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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 computationThu, 14 May 2009 01:30:57 -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/2009/May/14/t1242286350cgzygcb1bkncdxd.htm/, Retrieved Tue, 14 May 2024 03:22:49 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=39924, Retrieved Tue, 14 May 2024 03:22:49 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact137
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Centrummaten 5b -...] [2009-05-14 07:30:57] [8c726525c89fb87c09aaacaddee1db18] [Current]
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Dataseries X:
104.9
110.9
104.8
94.1
95.8
99.3
101.1
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
166.7




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'George Udny Yule' @ 72.249.76.132

\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 & 2 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=39924&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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=39924&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=39924&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 time2 seconds
R Server'George Udny Yule' @ 72.249.76.132







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean194.6383561643849.084886891177221.4244116075245
Geometric Mean180.883989779186
Harmonic Mean168.612182733680
Quadratic Mean209.348087924892
Winsorized Mean ( 1 / 24 )194.5726027397269.0519108497313421.4951965358233
Winsorized Mean ( 2 / 24 )194.0054794520558.8344625129940321.9600772731454
Winsorized Mean ( 3 / 24 )193.1753424657538.591742739748422.4838369021522
Winsorized Mean ( 4 / 24 )192.4520547945218.3580414776683223.0259750814505
Winsorized Mean ( 5 / 24 )191.6986301369868.0889465265886323.6988376059684
Winsorized Mean ( 6 / 24 )190.7863013698637.846079039738624.3161329886653
Winsorized Mean ( 7 / 24 )189.8753424657537.6352210933724824.8683489507028
Winsorized Mean ( 8 / 24 )188.0780821917817.2290555198054626.0169646887485
Winsorized Mean ( 9 / 24 )187.3260273972607.000882208866626.7574888147686
Winsorized Mean ( 10 / 24 )187.2301369863016.806788201492927.5063850150703
Winsorized Mean ( 11 / 24 )184.6082191780826.3042756725734629.2830181873572
Winsorized Mean ( 12 / 24 )183.0794520547955.702773084052132.1035835297005
Winsorized Mean ( 13 / 24 )182.2602739726035.4802307428055733.2577737190854
Winsorized Mean ( 14 / 24 )182.8739726027405.1080401255909435.8012012643662
Winsorized Mean ( 15 / 24 )182.1136986301374.930697538445636.9346724697999
Winsorized Mean ( 16 / 24 )182.2890410958904.6748906504616938.9932203179742
Winsorized Mean ( 17 / 24 )182.5917808219184.5273482993228540.3308446247062
Winsorized Mean ( 18 / 24 )182.3452054794524.3989205993609541.4522611537799
Winsorized Mean ( 19 / 24 )181.8767123287674.1986822607325743.3175699027613
Winsorized Mean ( 20 / 24 )182.8904109589044.0293138035510445.3899646132606
Winsorized Mean ( 21 / 24 )182.5739726027403.9044826652901446.7600930145691
Winsorized Mean ( 22 / 24 )182.2123287671233.6621370658277949.7557370168875
Winsorized Mean ( 23 / 24 )182.7479452054793.4484263443811552.99459143248
Winsorized Mean ( 24 / 24 )182.1232876712333.017479847352460.3560908057204
Trimmed Mean ( 1 / 24 )192.9704225352118.6927797681784822.1989314904324
Trimmed Mean ( 2 / 24 )191.2753623188418.2592187780909123.1590138798882
Trimmed Mean ( 3 / 24 )189.7880597014937.8797688847462524.0854855614974
Trimmed Mean ( 4 / 24 )188.527.5379517979151525.0094462068782
Trimmed Mean ( 5 / 24 )187.3809523809527.2146505157369625.9722840312539
Trimmed Mean ( 6 / 24 )186.3475409836076.9119333754494726.9602629049486
Trimmed Mean ( 7 / 24 )185.4322033898316.6159122426409128.0282138863152
Trimmed Mean ( 8 / 24 )184.6192982456146.3117478278869129.2501068293506
Trimmed Mean ( 9 / 24 )184.0454545454556.0468773799674830.4364456198786
Trimmed Mean ( 10 / 24 )183.5433962264155.775798130582431.7780144106088
Trimmed Mean ( 11 / 24 )183.0156862745105.4832360364803733.3773131517398
Trimmed Mean ( 12 / 24 )182.85.2419496100483234.8725214087503
Trimmed Mean ( 13 / 24 )182.7638297872345.0788886894126935.985003996685
Trimmed Mean ( 14 / 24 )182.8266666666674.9192883611146437.1652672593563
Trimmed Mean ( 15 / 24 )182.8209302325584.7960376758356238.1191605632466
Trimmed Mean ( 16 / 24 )182.9048780487804.671491054621539.1534257285654
Trimmed Mean ( 17 / 24 )182.9769230769234.5621446846111840.1076545630244
Trimmed Mean ( 18 / 24 )183.0216216216224.4453355368365741.1716101304391
