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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 computationSun, 20 Apr 2008 03:12:13 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/Apr/20/t1208682788nfyzkxachqa3o5q.htm/, Retrieved Mon, 13 May 2024 00:36:31 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=10305, Retrieved Mon, 13 May 2024 00:36:31 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact233
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [centrummaten eige...] [2008-04-20 09:12:13] [3e68c9212ad297cb41373898449ccda3] [Current]
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Dataseries X:
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
289,7
322,7
315
320,2




Summary of compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=10305&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]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=10305&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=10305&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'Sir Ronald Aylmer Fisher' @ 193.190.124.24







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean166.8452054794527.9330002234984821.0317913499154
Geometric Mean153.322695450361
Harmonic Mean140.699944865588
Quadratic Mean179.912373267640
Winsorized Mean ( 1 / 24 )166.8410958904117.9185810796588521.0695696883107
Winsorized Mean ( 2 / 24 )167.063013698637.8230308493510721.3552799312415
Winsorized Mean ( 3 / 24 )166.1506849315077.549316328599122.008706179403
Winsorized Mean ( 4 / 24 )165.0931506849327.3213962955688922.5494077932717
Winsorized Mean ( 5 / 24 )164.5246575342477.1564549155980522.9896868595724
Winsorized Mean ( 6 / 24 )164.2287671232887.0865876165204723.1745906507150
Winsorized Mean ( 7 / 24 )164.0465753424667.038871491971323.3058062687437
Winsorized Mean ( 8 / 24 )163.4986301369866.9375753984550823.5671139766489
Winsorized Mean ( 9 / 24 )162.8698630136996.8144967253629923.9004976563435
Winsorized Mean ( 10 / 24 )163.0890410958906.732724259729424.2233358748076
Winsorized Mean ( 11 / 24 )163.1342465753426.7126295750011424.3025843676641
Winsorized Mean ( 12 / 24 )163.3150684931516.6624537690997524.5127507301590
Winsorized Mean ( 13 / 24 )161.6410958904116.3766288800376925.3489890867626
Winsorized Mean ( 14 / 24 )161.736986301376.3464276756453225.4847285067224
Winsorized Mean ( 15 / 24 )159.9904109589045.9666510944618226.8141053374824
Winsorized Mean ( 16 / 24 )159.9465753424665.9059321499090627.0823591065008
Winsorized Mean ( 17 / 24 )160.2027397260275.870388170963527.289973858702
Winsorized Mean ( 18 / 24 )160.2027397260275.822948673171627.5123049708713
Winsorized Mean ( 19 / 24 )160.2547945205485.6808917079783728.2094436504541
Winsorized Mean ( 20 / 24 )160.336986301375.640030571816528.4283895733795
Winsorized Mean ( 21 / 24 )160.2219178082195.5623873602315628.8045235672959
Winsorized Mean ( 22 / 24 )159.6493150684935.4052141392126729.5361684027097
Winsorized Mean ( 23 / 24 )158.7671232876715.064726427495131.3476207571183
Winsorized Mean ( 24 / 24 )158.7342465753425.0173709737771131.6369364364234
Trimmed Mean ( 1 / 24 )166.036619718317.727040825390421.4877368284024
Trimmed Mean ( 2 / 24 )165.1855072463777.4985094498841122.0291123656488
Trimmed Mean ( 3 / 24 )164.1626865671647.2852691267897122.5335102533821
Trimmed Mean ( 4 / 24 )163.4184615384627.154688448139522.8407515886952
Trimmed Mean ( 5 / 24 )162.9333333333337.0780449220158823.0195393118427
Trimmed Mean ( 6 / 24 )162.5524590163937.0311533953270823.1188895870806
Trimmed Mean ( 7 / 24 )162.2067796610176.9871464458195623.2150250347287
Trimmed Mean ( 8 / 24 )161.8701754385966.9388074373290223.3282414738556
Trimmed Mean ( 9 / 24 )161.66.8962113250487523.4331566106492
Trimmed Mean ( 10 / 24 )161.4056603773586.862901897941723.5185731601040
Trimmed Mean ( 11 / 24 )161.1647058823536.829513130253823.5982716203320
Trimmed Mean ( 12 / 24 )160.8979591836736.7822933042040423.7232381389257
Trimmed Mean ( 13 / 24 )160.5851063829796.723167436314523.8853349859465
Trimmed Mean ( 14 / 24 )160.4533333333336.6967138028719523.9600105449514
Trimmed Mean ( 15 / 24 )160.2976744186056.655862359394124.0836822883454
Trimmed Mean ( 16 / 24 )160.3341463414636.6655929509136324.0539960243877
Trimmed Mean ( 17 / 24 )160.3794871794876.6714208886294424.0397795097642
Trimmed Mean ( 18 / 24 )160.46.6658704479481824.0628738965926
Trimmed Mean ( 19 / 24 )160.4228571428576.6467292591121524.1356087917873
