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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, 10 Oct 2013 12:51:38 -0400
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2013/Oct/10/t1381423921et60rhxa4gjl2dg.htm/, Retrieved Thu, 02 May 2024 07:54:47 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=214655, Retrieved Thu, 02 May 2024 07:54:47 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact69
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2013-10-10 16:51:38] [354a1e9bb909abf3036d55f04d250334] [Current]
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Dataseries X:
15579
16348
15928
16171
15937
15713
15594
15683
16438
17032
17696
17745
19394
20148
20108
18584
18441
18391
19178
18079
18483
19644
19195
19650
20830
23595
22937
21814
21928
21777
21383
21467
22052
22680
24320
24977
25204
25739
26434
27525
30695
32436
30160
30236
31293
31077
32226
33865
32810
32242
32700
32819
33947
34148
35261
39506
41591
39148
41216
40225
41126
42362
40740
40256
39804
41002
41702
42254
43605
43271
43221
41373




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Herman Ole Andreas Wold' @ wold.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 & 3 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=214655&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=214655&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=214655&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 time3 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean27613.02777777781114.5271564487524.7755540257645
Geometric Mean26042.1647044531
Harmonic Mean24579.5324210149
Quadratic Mean29166.306393013
Winsorized Mean ( 1 / 24 )27608.59722222221113.5672554181424.7929319831296
Winsorized Mean ( 2 / 24 )27609.68055555561112.9180677475524.808367619941
Winsorized Mean ( 3 / 24 )27575.13888888891105.8226995511324.9363111284314
Winsorized Mean ( 4 / 24 )27581.08333333331102.9044747477625.0076810502028
Winsorized Mean ( 5 / 24 )27543.3751095.7313568355625.1369779902479
Winsorized Mean ( 6 / 24 )27553.6251091.1644713496725.2515782207597
Winsorized Mean ( 7 / 24 )27549.63888888891084.8268686835825.3954245457802
Winsorized Mean ( 8 / 24 )27542.19444444441080.2553927075525.4960027326619
Winsorized Mean ( 9 / 24 )27605.19444444441067.695202040225.8549391171706
Winsorized Mean ( 10 / 24 )27680.19444444441052.0265397005526.311308127572
Winsorized Mean ( 11 / 24 )27647.65277777781043.9211944186126.484425189945
Winsorized Mean ( 12 / 24 )27622.65277777781022.3974630451727.0175286776482
Winsorized Mean ( 13 / 24 )27673.38888888891014.0877893097127.2889479398289
Winsorized Mean ( 14 / 24 )27601.25998.65285467916327.63848305312
Winsorized Mean ( 15 / 24 )27547.9166666667986.88140858599427.9141104766959
Winsorized Mean ( 16 / 24 )27490.8055555556970.46008453738928.3276004789627
Winsorized Mean ( 17 / 24 )26713.2916666667805.07153728092233.1812645580405
Winsorized Mean ( 18 / 24 )26439.2916666667763.90206236862734.6108394899295
Winsorized Mean ( 19 / 24 )26438.7638888889749.4062029891835.2796170934158
Winsorized Mean ( 20 / 24 )26485.4305555556737.05595815808635.9340837861796
Winsorized Mean ( 21 / 24 )26182.0972222222694.76168501654437.6850044941652
Winsorized Mean ( 22 / 24 )26319.2916666667676.06767222853638.9299662560551
Winsorized Mean ( 23 / 24 )26296.9305555556669.67285601777739.2683238080318
Winsorized Mean ( 24 / 24 )26436.2638888889628.84858669592242.0391560833261
Trimmed Mean ( 1 / 24 )27556.48571428571109.8273838033124.8295240471103
Trimmed Mean ( 2 / 24 )27501.30882352941104.597523677324.8971306145746
Trimmed Mean ( 3 / 24 )27442.1969696971097.987825693224.9931705320791
Trimmed Mean ( 4 / 24 )27392.343751092.4062405779925.0752355053434
Trimmed Mean ( 5 / 24 )27337.54838709681085.8333294736325.1765603845933
Trimmed Mean ( 6 / 24 )27288.151079.1619310128825.2864275654978
Trimmed Mean ( 7 / 24 )27233.2241379311071.3099494966725.4204902612226
Trimmed Mean ( 8 / 24 )27175.10714285711062.2969241158925.5814608194163
Trimmed Mean ( 9 / 24 )27113.92592592591051.2825307049425.7912836311897
Trimmed Mean ( 10 / 24 )27038.34615384621039.3443162668126.0148111945851
Trimmed Mean ( 11 / 24 )26945.921026.6047256498126.2476095489858
Trimmed Mean ( 12 / 24 )26850.22916666671011.1795738302626.553373764227
Trimmed Mean ( 13 / 24 )26749.4782608696995.0622322873926.8822164010581
Trimmed Mean ( 14 / 24 )26633.1818181818974.72259092131227.3238581584613
Trimmed Mean ( 15 / 24 )26514.6428571429950.69713269796227.8896842592736
Trimmed Mean ( 16 / 24 )26390.65920.73308971710128.6626496807111
Trimmed Mean ( 17 / 24 )26260.3684210526883.76793828215729.7140994638217
Trimmed Mean ( 18 / 24 )26207.0833333333875.99232834848329.9170237971625
Trimmed Mean ( 19 / 24 )26179.7647058824872.75251473514129.9967794579512
Trimmed Mean ( 20 / 24 )26149.09375868.47644841432130.1091570159945
Trimmed Mean ( 21 / 24 )26108.7333333333861.91247379906430.2916295180803
Trimmed Mean ( 22 / 24 )26099.75860.33387856449130.3367688408932
Trimmed Mean ( 23 / 24 )26072.1153846154858.10475840105530.3833711785921
