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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, 12 Oct 2014 17:08:52 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2014/Oct/12/t1413130148eiuh4ksbeza1rpx.htm/, Retrieved Wed, 15 May 2024 08:56:10 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=240606, Retrieved Wed, 15 May 2024 08:56:10 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact84
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2014-10-12 16:08:52] [0c3693ead1e3fa463b40b3108c1b2028] [Current]
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Dataseries X:
11236
10954
9580
10337
8961
10372
12782
15119
19940
13957
10849
9429
11816
11329
11334
9898
8961
10783
13149
16244
20067
13601
10573
8623
10962
11911
11677
9679
9116
11394
13240
18983
21545
14360
11839
9726
12347
12624
11918
10028
10228
11026
13878
22165
23533
13445
12164
9606
12177
13142
11210
9485
10082
10680
13579
21709
22205
14687
11222
8196
12794
12627
11080
10425
10865
10771
14771
20993
23882
14825
11648
10091




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

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=240606&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=240606&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=240606&T=0

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

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







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean12922.6944444444457.86536401491528.223786859806
Geometric Mean12451.9267518897
Harmonic Mean12069.8417165577
Quadratic Mean13486.3086426774
Winsorized Mean ( 1 / 24 )12923.7777777778455.4274223404328.3772499059516
Winsorized Mean ( 2 / 24 )12896.2777777778442.69223529294429.1314749833909
Winsorized Mean ( 3 / 24 )12894.6111111111442.19937338247929.1601749963538
Winsorized Mean ( 4 / 24 )12877.8888888889433.76053227170629.6889364771026
Winsorized Mean ( 5 / 24 )12888.2361111111427.93963497065430.1169488822762
Winsorized Mean ( 6 / 24 )12846.9027777778414.48477980692830.9948721971457
Winsorized Mean ( 7 / 24 )12766.1111111111389.04896509817132.8136359593959
Winsorized Mean ( 8 / 24 )12754.8888888889384.99645576664433.1298865167214
Winsorized Mean ( 9 / 24 )12644.3888888889353.05932913423435.8137792871676
Winsorized Mean ( 10 / 24 )12270.5262.47325595933946.749524842641
Winsorized Mean ( 11 / 24 )12124.9027777778224.18582842140854.0841625144399
Winsorized Mean ( 12 / 24 )12097.5694444444212.13084553755457.0288088645872
Winsorized Mean ( 13 / 24 )12097.5694444444209.03789297373957.8726147319341
Winsorized Mean ( 14 / 24 )12082.9861111111205.87375483911358.6912407584626
Winsorized Mean ( 15 / 24 )12043.4027777778190.08442718956663.3581769734732
Winsorized Mean ( 16 / 24 )11978.0694444444171.85674253735669.6979895440575
Winsorized Mean ( 17 / 24 )11967.6805555556167.73860778725271.3472033268245
Winsorized Mean ( 18 / 24 )11911.6805555556155.08093301554676.8094460352614
Winsorized Mean ( 19 / 24 )11944.9305555556149.01640125461180.1584956755622
Winsorized Mean ( 20 / 24 )11937.4305555556139.49248052493985.5775917858266
Winsorized Mean ( 21 / 24 )11904.1805555556127.16115077102193.6149168466664
Winsorized Mean ( 22 / 24 )11880.0416666667122.61598488219596.8881967394429
Winsorized Mean ( 23 / 24 )11898.8888888889119.65799521911499.4408176996451
Winsorized Mean ( 24 / 24 )11788.2222222222102.447937505584115.065490914151
Trimmed Mean ( 1 / 24 )12833.6571428571438.48984722847229.2678547153915
Trimmed Mean ( 2 / 24 )12738.2352941176417.95089635467130.4778274319289
Trimmed Mean ( 3 / 24 )12652.0303030303401.47685461024731.5137227906024
Trimmed Mean ( 4 / 24 )12561.0625381.50054080749232.9254120411284
Trimmed Mean ( 5 / 24 )12469.0806451613360.22138978052634.6150478536502
Trimmed Mean ( 6 / 24 )12368.4833333333335.52751576748536.8627988826541
Trimmed Mean ( 7 / 24 )12269.5308.80583790351339.7320856474016
Trimmed Mean ( 8 / 24 )12178.2857142857283.05113887258743.0250369696186
Trimmed Mean ( 9 / 24 )12082.1851851852250.36919499887448.2574750669287
Trimmed Mean ( 10 / 24 )11995.6923076923217.64036149593855.1170390695946
Trimmed Mean ( 11 / 24 )11956.12204.38082828736358.4992247080508
Trimmed Mean ( 12 / 24 )11933.1041666667197.58643014012260.394350756801
Trimmed Mean ( 13 / 24 )11911.652173913191.68901499801662.1405048903629
Trimmed Mean ( 14 / 24 )11888.25184.65711646366864.3801345307971
Trimmed Mean ( 15 / 24 )11864.4047619048176.14219937682567.3569695614108
Trimmed Mean ( 16 / 24 )11842.925168.90034380610570.1178264835002
Trimmed Mean ( 17 / 24 )11826.9210526316163.86983689695872.1726540807407