Trimmed Mean ( 19 / 24 )183.14.3125340091217842.4576361862216
Trimmed Mean ( 20 / 24 )183.2424242424244.1757371656931843.8826528038925
Trimmed Mean ( 21 / 24 )183.2838709677424.0250214633080145.5361226365009
Trimmed Mean ( 22 / 24 )183.3689655172413.8389118155145847.7658707283074
Trimmed Mean ( 23 / 24 )183.5111111111113.6400601625116950.4143071592767
Trimmed Mean ( 24 / 24 )183.6083.4123204226254453.8073736518366
Median190
Midrange253.85
Midmean - Weighted Average at Xnp181.788888888889
Midmean - Weighted Average at X(n+1)p183.021621621622
Midmean - Empirical Distribution Function183.021621621622
Midmean - Empirical Distribution Function - Averaging183.021621621622
Midmean - Empirical Distribution Function - Interpolation183.021621621622
Midmean - Closest Observation181.747368421053
Midmean - True Basic - Statistics Graphics Toolkit183.021621621622
Midmean - MS Excel (old versions)183.021621621622
Number of observations73

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 194.638356164384 & 9.0848868911772 & 21.4244116075245 \tabularnewline
Geometric Mean & 180.883989779186 &  &  \tabularnewline
Harmonic Mean & 168.612182733680 &  &  \tabularnewline
Quadratic Mean & 209.348087924892 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 194.572602739726 & 9.05191084973134 & 21.4951965358233 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 194.005479452055 & 8.83446251299403 & 21.9600772731454 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 193.175342465753 & 8.5917427397484 & 22.4838369021522 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 192.452054794521 & 8.35804147766832 & 23.0259750814505 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 191.698630136986 & 8.08894652658863 & 23.6988376059684 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 190.786301369863 & 7.8460790397386 & 24.3161329886653 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 189.875342465753 & 7.63522109337248 & 24.8683489507028 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 188.078082191781 & 7.22905551980546 & 26.0169646887485 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 187.326027397260 & 7.0008822088666 & 26.7574888147686 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 187.230136986301 & 6.8067882014929 & 27.5063850150703 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 184.608219178082 & 6.30427567257346 & 29.2830181873572 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 183.079452054795 & 5.7027730840521 & 32.1035835297005 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 182.260273972603 & 5.48023074280557 & 33.2577737190854 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 182.873972602740 & 5.10804012559094 & 35.8012012643662 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 182.113698630137 & 4.9306975384456 & 36.9346724697999 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 182.289041095890 & 4.67489065046169 & 38.9932203179742 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 182.591780821918 & 4.52734829932285 & 40.3308446247062 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 182.345205479452 & 4.39892059936095 & 41.4522611537799 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 181.876712328767 & 4.19868226073257 & 43.3175699027613 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 182.890410958904 & 4.02931380355104 & 45.3899646132606 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 182.573972602740 & 3.90448266529014 & 46.7600930145691 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 182.212328767123 & 3.66213706582779 & 49.7557370168875 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 182.747945205479 & 3.44842634438115 & 52.99459143248 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 182.123287671233 & 3.0174798473524 & 60.3560908057204 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 192.970422535211 & 8.69277976817848 & 22.1989314904324 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 191.275362318841 & 8.25921877809091 & 23.1590138798882 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 189.788059701493 & 7.87976888474625 & 24.0854855614974 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 188.52 & 7.53795179791515 & 25.0094462068782 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 187.380952380952 & 7.21465051573696 & 25.9722840312539 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 186.347540983607 & 6.91193337544947 & 26.9602629049486 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 