520750.007582405933925941123.75281332217
Winsorized Mean ( 16 / 26 )8.520750.006991801256480821218.67737474688
Winsorized Mean ( 17 / 26 )8.5228750.00664943547142221281.74414754898
Winsorized Mean ( 18 / 26 )8.5228750.00664943547142221281.74414754898
Winsorized Mean ( 19 / 26 )8.5228750.00664943547142221281.74414754898
Winsorized Mean ( 20 / 26 )8.5253750.006261555772825381361.54261166201
Winsorized Mean ( 21 / 26 )8.5306250.004781106506906081784.23655437877
Winsorized Mean ( 22 / 26 )8.5278750.00443552171092661922.63177947978
Winsorized Mean ( 23 / 26 )8.5278750.00443552171092661922.63177947978
Winsorized Mean ( 24 / 26 )8.5278750.00443552171092661922.63177947978
Winsorized Mean ( 25 / 26 )8.5278750.00443552171092661922.63177947978
Winsorized Mean ( 26 / 26 )8.5311250.004001557252250432131.95125352816
Trimmed Mean ( 1 / 26 )8.520641025641020.0151387629165557562.836017223237
Trimmed Mean ( 2 / 26 )8.521578947368420.0141161256942833603.676896332785
Trimmed Mean ( 3 / 26 )8.522027027027030.0130784941646987651.606134445475
Trimmed Mean ( 4 / 26 )8.523055555555550.0120893240595291705.006790585404
Trimmed Mean ( 5 / 26 )8.524285714285710.0112206763977415759.694461556834
Trimmed Mean ( 6 / 26 )8.5250.0105812214600017805.672580639721
Trimmed Mean ( 7 / 26 )8.525909090909090.0098448980378957866.023097252053
Trimmed Mean ( 8 / 26 )8.526250.00937400788401224909.562921804437
Trimmed Mean ( 9 / 26 )8.525967741935480.00899632593618334947.716634814656
Trimmed Mean ( 10 / 26 )8.525833333333330.0085875078982247992.81810676365
Trimmed Mean ( 11 / 26 )8.525862068965520.008139120361788451047.51640103429
Trimmed Mean ( 12 / 26 )8.525892857142860.007698780413258781107.43421678317
Trimmed Mean ( 13 / 26 )8.526111111111110.007327883751139031163.51615291193
Trimmed Mean ( 14 / 26 )8.526730769230770.007085563860567741203.39480908264
Trimmed Mean ( 15 / 26 )8.52720.00684546624878581245.67117711120
Trimmed Mean ( 16 / 26 )8.527916666666670.006590601069601241293.95127646266
Trimmed Mean ( 17 / 26 )8.528695652173910.006389973242043091334.69974428985
Trimmed Mean ( 18 / 26 )8.529318181818180.006206435717912851374.26996258111
Trimmed Mean ( 19 / 26 )8.530.005961549268974571430.8361157715
Trimmed Mean ( 20 / 26 )8.530750.005631726747086211514.76632001254
Trimmed Mean ( 21 / 26 )8.531315789473680.005295950473025821610.91306139035
Trimmed Mean ( 22 / 26 )8.531388888888890.005227412145842761632.04825846259
Trimmed Mean ( 23 / 26 )8.531764705882350.005196162512352381641.93569496730
Trimmed Mean ( 24 / 26 )8.53218750.005133978661346521661.90552450840
Trimmed Mean ( 25 / 26 )8.532666666666670.005027129464350521697.32383603314
Trimmed Mean ( 26 / 26 )8.533214285714290.004853776455562681758.05671394997
Median8.54
Midrange8.48
Midmean - Weighted Average at Xnp8.53
Midmean - Weighted Average at X(n+1)p8.53613636363636
Midmean - Empirical Distribution Function8.53
Midmean - Empirical Distribution Function - Averaging8.53613636363636
Midmean - Empirical Distribution Function - Interpolation8.53613636363636
Midmean - Closest Observation8.53
Midmean - True Basic - Statistics Graphics Toolkit8.53613636363636
Midmean - MS Excel (old versions)8.53
Number of observations80

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 8.519625 & 0.016174917828915 & 526.718286306837 \tabularnewline
Geometric Mean & 8.51840503330904 &  &  \tabularnewline
Harmonic Mean & 8.5171778322452 &  &  \tabularnewline
Quadratic Mean & 8.5208379136092 &  &  \tabularnewline