Trimmed Mean ( 18 / 24 )11810.3611111111157.91845470920374.7877196041411
Trimmed Mean ( 19 / 24 )11798.4411764706153.07815039016677.0746259110049
Trimmed Mean ( 20 / 24 )11781.09375147.59500329868979.8204104928847
Trimmed Mean ( 21 / 24 )11762.3333333333142.30637446916982.6549996597774
Trimmed Mean ( 22 / 24 )11744.9642857143138.22271808219184.9713017416605
Trimmed Mean ( 23 / 24 )11727.9615384615133.24104796910588.020634160585
Trimmed Mean ( 24 / 24 )11705.6666666667125.94251430002792.9445210120292
Median11662.5
Midrange16039
Midmean - Weighted Average at Xnp11771.4864864865
Midmean - Weighted Average at X(n+1)p11810.3611111111
Midmean - Empirical Distribution Function11771.4864864865
Midmean - Empirical Distribution Function - Averaging11810.3611111111
Midmean - Empirical Distribution Function - Interpolation11810.3611111111
Midmean - Closest Observation11771.4864864865
Midmean - True Basic - Statistics Graphics Toolkit11810.3611111111
Midmean - MS Excel (old versions)11826.9210526316
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 12922.6944444444 & 457.865364014915 & 28.223786859806 \tabularnewline
Geometric Mean & 12451.9267518897 &  &  \tabularnewline
Harmonic Mean & 12069.8417165577 &  &  \tabularnewline
Quadratic Mean & 13486.3086426774 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 12923.7777777778 & 455.42742234043 & 28.3772499059516 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 12896.2777777778 & 442.692235292944 & 29.1314749833909 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 12894.6111111111 & 442.199373382479 & 29.1601749963538 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 12877.8888888889 & 433.760532271706 & 29.6889364771026 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 12888.2361111111 & 427.939634970654 & 30.1169488822762 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 12846.9027777778 & 414.484779806928 & 30.9948721971457 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 12766.1111111111 & 389.048965098171 & 32.8136359593959 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 12754.8888888889 & 384.996455766644 & 33.1298865167214 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 12644.3888888889 & 353.059329134234 & 35.8137792871676 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 12270.5 & 262.473255959339 & 46.749524842641 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 12124.9027777778 & 224.185828421408 & 54.0841625144399 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 12097.5694444444 & 212.130845537554 & 57.0288088645872 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 12097.5694444444 & 209.037892973739 & 57.8726147319341 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 12082.9861111111 & 205.873754839113 & 58.6912407584626 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 12043.4027777778 & 190.084427189566 & 63.3581769734732 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 11978.0694444444 & 171.856742537356 & 69.6979895440575 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 11967.6805555556 & 167.738607787252 & 71.3472033268245 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 11911.6805555556 & 155.080933015546 & 76.8094460352614 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 11944.9305555556 & 149.016401254611 & 80.1584956755622 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 11937.4305555556 & 139.492480524939 & 85.5775917858266 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 11904.1805555556 & 127.161150771021 & 93.6149168466664 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 11880.0416666667 & 122.615984882195 & 96.8881967394429 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 11898.8888888889 & 119.657995219114 & 99.4408176996451 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 11788.2222222222 & 102.447937505584 & 115.065490914151 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 12833.6571428571 & 438.489847228472 & 29.2678547153915 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 12738.2352941176 & 417.950896354671 & 30.4778274319289 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 12652.0303030303 & 401.476854610247 & 31.5137227906024 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 12561.0625 & 381.500540807492 & 32.9254120411284 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 12469.0806451613 & 360.221389780526 & 34.6150478536502 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 12368.4833333333 & 335.527515767485 & 