185.432203389831 & 6.61591224264091 & 28.0282138863152 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 184.619298245614 & 6.31174782788691 & 29.2501068293506 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 184.045454545455 & 6.04687737996748 & 30.4364456198786 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 183.543396226415 & 5.7757981305824 & 31.7780144106088 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 183.015686274510 & 5.48323603648037 & 33.3773131517398 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 182.8 & 5.24194961004832 & 34.8725214087503 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 182.763829787234 & 5.07888868941269 & 35.985003996685 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 182.826666666667 & 4.91928836111464 & 37.1652672593563 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 182.820930232558 & 4.79603767583562 & 38.1191605632466 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 182.904878048780 & 4.6714910546215 & 39.1534257285654 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 182.976923076923 & 4.56214468461118 & 40.1076545630244 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 183.021621621622 & 4.44533553683657 & 41.1716101304391 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 183.1 & 4.31253400912178 & 42.4576361862216 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 183.242424242424 & 4.17573716569318 & 43.8826528038925 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 183.283870967742 & 4.02502146330801 & 45.5361226365009 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 183.368965517241 & 3.83891181551458 & 47.7658707283074 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 183.511111111111 & 3.64006016251169 & 50.4143071592767 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 183.608 & 3.41232042262544 & 53.8073736518366 \tabularnewline
Median & 190 &  &  \tabularnewline
Midrange & 253.85 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 181.788888888889 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 183.021621621622 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 183.021621621622 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 183.021621621622 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 183.021621621622 &  &  \tabularnewline
Midmean - Closest Observation & 181.747368421053 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 183.021621621622 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 183.021621621622 &  &  \tabularnewline
Number of observations & 73 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=39924&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]194.638356164384[/C][C]9.0848868911772[/C][C]21.4244116075245[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]180.883989779186[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]168.612182733680[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]209.348087924892[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]194.572602739726[/C][C]9.05191084973134[/C][C]21.4951965358233[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]194.005479452055[/C][C]8.83446251299403[/C][C]21.9600772731454[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]193.175342465753[/C][C]8.5917427397484[/C][C]22.4838369021522[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]192.452054794521[/C][C]8.35804147766832[/C][C]23.0259750814505[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]191.698630136986[/C][C]8.08894652658863[/C][C]23.6988376059684[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]190.786301369863[/C][C]7.8460790397386[/C][C]24.3161329886653[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]189.875342465753[/C][C]7.63522109337248[/C][C]24.8683489507028[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]188.078082191781[/C][C]7.22905551980546[/C][C]26.0169646887485[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]187.326027397260[/C][C]7.0008822088666[/C][C]26.7574888147686[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]187.230136986301[/C][C]6.8067882014929[/C][C]27.5063850150703[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]184.608219178082[/C][C]6.30427567257346[/C][C]29.2830181873572[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]183.079452054795[/C][C]5.7027730840521[/C][C]32.1035835297005[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]182.260273972603[/C][C]5.48023074280557[/C][C]33.2577737190854[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