Winsorized Mean ( 1 / 26 ) & 8.51975 & 0.0159954255723474 & 532.63665674071 \tabularnewline
Winsorized Mean ( 2 / 26 ) & 8.52075 & 0.015707749236474 & 542.455183853743 \tabularnewline
Winsorized Mean ( 3 / 26 ) & 8.51925 & 0.015166559442288 & 561.712762371556 \tabularnewline
Winsorized Mean ( 4 / 26 ) & 8.51875 & 0.0143491443312127 & 593.676515014887 \tabularnewline
Winsorized Mean ( 5 / 26 ) & 8.52125 & 0.0131764738084708 & 646.701850879248 \tabularnewline
Winsorized Mean ( 6 / 26 ) & 8.5205 & 0.0130358561016835 & 653.620286503443 \tabularnewline
Winsorized Mean ( 7 / 26 ) & 8.524 & 0.0115692740163686 & 736.779160726933 \tabularnewline
Winsorized Mean ( 8 / 26 ) & 8.528 & 0.0108184090643469 & 788.285962314442 \tabularnewline
Winsorized Mean ( 9 / 26 ) & 8.526875 & 0.0106089789860562 & 803.741341292807 \tabularnewline
Winsorized Mean ( 10 / 26 ) & 8.525625 & 0.0103847559742908 & 820.974996534014 \tabularnewline
Winsorized Mean ( 11 / 26 ) & 8.525625 & 0.00990435869718638 & 860.795257993024 \tabularnewline
Winsorized Mean ( 12 / 26 ) & 8.524125 & 0.00914664936576522 & 931.939627193402 \tabularnewline
Winsorized Mean ( 13 / 26 ) & 8.520875 & 0.0081349257774772 & 1047.44348419150 \tabularnewline
Winsorized Mean ( 14 / 26 ) & 8.522625 & 0.00783885112917169 & 1087.22883743559 \tabularnewline
Winsorized Mean ( 15 / 26 ) & 8.52075 & 0.00758240593392594 & 1123.75281332217 \tabularnewline
Winsorized Mean ( 16 / 26 ) & 8.52075 & 0.00699180125648082 & 1218.67737474688 \tabularnewline
Winsorized Mean ( 17 / 26 ) & 8.522875 & 0.0066494354714222 & 1281.74414754898 \tabularnewline
Winsorized Mean ( 18 / 26 ) & 8.522875 & 0.0066494354714222 & 1281.74414754898 \tabularnewline
Winsorized Mean ( 19 / 26 ) & 8.522875 & 0.0066494354714222 & 1281.74414754898 \tabularnewline
Winsorized Mean ( 20 / 26 ) & 8.525375 & 0.00626155577282538 & 1361.54261166201 \tabularnewline
Winsorized Mean ( 21 / 26 ) & 8.530625 & 0.00478110650690608 & 1784.23655437877 \tabularnewline
Winsorized Mean ( 22 / 26 ) & 8.527875 & 0.0044355217109266 & 1922.63177947978 \tabularnewline
Winsorized Mean ( 23 / 26 ) & 8.527875 & 0.0044355217109266 & 1922.63177947978 \tabularnewline
Winsorized Mean ( 24 / 26 ) & 8.527875 & 0.0044355217109266 & 1922.63177947978 \tabularnewline
Winsorized Mean ( 25 / 26 ) & 8.527875 & 0.0044355217109266 & 1922.63177947978 \tabularnewline
Winsorized Mean ( 26 / 26 ) & 8.531125 & 0.00400155725225043 & 2131.95125352816 \tabularnewline
Trimmed Mean ( 1 / 26 ) & 8.52064102564102 & 0.0151387629165557 & 562.836017223237 \tabularnewline
Trimmed Mean ( 2 / 26 ) & 8.52157894736842 & 0.0141161256942833 & 603.676896332785 \tabularnewline
Trimmed Mean ( 3 / 26 ) & 8.52202702702703 & 0.0130784941646987 & 651.606134445475 \tabularnewline
Trimmed Mean ( 4 / 26 ) & 8.52305555555555 & 0.0120893240595291 & 705.006790585404 \tabularnewline
Trimmed Mean ( 5 / 26 ) & 8.52428571428571 & 0.0112206763977415 & 759.694461556834 \tabularnewline
Trimmed Mean ( 6 / 26 ) & 8.525 & 0.0105812214600017 & 805.672580639721 \tabularnewline
Trimmed Mean ( 7 / 26 ) & 8.52590909090909 & 0.0098448980378957 & 866.023097252053 \tabularnewline
Trimmed Mean ( 8 / 26 ) & 8.52625 & 0.00937400788401224 & 909.562921804437 \tabularnewline
Trimmed Mean ( 9 / 26 ) & 8.52596774193548 & 0.00899632593618334 & 947.716634814656 \tabularnewline
Trimmed Mean ( 10 / 26 ) & 8.52583333333333 & 0.0085875078982247 & 992.81810676365 \tabularnewline
Trimmed Mean ( 11 / 26 ) & 8.52586206896552 & 0.00813912036178845 & 1047.51640103429 \tabularnewline
