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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationWed, 02 Dec 2009 10:55:45 -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/2009/Dec/02/t12597766477k1hooir071t5qo.htm/, Retrieved Sun, 28 Apr 2024 07:16:58 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=62497, Retrieved Sun, 28 Apr 2024 07:16:58 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact114
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2009-12-02 17:55:45] [21ab0ce05394a625ef1e345752188501] [Current]
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Dataseries X:
104.0
99.0
105.4
107.1
110.7
117.1
118.7
126.5
127.5
134.6
131.8
135.9
142.7
141.7
153.4
145.0
137.7
148.3
152.2
169.4
168.6
161.1
174.1
179.0
190.6
190.0
181.6
174.8
180.5
196.8
193.8
197.0
216.3
221.4
217.9
229.7
227.4
204.2
196.6
198.8
207.5
190.7
201.6
210.5
223.5
223.8
231.2
244.0
234.7
250.2
265.7
287.6
283.3
295.4
312.3
333.8
347.7
383.2
407.1
413.6
362.7
321.9
239.4
191.0
159.7
163.4
157.6
166.2
176.7
198.3
226.2
216.2
235.9




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=62497&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]1 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=62497&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=62497&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 time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean203.7191780821928.4219938061591324.1889489319274
Geometric Mean192.501099940956
Harmonic Mean182.364264969619
Quadratic Mean215.889930415465
Winsorized Mean ( 1 / 24 )203.6986301369868.380001174507324.3077090199767
Winsorized Mean ( 2 / 24 )203.0821917808228.1628062216820524.87896763265
Winsorized Mean ( 3 / 24 )202.3095890410967.9031627592776525.5985603742757
Winsorized Mean ( 4 / 24 )201.6849315068497.6453960119623226.3799195216682
Winsorized Mean ( 5 / 24 )201.1712328767127.3281502748982927.4518432797156
Winsorized Mean ( 6 / 24 )200.3246575342477.0672424759005728.3455192343205
Winsorized Mean ( 7 / 24 )200.1520547945216.733842805217329.7233037040076
Winsorized Mean ( 8 / 24 )198.4095890410966.3043590909689331.4718096127043
Winsorized Mean ( 9 / 24 )197.9780821917816.0202275876970632.8854813722274
Winsorized Mean ( 10 / 24 )197.7726027397265.8413302198835233.8574597386261
Winsorized Mean ( 11 / 24 )195.3164383561645.2957314642666136.8818622458631
Winsorized Mean ( 12 / 24 )193.0643835616444.8021250250225240.2039477430595
Winsorized Mean ( 13 / 24 )192.6726027397264.5105542813427142.7159481345098
Winsorized Mean ( 14 / 24 )191.9821917808224.34375036216144.1973354300479
Winsorized Mean ( 15 / 24 )191.7356164383564.1621072633492846.0669570260102
Winsorized Mean ( 16 / 24 )192.1958904109594.0119927894885147.9053429294578
Winsorized Mean ( 17 / 24 )192.2890410958903.7569983209642851.1815616267129
Winsorized Mean ( 18 / 24 )192.2150684931513.6603726964807652.512430954901
Winsorized Mean ( 19 / 24 )192.7095890410963.4169969571857856.3973545940205
Winsorized Mean ( 20 / 24 )192.9561643835623.2892802379309358.6621237553592
Winsorized Mean ( 21 / 24 )192.6684931506853.1367918326195161.4221483067905
Winsorized Mean ( 22 / 24 )193.2712328767123.0283537577260163.8205600596146
Winsorized Mean ( 23 / 24 )193.4917808219182.8171399682214068.6837654516964
Winsorized Mean ( 24 / 24 )193.1301369863012.5546974408330775.5980469152241
Trimmed Mean ( 1 / 24 )202.2380281690147.9944164031246225.2974098384429
Trimmed Mean ( 2 / 24 )200.6927536231887.5273336296626.6618650769507
Trimmed Mean ( 3 / 24 )199.3910447761197.1069416290415528.0558157339206
Trimmed Mean ( 4 / 24 )198.2984615384626.7240253412625429.4910342353391
Trimmed Mean ( 5 / 24 )197.3174603174606.3606640217959731.0215190806048
Trimmed Mean ( 6 / 24 )196.3950819672136.0262383604708532.5899956522576
Trimmed Mean ( 7 / 24 )195.5847457627125.6976251953854734.3274152046921
Trimmed Mean ( 8 / 24 )194.7491228070185.387642573407336.1473724645866
Trimmed Mean ( 9 / 24 )194.1418181818185.1240462303175637.8883814578282
Trimmed Mean ( 10 / 24 )193.5547169811324.8691391892608439.751321426183
Trimmed Mean ( 11 / 24 )192.9509803921574.592927531989842.0104560867226
Trimmed Mean ( 12 / 24 )192.6306122448984.3857348418178443.9220835715309
Trimmed Mean ( 13 / 24 )192.5744680851064.242214906017345.3947931331702
Trimmed Mean ( 14 / 24 )192.5622222222224.1240478409976446.6925287112189
Trimmed Mean ( 15 / 24 )192.6325581395354.0068569701014948.0757260807979
Trimmed Mean ( 16 / 24 )192.7390243902443.8929076819399549.5102992769139
Trimmed Mean ( 17 / 24 )192.8025641025643.7748769759104751.075191412314
