Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationFri, 13 Mar 2009 08:22:07 -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/Mar/13/t1236954178jbmz2461klmgqpb.htm/, Retrieved Tue, 07 Feb 2023 18:28:15 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=39065, Retrieved Tue, 07 Feb 2023 18:28:15 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact144
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Brutoschuld van d...] [2009-03-13 14:22:07] [2eea656d1ea82c4ced0e8e79cdac0617] [Current]
-    D    [Central Tendency] [Bruto schuld van ...] [2009-06-06 16:53:22] [ef653b42671acc8de32235b938c43afe]
- RM D    [Mean versus Median] [Bruto schuld van ...] [2009-06-06 16:56:36] [ef653b42671acc8de32235b938c43afe]
- RMPD    [Univariate Data Series] [inschrijving nieu...] [2009-06-06 17:40:57] [ef653b42671acc8de32235b938c43afe]
- RMPD    [Mean Plot] [inschrijving nieu...] [2009-06-06 17:45:40] [ef653b42671acc8de32235b938c43afe]
- RMPD    [Mean Plot] [Bruto schuld van ...] [2009-06-06 17:56:26] [ef653b42671acc8de32235b938c43afe]
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Dataseries X:
321.935
310.215
309.030
305.333
294.735
289.351
288.225
289.648
290.155
288.301
289.148
289.741
287.595
285.226
287.816
283.519
290.304
282.166
280.041
282.500
279.913
277.793
281.229
275.363
273.547
270.601
273.338
271.917
273.985
273.911
270.798
271.115
271.344
274.525
276.663
273.784
274.027
269.160
270.491
270.846
270.333
272.599
272.764
270.674
268.175
268.351
272.482
268.714
269.419
265.518
264.101
267.179
271.322
270.157
271.296
269.907
271.244
266.844
270.911
269.829
269.285
263.018
266.680
265.814
268.457
269.508
270.223
264.676
265.521
262.971
266.003
267.722
266.433




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=39065&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=39065&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=39065&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 Mean276.4036164383561.37570031102332200.918480735642
Geometric Mean276.167753528262
Harmonic Mean275.941920589930
Quadratic Mean276.650000681540
Winsorized Mean ( 1 / 24 )276.2437123287671.30959356930805210.938507032167
Winsorized Mean ( 2 / 24 )276.2409178082191.29401661279846213.475557482075
Winsorized Mean ( 3 / 24 )276.1126164383561.23931084835674222.795287239249
Winsorized Mean ( 4 / 24 )275.5780410958901.06392270161276259.020735884433
Winsorized Mean ( 5 / 24 )275.2747534246580.993868134431353276.973115334015
Winsorized Mean ( 6 / 24 )275.2865890410960.988057593349755278.613909648533
Winsorized Mean ( 7 / 24 )275.265013698630.977426447869276281.622227737636
Winsorized Mean ( 8 / 24 )275.3019452054790.969234798935838284.040508561748
Winsorized Mean ( 9 / 24 )275.2957808219180.957902508529574287.394362547928
Winsorized Mean ( 10 / 24 )275.2904383561640.94945919698403289.944464417879
Winsorized Mean ( 11 / 24 )275.2132876712330.917689370235552299.898088173988
Winsorized Mean ( 12 / 24 )275.2900547945210.90459703914547304.323409077896
Winsorized Mean ( 13 / 24 )275.2978904109590.880958066180771312.498291325558
Winsorized Mean ( 14 / 24 )275.2892602739730.868839720360189316.847001607900
Winsorized Mean ( 15 / 24 )274.8242602739730.772874921709248355.586981223541
Winsorized Mean ( 16 / 24 )274.5064520547950.697810282709353393.382641180038
Winsorized Mean ( 17 / 24 )274.373013698630.643874189006145426.128300191905
Winsorized Mean ( 18 / 24 )274.3214794520550.62603319991299438.189986553719
Winsorized Mean ( 19 / 24 )274.1124794520550.580110937177427472.517344330327
Winsorized Mean ( 20 / 24 )273.8113835616440.522637507715561523.903048517257
Winsorized Mean ( 21 / 24 )273.8669041095890.506136332923723541.093152762977
Winsorized Mean ( 22 / 24 )273.2515068493150.399766176960656683.528328801582
Winsorized Mean ( 23 / 24 )272.9742465753420.335223782442985814.304535871555
Winsorized Mean ( 24 / 24 )272.5685479452050.2689503527662311013.45302261834
Trimmed Mean ( 1 / 24 )275.9515211267611.24302448842191222.000068137914
Trimmed Mean ( 2 / 24 )275.6423913043481.16163270486560237.28876619072
Trimmed Mean ( 3 / 24 )275.3163283582091.07142915593021256.961766286060
Trimmed Mean ( 4 / 24 )275.0182307692310.987455919602634278.511906516194
Trimmed Mean ( 5 / 24 )274.8560634920630.956775188499215287.273402149150
Trimmed Mean ( 6 / 24 )274.7558524590160.94221442335731291.606502350073
Trimmed Mean ( 7 / 24 )274.6464067796610.925550329638286296.738489507097
Trimmed Mean ( 8 / 24 )274.5332280701750.907388979800076302.552967009433
Trimmed Mean ( 9 / 24 )274.4056909090910.886331628761634309.597087596305
Trimmed Mean ( 10 / 24 )274.2694716981130.862278292576644318.075352307138
Trimmed Mean ( 11 / 24 )274.1233333333330.833502962186612328.881054740583