Trimmed Mean ( 12 / 26 ) & 8.52589285714286 & 0.00769878041325878 & 1107.43421678317 \tabularnewline
Trimmed Mean ( 13 / 26 ) & 8.52611111111111 & 0.00732788375113903 & 1163.51615291193 \tabularnewline
Trimmed Mean ( 14 / 26 ) & 8.52673076923077 & 0.00708556386056774 & 1203.39480908264 \tabularnewline
Trimmed Mean ( 15 / 26 ) & 8.5272 & 0.0068454662487858 & 1245.67117711120 \tabularnewline
Trimmed Mean ( 16 / 26 ) & 8.52791666666667 & 0.00659060106960124 & 1293.95127646266 \tabularnewline
Trimmed Mean ( 17 / 26 ) & 8.52869565217391 & 0.00638997324204309 & 1334.69974428985 \tabularnewline
Trimmed Mean ( 18 / 26 ) & 8.52931818181818 & 0.00620643571791285 & 1374.26996258111 \tabularnewline
Trimmed Mean ( 19 / 26 ) & 8.53 & 0.00596154926897457 & 1430.8361157715 \tabularnewline
Trimmed Mean ( 20 / 26 ) & 8.53075 & 0.00563172674708621 & 1514.76632001254 \tabularnewline
Trimmed Mean ( 21 / 26 ) & 8.53131578947368 & 0.00529595047302582 & 1610.91306139035 \tabularnewline
Trimmed Mean ( 22 / 26 ) & 8.53138888888889 & 0.00522741214584276 & 1632.04825846259 \tabularnewline
Trimmed Mean ( 23 / 26 ) & 8.53176470588235 & 0.00519616251235238 & 1641.93569496730 \tabularnewline
Trimmed Mean ( 24 / 26 ) & 8.5321875 & 0.00513397866134652 & 1661.90552450840 \tabularnewline
Trimmed Mean ( 25 / 26 ) & 8.53266666666667 & 0.00502712946435052 & 1697.32383603314 \tabularnewline
Trimmed Mean ( 26 / 26 ) & 8.53321428571429 & 0.00485377645556268 & 1758.05671394997 \tabularnewline
Median & 8.54 &  &  \tabularnewline
Midrange & 8.48 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 8.53 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 8.53613636363636 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 8.53 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 8.53613636363636 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 8.53613636363636 &  &  \tabularnewline
Midmean - Closest Observation & 8.53 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 8.53613636363636 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 8.53 &  &  \tabularnewline
Number of observations & 80 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=19711&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]8.519625[/C][C]0.016174917828915[/C][C]526.718286306837[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]8.51840503330904[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]8.5171778322452[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]8.5208379136092[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 26 )[/C][C]8.51975[/C][C]0.0159954255723474[/C][C]532.63665674071[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 26 )[/C][C]8.52075[/C][C]0.015707749236474[/C][C]542.455183853743[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 26 )[/C][C]8.51925[/C][C]0.015166559442288[/C][C]561.712762371556[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 26 )[/C][C]8.51875[/C][C]0.0143491443312127[/C][C]593.676515014887[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 26 )[/C][C]8.52125[/C][C]0.0131764738084708[/C][C]646.701850879248[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 26 )[/C][C]8.5205[/C][C]0.0130358561016835[/C][C]653.620286503443[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 26 )[/C][C]8.524[/C][C]0.0115692740163686[/C][C]736.779160726933[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 26 )[/C][C]8.528[/C][C]0.0108184090643469[/C][C]788.285962314442[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 26 )[/C][C]8.526875[/C][C]0.0106089789860562[/C][C]803.741341292807[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 26 )[/C][C]8.525625[/C][C]0.0103847559742908[/C][C]820.974996534014[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 26 )[/C][C]8.525625[/C][C]0.00990435869718638[/C][C]860.795257993024[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 26 )[/C][C]8.524125[/C][C]0.00914664936576522[/C][C]931.939627193402[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 26 )[/C][C]8.520875[/C][C]0.0081349257774772[/C][C]1047.44348419150[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 26 )[/C][C]8.522625[/C][C]0.00783885112917169[/C][C]1087.22883743559[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 26 )[/C][C]8.52075[/C][C]0.00758240593392594[/C][C]1123.75281332217[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 26 )[/C][C]8.52075[/C][C]0.00699180125648082[/C][C]1218.67737474688[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 26 )[/C][C]8.522875[/C][C]0.0066494354714222[/C][C]1281.74414754898[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 26 )[/C][C]8.522875[/C][C]0.0066494354714222[/C][C]1281.74414754898[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 26 )[/C][C]8.522875[/C][C]0.0066494354714222[/C][C]1281.74414754898[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 26 )[/C][C]8.525375[/C][C]0.00626155577282538[/C][C]1361.54261166201[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 26 )[/C][C]8.530625[/C][C]0.00478110650690608[/C][C]1784.23655437877[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 26 )[/C][C]8.527875[/C][C]0.0044355217109266[/C][C]1922.63177947978[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 26 )[/C][C]8.527875[/C][C]0.0044355217109266[/C][C]1922.63177947978[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 26 )[/C][C]8.527875[/C][C]0.0044355217109266[/C][C]1922.63177947978[/C][/ROW]
[ROW][C]Winsorized Mean ( 25 / 26 )[/C][C]8.527875[/C][C]0.0044355217109266[/C][C]1922.63177947978[/C][/ROW]
[ROW][C]Winsorized Mean ( 26 / 26 )[/C][C]8.531125[/C][C]0.00400155725225043[/C][C]2131.95125352816[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 26 )[/C][C]8.52064102564102[/C][C]0.0151387629165557[/C][C]562.836017223237[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 26 )[/C][C]8.52157894736842[/C][C]0.0141161256942833[/C][C]603.676896332785[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 26 )[/C][C]8.52202702702703[/C][C]0.0130784941646987[/C][C]651.606134445475[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 26 )[/C][C]8.52305555555555[/C][C]0.0120893240595291[/C][C]705.006790585404[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 26 )[/C][C]8.52428571428571[/C][C]0.0112206763977415[/C][C]759.694461556834[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 26 )[/C][C]8.525[/C][C]0.0105812214600017[/C][C]805.672580639721[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 26 )[/C][C]8.52590909090909[/C][C]0.0098448980378957[/C][C]866.023097252053[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 26 )[/C][C]8.52625[/C][C]0.00937400788401224[/C][C]909.562921804437[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 26 )[/C][C]8.52596774193548[/C][C]0.00899632593618334[/C][C]947.716634814656[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 26 )[/C][C]8.52583333333333[/C][C]0.0085875078982247[/C][C]992.81810676365[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 26 )[/C][C]8.52586206896552[/C][C]0.00813912036178845[/C][C]1047.51640103429[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 