Trimmed Mean ( 18 / 24 )192.8621621621623.6755611844030852.4714873420026
Trimmed Mean ( 19 / 24 )192.9371428571433.5598722612204154.1977713523349
Trimmed Mean ( 20 / 24 )192.9636363636363.4602828153973855.7652789260453
Trimmed Mean ( 21 / 24 )192.9645161290323.34936215525257.6123175651377
Trimmed Mean ( 22 / 24 )1933.2290896092294359.7691682040549
Trimmed Mean ( 23 / 24 )192.9666666666673.0801959089653462.647530342148
Trimmed Mean ( 24 / 24 )192.92.9255426846997165.9364845397222
Median193.8
Midrange256.3
Midmean - Weighted Average at Xnp191.838888888889
Midmean - Weighted Average at X(n+1)p192.862162162162
Midmean - Empirical Distribution Function192.862162162162
Midmean - Empirical Distribution Function - Averaging192.862162162162
Midmean - Empirical Distribution Function - Interpolation192.862162162162
Midmean - Closest Observation191.792105263158
Midmean - True Basic - Statistics Graphics Toolkit192.862162162162
Midmean - MS Excel (old versions)192.862162162162
Number of observations73

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 203.719178082192 & 8.42199380615913 & 24.1889489319274 \tabularnewline
Geometric Mean & 192.501099940956 &  &  \tabularnewline
Harmonic Mean & 182.364264969619 &  &  \tabularnewline
Quadratic Mean & 215.889930415465 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 203.698630136986 & 8.3800011745073 & 24.3077090199767 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 203.082191780822 & 8.16280622168205 & 24.87896763265 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 202.309589041096 & 7.90316275927765 & 25.5985603742757 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 201.684931506849 & 7.64539601196232 & 26.3799195216682 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 201.171232876712 & 7.32815027489829 & 27.4518432797156 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 200.324657534247 & 7.06724247590057 & 28.3455192343205 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 200.152054794521 & 6.7338428052173 & 29.7233037040076 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 198.409589041096 & 6.30435909096893 & 31.4718096127043 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 197.978082191781 & 6.02022758769706 & 32.8854813722274 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 197.772602739726 & 5.84133021988352 & 33.8574597386261 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 195.316438356164 & 5.29573146426661 & 36.8818622458631 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 193.064383561644 & 4.80212502502252 & 40.2039477430595 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 192.672602739726 & 4.51055428134271 & 42.7159481345098 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 191.982191780822 & 4.343750362161 & 44.1973354300479 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 191.735616438356 & 4.16210726334928 & 46.0669570260102 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 192.195890410959 & 4.01199278948851 & 47.9053429294578 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 192.289041095890 & 3.75699832096428 & 51.1815616267129 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 192.215068493151 & 3.66037269648076 & 52.512430954901 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 192.709589041096 & 3.41699695718578 & 56.3973545940205 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 192.956164383562 & 3.28928023793093 & 58.6621237553592 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 192.668493150685 & 3.13679183261951 & 61.4221483067905 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 193.271232876712 & 3.02835375772601 & 63.8205600596146 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 193.491780821918 & 2.81713996822140 & 68.6837654516964 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 193.130136986301 & 2.55469744083307 & 75.5980469152241 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 202.238028169014 & 7.99441640312462 & 25.2974098384429 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 200.692753623188 & 7.52733362966 & 26.6618650769507 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 199.391044776119 & 7.10694162904155 & 28.0558157339206 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 198.298461538462 & 6.72402534126254 & 29.4910342353391 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 197.317460317460 & 6.36066402179597 & 31.0215190806048 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 196.395081967213 & 6.02623836047085 & 32.5899956522576 