Trimmed Mean ( 12 / 24 )273.9757142857140.804234264720809340.666552401650
Trimmed Mean ( 13 / 24 )273.8055957446810.76876622846198356.162361986771
Trimmed Mean ( 14 / 24 )273.6193777777780.727591074023643376.062032021144
Trimmed Mean ( 15 / 24 )273.416883720930.675202598863454404.940508495026
Trimmed Mean ( 16 / 24 )273.2498292682930.633492502797417431.338694714868
Trimmed Mean ( 17 / 24 )273.1028205128210.598739367159449456.129721031173
Trimmed Mean ( 18 / 24 )272.9554054054050.565939898892407482.304580291304
Trimmed Mean ( 19 / 24 )272.7971142857140.524556382036454520.052988825816
Trimmed Mean ( 20 / 24 )272.6439696969700.480842628615675567.012892517246
Trimmed Mean ( 21 / 24 )272.5065161290320.438743699819284621.106391365338
Trimmed Mean ( 22 / 24 )272.3434482758620.378330974897658719.855011473838
Trimmed Mean ( 23 / 24 )272.2318518518520.338117225847945805.140439589071
Trimmed Mean ( 24 / 24 )272.13760.305757959830975890.042568803245
Median271.344
Midrange292.453
Midmean - Weighted Average at Xnp272.699555555556
Midmean - Weighted Average at X(n+1)p272.955405405405
Midmean - Empirical Distribution Function272.955405405405
Midmean - Empirical Distribution Function - Averaging272.955405405405
Midmean - Empirical Distribution Function - Interpolation272.955405405405
Midmean - Closest Observation272.855526315789
Midmean - True Basic - Statistics Graphics Toolkit272.955405405405
Midmean - MS Excel (old versions)272.955405405405
Number of observations73

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 276.403616438356 & 1.37570031102332 & 200.918480735642 \tabularnewline
Geometric Mean & 276.167753528262 &  &  \tabularnewline
Harmonic Mean & 275.941920589930 &  &  \tabularnewline
Quadratic Mean & 276.650000681540 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 276.243712328767 & 1.30959356930805 & 210.938507032167 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 276.240917808219 & 1.29401661279846 & 213.475557482075 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 276.112616438356 & 1.23931084835674 & 222.795287239249 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 275.578041095890 & 1.06392270161276 & 259.020735884433 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 275.274753424658 & 0.993868134431353 & 276.973115334015 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 275.286589041096 & 0.988057593349755 & 278.613909648533 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 275.26501369863 & 0.977426447869276 & 281.622227737636 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 275.301945205479 & 0.969234798935838 & 284.040508561748 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 275.295780821918 & 0.957902508529574 & 287.394362547928 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 275.290438356164 & 0.94945919698403 & 289.944464417879 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 275.213287671233 & 0.917689370235552 & 299.898088173988 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 275.290054794521 & 0.90459703914547 & 304.323409077896 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 275.297890410959 & 0.880958066180771 & 312.498291325558 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 275.289260273973 & 0.868839720360189 & 316.847001607900 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 274.824260273973 & 0.772874921709248 & 355.586981223541 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 274.506452054795 & 0.697810282709353 & 393.382641180038 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 274.37301369863 & 0.643874189006145 & 426.128300191905 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 274.321479452055 & 0.62603319991299 & 438.189986553719 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 274.112479452055 & 0.580110937177427 & 472.517344330327 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 273.811383561644 & 0.522637507715561 & 523.903048517257 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 273.866904109589 & 0.506136332923723 & 541.093152762977 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 273.251506849315 & 0.399766176960656 & 683.528328801582 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 272.974246575342 & 0.335223782442985 & 814.304535871555 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 272.568547945205 & 0.268950352766231 & 1013.45302261834 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 275.951521126761 & 1.24302448842191 & 222.000068137914 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 275.642391304348 & 1.16163270486560 & 237.28876619072 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 275.316328358209 & 1.07142915593021 & 256.961766286060 