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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationThu, 29 Nov 2007 02:38:15 -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/Nov/29/t11963285141s95foltl3mbx8x.htm/, Retrieved Fri, 03 May 2024 09:30:23 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=7308, Retrieved Fri, 03 May 2024 09:30:23 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact228
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Central Tendency ...] [2007-11-29 09:38:15] [7c5c775a3769ba2649d285a4261e023c] [Current]
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Dataseries X:
90.8
96.4
90
92.1
97.2
95.1
88.5
91
90.5
75
66.3
66
68.4
70.6
83.9
90.1
90.6
87.1
90.8
94.1
99.8
96.8
87
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
145.8
164.4
149.8
137.7
151.7
156.8
180
180.4
170.4
191.6
199.5
218.2
217.5
205
194
199.3
219.3
211.1
215.2
240.2
242.2
240.7
255.4
253
218.2
203.7
205.6
215.6
188.5
202.9
214
230.3
230
241
259.6
247.8
270.3




Summary of compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=7308&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]2 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=7308&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=7308&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 time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean147.790123456796.7492545553030221.8972513550654
Geometric Mean135.858588543141
Harmonic Mean125.183317632445
Quadratic Mean159.643714425453
Winsorized Mean ( 1 / 27 )147.6617283950626.7199519967929321.9736284523361
Winsorized Mean ( 2 / 27 )147.6098765432106.6909526635678622.0611150556996
Winsorized Mean ( 3 / 27 )147.6024691358026.661296210779322.1582203320958
Winsorized Mean ( 4 / 27 )147.5629629629636.5807733992469322.4233466206038
Winsorized Mean ( 5 / 27 )147.7666666666676.4442617311263222.9299604565937
Winsorized Mean ( 6 / 27 )147.9074074074076.4001561945103323.109968399564
Winsorized Mean ( 7 / 27 )147.890123456796.3944199741153323.1279966057048
Winsorized Mean ( 8 / 27 )147.9790123456796.369185006115623.2335867467489
Winsorized Mean ( 9 / 27 )146.990123456796.1636443056322423.8479244044750
Winsorized Mean ( 10 / 27 )147.0148148148156.150217077146323.9040041954145
Winsorized Mean ( 11 / 27 )145.5753086419755.9126696282049224.6209103156288
Winsorized Mean ( 12 / 27 )145.4716049382725.8804352936235524.7382375070114
Winsorized Mean ( 13 / 27 )145.4876543209885.8785610123808524.7488550369003
Winsorized Mean ( 14 / 27 )145.4012345679015.8558658714493124.8300145119128
Winsorized Mean ( 15 / 27 )145.0493827160495.8020489472235424.9996827044108
Winsorized Mean ( 16 / 27 )145.009876543215.7854392592653625.0646269098715
Winsorized Mean ( 17 / 27 )144.8209876543215.7400280454990325.2300139487786
Winsorized Mean ( 18 / 27 )144.3543209876545.6229811327339925.6722044019142
Winsorized Mean ( 19 / 27 )143.5333333333335.3799909357856526.6791031893017
Winsorized Mean ( 20 / 27 )143.5333333333335.3416815450188626.8704399773099
Winsorized Mean ( 21 / 27 )143.35.2815109603873227.1323871283780
Winsorized Mean ( 22 / 27 )143.4086419753095.2134856582164527.5072478140027
Winsorized Mean ( 23 / 27 )142.4716049382725.0735796633657228.0810816802586
Winsorized Mean ( 24 / 27 )142.5308641975315.0518226884197428.2137503606873
Winsorized Mean ( 25 / 27 )141.0185185185194.8102588131106229.3162018921238
Winsorized Mean ( 26 / 27 )140.3765432098774.6900058805159829.9309951386314
Winsorized Mean ( 27 / 27 )140.0765432098774.4662880822164431.3630783844024
Trimmed Mean ( 1 / 27 )147.2746835443046.6617213404860822.1076019270355
