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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationMon, 10 Dec 2007 14:58:37 -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/2007/Dec/10/t1197323057qbinafijk8w8uju.htm/, Retrieved Mon, 06 May 2024 22:57:50 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=3066, Retrieved Mon, 06 May 2024 22:57:50 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact219
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Paper] [2007-12-10 21:58:37] [3463f71ebce131edf0c83e066f45702c] [Current]
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Dataseries X:
99,8
96,8
87,0
96,3
107,1
115,2
106,1
89,5
91,3
97,6
100,7
104,6
94,7
101,8
102,5
105,3
110,3
109,8
117,3
118,8
131,3
125,9
133,1
147,0
145,8
164,4
149,8
137,7
151,7
156,8
180,0
180,4
170,4
191,6
199,5
218,2
217,5
205,0
194,0
199,3
219,3
211,1
215,2
240,2
242,2
240,7
255,4
253,0
218,2
203,7
205,6
215,6
188,5
202,9
214,0
230,3
230,0
241,0
259,6
247,8
270,3




Summary of compuational 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 compuational 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=3066&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]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=3066&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=3066&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 time4 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean168.1393442622957.2210939783525623.2844697446598
Geometric Mean158.391366305041
Harmonic Mean148.771220525722
Quadratic Mean177.199015188027
Winsorized Mean ( 1 / 20 )168.0049180327877.174169446504323.4180303776696
Winsorized Mean ( 2 / 20 )167.9262295081977.1347839167709123.5362740437692
Winsorized Mean ( 3 / 20 )167.9754098360667.081528213220123.7202203787710
Winsorized Mean ( 4 / 20 )167.7393442622956.9969135579265123.9733337954805
Winsorized Mean ( 5 / 20 )167.3213114754106.9046725743739724.2330551772153
Winsorized Mean ( 6 / 20 )167.2819672131156.8701025311097224.3492679265871
Winsorized Mean ( 7 / 20 )167.56.8217267816992724.5539004067642
Winsorized Mean ( 8 / 20 )167.5524590163936.7905718980435924.6742780331457
Winsorized Mean ( 9 / 20 )166.2540983606566.5137540793613125.5235454601254
Winsorized Mean ( 10 / 20 )166.3196721311486.486830214189125.6395907769167
Winsorized Mean ( 11 / 20 )164.7688524590166.123309197198926.9084652028334
Winsorized Mean ( 12 / 20 )164.6901639344266.0688435286723627.1369929305879
Winsorized Mean ( 13 / 20 )164.8606557377056.0411201503056627.2897495225887
Winsorized Mean ( 14 / 20 )164.9295081967215.9804327311413327.5781896747872
Winsorized Mean ( 15 / 20 )165.1262295081975.8061216524318528.4400223407367
Winsorized Mean ( 16 / 20 )165.1524590163935.770133961830728.6219453671047
Winsorized Mean ( 17 / 20 )166.1836065573775.5081931921664530.1702574255597
Winsorized Mean ( 18 / 20 )165.9475409836075.2901101698927931.3693922535019
Winsorized Mean ( 19 / 20 )164.7016393442624.9791672509151833.0781496271269
Winsorized Mean ( 20 / 20 )166.8327868852464.6004227183482236.2646645969845
Trimmed Mean ( 1 / 20 )167.7830508474587.1270486621890623.5417293749645
Trimmed Mean ( 2 / 20 )167.5456140350887.0634894100019423.7199497740936
Trimmed Mean ( 3 / 20 )167.3345454545457.0046604102200323.8890303961629
Trimmed Mean ( 4 / 20 )167.0886792452836.9495980715019424.0429270191120
Trimmed Mean ( 5 / 20 )166.8941176470596.904928851567824.1702878095789
Trimmed Mean ( 6 / 20 )166.7877551020416.8696034061606624.2790952025652
Trimmed Mean ( 7 / 20 )166.6808510638306.8247303188514124.4230677662706
Trimmed Mean ( 8 / 20 )166.5222222222226.769895399941624.5974586584689
Trimmed Mean ( 9 / 20 )166.3395348837216.6963868040624924.8401921440392
Trimmed Mean ( 10 / 20 )166.3536585365856.6592875704436724.9806990277643
Trimmed Mean ( 11 / 20 )166.3589743589746.6022260568834325.1974065906952
Trimmed Mean ( 12 / 20 )166.5972972972976.5976409544215725.2510402503259
Trimmed Mean ( 13 / 20 )166.8742857142866.582225036761825.3522607905824
Trimmed Mean ( 14 / 20 )167.1606060606066.544357590810625.5427066356105
Trimmed Mean ( 15 / 20 )167.4741935483876.4826185598336525.8343433294160
Trimmed Mean ( 16 / 20 )167.8034482758626.4170617763385626.1495765701678
Trimmed Mean ( 17 / 20 )168.1777777777786.3020173438423126.6863400403212
Trimmed Mean ( 18 / 20 )168.4646.1876028745656727.2260523849190
Trimmed Mean ( 19 / 20 )168.8347826086966.0519999918220427.8973534099206
Trimmed Mean ( 20 / 20 )169.4666666666675.9099525956254228.6747928895583
Median170.4
Midrange178.65
Midmean - Weighted Average at Xnp165.87
Midmean - Weighted Average at X(n+1)p167.474193548387
Midmean - Empirical Distribution Function167.474193548387
Midmean - Empirical Distribution Function - Averaging167.474193548387
Midmean - Empirical Distribution Function - Interpolation167.474193548387
Midmean - Closest Observation165.5875
Midmean - True Basic - Statistics Graphics Toolkit167.474193548387
Midmean - MS Excel (old versions)167.474193548387