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 275.018230769231 & 0.987455919602634 & 278.511906516194 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 274.856063492063 & 0.956775188499215 & 287.273402149150 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 274.755852459016 & 0.94221442335731 & 291.606502350073 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 274.646406779661 & 0.925550329638286 & 296.738489507097 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 274.533228070175 & 0.907388979800076 & 302.552967009433 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 274.405690909091 & 0.886331628761634 & 309.597087596305 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 274.269471698113 & 0.862278292576644 & 318.075352307138 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 274.123333333333 & 0.833502962186612 & 328.881054740583 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 273.975714285714 & 0.804234264720809 & 340.666552401650 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 273.805595744681 & 0.76876622846198 & 356.162361986771 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 273.619377777778 & 0.727591074023643 & 376.062032021144 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 273.41688372093 & 0.675202598863454 & 404.940508495026 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 273.249829268293 & 0.633492502797417 & 431.338694714868 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 273.102820512821 & 0.598739367159449 & 456.129721031173 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 272.955405405405 & 0.565939898892407 & 482.304580291304 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 272.797114285714 & 0.524556382036454 & 520.052988825816 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 272.643969696970 & 0.480842628615675 & 567.012892517246 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 272.506516129032 & 0.438743699819284 & 621.106391365338 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 272.343448275862 & 0.378330974897658 & 719.855011473838 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 272.231851851852 & 0.338117225847945 & 805.140439589071 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 272.1376 & 0.305757959830975 & 890.042568803245 \tabularnewline
Median & 271.344 &  &  \tabularnewline
Midrange & 292.453 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 272.699555555556 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 272.955405405405 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 272.955405405405 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 272.955405405405 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 272.955405405405 &  &  \tabularnewline
Midmean - Closest Observation & 272.855526315789 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 272.955405405405 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 272.955405405405 &  &  \tabularnewline
Number of observations & 73 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=39065&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]276.403616438356[/C][C]1.37570031102332[/C][C]200.918480735642[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]276.167753528262[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]275.941920589930[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]276.650000681540[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]276.243712328767[/C][C]1.30959356930805[/C][C]210.938507032167[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]276.240917808219[/C][C]1.29401661279846[/C][C]213.475557482075[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]276.112616438356[/C][C]1.23931084835674[/C][C]222.795287239249[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]275.578041095890[/C][C]1.06392270161276[/C][C]259.020735884433[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]275.274753424658[/C][C]0.993868134431353[/C][C]276.973115334015[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]275.286589041096[/C][C]0.988057593349755[/C][C]278.613909648533[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]275.26501369863[/C][C]0.977426447869276[/C][C]281.622227737636[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]275.301945205479[/C][C]0.969234798935838[/C][C]284.040508561748[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]275.295780821918[/C][C]0.957902508529574[/C][C]287.394362547928[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]275.290438356164[/C][C]0.94945919698403[/C][C]289.944464417879[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]275.213287671233[/C][C]0.917689370235552[/C][C]299.898088173988[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