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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 computationMon, 17 Oct 2011 08:46:52 -0400
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Oct/17/t1318855663o42le3ujur3jej2.htm/, Retrieved Wed, 15 May 2024 16:34:05 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=130401, Retrieved Wed, 15 May 2024 16:34:05 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDG2011W52a
Estimated Impact78
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [opgave 5] [2011-10-17 12:46:52] [824ef6e68de890e55183bcf963376e73] [Current]
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Dataseries X:
162,9
164,7
165
167,2
168,6
169,5
169,8
171,9
172
173,7
173,9
175,9
175,6
176,1
176,3
179,4
179,7
179,9
180,4
182,5
183,6
183,9
184,5
187,6
188
188,5
188,6
191,9
193,5
194,9
194,9
196,2
196,2
198
198,6
201,3
203,5
204,1
204,8
206,5
207,8
208,6
209,7
210
211,7
212,4
213,7
214,8
216,4
217,5
218,6
220,4
221,8
222,5
223,4
225,5
226,5
227,8
228,5
229,1
229,9
230,8
231,9
236
237,5
239,1
240,5
241,4
243,2
243,6
244,3
244,5
245,1
245,8
246,7
247,7
248,5




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

\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' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=130401&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' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=130401&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=130401&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' @ jenkins.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean205.4194805194812.9540870577977269.5373821083734
Geometric Mean203.801219511559
Harmonic Mean202.188646439282
Quadratic Mean207.027502721539
Winsorized Mean ( 1 / 25 )205.4324675324682.9477712896476969.6907756222227
Winsorized Mean ( 2 / 25 )205.4142857142862.9415098549113169.8329415321571
Winsorized Mean ( 3 / 25 )205.4649350649352.9199462339230270.3659994413279
Winsorized Mean ( 4 / 25 )205.5012987012992.90101892057570.8376278568245
Winsorized Mean ( 5 / 25 )205.5207792207792.8843636115826471.2534225558374
Winsorized Mean ( 6 / 25 )205.5285714285712.8777666453605871.4194709845277
Winsorized Mean ( 7 / 25 )205.6558441558442.8359765753091672.5167640474691
Winsorized Mean ( 8 / 25 )205.6246753246752.8270578649394872.7345123970701
Winsorized Mean ( 9 / 25 )205.6129870129872.7600399901566174.4963796706875
Winsorized Mean ( 10 / 25 )205.5220779220782.7362885187323575.1097980037904
Winsorized Mean ( 11 / 25 )205.5649350649352.6664914997224777.0919146325164
Winsorized Mean ( 12 / 25 )205.3623376623382.6188072079902178.4182726531986
Winsorized Mean ( 13 / 25 )205.1428571428572.5733726607107479.7175085734372
Winsorized Mean ( 14 / 25 )204.4337662337662.4541430718941583.3014866064758
Winsorized Mean ( 15 / 25 )204.8233766233772.3337884093003187.7643302225434
Winsorized Mean ( 16 / 25 )204.6987012987012.2976677627554889.0897738205701
Winsorized Mean ( 17 / 25 )204.5662337662342.2660181022244890.2756397071219
Winsorized Mean ( 18 / 25 )204.5428571428572.2294128623407691.7474105393374
Winsorized Mean ( 19 / 25 )204.8883116883122.1322531910232396.0900481007086
Winsorized Mean ( 20 / 25 )204.8363636363642.04559435992121100.135377594732
Winsorized Mean ( 21 / 25 )204.6454545454551.99666805968916102.493478348782
Winsorized Mean ( 22 / 25 )204.2168831168831.89191122990394107.942106315026
Winsorized Mean ( 23 / 25 )204.8740259740261.73159830257122118.314984295036
Winsorized Mean ( 24 / 25 )204.7805194805191.68615146513192121.448472284486
Winsorized Mean ( 25 / 25 )204.4883116883121.60504052031689127.403831305106
Trimmed Mean ( 1 / 25 )205.4122.9225559343131870.2850534315858
Trimmed Mean ( 2 / 25 )205.3904109589042.8919738591606271.020839385636
Trimmed Mean ( 3 / 25 )205.3774647887322.8588787865577371.8384653992344
Trimmed Mean ( 4 / 25 )205.3449275362322.8281698119485172.6070007072016
Trimmed Mean ( 5 / 25 )205.3449275362322.7971677541032873.4117312896242