Number of observations61

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 168.139344262295 & 7.22109397835256 & 23.2844697446598 \tabularnewline
Geometric Mean & 158.391366305041 &  &  \tabularnewline
Harmonic Mean & 148.771220525722 &  &  \tabularnewline
Quadratic Mean & 177.199015188027 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 168.004918032787 & 7.1741694465043 & 23.4180303776696 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 167.926229508197 & 7.13478391677091 & 23.5362740437692 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 167.975409836066 & 7.0815282132201 & 23.7202203787710 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 167.739344262295 & 6.99691355792651 & 23.9733337954805 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 167.321311475410 & 6.90467257437397 & 24.2330551772153 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 167.281967213115 & 6.87010253110972 & 24.3492679265871 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 167.5 & 6.82172678169927 & 24.5539004067642 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 167.552459016393 & 6.79057189804359 & 24.6742780331457 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 166.254098360656 & 6.51375407936131 & 25.5235454601254 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 166.319672131148 & 6.4868302141891 & 25.6395907769167 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 164.768852459016 & 6.1233091971989 & 26.9084652028334 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 164.690163934426 & 6.06884352867236 & 27.1369929305879 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 164.860655737705 & 6.04112015030566 & 27.2897495225887 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 164.929508196721 & 5.98043273114133 & 27.5781896747872 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 165.126229508197 & 5.80612165243185 & 28.4400223407367 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 165.152459016393 & 5.7701339618307 & 28.6219453671047 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 166.183606557377 & 5.50819319216645 & 30.1702574255597 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 165.947540983607 & 5.29011016989279 & 31.3693922535019 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 164.701639344262 & 4.97916725091518 & 33.0781496271269 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 166.832786885246 & 4.60042271834822 & 36.2646645969845 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 167.783050847458 & 7.12704866218906 & 23.5417293749645 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 167.545614035088 & 7.06348941000194 & 23.7199497740936 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 167.334545454545 & 7.00466041022003 & 23.8890303961629 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 167.088679245283 & 6.94959807150194 & 24.0429270191120 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 166.894117647059 & 6.9049288515678 & 24.1702878095789 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 166.787755102041 & 6.86960340616066 & 24.2790952025652 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 166.680851063830 & 6.82473031885141 & 24.4230677662706 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 166.522222222222 & 6.7698953999416 & 24.5974586584689 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 166.339534883721 & 6.69638680406249 & 24.8401921440392 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 166.353658536585 & 6.65928757044367 & 24.9806990277643 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 166.358974358974 & 6.60222605688343 & 25.1974065906952 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 166.597297297297 & 6.59764095442157 & 25.2510402503259 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 166.874285714286 & 6.5822250367618 & 25.3522607905824 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 167.160606060606 & 6.5443575908106 & 25.5427066356105 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 167.474193548387 & 6.48261855983365 & 25.8343433294160 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 167.803448275862 & 6.41706177633856 & 26.1495765701678 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 168.177777777778 & 6.30201734384231 & 26.6863400403212 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 168.464 & 6.18760287456567 & 27.2260523849190 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 168.834782608696 & 6.05199999182204 & 27.8973534099206 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 169.466666666667 & 5.90995259562542 & 28.6747928895583 \tabularnewline
Median & 170.4 &  &  \tabularnewline
Midrange & 178.65 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 165.87 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 167.474193548387 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 167.474193548387 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 167.474193548387 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 167.474193548387 &  &  \tabularnewline