Trimmed Mean ( 2 / 27 )146.8675324675326.591719323643122.2806107567035
Trimmed Mean ( 3 / 27 )146.4666666666676.5254231393180322.4455431532328
Trimmed Mean ( 4 / 27 )146.0465753424666.4580277824882722.6147332067058
Trimmed Mean ( 5 / 27 )145.6140845070426.4034812890186122.7398313409234
Trimmed Mean ( 6 / 27 )145.1086956521746.3741946114226922.7650243674920
Trimmed Mean ( 7 / 27 )144.5447761194036.3453413801096322.7796689666689
Trimmed Mean ( 8 / 27 )143.9492307692316.3069669669727322.8238440954329
Trimmed Mean ( 9 / 27 )143.3015873015876.2608948532014422.8883555245001
Trimmed Mean ( 10 / 27 )142.7573770491806.242572180305122.8683582545622
Trimmed Mean ( 11 / 27 )142.1728813559326.21583253568522.8727013702058
Trimmed Mean ( 12 / 27 )141.7333333333336.2212538593348722.7821170037396
Trimmed Mean ( 13 / 27 )141.2745454545456.2241947909618922.6976420563973
Trimmed Mean ( 14 / 27 )140.7792452830196.2181305662883222.6401237127853
Trimmed Mean ( 15 / 27 )140.2549019607846.2044615912311622.6054912095851
Trimmed Mean ( 16 / 27 )139.7265306122456.1868158424139222.5845627494429
Trimmed Mean ( 17 / 27 )139.1574468085116.1563439784612822.6039102583238
Trimmed Mean ( 18 / 27 )138.5577777777786.1147738702037222.6595096922467
Trimmed Mean ( 19 / 27 )137.9511627906986.0724942852903522.7173804222200
Trimmed Mean ( 20 / 27 )137.3707317073176.0527903703253222.6954385172163
Trimmed Mean ( 21 / 27 )136.7307692307696.018023036386622.7202136655273
Trimmed Mean ( 22 / 27 )136.0459459459465.967734308067922.7969173765030
Trimmed Mean ( 23 / 27 )135.2714285714295.8959786486799922.9429983776677
Trimmed Mean ( 24 / 27 )134.5030303030305.8153133218444323.1291115128377
Trimmed Mean ( 25 / 27 )133.6290322580655.6860349462206723.5012681986563
Trimmed Mean ( 26 / 27 )132.8034482758625.5571736861727823.8976601732460
Trimmed Mean ( 27 / 27 )131.9296296296305.3853494804017224.4978770848105
Median125.9
Midrange168.15
Midmean - Weighted Average at Xnp135.68
Midmean - Weighted Average at X(n+1)p137.370731707317
Midmean - Empirical Distribution Function137.370731707317
Midmean - Empirical Distribution Function - Averaging137.370731707317
Midmean - Empirical Distribution Function - Interpolation137.370731707317
Midmean - Closest Observation136.340476190476
Midmean - True Basic - Statistics Graphics Toolkit137.370731707317
Midmean - MS Excel (old versions)137.370731707317
Number of observations81

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 147.79012345679 & 6.74925455530302 & 21.8972513550654 \tabularnewline
Geometric Mean & 135.858588543141 &  &  \tabularnewline
Harmonic Mean & 125.183317632445 &  &  \tabularnewline
Quadratic Mean & 159.643714425453 &  &  \tabularnewline
Winsorized Mean ( 1 / 27 ) & 147.661728395062 & 6.71995199679293 & 21.9736284523361 \tabularnewline
Winsorized Mean ( 2 / 27 ) & 147.609876543210 & 6.69095266356786 & 22.0611150556996 \tabularnewline
Winsorized Mean ( 3 / 27 ) & 147.602469135802 & 6.6612962107793 & 22.1582203320958 \tabularnewline
Winsorized Mean ( 4 / 27 ) & 147.562962962963 & 6.58077339924693 & 22.4233466206038 \tabularnewline
Winsorized Mean ( 5 / 27 ) & 147.766666666667 & 6.44426173112632 & 22.9299604565937 \tabularnewline
Winsorized Mean ( 6 / 27 ) & 147.907407407407 & 6.40015619451033 & 23.109968399564 \tabularnewline
Winsorized Mean ( 7 / 27 ) & 147.89012345679 & 6.39441997411533 & 23.1279966057048 \tabularnewline
Winsorized Mean ( 8 / 27 ) & 147.979012345679 & 6.3691850061156 & 23.2335867467489 \tabularnewline
Winsorized Mean ( 9 / 27 ) & 146.99012345679 & 6.16364430563224 & 23.8479244044750 \tabularnewline