Trimmed Mean ( 6 / 25 )205.2476923076922.7639472433288874.2589037482833
Trimmed Mean ( 7 / 25 )205.1904761904762.7246994829390475.3075623478095
Trimmed Mean ( 8 / 25 )205.1065573770492.6864422496942776.3487684875383
Trimmed Mean ( 9 / 25 )205.0220338983052.640916932262977.6328976476477
Trimmed Mean ( 10 / 25 )205.0220338983052.5990206046879178.8843434055514
Trimmed Mean ( 11 / 25 )204.8509090909092.5513736614719980.2904381213695
Trimmed Mean ( 12 / 25 )204.7566037735852.5057372620970481.7151131009742
Trimmed Mean ( 13 / 25 )204.6803921568632.4574034113950583.2913274262394
Trimmed Mean ( 14 / 25 )204.6244897959182.4047422157590685.0920686861766
Trimmed Mean ( 15 / 25 )204.6468085106382.3613109826020786.6666059737398
Trimmed Mean ( 16 / 25 )204.6266666666672.3282897872329787.8871125874126
Trimmed Mean ( 17 / 25 )204.6186046511632.2903047034632889.3412148792906
Trimmed Mean ( 18 / 25 )204.6243902439022.2446434354458991.161200488511
Trimmed Mean ( 19 / 25 )204.6333333333332.1897421675242893.4508803676607
Trimmed Mean ( 20 / 25 )204.6333333333332.13640314725495.7840441287294
Trimmed Mean ( 21 / 25 )204.582.0821199603797598.2556259451485
Trimmed Mean ( 22 / 25 )204.5727272727272.01641123191633101.453872124243
Trimmed Mean ( 23 / 25 )204.6129032258061.94995859859818104.931921822803
Trimmed Mean ( 24 / 25 )204.582758620691.89852203966961107.758958993329
Trimmed Mean ( 25 / 25 )204.5592592592591.83171069807991111.676619825221
Median204.8
Midrange205.7
Midmean - Weighted Average at Xnp204.023684210526
Midmean - Weighted Average at X(n+1)p204.633333333333
Midmean - Empirical Distribution Function204.633333333333
Midmean - Empirical Distribution Function - Averaging204.633333333333
Midmean - Empirical Distribution Function - Interpolation204.633333333333
Midmean - Closest Observation204.0275
Midmean - True Basic - Statistics Graphics Toolkit204.633333333333
Midmean - MS Excel (old versions)204.633333333333
Number of observations77

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 205.419480519481 & 2.95408705779772 & 69.5373821083734 \tabularnewline
Geometric Mean & 203.801219511559 &  &  \tabularnewline
Harmonic Mean & 202.188646439282 &  &  \tabularnewline
Quadratic Mean & 207.027502721539 &  &  \tabularnewline
Winsorized Mean ( 1 / 25 ) & 205.432467532468 & 2.94777128964769 & 69.6907756222227 \tabularnewline
Winsorized Mean ( 2 / 25 ) & 205.414285714286 & 2.94150985491131 & 69.8329415321571 \tabularnewline
Winsorized Mean ( 3 / 25 ) & 205.464935064935 & 2.91994623392302 & 70.3659994413279 \tabularnewline
Winsorized Mean ( 4 / 25 ) & 205.501298701299 & 2.901018920575 & 70.8376278568245 \tabularnewline
Winsorized Mean ( 5 / 25 ) & 205.520779220779 & 2.88436361158264 & 71.2534225558374 \tabularnewline
Winsorized Mean ( 6 / 25 ) & 205.528571428571 & 2.87776664536058 & 71.4194709845277 \tabularnewline
Winsorized Mean ( 7 / 25 ) & 205.655844155844 & 2.83597657530916 & 72.5167640474691 \tabularnewline
Winsorized Mean ( 8 / 25 ) & 205.624675324675 & 2.82705786493948 & 72.7345123970701 \tabularnewline
Winsorized Mean ( 9 / 25 ) & 205.612987012987 & 2.76003999015661 & 74.4963796706875 \tabularnewline
Winsorized Mean ( 10 / 25 ) & 205.522077922078 & 2.73628851873235 & 75.1097980037904 \tabularnewline
Winsorized Mean ( 11 / 25 ) & 205.564935064935 & 2.66649149972247 & 77.0919146325164 \tabularnewline
Winsorized Mean ( 12 / 25 ) & 205.362337662338 & 2.61880720799021 & 78.4182726531986 \tabularnewline
Winsorized Mean ( 13 / 25 ) & 205.142857142857 & 2.57337266071074 & 79.7175085734372 \tabularnewline
Winsorized Mean ( 14 / 25 ) & 204.433766233766 & 2.45414307189415 & 83.3014866064758 \tabularnewline
Winsorized Mean ( 15 / 25 ) & 204.823376623377 & 2.33378840930031 & 87.7643302225434 \tabularnewline
Winsorized Mean ( 16 / 25 ) & 204.698701298701 & 2.29766776275548 & 89.0897738205701 \tabularnewline
Winsorized Mean ( 17 / 25 ) & 204.566233766234 & 2.26601810222448 & 90.2756397071219 \tabularnewline