36.8627988826541 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 12269.5 & 308.805837903513 & 39.7320856474016 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 12178.2857142857 & 283.051138872587 & 43.0250369696186 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 12082.1851851852 & 250.369194998874 & 48.2574750669287 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 11995.6923076923 & 217.640361495938 & 55.1170390695946 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 11956.12 & 204.380828287363 & 58.4992247080508 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 11933.1041666667 & 197.586430140122 & 60.394350756801 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 11911.652173913 & 191.689014998016 & 62.1405048903629 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 11888.25 & 184.657116463668 & 64.3801345307971 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 11864.4047619048 & 176.142199376825 & 67.3569695614108 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 11842.925 & 168.900343806105 & 70.1178264835002 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 11826.9210526316 & 163.869836896958 & 72.1726540807407 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 11810.3611111111 & 157.918454709203 & 74.7877196041411 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 11798.4411764706 & 153.078150390166 & 77.0746259110049 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 11781.09375 & 147.595003298689 & 79.8204104928847 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 11762.3333333333 & 142.306374469169 & 82.6549996597774 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 11744.9642857143 & 138.222718082191 & 84.9713017416605 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 11727.9615384615 & 133.241047969105 & 88.020634160585 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 11705.6666666667 & 125.942514300027 & 92.9445210120292 \tabularnewline
Median & 11662.5 &  &  \tabularnewline
Midrange & 16039 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 11771.4864864865 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 11810.3611111111 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 11771.4864864865 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 11810.3611111111 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 11810.3611111111 &  &  \tabularnewline
Midmean - Closest Observation & 11771.4864864865 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 11810.3611111111 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 11826.9210526316 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=240606&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]12922.6944444444[/C][C]457.865364014915[/C][C]28.223786859806[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]12451.9267518897[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]12069.8417165577[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]13486.3086426774[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]12923.7777777778[/C][C]455.42742234043[/C][C]28.3772499059516[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]12896.2777777778[/C][C]442.692235292944[/C][C]29.1314749833909[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]12894.6111111111[/C][C]442.199373382479[/C][C]29.1601749963538[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]12877.8888888889[/C][C]433.760532271706[/C][C]29.6889364771026[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]12888.2361111111[/C][C]427.939634970654[/C][C]30.1169488822762[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]12846.9027777778[/C][C]414.484779806928[/C][C]30.9948721971457[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]12766.1111111111[/C][C]389.048965098171[/C][C]32.8136359593959[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]12754.8888888889[/C][C]384.996455766644[/C][C]33.1298865167214[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]12644.3888888889[/C][C]353.059329134234[/C][C]35.8137792871676[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]12270.5[/C][C]262.473255959339[/C][C]46.749524842641[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]12124.9027777778[/C][C]224.185828421408[/C][C]54.0841625144399[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]12097.5694444444[/C][C]212.130845537554[/C][C]57.0288088645872[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]12097.5694444444[/C][C]209.037892973739[/C][C]57.8726147319341[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]12082.9861111111[/C][C