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 195.584745762712 & 5.69762519538547 & 34.3274152046921 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 194.749122807018 & 5.3876425734073 & 36.1473724645866 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 194.141818181818 & 5.12404623031756 & 37.8883814578282 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 193.554716981132 & 4.86913918926084 & 39.751321426183 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 192.950980392157 & 4.5929275319898 & 42.0104560867226 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 192.630612244898 & 4.38573484181784 & 43.9220835715309 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 192.574468085106 & 4.2422149060173 & 45.3947931331702 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 192.562222222222 & 4.12404784099764 & 46.6925287112189 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 192.632558139535 & 4.00685697010149 & 48.0757260807979 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 192.739024390244 & 3.89290768193995 & 49.5102992769139 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 192.802564102564 & 3.77487697591047 & 51.075191412314 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 192.862162162162 & 3.67556118440308 & 52.4714873420026 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 192.937142857143 & 3.55987226122041 & 54.1977713523349 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 192.963636363636 & 3.46028281539738 & 55.7652789260453 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 192.964516129032 & 3.349362155252 & 57.6123175651377 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 193 & 3.22908960922943 & 59.7691682040549 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 192.966666666667 & 3.08019590896534 & 62.647530342148 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 192.9 & 2.92554268469971 & 65.9364845397222 \tabularnewline
Median & 193.8 &  &  \tabularnewline
Midrange & 256.3 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 191.838888888889 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 192.862162162162 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 192.862162162162 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 192.862162162162 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 192.862162162162 &  &  \tabularnewline
Midmean - Closest Observation & 191.792105263158 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 192.862162162162 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 192.862162162162 &  &  \tabularnewline
Number of observations & 73 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=62497&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]203.719178082192[/C][C]8.42199380615913[/C][C]24.1889489319274[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]192.501099940956[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]182.364264969619[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]215.889930415465[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]203.698630136986[/C][C]8.3800011745073[/C][C]24.3077090199767[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]203.082191780822[/C][C]8.16280622168205[/C][C]24.87896763265[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]202.309589041096[/C][C]7.90316275927765[/C][C]25.5985603742757[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]201.684931506849[/C][C]7.64539601196232[/C][C]26.3799195216682[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]201.171232876712[/C][C]7.32815027489829[/C][C]27.4518432797156[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]200.324657534247[/C][C]7.06724247590057[/C][C]28.3455192343205[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]200.152054794521[/C][C]6.7338428052173[/C][C]29.7233037040076[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]198.409589041096[/C][C]6.30435909096893[/C][C]31.4718096127043[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]197.978082191781[/C][C]6.02022758769706[/C][C]32.8854813722274[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]197.772602739726[/C][C]5.84133021988352[/C][C]33.8574597386261[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]195.316438356164[/C][C]5.29573146426661[/C][C]36.8818622458631[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]193.064383561644[/C][C]4.80212502502252[/C][C]40.2039477430595[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]192.672602739726[/C][C]4.51055428134271[/C][C]42.7159481345098[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]191.982