Winsorized Mean ( 10 / 27 ) & 147.014814814815 & 6.1502170771463 & 23.9040041954145 \tabularnewline
Winsorized Mean ( 11 / 27 ) & 145.575308641975 & 5.91266962820492 & 24.6209103156288 \tabularnewline
Winsorized Mean ( 12 / 27 ) & 145.471604938272 & 5.88043529362355 & 24.7382375070114 \tabularnewline
Winsorized Mean ( 13 / 27 ) & 145.487654320988 & 5.87856101238085 & 24.7488550369003 \tabularnewline
Winsorized Mean ( 14 / 27 ) & 145.401234567901 & 5.85586587144931 & 24.8300145119128 \tabularnewline
Winsorized Mean ( 15 / 27 ) & 145.049382716049 & 5.80204894722354 & 24.9996827044108 \tabularnewline
Winsorized Mean ( 16 / 27 ) & 145.00987654321 & 5.78543925926536 & 25.0646269098715 \tabularnewline
Winsorized Mean ( 17 / 27 ) & 144.820987654321 & 5.74002804549903 & 25.2300139487786 \tabularnewline
Winsorized Mean ( 18 / 27 ) & 144.354320987654 & 5.62298113273399 & 25.6722044019142 \tabularnewline
Winsorized Mean ( 19 / 27 ) & 143.533333333333 & 5.37999093578565 & 26.6791031893017 \tabularnewline
Winsorized Mean ( 20 / 27 ) & 143.533333333333 & 5.34168154501886 & 26.8704399773099 \tabularnewline
Winsorized Mean ( 21 / 27 ) & 143.3 & 5.28151096038732 & 27.1323871283780 \tabularnewline
Winsorized Mean ( 22 / 27 ) & 143.408641975309 & 5.21348565821645 & 27.5072478140027 \tabularnewline
Winsorized Mean ( 23 / 27 ) & 142.471604938272 & 5.07357966336572 & 28.0810816802586 \tabularnewline
Winsorized Mean ( 24 / 27 ) & 142.530864197531 & 5.05182268841974 & 28.2137503606873 \tabularnewline
Winsorized Mean ( 25 / 27 ) & 141.018518518519 & 4.81025881311062 & 29.3162018921238 \tabularnewline
Winsorized Mean ( 26 / 27 ) & 140.376543209877 & 4.69000588051598 & 29.9309951386314 \tabularnewline
Winsorized Mean ( 27 / 27 ) & 140.076543209877 & 4.46628808221644 & 31.3630783844024 \tabularnewline
Trimmed Mean ( 1 / 27 ) & 147.274683544304 & 6.66172134048608 & 22.1076019270355 \tabularnewline
Trimmed Mean ( 2 / 27 ) & 146.867532467532 & 6.5917193236431 & 22.2806107567035 \tabularnewline
Trimmed Mean ( 3 / 27 ) & 146.466666666667 & 6.52542313931803 & 22.4455431532328 \tabularnewline
Trimmed Mean ( 4 / 27 ) & 146.046575342466 & 6.45802778248827 & 22.6147332067058 \tabularnewline
Trimmed Mean ( 5 / 27 ) & 145.614084507042 & 6.40348128901861 & 22.7398313409234 \tabularnewline
Trimmed Mean ( 6 / 27 ) & 145.108695652174 & 6.37419461142269 & 22.7650243674920 \tabularnewline
Trimmed Mean ( 7 / 27 ) & 144.544776119403 & 6.34534138010963 & 22.7796689666689 \tabularnewline
Trimmed Mean ( 8 / 27 ) & 143.949230769231 & 6.30696696697273 & 22.8238440954329 \tabularnewline
Trimmed Mean ( 9 / 27 ) & 143.301587301587 & 6.26089485320144 & 22.8883555245001 \tabularnewline
Trimmed Mean ( 10 / 27 ) & 142.757377049180 & 6.2425721803051 & 22.8683582545622 \tabularnewline
Trimmed Mean ( 11 / 27 ) & 142.172881355932 & 6.215832535685 & 22.8727013702058 \tabularnewline
Trimmed Mean ( 12 / 27 ) & 141.733333333333 & 6.22125385933487 & 22.7821170037396 \tabularnewline
Trimmed Mean ( 13 / 27 ) & 141.274545454545 & 6.22419479096189 & 22.6976420563973 \tabularnewline
Trimmed Mean ( 14 / 27 ) & 140.779245283019 & 6.21813056628832 & 22.6401237127853 \tabularnewline
Trimmed Mean ( 15 / 27 ) & 140.254901960784 & 6.20446159123116 & 22.6054912095851 \tabularnewline
Trimmed Mean ( 16 / 27 ) & 139.726530612245 & 6.18681584241392 & 22.5845627494429 \tabularnewline
Trimmed Mean ( 17 / 27 ) & 139.157446808511 & 6.15634397846128 & 22.6039102583238 \tabularnewline
Trimmed Mean ( 18 / 27 ) & 138.557777777778 & 6.11477387020372 & 22.6595096922467 \tabularnewline