Trimmed Mean ( 20 / 24 )160.4424242424246.629558223636624.2010732586061
Trimmed Mean ( 21 / 24 )160.4548387096776.5887829716511324.3527278709968
Trimmed Mean ( 22 / 24 )160.4827586206906.523136294557824.6020857719283
Trimmed Mean ( 23 / 24 )160.5851851851856.442773959084324.9248516562901
Trimmed Mean ( 24 / 24 )160.8166.394366478914625.1496376584436
Median156.8
Midrange195.55
Midmean - Weighted Average at Xnp158.813888888889
Midmean - Weighted Average at X(n+1)p160.4
Midmean - Empirical Distribution Function160.4
Midmean - Empirical Distribution Function - Averaging160.4
Midmean - Empirical Distribution Function - Interpolation160.4
Midmean - Closest Observation158.857894736842
Midmean - True Basic - Statistics Graphics Toolkit160.4
Midmean - MS Excel (old versions)160.4
Number of observations73

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 166.845205479452 & 7.93300022349848 & 21.0317913499154 \tabularnewline
Geometric Mean & 153.322695450361 &  &  \tabularnewline
Harmonic Mean & 140.699944865588 &  &  \tabularnewline
Quadratic Mean & 179.912373267640 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 166.841095890411 & 7.91858107965885 & 21.0695696883107 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 167.06301369863 & 7.82303084935107 & 21.3552799312415 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 166.150684931507 & 7.5493163285991 & 22.008706179403 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 165.093150684932 & 7.32139629556889 & 22.5494077932717 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 164.524657534247 & 7.15645491559805 & 22.9896868595724 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 164.228767123288 & 7.08658761652047 & 23.1745906507150 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 164.046575342466 & 7.0388714919713 & 23.3058062687437 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 163.498630136986 & 6.93757539845508 & 23.5671139766489 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 162.869863013699 & 6.81449672536299 & 23.9004976563435 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 163.089041095890 & 6.7327242597294 & 24.2233358748076 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 163.134246575342 & 6.71262957500114 & 24.3025843676641 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 163.315068493151 & 6.66245376909975 & 24.5127507301590 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 161.641095890411 & 6.37662888003769 & 25.3489890867626 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 161.73698630137 & 6.34642767564532 & 25.4847285067224 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 159.990410958904 & 5.96665109446182 & 26.8141053374824 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 159.946575342466 & 5.90593214990906 & 27.0823591065008 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 160.202739726027 & 5.8703881709635 & 27.289973858702 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 160.202739726027 & 5.8229486731716 & 27.5123049708713 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 160.254794520548 & 5.68089170797837 & 28.2094436504541 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 160.33698630137 & 5.6400305718165 & 28.4283895733795 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 160.221917808219 & 5.56238736023156 & 28.8045235672959 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 159.649315068493 & 5.40521413921267 & 29.5361684027097 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 158.767123287671 & 5.0647264274951 & 31.3476207571183 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 158.734246575342 & 5.01737097377711 & 31.6369364364234 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 166.03661971831 & 7.7270408253904 & 21.4877368284024 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 165.185507246377 & 7.49850944988411 & 22.0291123656488 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 164.162686567164 & 7.28526912678971 & 22.5335102533821 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 163.418461538462 & 7.1546884481395 & 22.8407515886952 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 162.933333333333 & 7.07804492201588 & 23.0195393118427 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 162.552459016393 & 7.03115339532708 & 23.1188895870806 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 162.206779661017 & 6.98714644581956 & 23.2150250347287 