Midmean - Closest Observation & 165.5875 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 167.474193548387 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 167.474193548387 &  &  \tabularnewline
Number of observations & 61 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=3066&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]168.139344262295[/C][C]7.22109397835256[/C][C]23.2844697446598[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]158.391366305041[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]148.771220525722[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]177.199015188027[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]168.004918032787[/C][C]7.1741694465043[/C][C]23.4180303776696[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]167.926229508197[/C][C]7.13478391677091[/C][C]23.5362740437692[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]167.975409836066[/C][C]7.0815282132201[/C][C]23.7202203787710[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]167.739344262295[/C][C]6.99691355792651[/C][C]23.9733337954805[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]167.321311475410[/C][C]6.90467257437397[/C][C]24.2330551772153[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]167.281967213115[/C][C]6.87010253110972[/C][C]24.3492679265871[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]167.5[/C][C]6.82172678169927[/C][C]24.5539004067642[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]167.552459016393[/C][C]6.79057189804359[/C][C]24.6742780331457[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]166.254098360656[/C][C]6.51375407936131[/C][C]25.5235454601254[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]166.319672131148[/C][C]6.4868302141891[/C][C]25.6395907769167[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]164.768852459016[/C][C]6.1233091971989[/C][C]26.9084652028334[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]164.690163934426[/C][C]6.06884352867236[/C][C]27.1369929305879[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]164.860655737705[/C][C]6.04112015030566[/C][C]27.2897495225887[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]164.929508196721[/C][C]5.98043273114133[/C][C]27.5781896747872[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]165.126229508197[/C][C]5.80612165243185[/C][C]28.4400223407367[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]165.152459016393[/C][C]5.7701339618307[/C][C]28.6219453671047[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]166.183606557377[/C][C]5.50819319216645[/C][C]30.1702574255597[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]165.947540983607[/C][C]5.29011016989279[/C][C]31.3693922535019[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]164.701639344262[/C][C]4.97916725091518[/C][C]33.0781496271269[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]166.832786885246[/C][C]4.60042271834822[/C][C]36.2646645969845[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]167.783050847458[/C][C]7.12704866218906[/C][C]23.5417293749645[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]167.545614035088[/C][C]7.06348941000194[/C][C]23.7199497740936[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]167.334545454545[/C][C]7.00466041022003[/C][C]23.8890303961629[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]167.088679245283[/C][C]6.94959807150194[/C][C]24.0429270191120[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]166.894117647059[/C][C]6.9049288515678[/C][C]24.1702878095789[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]166.787755102041[/C][C]6.86960340616066[/C][C]24.2790952025652[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]166.680851063830[/C][C]6.82473031885141[/C][C]24.4230677662706[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]166.522222222222[/C][C]6.7698953999416[/C][C]24.5974586584689[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]166.339534883721[/C][C]6.69638680406249[/C][C]24.8401921440392[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]166.353658536585[/C][C]6.65928757044367[/C][C]24.9806990277643[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]166.358974358974[/C][C]6.60222605688343[/C][C]25.1974065906952[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]166.597297297297[/C][C]6.59764095442157[/C][C]25.2510402503259[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]166.874285714286[/C][C]6.5822250367618[/C][C]25.3522607905824[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]167.160606060606[/C][C]6.5443575908106[/C][C]25.5427066356105[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]167.474193548387[/C][C]6.48261855983365[/C][C]25.8343433294160[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]167.803448275862[/C][C]6.41706177633856[/C][C]26.1495765701678[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]168.177777777778[/C][C]6.30201734384231[/C][C]26.6863400403212[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]168.464[/C][C]6.18760287456567[/C][C]27.2260523849190[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]168.834782608696[/C][C]6.05199999182204[/C][C]27.8973534099206[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]169.466666666667[/C][C]5.90995259562542[/C][C]28.6747928895583[/C][/ROW]