Trimmed Mean ( 19 / 27 ) & 137.951162790698 & 6.07249428529035 & 22.7173804222200 \tabularnewline
Trimmed Mean ( 20 / 27 ) & 137.370731707317 & 6.05279037032532 & 22.6954385172163 \tabularnewline
Trimmed Mean ( 21 / 27 ) & 136.730769230769 & 6.0180230363866 & 22.7202136655273 \tabularnewline
Trimmed Mean ( 22 / 27 ) & 136.045945945946 & 5.9677343080679 & 22.7969173765030 \tabularnewline
Trimmed Mean ( 23 / 27 ) & 135.271428571429 & 5.89597864867999 & 22.9429983776677 \tabularnewline
Trimmed Mean ( 24 / 27 ) & 134.503030303030 & 5.81531332184443 & 23.1291115128377 \tabularnewline
Trimmed Mean ( 25 / 27 ) & 133.629032258065 & 5.68603494622067 & 23.5012681986563 \tabularnewline
Trimmed Mean ( 26 / 27 ) & 132.803448275862 & 5.55717368617278 & 23.8976601732460 \tabularnewline
Trimmed Mean ( 27 / 27 ) & 131.929629629630 & 5.38534948040172 & 24.4978770848105 \tabularnewline
Median & 125.9 &  &  \tabularnewline
Midrange & 168.15 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 135.68 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 137.370731707317 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 137.370731707317 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 137.370731707317 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 137.370731707317 &  &  \tabularnewline
Midmean - Closest Observation & 136.340476190476 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 137.370731707317 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 137.370731707317 &  &  \tabularnewline
Number of observations & 81 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=7308&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]147.79012345679[/C][C]6.74925455530302[/C][C]21.8972513550654[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]135.858588543141[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]125.183317632445[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]159.643714425453[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 27 )[/C][C]147.661728395062[/C][C]6.71995199679293[/C][C]21.9736284523361[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 27 )[/C][C]147.609876543210[/C][C]6.69095266356786[/C][C]22.0611150556996[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 27 )[/C][C]147.602469135802[/C][C]6.6612962107793[/C][C]22.1582203320958[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 27 )[/C][C]147.562962962963[/C][C]6.58077339924693[/C][C]22.4233466206038[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 27 )[/C][C]147.766666666667[/C][C]6.44426173112632[/C][C]22.9299604565937[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 27 )[/C][C]147.907407407407[/C][C]6.40015619451033[/C][C]23.109968399564[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 27 )[/C][C]147.89012345679[/C][C]6.39441997411533[/C][C]23.1279966057048[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 27 )[/C][C]147.979012345679[/C][C]6.3691850061156[/C][C]23.2335867467489[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 27 )[/C][C]146.99012345679[/C][C]6.16364430563224[/C][C]23.8479244044750[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 27 )[/C][C]147.014814814815[/C][C]6.1502170771463[/C][C]23.9040041954145[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 27 )[/C][C]145.575308641975[/C][C]5.91266962820492[/C][C]24.6209103156288[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 27 )[/C][C]145.471604938272[/C][C]5.88043529362355[/C][C]24.7382375070114[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 27 )[/C][C]145.487654320988[/C][C]5.87856101238085[/C][C]24.7488550369003[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 27 )[/C][C]145.401234567901[/C][C]5.85586587144931[/C][C]24.8300145119128[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 27 )[/C][C]145.049382716049[/C][C]5.80204894722354[/C][C]24.9996827044108[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 27 )[/C][C]145.00987654321[/C][C]5.78543925926536[/C][C]25.0646269098715[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 27 )[/C][C]144.820987654321[/C][C]5.74002804549903[/C][C]25.2300139487786[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 27 )[/C][C]144.354320987654[/C][C]5.62298113273399[/C][C]25.6722044019142[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 27 )[/C][C]143.533333333333[/C][C]5.37999093578565[/C][C]26.6791031893017[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 27 )[/C][C]143.533333333333[/C][C]5.34168154501886[/C][C]26.8704399773099[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 27 )[/C][C]143.3[/C][C]5.28151096038732[/C][C]27.1323871283780[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 27 )[/C][C]143.408641975309[/C][C]5.21348565821645[/C][C]27.5072478140027[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 27 )[/C][C]142.471604938272[/C][C]5.07357966336572[/C][C]28.0810816802586[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 27 )[/C][C]142.530864197531[/C][C]5.05182268841974[/C][C]28.2137503606873[/C][/ROW]
[ROW][C]Winsorized Mean ( 25 / 27 )[/C][C]141.018518518519[/C][C]4.81025881311062[/C][C]29.3162018921238[/C][/ROW]
[ROW][C]Winsorized Mean ( 26 / 27 )[/C][C]140.376543209877[/C][C]4.69000588051598[/C][C]29.9309951386314[/C][/ROW]
[ROW][C]Winsorized Mean ( 27 / 27 )[/C][C]140.076543209877[/C][C]4.46628808221644[/C][C]31.3630783844024[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 27 )[/C][C]147.274683544304[/C][C]6.66172134048608[/C][C]22.1076019270355[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 27 )[/C][C]146.867532467532[/C][C]6.5917193236431[/C][C]22.2806107567035[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 27 )[/C][C]146.466666666667[/C][C]6.52542313931803[/C][C]22.4455431532328[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 27 )[/C][C]146.046575342466[/C][C]6.45802778248827[/C][C]22.6147332067058[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 27 )[/C][C]145.614084507042[/C][C]6.40348128901861[/C][C]22.7398313409234[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 27 )[/C][C]145.108695652174[/C][C]6.37419461142269[/C][C]22.7650243674920[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 27 )[/C][C]144.544776119403[/C][C]6.34534138010963[/C][C]22.7796689666689[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 27 )[/C][C]143.949230769231[/C][C]6.30696696697273[/C][C]22.8238440954329[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 27 )[/C][C]143.301587301587[/C][C]6.26089485320144[/C][C]22.8883555245001[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 27 )[/C][C]142.757377049180[/C][C]6.2425721803051[/C][C]22.8683582545622[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 27 )[/C][C]142.172881355932[/C][C]6.215832535685[/C][C]22.8727013702058[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 27 )[/C][C]141.733333333333[/C][C]6.22125385933487[/C][C]22.7821170037396[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 27 )[/C][C]141.274545454545[/C][C]6.22419479096189[/C][C]22.6976420563973[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 27 )[/C][C]140.779245283019[/C][C]6.21813056628832[/C][C]22.6401237127853[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 