]205.873754839113[/C][C]58.6912407584626[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]12043.4027777778[/C][C]190.084427189566[/C][C]63.3581769734732[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]11978.0694444444[/C][C]171.856742537356[/C][C]69.6979895440575[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]11967.6805555556[/C][C]167.738607787252[/C][C]71.3472033268245[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]11911.6805555556[/C][C]155.080933015546[/C][C]76.8094460352614[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]11944.9305555556[/C][C]149.016401254611[/C][C]80.1584956755622[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]11937.4305555556[/C][C]139.492480524939[/C][C]85.5775917858266[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]11904.1805555556[/C][C]127.161150771021[/C][C]93.6149168466664[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]11880.0416666667[/C][C]122.615984882195[/C][C]96.8881967394429[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]11898.8888888889[/C][C]119.657995219114[/C][C]99.4408176996451[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]11788.2222222222[/C][C]102.447937505584[/C][C]115.065490914151[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]12833.6571428571[/C][C]438.489847228472[/C][C]29.2678547153915[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]12738.2352941176[/C][C]417.950896354671[/C][C]30.4778274319289[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]12652.0303030303[/C][C]401.476854610247[/C][C]31.5137227906024[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]12561.0625[/C][C]381.500540807492[/C][C]32.9254120411284[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]12469.0806451613[/C][C]360.221389780526[/C][C]34.6150478536502[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]12368.4833333333[/C][C]335.527515767485[/C][C]36.8627988826541[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]12269.5[/C][C]308.805837903513[/C][C]39.7320856474016[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]12178.2857142857[/C][C]283.051138872587[/C][C]43.0250369696186[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]12082.1851851852[/C][C]250.369194998874[/C][C]48.2574750669287[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]11995.6923076923[/C][C]217.640361495938[/C][C]55.1170390695946[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]11956.12[/C][C]204.380828287363[/C][C]58.4992247080508[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]11933.1041666667[/C][C]197.586430140122[/C][C]60.394350756801[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]11911.652173913[/C][C]191.689014998016[/C][C]62.1405048903629[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]11888.25[/C][C]184.657116463668[/C][C]64.3801345307971[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]11864.4047619048[/C][C]176.142199376825[/C][C]67.3569695614108[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]11842.925[/C][C]168.900343806105[/C][C]70.1178264835002[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]11826.9210526316[/C][C]163.869836896958[/C][C]72.1726540807407[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]11810.3611111111[/C][C]157.918454709203[/C][C]74.7877196041411[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]11798.4411764706[/C][C]153.078150390166[/C][C]77.0746259110049[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]11781.09375[/C][C]147.595003298689[/C][C]79.8204104928847[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]11762.3333333333[/C][C]142.306374469169[/C][C]82.6549996597774[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]11744.9642857143[/C][C]138.222718082191[/C][C]84.9713017416605[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]11727.9615384615[/C][C]133.241047969105[/C][C]88.020634160585[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]11705.6666666667[/C][C]125.942514300027[/C][C]92.9445210120292[/C][/ROW]
[ROW][C]Median[/C][C]11662.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]16039[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]11771.4864864865[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]11810.3611111111[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]11771.4864864865[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]11810.3611111111[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]11810.3611111111[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]11771.4864864865[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]11810.3611111111[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]11826.9210526316[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]72[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=240606&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=240606&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 Mean12922.6944444444457.86536401491528.223786859806