[ROW][C]Median[/C][C]170.4[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]178.65[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]165.87[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]167.474193548387[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]167.474193548387[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]167.474193548387[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]167.474193548387[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]165.5875[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]167.474193548387[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]167.474193548387[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]61[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=3066&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=3066&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 Mean168.1393442622957.2210939783525623.2844697446598
Geometric Mean158.391366305041
Harmonic Mean148.771220525722
Quadratic Mean177.199015188027
Winsorized Mean ( 1 / 20 )168.0049180327877.174169446504323.4180303776696
Winsorized Mean ( 2 / 20 )167.9262295081977.1347839167709123.5362740437692
Winsorized Mean ( 3 / 20 )167.9754098360667.081528213220123.7202203787710
Winsorized Mean ( 4 / 20 )167.7393442622956.9969135579265123.9733337954805
Winsorized Mean ( 5 / 20 )167.3213114754106.9046725743739724.2330551772153
Winsorized Mean ( 6 / 20 )167.2819672131156.8701025311097224.3492679265871
Winsorized Mean ( 7 / 20 )167.56.8217267816992724.5539004067642
Winsorized Mean ( 8 / 20 )167.5524590163936.7905718980435924.6742780331457
Winsorized Mean ( 9 / 20 )166.2540983606566.5137540793613125.5235454601254
Winsorized Mean ( 10 / 20 )166.3196721311486.486830214189125.6395907769167
Winsorized Mean ( 11 / 20 )164.7688524590166.123309197198926.9084652028334
Winsorized Mean ( 12 / 20 )164.6901639344266.0688435286723627.1369929305879
Winsorized Mean ( 13 / 20 )164.8606557377056.0411201503056627.2897495225887
Winsorized Mean ( 14 / 20 )164.9295081967215.9804327311413327.5781896747872
Winsorized Mean ( 15 / 20 )165.1262295081975.8061216524318528.4400223407367
Winsorized Mean ( 16 / 20 )165.1524590163935.770133961830728.6219453671047
Winsorized Mean ( 17 / 20 )166.1836065573775.5081931921664530.1702574255597
Winsorized Mean ( 18 / 20 )165.9475409836075.2901101698927931.3693922535019
Winsorized Mean ( 19 / 20 )164.7016393442624.9791672509151833.0781496271269
Winsorized Mean ( 20 / 20 )166.8327868852464.6004227183482236.2646645969845
Trimmed Mean ( 1 / 20 )167.7830508474587.1270486621890623.5417293749645
Trimmed Mean ( 2 / 20 )167.5456140350887.0634894100019423.7199497740936
Trimmed Mean ( 3 / 20 )167.3345454545457.0046604102200323.8890303961629
Trimmed Mean ( 4 / 20 )167.0886792452836.9495980715019424.0429270191120
Trimmed Mean ( 5 / 20 )166.8941176470596.904928851567824.1702878095789
Trimmed Mean ( 6 / 20 )166.7877551020416.8696034061606624.2790952025652
Trimmed Mean ( 7 / 20 )166.6808510638306.8247303188514124.4230677662706
Trimmed Mean ( 8 / 20 )166.5222222222226.769895399941624.5974586584689
Trimmed Mean ( 9 / 20 )166.3395348837216.6963868040624924.8401921440392
Trimmed Mean ( 10 / 20 )166.3536585365856.6592875704436724.9806990277643
Trimmed Mean ( 11 / 20 )166.3589743589746.6022260568834325.1974065906952
Trimmed Mean ( 12 / 20 )166.5972972972976.5976409544215725.2510402503259
Trimmed Mean ( 13 / 20 )166.8742857142866.582225036761825.3522607905824
Trimmed Mean ( 14 / 20 )167.1606060606066.544357590810625.5427066356105
Trimmed Mean ( 15 / 20 )167.4741935483876.4826185598336525.8343433294160
Trimmed Mean ( 16 / 20 )167.8034482758626.4170617763385626.1495765701678
Trimmed Mean ( 17 / 20 )168.1777777777786.3020173438423126.6863400403212
Trimmed Mean ( 18 / 20 )168.4646.1876028745656727.2260523849190
Trimmed Mean ( 19 / 20 )168.8347826086966.0519999918220427.8973534099206
Trimmed Mean ( 20 / 20 )169.4666666666675.9099525956254228.6747928895583
Median170.4
Midrange178.65
Midmean - Weighted Average at Xnp165.87
Midmean - Weighted Average at X(n+1)p167.474193548387
Midmean - Empirical Distribution Function167.474193548387
Midmean - Empirical Distribution Function - Averaging167.474193548387
Midmean - Empirical Distribution Function - Interpolation167.474193548387
Midmean - Closest Observation165.5875
Midmean - True Basic - Statistics Graphics Toolkit167.474193548387
Midmean - MS Excel (old versions)167.474193548387
Number of observations61



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')