26 )[/C][C]8.52589285714286[/C][C]0.00769878041325878[/C][C]1107.43421678317[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 26 )[/C][C]8.52611111111111[/C][C]0.00732788375113903[/C][C]1163.51615291193[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 26 )[/C][C]8.52673076923077[/C][C]0.00708556386056774[/C][C]1203.39480908264[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 26 )[/C][C]8.5272[/C][C]0.0068454662487858[/C][C]1245.67117711120[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 26 )[/C][C]8.52791666666667[/C][C]0.00659060106960124[/C][C]1293.95127646266[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 26 )[/C][C]8.52869565217391[/C][C]0.00638997324204309[/C][C]1334.69974428985[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 26 )[/C][C]8.52931818181818[/C][C]0.00620643571791285[/C][C]1374.26996258111[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 26 )[/C][C]8.53[/C][C]0.00596154926897457[/C][C]1430.8361157715[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 26 )[/C][C]8.53075[/C][C]0.00563172674708621[/C][C]1514.76632001254[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 26 )[/C][C]8.53131578947368[/C][C]0.00529595047302582[/C][C]1610.91306139035[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 26 )[/C][C]8.53138888888889[/C][C]0.00522741214584276[/C][C]1632.04825846259[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 26 )[/C][C]8.53176470588235[/C][C]0.00519616251235238[/C][C]1641.93569496730[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 26 )[/C][C]8.5321875[/C][C]0.00513397866134652[/C][C]1661.90552450840[/C][/ROW]
[ROW][C]Trimmed Mean ( 25 / 26 )[/C][C]8.53266666666667[/C][C]0.00502712946435052[/C][C]1697.32383603314[/C][/ROW]
[ROW][C]Trimmed Mean ( 26 / 26 )[/C][C]8.53321428571429[/C][C]0.00485377645556268[/C][C]1758.05671394997[/C][/ROW]
[ROW][C]Median[/C][C]8.54[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]8.48[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]8.53[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]8.53613636363636[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]8.53[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]8.53613636363636[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]8.53613636363636[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]8.53[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]8.53613636363636[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]8.53[/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=19711&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=19711&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 Mean8.5196250.016174917828915526.718286306837
Geometric Mean8.51840503330904
Harmonic Mean8.5171778322452
Quadratic Mean8.5208379136092
Winsorized Mean ( 1 / 26 )8.519750.0159954255723474532.63665674071
Winsorized Mean ( 2 / 26 )8.520750.015707749236474542.455183853743
Winsorized Mean ( 3 / 26 )8.519250.015166559442288561.712762371556
Winsorized Mean ( 4 / 26 )8.518750.0143491443312127593.676515014887
Winsorized Mean ( 5 / 26 )8.521250.0131764738084708646.701850879248
Winsorized Mean ( 6 / 26 )8.52050.0130358561016835653.620286503443
Winsorized Mean ( 7 / 26 )8.5240.0115692740163686736.779160726933
Winsorized Mean ( 8 / 26 )8.5280.0108184090643469788.285962314442
Winsorized Mean ( 9 / 26 )8.5268750.0106089789860562803.741341292807
Winsorized Mean ( 10 / 26 )8.5256250.0103847559742908820.974996534014