Trimmed Mean ( 24 / 24 )26042.7916666667850.80824739629830.6094725178847
Median25090.5
Midrange29592
Midmean - Weighted Average at Xnp26017.1081081081
Midmean - Weighted Average at X(n+1)p26207.0833333333
Midmean - Empirical Distribution Function26017.1081081081
Midmean - Empirical Distribution Function - Averaging26207.0833333333
Midmean - Empirical Distribution Function - Interpolation26207.0833333333
Midmean - Closest Observation26017.1081081081
Midmean - True Basic - Statistics Graphics Toolkit26207.0833333333
Midmean - MS Excel (old versions)26260.3684210526
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 27613.0277777778 & 1114.52715644875 & 24.7755540257645 \tabularnewline
Geometric Mean & 26042.1647044531 &  &  \tabularnewline
Harmonic Mean & 24579.5324210149 &  &  \tabularnewline
Quadratic Mean & 29166.306393013 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 27608.5972222222 & 1113.56725541814 & 24.7929319831296 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 27609.6805555556 & 1112.91806774755 & 24.808367619941 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 27575.1388888889 & 1105.82269955113 & 24.9363111284314 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 27581.0833333333 & 1102.90447474776 & 25.0076810502028 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 27543.375 & 1095.73135683556 & 25.1369779902479 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 27553.625 & 1091.16447134967 & 25.2515782207597 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 27549.6388888889 & 1084.82686868358 & 25.3954245457802 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 27542.1944444444 & 1080.25539270755 & 25.4960027326619 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 27605.1944444444 & 1067.6952020402 & 25.8549391171706 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 27680.1944444444 & 1052.02653970055 & 26.311308127572 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 27647.6527777778 & 1043.92119441861 & 26.484425189945 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 27622.6527777778 & 1022.39746304517 & 27.0175286776482 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 27673.3888888889 & 1014.08778930971 & 27.2889479398289 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 27601.25 & 998.652854679163 & 27.63848305312 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 27547.9166666667 & 986.881408585994 & 27.9141104766959 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 27490.8055555556 & 970.460084537389 & 28.3276004789627 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 26713.2916666667 & 805.071537280922 & 33.1812645580405 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 26439.2916666667 & 763.902062368627 & 34.6108394899295 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 26438.7638888889 & 749.40620298918 & 35.2796170934158 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 26485.4305555556 & 737.055958158086 & 35.9340837861796 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 26182.0972222222 & 694.761685016544 & 37.6850044941652 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 26319.2916666667 & 676.067672228536 & 38.9299662560551 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 26296.9305555556 & 669.672856017777 & 39.2683238080318 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 26436.2638888889 & 628.848586695922 & 42.0391560833261 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 27556.4857142857 & 1109.82738380331 & 24.8295240471103 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 27501.3088235294 & 1104.5975236773 & 24.8971306145746 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 27442.196969697 & 1097.9878256932 & 24.9931705320791 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 27392.34375 & 1092.40624057799 & 25.0752355053434 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 27337.5483870968 & 1085.83332947363 & 25.1765603845933 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 27288.15 & 1079.16193101288 & 25.2864275654978 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 27233.224137931 & 1071.30994949667 & 25.4204902612226 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 27175.1071428571 & 1062.29692411589 & 25.5814608194163 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 27113.9259259259 & 1051.28253070494 & 25.7912836311897 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 27038.3461538462 & 1039.34431626681 & 26.0148111945851 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 26945.92 & 1026.60472564981 & 26.2476095489858 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 26850.2291666667 & 1011.17957383026 & 26.553373764227 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 26749.4782608696 & 995.06223228739 & 26.8822164010581 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 26633.1818181818 & 974.722590921312 & 27.3238581584613 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 26514.6428571429 & 950.697132697962 & 27.8896842592736 