Winsorized Mean ( 18 / 25 ) & 204.542857142857 & 2.22941286234076 & 91.7474105393374 \tabularnewline
Winsorized Mean ( 19 / 25 ) & 204.888311688312 & 2.13225319102323 & 96.0900481007086 \tabularnewline
Winsorized Mean ( 20 / 25 ) & 204.836363636364 & 2.04559435992121 & 100.135377594732 \tabularnewline
Winsorized Mean ( 21 / 25 ) & 204.645454545455 & 1.99666805968916 & 102.493478348782 \tabularnewline
Winsorized Mean ( 22 / 25 ) & 204.216883116883 & 1.89191122990394 & 107.942106315026 \tabularnewline
Winsorized Mean ( 23 / 25 ) & 204.874025974026 & 1.73159830257122 & 118.314984295036 \tabularnewline
Winsorized Mean ( 24 / 25 ) & 204.780519480519 & 1.68615146513192 & 121.448472284486 \tabularnewline
Winsorized Mean ( 25 / 25 ) & 204.488311688312 & 1.60504052031689 & 127.403831305106 \tabularnewline
Trimmed Mean ( 1 / 25 ) & 205.412 & 2.92255593431318 & 70.2850534315858 \tabularnewline
Trimmed Mean ( 2 / 25 ) & 205.390410958904 & 2.89197385916062 & 71.020839385636 \tabularnewline
Trimmed Mean ( 3 / 25 ) & 205.377464788732 & 2.85887878655773 & 71.8384653992344 \tabularnewline
Trimmed Mean ( 4 / 25 ) & 205.344927536232 & 2.82816981194851 & 72.6070007072016 \tabularnewline
Trimmed Mean ( 5 / 25 ) & 205.344927536232 & 2.79716775410328 & 73.4117312896242 \tabularnewline
Trimmed Mean ( 6 / 25 ) & 205.247692307692 & 2.76394724332888 & 74.2589037482833 \tabularnewline
Trimmed Mean ( 7 / 25 ) & 205.190476190476 & 2.72469948293904 & 75.3075623478095 \tabularnewline
Trimmed Mean ( 8 / 25 ) & 205.106557377049 & 2.68644224969427 & 76.3487684875383 \tabularnewline
Trimmed Mean ( 9 / 25 ) & 205.022033898305 & 2.6409169322629 & 77.6328976476477 \tabularnewline
Trimmed Mean ( 10 / 25 ) & 205.022033898305 & 2.59902060468791 & 78.8843434055514 \tabularnewline
Trimmed Mean ( 11 / 25 ) & 204.850909090909 & 2.55137366147199 & 80.2904381213695 \tabularnewline
Trimmed Mean ( 12 / 25 ) & 204.756603773585 & 2.50573726209704 & 81.7151131009742 \tabularnewline
Trimmed Mean ( 13 / 25 ) & 204.680392156863 & 2.45740341139505 & 83.2913274262394 \tabularnewline
Trimmed Mean ( 14 / 25 ) & 204.624489795918 & 2.40474221575906 & 85.0920686861766 \tabularnewline
Trimmed Mean ( 15 / 25 ) & 204.646808510638 & 2.36131098260207 & 86.6666059737398 \tabularnewline
Trimmed Mean ( 16 / 25 ) & 204.626666666667 & 2.32828978723297 & 87.8871125874126 \tabularnewline
Trimmed Mean ( 17 / 25 ) & 204.618604651163 & 2.29030470346328 & 89.3412148792906 \tabularnewline
Trimmed Mean ( 18 / 25 ) & 204.624390243902 & 2.24464343544589 & 91.161200488511 \tabularnewline
Trimmed Mean ( 19 / 25 ) & 204.633333333333 & 2.18974216752428 & 93.4508803676607 \tabularnewline
Trimmed Mean ( 20 / 25 ) & 204.633333333333 & 2.136403147254 & 95.7840441287294 \tabularnewline
Trimmed Mean ( 21 / 25 ) & 204.58 & 2.08211996037975 & 98.2556259451485 \tabularnewline
Trimmed Mean ( 22 / 25 ) & 204.572727272727 & 2.01641123191633 & 101.453872124243 \tabularnewline
Trimmed Mean ( 23 / 25 ) & 204.612903225806 & 1.94995859859818 & 104.931921822803 \tabularnewline
Trimmed Mean ( 24 / 25 ) & 204.58275862069 & 1.89852203966961 & 107.758958993329 \tabularnewline
Trimmed Mean ( 25 / 25 ) & 204.559259259259 & 1.83171069807991 & 111.676619825221 \tabularnewline
Median & 204.8 &  &  \tabularnewline
Midrange & 205.7 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 204.023684210526 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 204.633333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 204.633333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 204.633333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 204.633333333333 &  &  \tabularnewline
Midmean - Closest Observation & 204.0275 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 204.633333333333 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 204.633333333333 &  &  \tabularnewline