]182.873972602740[/C][C]5.10804012559094[/C][C]35.8012012643662[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]182.113698630137[/C][C]4.9306975384456[/C][C]36.9346724697999[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]182.289041095890[/C][C]4.67489065046169[/C][C]38.9932203179742[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]182.591780821918[/C][C]4.52734829932285[/C][C]40.3308446247062[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]182.345205479452[/C][C]4.39892059936095[/C][C]41.4522611537799[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]181.876712328767[/C][C]4.19868226073257[/C][C]43.3175699027613[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]182.890410958904[/C][C]4.02931380355104[/C][C]45.3899646132606[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]182.573972602740[/C][C]3.90448266529014[/C][C]46.7600930145691[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]182.212328767123[/C][C]3.66213706582779[/C][C]49.7557370168875[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]182.747945205479[/C][C]3.44842634438115[/C][C]52.99459143248[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]182.123287671233[/C][C]3.0174798473524[/C][C]60.3560908057204[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]192.970422535211[/C][C]8.69277976817848[/C][C]22.1989314904324[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]191.275362318841[/C][C]8.25921877809091[/C][C]23.1590138798882[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]189.788059701493[/C][C]7.87976888474625[/C][C]24.0854855614974[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]188.52[/C][C]7.53795179791515[/C][C]25.0094462068782[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]187.380952380952[/C][C]7.21465051573696[/C][C]25.9722840312539[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]186.347540983607[/C][C]6.91193337544947[/C][C]26.9602629049486[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]185.432203389831[/C][C]6.61591224264091[/C][C]28.0282138863152[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]184.619298245614[/C][C]6.31174782788691[/C][C]29.2501068293506[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]184.045454545455[/C][C]6.04687737996748[/C][C]30.4364456198786[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]183.543396226415[/C][C]5.7757981305824[/C][C]31.7780144106088[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]183.015686274510[/C][C]5.48323603648037[/C][C]33.3773131517398[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]182.8[/C][C]5.24194961004832[/C][C]34.8725214087503[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]182.763829787234[/C][C]5.07888868941269[/C][C]35.985003996685[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]182.826666666667[/C][C]4.91928836111464[/C][C]37.1652672593563[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]182.820930232558[/C][C]4.79603767583562[/C][C]38.1191605632466[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]182.904878048780[/C][C]4.6714910546215[/C][C]39.1534257285654[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]182.976923076923[/C][C]4.56214468461118[/C][C]40.1076545630244[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]183.021621621622[/C][C]4.44533553683657[/C][C]41.1716101304391[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]183.1[/C][C]4.31253400912178[/C][C]42.4576361862216[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]183.242424242424[/C][C]4.17573716569318[/C][C]43.8826528038925[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]183.283870967742[/C][C]4.02502146330801[/C][C]45.5361226365009[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]183.368965517241[/C][C]3.83891181551458[/C][C]47.7658707283074[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]183.511111111111[/C][C]3.64006016251169[/C][C]50.4143071592767[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]183.608[/C][C]3.41232042262544[/C][C]53.8073736518366[/C][/ROW]
[ROW][C]Median[/C][C]190[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]253.85[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]181.788888888889[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]183.021621621622[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]183.021621621622[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]183.021621621622[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]183.021621621622[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]181.747368421053[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]183.021621621622[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]183.021621621622[/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=39924&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=39924&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 Mean194.6383561643849.084886891177221.4244116075245