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 26390.65 & 920.733089717101 & 28.6626496807111 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 26260.3684210526 & 883.767938282157 & 29.7140994638217 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 26207.0833333333 & 875.992328348483 & 29.9170237971625 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 26179.7647058824 & 872.752514735141 & 29.9967794579512 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 26149.09375 & 868.476448414321 & 30.1091570159945 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 26108.7333333333 & 861.912473799064 & 30.2916295180803 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 26099.75 & 860.333878564491 & 30.3367688408932 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 26072.1153846154 & 858.104758401055 & 30.3833711785921 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 26042.7916666667 & 850.808247396298 & 30.6094725178847 \tabularnewline
Median & 25090.5 &  &  \tabularnewline
Midrange & 29592 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 26017.1081081081 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 26207.0833333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 26017.1081081081 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 26207.0833333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 26207.0833333333 &  &  \tabularnewline
Midmean - Closest Observation & 26017.1081081081 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 26207.0833333333 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 26260.3684210526 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=214655&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]27613.0277777778[/C][C]1114.52715644875[/C][C]24.7755540257645[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]26042.1647044531[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]24579.5324210149[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]29166.306393013[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]27608.5972222222[/C][C]1113.56725541814[/C][C]24.7929319831296[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]27609.6805555556[/C][C]1112.91806774755[/C][C]24.808367619941[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]27575.1388888889[/C][C]1105.82269955113[/C][C]24.9363111284314[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]27581.0833333333[/C][C]1102.90447474776[/C][C]25.0076810502028[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]27543.375[/C][C]1095.73135683556[/C][C]25.1369779902479[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]27553.625[/C][C]1091.16447134967[/C][C]25.2515782207597[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]27549.6388888889[/C][C]1084.82686868358[/C][C]25.3954245457802[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]27542.1944444444[/C][C]1080.25539270755[/C][C]25.4960027326619[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]27605.1944444444[/C][C]1067.6952020402[/C][C]25.8549391171706[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]27680.1944444444[/C][C]1052.02653970055[/C][C]26.311308127572[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]27647.6527777778[/C][C]1043.92119441861[/C][C]26.484425189945[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]27622.6527777778[/C][C]1022.39746304517[/C][C]27.0175286776482[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]27673.3888888889[/C][C]1014.08778930971[/C][C]27.2889479398289[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]27601.25[/C][C]998.652854679163[/C][C]27.63848305312[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]27547.9166666667[/C][C]986.881408585994[/C][C]27.9141104766959[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]27490.8055555556[/C][C]970.460084537389[/C][C]28.3276004789627[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]26713.2916666667[/C][C]805.071537280922[/C][C]33.1812645580405[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]26439.2916666667[/C][C]763.902062368627[/C][C]34.6108394899295[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]26438.7638888889[/C][C]749.40620298918[/C][C]35.2796170934158[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]26485.4305555556[/C][C]737.055958158086[/C][C]35.9340837861796[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]26182.0972222222[/C][C]694.761685016544[/C][C]37.6850044941652[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]26319.2916666667[/C][C]676.067672228536[/C][C]38.9299662560551[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]26296.9305555556[/C][C]669.672856017777[/C][C]39.2683238080318[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]26436.2638888889[/C][C]628.848586695922[/C][C]42.0391560833261[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]27556.4857142857[/C][C]1109.82738380331[/C][C]24.8295240471103[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]27501.3088235294[/C][C]1104.5975236773[/C][C]24.8971306145746[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