Number of observations & 77 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=130401&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]205.419480519481[/C][C]2.95408705779772[/C][C]69.5373821083734[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]203.801219511559[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]202.188646439282[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]207.027502721539[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 25 )[/C][C]205.432467532468[/C][C]2.94777128964769[/C][C]69.6907756222227[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 25 )[/C][C]205.414285714286[/C][C]2.94150985491131[/C][C]69.8329415321571[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 25 )[/C][C]205.464935064935[/C][C]2.91994623392302[/C][C]70.3659994413279[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 25 )[/C][C]205.501298701299[/C][C]2.901018920575[/C][C]70.8376278568245[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 25 )[/C][C]205.520779220779[/C][C]2.88436361158264[/C][C]71.2534225558374[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 25 )[/C][C]205.528571428571[/C][C]2.87776664536058[/C][C]71.4194709845277[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 25 )[/C][C]205.655844155844[/C][C]2.83597657530916[/C][C]72.5167640474691[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 25 )[/C][C]205.624675324675[/C][C]2.82705786493948[/C][C]72.7345123970701[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 25 )[/C][C]205.612987012987[/C][C]2.76003999015661[/C][C]74.4963796706875[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 25 )[/C][C]205.522077922078[/C][C]2.73628851873235[/C][C]75.1097980037904[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 25 )[/C][C]205.564935064935[/C][C]2.66649149972247[/C][C]77.0919146325164[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 25 )[/C][C]205.362337662338[/C][C]2.61880720799021[/C][C]78.4182726531986[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 25 )[/C][C]205.142857142857[/C][C]2.57337266071074[/C][C]79.7175085734372[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 25 )[/C][C]204.433766233766[/C][C]2.45414307189415[/C][C]83.3014866064758[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 25 )[/C][C]204.823376623377[/C][C]2.33378840930031[/C][C]87.7643302225434[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 25 )[/C][C]204.698701298701[/C][C]2.29766776275548[/C][C]89.0897738205701[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 25 )[/C][C]204.566233766234[/C][C]2.26601810222448[/C][C]90.2756397071219[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 25 )[/C][C]204.542857142857[/C][C]2.22941286234076[/C][C]91.7474105393374[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 25 )[/C][C]204.888311688312[/C][C]2.13225319102323[/C][C]96.0900481007086[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 25 )[/C][C]204.836363636364[/C][C]2.04559435992121[/C][C]100.135377594732[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 25 )[/C][C]204.645454545455[/C][C]1.99666805968916[/C][C]102.493478348782[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 25 )[/C][C]204.216883116883[/C][C]1.89191122990394[/C][C]107.942106315026[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 25 )[/C][C]204.874025974026[/C][C]1.73159830257122[/C][C]118.314984295036[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 25 )[/C][C]204.780519480519[/C][C]1.68615146513192[/C][C]121.448472284486[/C][/ROW]