191780822[/C][C]4.343750362161[/C][C]44.1973354300479[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]191.735616438356[/C][C]4.16210726334928[/C][C]46.0669570260102[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]192.195890410959[/C][C]4.01199278948851[/C][C]47.9053429294578[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]192.289041095890[/C][C]3.75699832096428[/C][C]51.1815616267129[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]192.215068493151[/C][C]3.66037269648076[/C][C]52.512430954901[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]192.709589041096[/C][C]3.41699695718578[/C][C]56.3973545940205[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]192.956164383562[/C][C]3.28928023793093[/C][C]58.6621237553592[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]192.668493150685[/C][C]3.13679183261951[/C][C]61.4221483067905[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]193.271232876712[/C][C]3.02835375772601[/C][C]63.8205600596146[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]193.491780821918[/C][C]2.81713996822140[/C][C]68.6837654516964[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]193.130136986301[/C][C]2.55469744083307[/C][C]75.5980469152241[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]202.238028169014[/C][C]7.99441640312462[/C][C]25.2974098384429[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]200.692753623188[/C][C]7.52733362966[/C][C]26.6618650769507[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]199.391044776119[/C][C]7.10694162904155[/C][C]28.0558157339206[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]198.298461538462[/C][C]6.72402534126254[/C][C]29.4910342353391[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]197.317460317460[/C][C]6.36066402179597[/C][C]31.0215190806048[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]196.395081967213[/C][C]6.02623836047085[/C][C]32.5899956522576[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]195.584745762712[/C][C]5.69762519538547[/C][C]34.3274152046921[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]194.749122807018[/C][C]5.3876425734073[/C][C]36.1473724645866[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]194.141818181818[/C][C]5.12404623031756[/C][C]37.8883814578282[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]193.554716981132[/C][C]4.86913918926084[/C][C]39.751321426183[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]192.950980392157[/C][C]4.5929275319898[/C][C]42.0104560867226[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]192.630612244898[/C][C]4.38573484181784[/C][C]43.9220835715309[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]192.574468085106[/C][C]4.2422149060173[/C][C]45.3947931331702[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]192.562222222222[/C][C]4.12404784099764[/C][C]46.6925287112189[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]192.632558139535[/C][C]4.00685697010149[/C][C]48.0757260807979[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]192.739024390244[/C][C]3.89290768193995[/C][C]49.5102992769139[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]192.802564102564[/C][C]3.77487697591047[/C][C]51.075191412314[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]192.862162162162[/C][C]3.67556118440308[/C][C]52.4714873420026[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]192.937142857143[/C][C]3.55987226122041[/C][C]54.1977713523349[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]192.963636363636[/C][C]3.46028281539738[/C][C]55.7652789260453[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]192.964516129032[/C][C]3.349362155252[/C][C]57.6123175651377[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]193[/C][C]3.22908960922943[/C][C]59.7691682040549[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]192.966666666667[/C][C]3.08019590896534[/C][C]62.647530342148[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]192.9[/C][C]2.92554268469971[/C][C]65.9364845397222[/C][/ROW]
[ROW][C]Median[/C][C]193.8[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]256.3[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]191.838888888889[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]192.862162162162[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]192.862162162162[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]192.862162162162[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]192.862162162162[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]191.792105263158[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]192.862162162162[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]192.862162162162[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]73[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=62497&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=62497&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 Mean203.7191780821928.4219938061591324.1889489319274