Geometric Mean12451.9267518897
Harmonic Mean12069.8417165577
Quadratic Mean13486.3086426774
Winsorized Mean ( 1 / 24 )12923.7777777778455.4274223404328.3772499059516
Winsorized Mean ( 2 / 24 )12896.2777777778442.69223529294429.1314749833909
Winsorized Mean ( 3 / 24 )12894.6111111111442.19937338247929.1601749963538
Winsorized Mean ( 4 / 24 )12877.8888888889433.76053227170629.6889364771026
Winsorized Mean ( 5 / 24 )12888.2361111111427.93963497065430.1169488822762
Winsorized Mean ( 6 / 24 )12846.9027777778414.48477980692830.9948721971457
Winsorized Mean ( 7 / 24 )12766.1111111111389.04896509817132.8136359593959
Winsorized Mean ( 8 / 24 )12754.8888888889384.99645576664433.1298865167214
Winsorized Mean ( 9 / 24 )12644.3888888889353.05932913423435.8137792871676
Winsorized Mean ( 10 / 24 )12270.5262.47325595933946.749524842641
Winsorized Mean ( 11 / 24 )12124.9027777778224.18582842140854.0841625144399
Winsorized Mean ( 12 / 24 )12097.5694444444212.13084553755457.0288088645872
Winsorized Mean ( 13 / 24 )12097.5694444444209.03789297373957.8726147319341
Winsorized Mean ( 14 / 24 )12082.9861111111205.87375483911358.6912407584626
Winsorized Mean ( 15 / 24 )12043.4027777778190.08442718956663.3581769734732
Winsorized Mean ( 16 / 24 )11978.0694444444171.85674253735669.6979895440575
Winsorized Mean ( 17 / 24 )11967.6805555556167.73860778725271.3472033268245
Winsorized Mean ( 18 / 24 )11911.6805555556155.08093301554676.8094460352614
Winsorized Mean ( 19 / 24 )11944.9305555556149.01640125461180.1584956755622
Winsorized Mean ( 20 / 24 )11937.4305555556139.49248052493985.5775917858266
Winsorized Mean ( 21 / 24 )11904.1805555556127.16115077102193.6149168466664
Winsorized Mean ( 22 / 24 )11880.0416666667122.61598488219596.8881967394429
Winsorized Mean ( 23 / 24 )11898.8888888889119.65799521911499.4408176996451
Winsorized Mean ( 24 / 24 )11788.2222222222102.447937505584115.065490914151
Trimmed Mean ( 1 / 24 )12833.6571428571438.48984722847229.2678547153915
Trimmed Mean ( 2 / 24 )12738.2352941176417.95089635467130.4778274319289
Trimmed Mean ( 3 / 24 )12652.0303030303401.47685461024731.5137227906024
Trimmed Mean ( 4 / 24 )12561.0625381.50054080749232.9254120411284
Trimmed Mean ( 5 / 24 )12469.0806451613360.22138978052634.6150478536502
Trimmed Mean ( 6 / 24 )12368.4833333333335.52751576748536.8627988826541
Trimmed Mean ( 7 / 24 )12269.5308.80583790351339.7320856474016
Trimmed Mean ( 8 / 24 )12178.2857142857283.05113887258743.0250369696186
Trimmed Mean ( 9 / 24 )12082.1851851852250.36919499887448.2574750669287
Trimmed Mean ( 10 / 24 )11995.6923076923217.64036149593855.1170390695946
Trimmed Mean ( 11 / 24 )11956.12204.38082828736358.4992247080508
Trimmed Mean ( 12 / 24 )11933.1041666667197.58643014012260.394350756801
Trimmed Mean ( 13 / 24 )11911.652173913191.68901499801662.1405048903629
Trimmed Mean ( 14 / 24 )11888.25184.65711646366864.3801345307971
Trimmed Mean ( 15 / 24 )11864.4047619048176.14219937682567.3569695614108
Trimmed Mean ( 16 / 24 )11842.925168.90034380610570.1178264835002
Trimmed Mean ( 17 / 24 )11826.9210526316163.86983689695872.1726540807407
Trimmed Mean ( 18 / 24 )11810.3611111111157.91845470920374.7877196041411
Trimmed Mean ( 19 / 24 )11798.4411764706153.07815039016677.0746259110049
Trimmed Mean ( 20 / 24 )11781.09375147.59500329868979.8204104928847
Trimmed Mean ( 21 / 24 )11762.3333333333142.30637446916982.6549996597774
Trimmed Mean ( 22 / 24 )11744.9642857143138.22271808219184.9713017416605
Trimmed Mean ( 23 / 24 )11727.9615384615133.24104796910588.020634160585
Trimmed Mean ( 24 / 24 )11705.6666666667125.94251430002792.9445210120292
Median11662.5
Midrange16039
Midmean - Weighted Average at Xnp11771.4864864865
Midmean - Weighted Average at X(n+1)p11810.3611111111
Midmean - Empirical Distribution Function11771.4864864865
Midmean - Empirical Distribution Function - Averaging11810.3611111111
Midmean - Empirical Distribution Function - Interpolation11810.3611111111
Midmean - Closest Observation11771.4864864865
Midmean - True Basic - Statistics Graphics Toolkit11810.3611111111
Midmean - MS Excel (old versions)11826.9210526316
Number of observations72



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')