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 161.870175438596 & 6.93880743732902 & 23.3282414738556 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 161.6 & 6.89621132504875 & 23.4331566106492 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 161.405660377358 & 6.8629018979417 & 23.5185731601040 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 161.164705882353 & 6.8295131302538 & 23.5982716203320 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 160.897959183673 & 6.78229330420404 & 23.7232381389257 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 160.585106382979 & 6.7231674363145 & 23.8853349859465 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 160.453333333333 & 6.69671380287195 & 23.9600105449514 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 160.297674418605 & 6.6558623593941 & 24.0836822883454 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 160.334146341463 & 6.66559295091363 & 24.0539960243877 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 160.379487179487 & 6.67142088862944 & 24.0397795097642 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 160.4 & 6.66587044794818 & 24.0628738965926 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 160.422857142857 & 6.64672925911215 & 24.1356087917873 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 160.442424242424 & 6.6295582236366 & 24.2010732586061 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 160.454838709677 & 6.58878297165113 & 24.3527278709968 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 160.482758620690 & 6.5231362945578 & 24.6020857719283 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 160.585185185185 & 6.4427739590843 & 24.9248516562901 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 160.816 & 6.3943664789146 & 25.1496376584436 \tabularnewline
Median & 156.8 &  &  \tabularnewline
Midrange & 195.55 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 158.813888888889 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 160.4 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 160.4 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 160.4 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 160.4 &  &  \tabularnewline
Midmean - Closest Observation & 158.857894736842 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 160.4 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 160.4 &  &  \tabularnewline
Number of observations & 73 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=10305&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]166.845205479452[/C][C]7.93300022349848[/C][C]21.0317913499154[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]153.322695450361[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]140.699944865588[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]179.912373267640[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]166.841095890411[/C][C]7.91858107965885[/C][C]21.0695696883107[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]167.06301369863[/C][C]7.82303084935107[/C][C]21.3552799312415[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]166.150684931507[/C][C]7.5493163285991[/C][C]22.008706179403[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]165.093150684932[/C][C]7.32139629556889[/C][C]22.5494077932717[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]164.524657534247[/C][C]7.15645491559805[/C][C]22.9896868595724[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]164.228767123288[/C][C]7.08658761652047[/C][C]23.1745906507150[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]164.046575342466[/C][C]7.0388714919713[/C][C]23.3058062687437[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]163.498630136986[/C][C]6.93757539845508[/C][C]23.5671139766489[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]162.869863013699[/C][C]6.81449672536299[/C][C]23.9004976563435[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]163.089041095890[/C][C]6.7327242597294[/C][C]24.2233358748076[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]163.134246575342[/C][C]6.71262957500114[/C][C]24.3025843676641[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]163.315068493151[/C][C]6.66245376909975[/C][C]24.5127507301590[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]161.641095890411[/C][C]6.37662888003769[/C][C]25.3489890867626[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]161.73698630137[/C][C]6.34642767564532