Geometric Mean192.501099940956
Harmonic Mean182.364264969619
Quadratic Mean215.889930415465
Winsorized Mean ( 1 / 24 )203.6986301369868.380001174507324.3077090199767
Winsorized Mean ( 2 / 24 )203.0821917808228.1628062216820524.87896763265
Winsorized Mean ( 3 / 24 )202.3095890410967.9031627592776525.5985603742757
Winsorized Mean ( 4 / 24 )201.6849315068497.6453960119623226.3799195216682
Winsorized Mean ( 5 / 24 )201.1712328767127.3281502748982927.4518432797156
Winsorized Mean ( 6 / 24 )200.3246575342477.0672424759005728.3455192343205
Winsorized Mean ( 7 / 24 )200.1520547945216.733842805217329.7233037040076
Winsorized Mean ( 8 / 24 )198.4095890410966.3043590909689331.4718096127043
Winsorized Mean ( 9 / 24 )197.9780821917816.0202275876970632.8854813722274
Winsorized Mean ( 10 / 24 )197.7726027397265.8413302198835233.8574597386261
Winsorized Mean ( 11 / 24 )195.3164383561645.2957314642666136.8818622458631
Winsorized Mean ( 12 / 24 )193.0643835616444.8021250250225240.2039477430595
Winsorized Mean ( 13 / 24 )192.6726027397264.5105542813427142.7159481345098
Winsorized Mean ( 14 / 24 )191.9821917808224.34375036216144.1973354300479
Winsorized Mean ( 15 / 24 )191.7356164383564.1621072633492846.0669570260102
Winsorized Mean ( 16 / 24 )192.1958904109594.0119927894885147.9053429294578
Winsorized Mean ( 17 / 24 )192.2890410958903.7569983209642851.1815616267129
Winsorized Mean ( 18 / 24 )192.2150684931513.6603726964807652.512430954901
Winsorized Mean ( 19 / 24 )192.7095890410963.4169969571857856.3973545940205
Winsorized Mean ( 20 / 24 )192.9561643835623.2892802379309358.6621237553592
Winsorized Mean ( 21 / 24 )192.6684931506853.1367918326195161.4221483067905
Winsorized Mean ( 22 / 24 )193.2712328767123.0283537577260163.8205600596146
Winsorized Mean ( 23 / 24 )193.4917808219182.8171399682214068.6837654516964
Winsorized Mean ( 24 / 24 )193.1301369863012.5546974408330775.5980469152241
Trimmed Mean ( 1 / 24 )202.2380281690147.9944164031246225.2974098384429
Trimmed Mean ( 2 / 24 )200.6927536231887.5273336296626.6618650769507
Trimmed Mean ( 3 / 24 )199.3910447761197.1069416290415528.0558157339206
Trimmed Mean ( 4 / 24 )198.2984615384626.7240253412625429.4910342353391
Trimmed Mean ( 5 / 24 )197.3174603174606.3606640217959731.0215190806048
Trimmed Mean ( 6 / 24 )196.3950819672136.0262383604708532.5899956522576
Trimmed Mean ( 7 / 24 )195.5847457627125.6976251953854734.3274152046921
Trimmed Mean ( 8 / 24 )194.7491228070185.387642573407336.1473724645866
Trimmed Mean ( 9 / 24 )194.1418181818185.1240462303175637.8883814578282
Trimmed Mean ( 10 / 24 )193.5547169811324.8691391892608439.751321426183
Trimmed Mean ( 11 / 24 )192.9509803921574.592927531989842.0104560867226
Trimmed Mean ( 12 / 24 )192.6306122448984.3857348418178443.9220835715309
Trimmed Mean ( 13 / 24 )192.5744680851064.242214906017345.3947931331702
Trimmed Mean ( 14 / 24 )192.5622222222224.1240478409976446.6925287112189
Trimmed Mean ( 15 / 24 )192.6325581395354.0068569701014948.0757260807979
Trimmed Mean ( 16 / 24 )192.7390243902443.8929076819399549.5102992769139
Trimmed Mean ( 17 / 24 )192.8025641025643.7748769759104751.075191412314
Trimmed Mean ( 18 / 24 )192.8621621621623.6755611844030852.4714873420026
Trimmed Mean ( 19 / 24 )192.9371428571433.5598722612204154.1977713523349
Trimmed Mean ( 20 / 24 )192.9636363636363.4602828153973855.7652789260453
Trimmed Mean ( 21 / 24 )192.9645161290323.34936215525257.6123175651377
Trimmed Mean ( 22 / 24 )1933.2290896092294359.7691682040549
Trimmed Mean ( 23 / 24 )192.9666666666673.0801959089653462.647530342148
Trimmed Mean ( 24 / 24 )192.92.9255426846997165.9364845397222
Median193.8
Midrange256.3
Midmean - Weighted Average at Xnp191.838888888889
Midmean - Weighted Average at X(n+1)p192.862162162162
Midmean - Empirical Distribution Function192.862162162162
Midmean - Empirical Distribution Function - Averaging192.862162162162
Midmean - Empirical Distribution Function - Interpolation192.862162162162
Midmean - Closest Observation191.792105263158
Midmean - True Basic - Statistics Graphics Toolkit192.862162162162
Midmean - MS Excel (old versions)192.862162162162
Number of observations73



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')