]275.290054794521[/C][C]0.90459703914547[/C][C]304.323409077896[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]275.297890410959[/C][C]0.880958066180771[/C][C]312.498291325558[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]275.289260273973[/C][C]0.868839720360189[/C][C]316.847001607900[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]274.824260273973[/C][C]0.772874921709248[/C][C]355.586981223541[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]274.506452054795[/C][C]0.697810282709353[/C][C]393.382641180038[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]274.37301369863[/C][C]0.643874189006145[/C][C]426.128300191905[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]274.321479452055[/C][C]0.62603319991299[/C][C]438.189986553719[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]274.112479452055[/C][C]0.580110937177427[/C][C]472.517344330327[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]273.811383561644[/C][C]0.522637507715561[/C][C]523.903048517257[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]273.866904109589[/C][C]0.506136332923723[/C][C]541.093152762977[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]273.251506849315[/C][C]0.399766176960656[/C][C]683.528328801582[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]272.974246575342[/C][C]0.335223782442985[/C][C]814.304535871555[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]272.568547945205[/C][C]0.268950352766231[/C][C]1013.45302261834[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]275.951521126761[/C][C]1.24302448842191[/C][C]222.000068137914[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]275.642391304348[/C][C]1.16163270486560[/C][C]237.28876619072[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]275.316328358209[/C][C]1.07142915593021[/C][C]256.961766286060[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]275.018230769231[/C][C]0.987455919602634[/C][C]278.511906516194[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]274.856063492063[/C][C]0.956775188499215[/C][C]287.273402149150[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]274.755852459016[/C][C]0.94221442335731[/C][C]291.606502350073[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]274.646406779661[/C][C]0.925550329638286[/C][C]296.738489507097[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]274.533228070175[/C][C]0.907388979800076[/C][C]302.552967009433[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]274.405690909091[/C][C]0.886331628761634[/C][C]309.597087596305[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]274.269471698113[/C][C]0.862278292576644[/C][C]318.075352307138[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]274.123333333333[/C][C]0.833502962186612[/C][C]328.881054740583[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]273.975714285714[/C][C]0.804234264720809[/C][C]340.666552401650[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]273.805595744681[/C][C]0.76876622846198[/C][C]356.162361986771[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]273.619377777778[/C][C]0.727591074023643[/C][C]376.062032021144[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]273.41688372093[/C][C]0.675202598863454[/C][C]404.940508495026[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]273.249829268293[/C][C]0.633492502797417[/C][C]431.338694714868[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]273.102820512821[/C][C]0.598739367159449[/C][C]456.129721031173[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]272.955405405405[/C][C]0.565939898892407[/C][C]482.304580291304[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]272.797114285714[/C][C]0.524556382036454[/C][C]520.052988825816[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]272.643969696970[/C][C]0.480842628615675[/C][C]567.012892517246[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]272.506516129032[/C][C]0.438743699819284[/C][C]621.106391365338[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]272.343448275862[/C][C]0.378330974897658[/C][C]719.855011473838[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]272.231851851852[/C][C]0.338117225847945[/C][C]805.140439589071[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]272.1376[/C][C]0.305757959830975[/C][C]890.042568803245[/C][/ROW]