27 )[/C][C]140.254901960784[/C][C]6.20446159123116[/C][C]22.6054912095851[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 27 )[/C][C]139.726530612245[/C][C]6.18681584241392[/C][C]22.5845627494429[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 27 )[/C][C]139.157446808511[/C][C]6.15634397846128[/C][C]22.6039102583238[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 27 )[/C][C]138.557777777778[/C][C]6.11477387020372[/C][C]22.6595096922467[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 27 )[/C][C]137.951162790698[/C][C]6.07249428529035[/C][C]22.7173804222200[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 27 )[/C][C]137.370731707317[/C][C]6.05279037032532[/C][C]22.6954385172163[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 27 )[/C][C]136.730769230769[/C][C]6.0180230363866[/C][C]22.7202136655273[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 27 )[/C][C]136.045945945946[/C][C]5.9677343080679[/C][C]22.7969173765030[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 27 )[/C][C]135.271428571429[/C][C]5.89597864867999[/C][C]22.9429983776677[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 27 )[/C][C]134.503030303030[/C][C]5.81531332184443[/C][C]23.1291115128377[/C][/ROW]
[ROW][C]Trimmed Mean ( 25 / 27 )[/C][C]133.629032258065[/C][C]5.68603494622067[/C][C]23.5012681986563[/C][/ROW]
[ROW][C]Trimmed Mean ( 26 / 27 )[/C][C]132.803448275862[/C][C]5.55717368617278[/C][C]23.8976601732460[/C][/ROW]
[ROW][C]Trimmed Mean ( 27 / 27 )[/C][C]131.929629629630[/C][C]5.38534948040172[/C][C]24.4978770848105[/C][/ROW]
[ROW][C]Median[/C][C]125.9[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]168.15[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]135.68[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]137.370731707317[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]137.370731707317[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]137.370731707317[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]137.370731707317[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]136.340476190476[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]137.370731707317[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]137.370731707317[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]81[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=7308&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=7308&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 Mean147.790123456796.7492545553030221.8972513550654
Geometric Mean135.858588543141
Harmonic Mean125.183317632445
Quadratic Mean159.643714425453
Winsorized Mean ( 1 / 27 )147.6617283950626.7199519967929321.9736284523361
Winsorized Mean ( 2 / 27 )147.6098765432106.6909526635678622.0611150556996
Winsorized Mean ( 3 / 27 )147.6024691358026.661296210779322.1582203320958
Winsorized Mean ( 4 / 27 )147.5629629629636.5807733992469322.4233466206038
Winsorized Mean ( 5 / 27 )147.7666666666676.4442617311263222.9299604565937
Winsorized Mean ( 6 / 27 )147.9074074074076.4001561945103323.109968399564
Winsorized Mean ( 7 / 27 )147.890123456796.3944199741153323.1279966057048
Winsorized Mean ( 8 / 27 )147.9790123456796.369185006115623.2335867467489
Winsorized Mean ( 9 / 27 )146.990123456796.1636443056322423.8479244044750
Winsorized Mean ( 10 / 27 )147.0148148148156.150217077146323.9040041954145
Winsorized Mean ( 11 / 27 )145.5753086419755.9126696282049224.6209103156288
Winsorized Mean ( 12 / 27 )145.4716049382725.8804352936235524.7382375070114
Winsorized Mean ( 13 / 27 )145.4876543209885.8785610123808524.7488550369003