[ROW][C]Winsorized Mean ( 25 / 25 )[/C][C]204.488311688312[/C][C]1.60504052031689[/C][C]127.403831305106[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 25 )[/C][C]205.412[/C][C]2.92255593431318[/C][C]70.2850534315858[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 25 )[/C][C]205.390410958904[/C][C]2.89197385916062[/C][C]71.020839385636[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 25 )[/C][C]205.377464788732[/C][C]2.85887878655773[/C][C]71.8384653992344[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 25 )[/C][C]205.344927536232[/C][C]2.82816981194851[/C][C]72.6070007072016[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 25 )[/C][C]205.344927536232[/C][C]2.79716775410328[/C][C]73.4117312896242[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 25 )[/C][C]205.247692307692[/C][C]2.76394724332888[/C][C]74.2589037482833[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 25 )[/C][C]205.190476190476[/C][C]2.72469948293904[/C][C]75.3075623478095[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 25 )[/C][C]205.106557377049[/C][C]2.68644224969427[/C][C]76.3487684875383[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 25 )[/C][C]205.022033898305[/C][C]2.6409169322629[/C][C]77.6328976476477[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 25 )[/C][C]205.022033898305[/C][C]2.59902060468791[/C][C]78.8843434055514[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 25 )[/C][C]204.850909090909[/C][C]2.55137366147199[/C][C]80.2904381213695[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 25 )[/C][C]204.756603773585[/C][C]2.50573726209704[/C][C]81.7151131009742[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 25 )[/C][C]204.680392156863[/C][C]2.45740341139505[/C][C]83.2913274262394[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 25 )[/C][C]204.624489795918[/C][C]2.40474221575906[/C][C]85.0920686861766[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 25 )[/C][C]204.646808510638[/C][C]2.36131098260207[/C][C]86.6666059737398[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 25 )[/C][C]204.626666666667[/C][C]2.32828978723297[/C][C]87.8871125874126[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 25 )[/C][C]204.618604651163[/C][C]2.29030470346328[/C][C]89.3412148792906[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 25 )[/C][C]204.624390243902[/C][C]2.24464343544589[/C][C]91.161200488511[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 25 )[/C][C]204.633333333333[/C][C]2.18974216752428[/C][C]93.4508803676607[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 25 )[/C][C]204.633333333333[/C][C]2.136403147254[/C][C]95.7840441287294[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 25 )[/C][C]204.58[/C][C]2.08211996037975[/C][C]98.2556259451485[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 25 )[/C][C]204.572727272727[/C][C]2.01641123191633[/C][C]101.453872124243[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 25 )[/C][C]204.612903225806[/C][C]1.94995859859818[/C][C]104.931921822803[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 25 )[/C][C]204.58275862069[/C][C]1.89852203966961[/C][C]107.758958993329[/C][/ROW]
[ROW][C]Trimmed Mean ( 25 / 25 )[/C][C]204.559259259259[/C][C]1.83171069807991[/C][C]111.676619825221[/C][/ROW]
[ROW][C]Median[/C][C]204.8[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]205.7[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]204.023684210526[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]204.633333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]204.633333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]204.633333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]204.633333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]204.0275[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]204.633333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]204.633333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]77[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=130401&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=130401&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 Mean205.4194805194812.9540870577977269.5373821083734
Geometric Mean203.801219511559
Harmonic Mean202.188646439282
Quadratic Mean207.027502721539
Winsorized Mean ( 1 / 25 )205.4324675324682.9477712896476969.6907756222227
Winsorized Mean ( 2 / 25 )205.4142857142862.9415098549113169.8329415321571
Winsorized Mean ( 3 / 25 )205.4649350649352.9199462339230270.3659994413279
Winsorized Mean ( 4 / 25 )205.5012987012992.90101892057570.8376278568245