Winsorized Mean ( 11 / 26 )8.5256250.00990435869718638860.795257993024
Winsorized Mean ( 12 / 26 )8.5241250.00914664936576522931.939627193402
Winsorized Mean ( 13 / 26 )8.5208750.00813492577747721047.44348419150
Winsorized Mean ( 14 / 26 )8.5226250.007838851129171691087.22883743559
Winsorized Mean ( 15 / 26 )8.520750.007582405933925941123.75281332217
Winsorized Mean ( 16 / 26 )8.520750.006991801256480821218.67737474688
Winsorized Mean ( 17 / 26 )8.5228750.00664943547142221281.74414754898
Winsorized Mean ( 18 / 26 )8.5228750.00664943547142221281.74414754898
Winsorized Mean ( 19 / 26 )8.5228750.00664943547142221281.74414754898
Winsorized Mean ( 20 / 26 )8.5253750.006261555772825381361.54261166201
Winsorized Mean ( 21 / 26 )8.5306250.004781106506906081784.23655437877
Winsorized Mean ( 22 / 26 )8.5278750.00443552171092661922.63177947978
Winsorized Mean ( 23 / 26 )8.5278750.00443552171092661922.63177947978
Winsorized Mean ( 24 / 26 )8.5278750.00443552171092661922.63177947978
Winsorized Mean ( 25 / 26 )8.5278750.00443552171092661922.63177947978
Winsorized Mean ( 26 / 26 )8.5311250.004001557252250432131.95125352816
Trimmed Mean ( 1 / 26 )8.520641025641020.0151387629165557562.836017223237
Trimmed Mean ( 2 / 26 )8.521578947368420.0141161256942833603.676896332785
Trimmed Mean ( 3 / 26 )8.522027027027030.0130784941646987651.606134445475
Trimmed Mean ( 4 / 26 )8.523055555555550.0120893240595291705.006790585404
Trimmed Mean ( 5 / 26 )8.524285714285710.0112206763977415759.694461556834
Trimmed Mean ( 6 / 26 )8.5250.0105812214600017805.672580639721
Trimmed Mean ( 7 / 26 )8.525909090909090.0098448980378957866.023097252053
Trimmed Mean ( 8 / 26 )8.526250.00937400788401224909.562921804437
Trimmed Mean ( 9 / 26 )8.525967741935480.00899632593618334947.716634814656
Trimmed Mean ( 10 / 26 )8.525833333333330.0085875078982247992.81810676365
Trimmed Mean ( 11 / 26 )8.525862068965520.008139120361788451047.51640103429
Trimmed Mean ( 12 / 26 )8.525892857142860.007698780413258781107.43421678317
Trimmed Mean ( 13 / 26 )8.526111111111110.007327883751139031163.51615291193
Trimmed Mean ( 14 / 26 )8.526730769230770.007085563860567741203.39480908264
Trimmed Mean ( 15 / 26 )8.52720.00684546624878581245.67117711120
Trimmed Mean ( 16 / 26 )8.527916666666670.006590601069601241293.95127646266
Trimmed Mean ( 17 / 26 )8.528695652173910.006389973242043091334.69974428985
Trimmed Mean ( 18 / 26 )8.529318181818180.006206435717912851374.26996258111
Trimmed Mean ( 19 / 26 )8.530.005961549268974571430.8361157715
Trimmed Mean ( 20 / 26 )8.530750.005631726747086211514.76632001254
Trimmed Mean ( 21 / 26 )8.531315789473680.005295950473025821610.91306139035
Trimmed Mean ( 22 / 26 )8.531388888888890.005227412145842761632.04825846259
Trimmed Mean ( 23 / 26 )8.531764705882350.005196162512352381641.93569496730
Trimmed Mean ( 24 / 26 )8.53218750.005133978661346521661.90552450840
Trimmed Mean ( 25 / 26 )8.532666666666670.005027129464350521697.32383603314
Trimmed Mean ( 26 / 26 )8.533214285714290.004853776455562681758.05671394997
Median8.54
Midrange8.48
Midmean - Weighted Average at Xnp8.53
Midmean - Weighted Average at X(n+1)p8.53613636363636
Midmean - Empirical Distribution Function8.53
Midmean - Empirical Distribution Function - Averaging8.53613636363636
Midmean - Empirical Distribution Function - Interpolation8.53613636363636
Midmean - Closest Observation8.53
Midmean - True Basic - Statistics Graphics Toolkit8.53613636363636
Midmean - MS Excel (old versions)8.53
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')