[/C][C]25.4847285067224[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]159.990410958904[/C][C]5.96665109446182[/C][C]26.8141053374824[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]159.946575342466[/C][C]5.90593214990906[/C][C]27.0823591065008[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]160.202739726027[/C][C]5.8703881709635[/C][C]27.289973858702[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]160.202739726027[/C][C]5.8229486731716[/C][C]27.5123049708713[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]160.254794520548[/C][C]5.68089170797837[/C][C]28.2094436504541[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]160.33698630137[/C][C]5.6400305718165[/C][C]28.4283895733795[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]160.221917808219[/C][C]5.56238736023156[/C][C]28.8045235672959[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]159.649315068493[/C][C]5.40521413921267[/C][C]29.5361684027097[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]158.767123287671[/C][C]5.0647264274951[/C][C]31.3476207571183[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]158.734246575342[/C][C]5.01737097377711[/C][C]31.6369364364234[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]166.03661971831[/C][C]7.7270408253904[/C][C]21.4877368284024[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]165.185507246377[/C][C]7.49850944988411[/C][C]22.0291123656488[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]164.162686567164[/C][C]7.28526912678971[/C][C]22.5335102533821[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]163.418461538462[/C][C]7.1546884481395[/C][C]22.8407515886952[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]162.933333333333[/C][C]7.07804492201588[/C][C]23.0195393118427[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]162.552459016393[/C][C]7.03115339532708[/C][C]23.1188895870806[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]162.206779661017[/C][C]6.98714644581956[/C][C]23.2150250347287[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]161.870175438596[/C][C]6.93880743732902[/C][C]23.3282414738556[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]161.6[/C][C]6.89621132504875[/C][C]23.4331566106492[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]161.405660377358[/C][C]6.8629018979417[/C][C]23.5185731601040[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]161.164705882353[/C][C]6.8295131302538[/C][C]23.5982716203320[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]160.897959183673[/C][C]6.78229330420404[/C][C]23.7232381389257[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]160.585106382979[/C][C]6.7231674363145[/C][C]23.8853349859465[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]160.453333333333[/C][C]6.69671380287195[/C][C]23.9600105449514[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]160.297674418605[/C][C]6.6558623593941[/C][C]24.0836822883454[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]160.334146341463[/C][C]6.66559295091363[/C][C]24.0539960243877[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]160.379487179487[/C][C]6.67142088862944[/C][C]24.0397795097642[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]160.4[/C][C]6.66587044794818[/C][C]24.0628738965926[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]160.422857142857[/C][C]6.64672925911215[/C][C]24.1356087917873[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]160.442424242424[/C][C]6.6295582236366[/C][C]24.2010732586061[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]160.454838709677[/C][C]6.58878297165113[/C][C]24.3527278709968[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]160.482758620690[/C][C]6.5231362945578[/C][C]24.6020857719283[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]160.585185185185[/C][C]6.4427739590843[/C][C]24.9248516562901[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]160.816[/C][C]6.3943664789146[/C][C]25.1496376584436[/C][/ROW]
[ROW][C]Median[/C][C]156.8[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]195.55[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]158.813888888889[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]160.4[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]160.4[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]160.4[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]160.4[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]158.857894736842[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]160.4[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]160.4[/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=10305&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=10305&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 Mean166.8452054794527.9330002234984821.0317913499154