Winsorized Mean ( 5 / 25 )205.5207792207792.8843636115826471.2534225558374
Winsorized Mean ( 6 / 25 )205.5285714285712.8777666453605871.4194709845277
Winsorized Mean ( 7 / 25 )205.6558441558442.8359765753091672.5167640474691
Winsorized Mean ( 8 / 25 )205.6246753246752.8270578649394872.7345123970701
Winsorized Mean ( 9 / 25 )205.6129870129872.7600399901566174.4963796706875
Winsorized Mean ( 10 / 25 )205.5220779220782.7362885187323575.1097980037904
Winsorized Mean ( 11 / 25 )205.5649350649352.6664914997224777.0919146325164
Winsorized Mean ( 12 / 25 )205.3623376623382.6188072079902178.4182726531986
Winsorized Mean ( 13 / 25 )205.1428571428572.5733726607107479.7175085734372
Winsorized Mean ( 14 / 25 )204.4337662337662.4541430718941583.3014866064758
Winsorized Mean ( 15 / 25 )204.8233766233772.3337884093003187.7643302225434
Winsorized Mean ( 16 / 25 )204.6987012987012.2976677627554889.0897738205701
Winsorized Mean ( 17 / 25 )204.5662337662342.2660181022244890.2756397071219
Winsorized Mean ( 18 / 25 )204.5428571428572.2294128623407691.7474105393374
Winsorized Mean ( 19 / 25 )204.8883116883122.1322531910232396.0900481007086
Winsorized Mean ( 20 / 25 )204.8363636363642.04559435992121100.135377594732
Winsorized Mean ( 21 / 25 )204.6454545454551.99666805968916102.493478348782
Winsorized Mean ( 22 / 25 )204.2168831168831.89191122990394107.942106315026
Winsorized Mean ( 23 / 25 )204.8740259740261.73159830257122118.314984295036
Winsorized Mean ( 24 / 25 )204.7805194805191.68615146513192121.448472284486
Winsorized Mean ( 25 / 25 )204.4883116883121.60504052031689127.403831305106
Trimmed Mean ( 1 / 25 )205.4122.9225559343131870.2850534315858
Trimmed Mean ( 2 / 25 )205.3904109589042.8919738591606271.020839385636
Trimmed Mean ( 3 / 25 )205.3774647887322.8588787865577371.8384653992344
Trimmed Mean ( 4 / 25 )205.3449275362322.8281698119485172.6070007072016
Trimmed Mean ( 5 / 25 )205.3449275362322.7971677541032873.4117312896242
Trimmed Mean ( 6 / 25 )205.2476923076922.7639472433288874.2589037482833
Trimmed Mean ( 7 / 25 )205.1904761904762.7246994829390475.3075623478095
Trimmed Mean ( 8 / 25 )205.1065573770492.6864422496942776.3487684875383
Trimmed Mean ( 9 / 25 )205.0220338983052.640916932262977.6328976476477
Trimmed Mean ( 10 / 25 )205.0220338983052.5990206046879178.8843434055514
Trimmed Mean ( 11 / 25 )204.8509090909092.5513736614719980.2904381213695
Trimmed Mean ( 12 / 25 )204.7566037735852.5057372620970481.7151131009742
Trimmed Mean ( 13 / 25 )204.6803921568632.4574034113950583.2913274262394
Trimmed Mean ( 14 / 25 )204.6244897959182.4047422157590685.0920686861766
Trimmed Mean ( 15 / 25 )204.6468085106382.3613109826020786.6666059737398
Trimmed Mean ( 16 / 25 )204.6266666666672.3282897872329787.8871125874126
Trimmed Mean ( 17 / 25 )204.6186046511632.2903047034632889.3412148792906
Trimmed Mean ( 18 / 25 )204.6243902439022.2446434354458991.161200488511
Trimmed Mean ( 19 / 25 )204.6333333333332.1897421675242893.4508803676607
Trimmed Mean ( 20 / 25 )204.6333333333332.13640314725495.7840441287294
Trimmed Mean ( 21 / 25 )204.582.0821199603797598.2556259451485
Trimmed Mean ( 22 / 25 )204.5727272727272.01641123191633101.453872124243
Trimmed Mean ( 23 / 25 )204.6129032258061.94995859859818104.931921822803
Trimmed Mean ( 24 / 25 )204.582758620691.89852203966961107.758958993329
Trimmed Mean ( 25 / 25 )204.5592592592591.83171069807991111.676619825221
Median204.8
Midrange205.7
Midmean - Weighted Average at Xnp204.023684210526
Midmean - Weighted Average at X(n+1)p204.633333333333
Midmean - Empirical Distribution Function204.633333333333
Midmean - Empirical Distribution Function - Averaging204.633333333333
Midmean - Empirical Distribution Function - Interpolation204.633333333333
Midmean - Closest Observation204.0275
Midmean - True Basic - Statistics Graphics Toolkit204.633333333333
Midmean - MS Excel (old versions)204.633333333333
Number of observations77



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')