[ROW][C]Median[/C][C]271.344[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]292.453[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]272.699555555556[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]272.955405405405[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]272.955405405405[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]272.955405405405[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]272.955405405405[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]272.855526315789[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]272.955405405405[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]272.955405405405[/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=39065&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=39065&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 Mean276.4036164383561.37570031102332200.918480735642
Geometric Mean276.167753528262
Harmonic Mean275.941920589930
Quadratic Mean276.650000681540
Winsorized Mean ( 1 / 24 )276.2437123287671.30959356930805210.938507032167
Winsorized Mean ( 2 / 24 )276.2409178082191.29401661279846213.475557482075
Winsorized Mean ( 3 / 24 )276.1126164383561.23931084835674222.795287239249
Winsorized Mean ( 4 / 24 )275.5780410958901.06392270161276259.020735884433
Winsorized Mean ( 5 / 24 )275.2747534246580.993868134431353276.973115334015
Winsorized Mean ( 6 / 24 )275.2865890410960.988057593349755278.613909648533
Winsorized Mean ( 7 / 24 )275.265013698630.977426447869276281.622227737636
Winsorized Mean ( 8 / 24 )275.3019452054790.969234798935838284.040508561748
Winsorized Mean ( 9 / 24 )275.2957808219180.957902508529574287.394362547928
Winsorized Mean ( 10 / 24 )275.2904383561640.94945919698403289.944464417879
Winsorized Mean ( 11 / 24 )275.2132876712330.917689370235552299.898088173988
Winsorized Mean ( 12 / 24 )275.2900547945210.90459703914547304.323409077896
Winsorized Mean ( 13 / 24 )275.2978904109590.880958066180771312.498291325558
Winsorized Mean ( 14 / 24 )275.2892602739730.868839720360189316.847001607900
Winsorized Mean ( 15 / 24 )274.8242602739730.772874921709248355.586981223541
Winsorized Mean ( 16 / 24 )274.5064520547950.697810282709353393.382641180038
Winsorized Mean ( 17 / 24 )274.373013698630.643874189006145426.128300191905
Winsorized Mean ( 18 / 24 )274.3214794520550.62603319991299438.189986553719
Winsorized Mean ( 19 / 24 )274.1124794520550.580110937177427472.517344330327
Winsorized Mean ( 20 / 24 )273.8113835616440.522637507715561523.903048517257
Winsorized Mean ( 21 / 24 )273.8669041095890.506136332923723541.093152762977
Winsorized Mean ( 22 / 24 )273.2515068493150.399766176960656683.528328801582
Winsorized Mean ( 23 / 24 )272.9742465753420.335223782442985814.304535871555
Winsorized Mean ( 24 / 24 )272.5685479452050.2689503527662311013.45302261834
Trimmed Mean ( 1 / 24 )275.9515211267611.24302448842191222.000068137914
Trimmed Mean ( 2 / 24 )275.6423913043481.16163270486560237.28876619072
Trimmed Mean ( 3 / 24 )275.3163283582091.07142915593021256.961766286060
Trimmed Mean ( 4 / 24 )275.0182307692310.987455919602634278.511906516194
Trimmed Mean ( 5 / 24 )274.8560634920630.956775188499215287.273402149150
Trimmed Mean ( 6 / 24 )274.7558524590160.94221442335731291.606502350073
Trimmed Mean ( 7 / 24 )274.6464067796610.925550329638286296.738489507097
Trimmed Mean ( 8 / 24 )274.5332280701750.907388979800076302.552967009433
Trimmed Mean ( 9 / 24 )274.4056909090910.886331628761634309.597087596305
Trimmed Mean ( 10 / 24 )274.2694716981130.862278292576644318.075352307138
Trimmed Mean ( 11 / 24 )274.1233333333330.833502962186612328.881054740583
Trimmed Mean ( 12 / 24 )273.9757142857140.804234264720809340.666552401650
Trimmed Mean ( 13 / 24 )273.8055957446810.76876622846198356.162361986771
Trimmed Mean ( 14 / 24 )273.6193777777780.727591074023643376.062032021144
Trimmed Mean ( 15 / 24 )273.416883720930.675202598863454404.940508495026
Trimmed Mean ( 16 / 24 )273.2498292682930.633492502797417431.338694714868
Trimmed Mean ( 17 / 24 )273.1028205128210.598739367159449456.129721031173
Trimmed Mean ( 18 / 24 )272.9554054054050.565939898892407482.304580291304
Trimmed Mean ( 19 / 24 )272.7971142857140.524556382036454520.052988825816
Trimmed Mean ( 20 / 24 )272.6439696969700.480842628615675567.012892517246
Trimmed Mean ( 21 / 24 )272.5065161290320.438743699819284621.106391365338
Trimmed Mean ( 22 / 24 )272.3434482758620.378330974897658719.855011473838
Trimmed Mean ( 23 / 24 )272.2318518518520.338117225847945805.140439589071
Trimmed Mean ( 24 / 24 )272.13760.305757959830975890.042568803245
Median271.344
Midrange292.453
Midmean - Weighted Average at Xnp272.699555555556
Midmean - Weighted Average at X(n+1)p272.955405405405
Midmean - Empirical Distribution Function272.955405405405
Midmean - Empirical Distribution Function - Averaging272.955405405405
Midmean - Empirical Distribution Function - Interpolation272.955405405405
Midmean - Closest Observation272.855526315789
Midmean - True Basic - Statistics Graphics Toolkit272.955405405405
Midmean - MS Excel (old versions)272.955405405405
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')