Winsorized Mean ( 14 / 27 )145.4012345679015.8558658714493124.8300145119128
Winsorized Mean ( 15 / 27 )145.0493827160495.8020489472235424.9996827044108
Winsorized Mean ( 16 / 27 )145.009876543215.7854392592653625.0646269098715
Winsorized Mean ( 17 / 27 )144.8209876543215.7400280454990325.2300139487786
Winsorized Mean ( 18 / 27 )144.3543209876545.6229811327339925.6722044019142
Winsorized Mean ( 19 / 27 )143.5333333333335.3799909357856526.6791031893017
Winsorized Mean ( 20 / 27 )143.5333333333335.3416815450188626.8704399773099
Winsorized Mean ( 21 / 27 )143.35.2815109603873227.1323871283780
Winsorized Mean ( 22 / 27 )143.4086419753095.2134856582164527.5072478140027
Winsorized Mean ( 23 / 27 )142.4716049382725.0735796633657228.0810816802586
Winsorized Mean ( 24 / 27 )142.5308641975315.0518226884197428.2137503606873
Winsorized Mean ( 25 / 27 )141.0185185185194.8102588131106229.3162018921238
Winsorized Mean ( 26 / 27 )140.3765432098774.6900058805159829.9309951386314
Winsorized Mean ( 27 / 27 )140.0765432098774.4662880822164431.3630783844024
Trimmed Mean ( 1 / 27 )147.2746835443046.6617213404860822.1076019270355
Trimmed Mean ( 2 / 27 )146.8675324675326.591719323643122.2806107567035
Trimmed Mean ( 3 / 27 )146.4666666666676.5254231393180322.4455431532328
Trimmed Mean ( 4 / 27 )146.0465753424666.4580277824882722.6147332067058
Trimmed Mean ( 5 / 27 )145.6140845070426.4034812890186122.7398313409234
Trimmed Mean ( 6 / 27 )145.1086956521746.3741946114226922.7650243674920
Trimmed Mean ( 7 / 27 )144.5447761194036.3453413801096322.7796689666689
Trimmed Mean ( 8 / 27 )143.9492307692316.3069669669727322.8238440954329
Trimmed Mean ( 9 / 27 )143.3015873015876.2608948532014422.8883555245001
Trimmed Mean ( 10 / 27 )142.7573770491806.242572180305122.8683582545622
Trimmed Mean ( 11 / 27 )142.1728813559326.21583253568522.8727013702058
Trimmed Mean ( 12 / 27 )141.7333333333336.2212538593348722.7821170037396
Trimmed Mean ( 13 / 27 )141.2745454545456.2241947909618922.6976420563973
Trimmed Mean ( 14 / 27 )140.7792452830196.2181305662883222.6401237127853
Trimmed Mean ( 15 / 27 )140.2549019607846.2044615912311622.6054912095851
Trimmed Mean ( 16 / 27 )139.7265306122456.1868158424139222.5845627494429
Trimmed Mean ( 17 / 27 )139.1574468085116.1563439784612822.6039102583238
Trimmed Mean ( 18 / 27 )138.5577777777786.1147738702037222.6595096922467
Trimmed Mean ( 19 / 27 )137.9511627906986.0724942852903522.7173804222200
Trimmed Mean ( 20 / 27 )137.3707317073176.0527903703253222.6954385172163
Trimmed Mean ( 21 / 27 )136.7307692307696.018023036386622.7202136655273
Trimmed Mean ( 22 / 27 )136.0459459459465.967734308067922.7969173765030
Trimmed Mean ( 23 / 27 )135.2714285714295.8959786486799922.9429983776677
Trimmed Mean ( 24 / 27 )134.5030303030305.8153133218444323.1291115128377
Trimmed Mean ( 25 / 27 )133.6290322580655.6860349462206723.5012681986563
Trimmed Mean ( 26 / 27 )132.8034482758625.5571736861727823.8976601732460
Trimmed Mean ( 27 / 27 )131.9296296296305.3853494804017224.4978770848105
Median125.9
Midrange168.15
Midmean - Weighted Average at Xnp135.68
Midmean - Weighted Average at X(n+1)p137.370731707317
Midmean - Empirical Distribution Function137.370731707317
Midmean - Empirical Distribution Function - Averaging137.370731707317
Midmean - Empirical Distribution Function - Interpolation137.370731707317
Midmean - Closest Observation136.340476190476
Midmean - True Basic - Statistics Graphics Toolkit137.370731707317
Midmean - MS Excel (old versions)137.370731707317
Number of observations81



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')