Geometric Mean180.883989779186
Harmonic Mean168.612182733680
Quadratic Mean209.348087924892
Winsorized Mean ( 1 / 24 )194.5726027397269.0519108497313421.4951965358233
Winsorized Mean ( 2 / 24 )194.0054794520558.8344625129940321.9600772731454
Winsorized Mean ( 3 / 24 )193.1753424657538.591742739748422.4838369021522
Winsorized Mean ( 4 / 24 )192.4520547945218.3580414776683223.0259750814505
Winsorized Mean ( 5 / 24 )191.6986301369868.0889465265886323.6988376059684
Winsorized Mean ( 6 / 24 )190.7863013698637.846079039738624.3161329886653
Winsorized Mean ( 7 / 24 )189.8753424657537.6352210933724824.8683489507028
Winsorized Mean ( 8 / 24 )188.0780821917817.2290555198054626.0169646887485
Winsorized Mean ( 9 / 24 )187.3260273972607.000882208866626.7574888147686
Winsorized Mean ( 10 / 24 )187.2301369863016.806788201492927.5063850150703
Winsorized Mean ( 11 / 24 )184.6082191780826.3042756725734629.2830181873572
Winsorized Mean ( 12 / 24 )183.0794520547955.702773084052132.1035835297005
Winsorized Mean ( 13 / 24 )182.2602739726035.4802307428055733.2577737190854
Winsorized Mean ( 14 / 24 )182.8739726027405.1080401255909435.8012012643662
Winsorized Mean ( 15 / 24 )182.1136986301374.930697538445636.9346724697999
Winsorized Mean ( 16 / 24 )182.2890410958904.6748906504616938.9932203179742
Winsorized Mean ( 17 / 24 )182.5917808219184.5273482993228540.3308446247062
Winsorized Mean ( 18 / 24 )182.3452054794524.3989205993609541.4522611537799
Winsorized Mean ( 19 / 24 )181.8767123287674.1986822607325743.3175699027613
Winsorized Mean ( 20 / 24 )182.8904109589044.0293138035510445.3899646132606
Winsorized Mean ( 21 / 24 )182.5739726027403.9044826652901446.7600930145691
Winsorized Mean ( 22 / 24 )182.2123287671233.6621370658277949.7557370168875
Winsorized Mean ( 23 / 24 )182.7479452054793.4484263443811552.99459143248
Winsorized Mean ( 24 / 24 )182.1232876712333.017479847352460.3560908057204
Trimmed Mean ( 1 / 24 )192.9704225352118.6927797681784822.1989314904324
Trimmed Mean ( 2 / 24 )191.2753623188418.2592187780909123.1590138798882
Trimmed Mean ( 3 / 24 )189.7880597014937.8797688847462524.0854855614974
Trimmed Mean ( 4 / 24 )188.527.5379517979151525.0094462068782
Trimmed Mean ( 5 / 24 )187.3809523809527.2146505157369625.9722840312539
Trimmed Mean ( 6 / 24 )186.3475409836076.9119333754494726.9602629049486
Trimmed Mean ( 7 / 24 )185.4322033898316.6159122426409128.0282138863152
Trimmed Mean ( 8 / 24 )184.6192982456146.3117478278869129.2501068293506
Trimmed Mean ( 9 / 24 )184.0454545454556.0468773799674830.4364456198786
Trimmed Mean ( 10 / 24 )183.5433962264155.775798130582431.7780144106088
Trimmed Mean ( 11 / 24 )183.0156862745105.4832360364803733.3773131517398
Trimmed Mean ( 12 / 24 )182.85.2419496100483234.8725214087503
Trimmed Mean ( 13 / 24 )182.7638297872345.0788886894126935.985003996685
Trimmed Mean ( 14 / 24 )182.8266666666674.9192883611146437.1652672593563
Trimmed Mean ( 15 / 24 )182.8209302325584.7960376758356238.1191605632466
Trimmed Mean ( 16 / 24 )182.9048780487804.671491054621539.1534257285654
Trimmed Mean ( 17 / 24 )182.9769230769234.5621446846111840.1076545630244
Trimmed Mean ( 18 / 24 )183.0216216216224.4453355368365741.1716101304391
Trimmed Mean ( 19 / 24 )183.14.3125340091217842.4576361862216
Trimmed Mean ( 20 / 24 )183.2424242424244.1757371656931843.8826528038925
Trimmed Mean ( 21 / 24 )183.2838709677424.0250214633080145.5361226365009
Trimmed Mean ( 22 / 24 )183.3689655172413.8389118155145847.7658707283074
Trimmed Mean ( 23 / 24 )183.5111111111113.6400601625116950.4143071592767
Trimmed Mean ( 24 / 24 )183.6083.4123204226254453.8073736518366
Median190
Midrange253.85
Midmean - Weighted Average at Xnp181.788888888889
Midmean - Weighted Average at X(n+1)p183.021621621622
Midmean - Empirical Distribution Function183.021621621622
Midmean - Empirical Distribution Function - Averaging183.021621621622
Midmean - Empirical Distribution Function - Interpolation183.021621621622
Midmean - Closest Observation181.747368421053
Midmean - True Basic - Statistics Graphics Toolkit183.021621621622
Midmean - MS Excel (old versions)183.021621621622
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')