Geometric Mean153.322695450361
Harmonic Mean140.699944865588
Quadratic Mean179.912373267640
Winsorized Mean ( 1 / 24 )166.8410958904117.9185810796588521.0695696883107
Winsorized Mean ( 2 / 24 )167.063013698637.8230308493510721.3552799312415
Winsorized Mean ( 3 / 24 )166.1506849315077.549316328599122.008706179403
Winsorized Mean ( 4 / 24 )165.0931506849327.3213962955688922.5494077932717
Winsorized Mean ( 5 / 24 )164.5246575342477.1564549155980522.9896868595724
Winsorized Mean ( 6 / 24 )164.2287671232887.0865876165204723.1745906507150
Winsorized Mean ( 7 / 24 )164.0465753424667.038871491971323.3058062687437
Winsorized Mean ( 8 / 24 )163.4986301369866.9375753984550823.5671139766489
Winsorized Mean ( 9 / 24 )162.8698630136996.8144967253629923.9004976563435
Winsorized Mean ( 10 / 24 )163.0890410958906.732724259729424.2233358748076
Winsorized Mean ( 11 / 24 )163.1342465753426.7126295750011424.3025843676641
Winsorized Mean ( 12 / 24 )163.3150684931516.6624537690997524.5127507301590
Winsorized Mean ( 13 / 24 )161.6410958904116.3766288800376925.3489890867626
Winsorized Mean ( 14 / 24 )161.736986301376.3464276756453225.4847285067224
Winsorized Mean ( 15 / 24 )159.9904109589045.9666510944618226.8141053374824
Winsorized Mean ( 16 / 24 )159.9465753424665.9059321499090627.0823591065008
Winsorized Mean ( 17 / 24 )160.2027397260275.870388170963527.289973858702
Winsorized Mean ( 18 / 24 )160.2027397260275.822948673171627.5123049708713
Winsorized Mean ( 19 / 24 )160.2547945205485.6808917079783728.2094436504541
Winsorized Mean ( 20 / 24 )160.336986301375.640030571816528.4283895733795
Winsorized Mean ( 21 / 24 )160.2219178082195.5623873602315628.8045235672959
Winsorized Mean ( 22 / 24 )159.6493150684935.4052141392126729.5361684027097
Winsorized Mean ( 23 / 24 )158.7671232876715.064726427495131.3476207571183
Winsorized Mean ( 24 / 24 )158.7342465753425.0173709737771131.6369364364234
Trimmed Mean ( 1 / 24 )166.036619718317.727040825390421.4877368284024
Trimmed Mean ( 2 / 24 )165.1855072463777.4985094498841122.0291123656488
Trimmed Mean ( 3 / 24 )164.1626865671647.2852691267897122.5335102533821
Trimmed Mean ( 4 / 24 )163.4184615384627.154688448139522.8407515886952
Trimmed Mean ( 5 / 24 )162.9333333333337.0780449220158823.0195393118427
Trimmed Mean ( 6 / 24 )162.5524590163937.0311533953270823.1188895870806
Trimmed Mean ( 7 / 24 )162.2067796610176.9871464458195623.2150250347287
Trimmed Mean ( 8 / 24 )161.8701754385966.9388074373290223.3282414738556
Trimmed Mean ( 9 / 24 )161.66.8962113250487523.4331566106492
Trimmed Mean ( 10 / 24 )161.4056603773586.862901897941723.5185731601040
Trimmed Mean ( 11 / 24 )161.1647058823536.829513130253823.5982716203320
Trimmed Mean ( 12 / 24 )160.8979591836736.7822933042040423.7232381389257
Trimmed Mean ( 13 / 24 )160.5851063829796.723167436314523.8853349859465
Trimmed Mean ( 14 / 24 )160.4533333333336.6967138028719523.9600105449514
Trimmed Mean ( 15 / 24 )160.2976744186056.655862359394124.0836822883454
Trimmed Mean ( 16 / 24 )160.3341463414636.6655929509136324.0539960243877
Trimmed Mean ( 17 / 24 )160.3794871794876.6714208886294424.0397795097642
Trimmed Mean ( 18 / 24 )160.46.6658704479481824.0628738965926
Trimmed Mean ( 19 / 24 )160.4228571428576.6467292591121524.1356087917873
Trimmed Mean ( 20 / 24 )160.4424242424246.629558223636624.2010732586061
Trimmed Mean ( 21 / 24 )160.4548387096776.5887829716511324.3527278709968
Trimmed Mean ( 22 / 24 )160.4827586206906.523136294557824.6020857719283
Trimmed Mean ( 23 / 24 )160.5851851851856.442773959084324.9248516562901
Trimmed Mean ( 24 / 24 )160.8166.394366478914625.1496376584436
Median156.8
Midrange195.55
Midmean - Weighted Average at Xnp158.813888888889
Midmean - Weighted Average at X(n+1)p160.4
Midmean - Empirical Distribution Function160.4
Midmean - Empirical Distribution Function - Averaging160.4
Midmean - Empirical Distribution Function - Interpolation160.4
Midmean - Closest Observation158.857894736842
Midmean - True Basic - Statistics Graphics Toolkit160.4
Midmean - MS Excel (old versions)160.4
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')