]27442.196969697[/C][C]1097.9878256932[/C][C]24.9931705320791[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]27392.34375[/C][C]1092.40624057799[/C][C]25.0752355053434[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]27337.5483870968[/C][C]1085.83332947363[/C][C]25.1765603845933[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]27288.15[/C][C]1079.16193101288[/C][C]25.2864275654978[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]27233.224137931[/C][C]1071.30994949667[/C][C]25.4204902612226[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]27175.1071428571[/C][C]1062.29692411589[/C][C]25.5814608194163[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]27113.9259259259[/C][C]1051.28253070494[/C][C]25.7912836311897[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]27038.3461538462[/C][C]1039.34431626681[/C][C]26.0148111945851[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]26945.92[/C][C]1026.60472564981[/C][C]26.2476095489858[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]26850.2291666667[/C][C]1011.17957383026[/C][C]26.553373764227[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]26749.4782608696[/C][C]995.06223228739[/C][C]26.8822164010581[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]26633.1818181818[/C][C]974.722590921312[/C][C]27.3238581584613[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]26514.6428571429[/C][C]950.697132697962[/C][C]27.8896842592736[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]26390.65[/C][C]920.733089717101[/C][C]28.6626496807111[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]26260.3684210526[/C][C]883.767938282157[/C][C]29.7140994638217[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]26207.0833333333[/C][C]875.992328348483[/C][C]29.9170237971625[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]26179.7647058824[/C][C]872.752514735141[/C][C]29.9967794579512[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]26149.09375[/C][C]868.476448414321[/C][C]30.1091570159945[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]26108.7333333333[/C][C]861.912473799064[/C][C]30.2916295180803[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]26099.75[/C][C]860.333878564491[/C][C]30.3367688408932[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]26072.1153846154[/C][C]858.104758401055[/C][C]30.3833711785921[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]26042.7916666667[/C][C]850.808247396298[/C][C]30.6094725178847[/C][/ROW]
[ROW][C]Median[/C][C]25090.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]29592[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]26017.1081081081[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]26207.0833333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]26017.1081081081[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]26207.0833333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]26207.0833333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]26017.1081081081[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]26207.0833333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]26260.3684210526[/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=214655&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=214655&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 Mean27613.02777777781114.5271564487524.7755540257645
Geometric Mean26042.1647044531
Harmonic Mean24579.5324210149
Quadratic Mean29166.306393013
Winsorized Mean ( 1 / 24 )27608.59722222221113.5672554181424.7929319831296
Winsorized Mean ( 2 / 24 )27609.68055555561112.9180677475524.808367619941
Winsorized Mean ( 3 / 24 )27575.13888888891105.8226995511324.9363111284314
Winsorized Mean ( 4 / 24 )27581.08333333331102.9044747477625.0076810502028
Winsorized Mean ( 5 / 24 )27543.3751095.7313568355625.1369779902479
Winsorized Mean ( 6 / 24 )27553.6251091.1644713496725.2515782207597
Winsorized Mean ( 7 / 24 )27549.63888888891084.8268686835825.3954245457802
Winsorized Mean ( 8 / 24 )27542.19444444441080.2553927075525.4960027326619
Winsorized Mean ( 9 / 24 )27605.19444444441067.695202040225.8549391171706
Winsorized Mean ( 10 / 24 )27680.19444444441052.0265397005526.311308127572
Winsorized Mean ( 11 / 24 )27647.65277777781043.9211944186126.484425189945
Winsorized Mean ( 12 / 24 )27622.65277777781022.3974630451727.0175286776482
Winsorized Mean ( 13 / 24 )27673.38888888891014.0877893097127.2889479398289
Winsorized Mean ( 14 / 24 )27601.25998.65285467916327.63848305312
Winsorized Mean ( 15 / 24 )27547.9166666667986.88140858599427.9141104766959
Winsorized Mean ( 16 / 24 )27490.8055555556970.46008453738928.3276004789627
Winsorized Mean ( 17 / 24 )26713.2916666667805.07153728092233.1812645580405
Winsorized Mean ( 18 / 24 )26439.2916666667763.90206236862734.6108394899295
Winsorized Mean ( 19 / 24 )26438.7638888889749.4062029891835.2796170934158
Winsorized Mean ( 20 / 24 )26485.4305555556737.05595815808635.9340837861796
Winsorized Mean ( 21 / 24 )26182.0972222222694.76168501654437.6850044941652
Winsorized Mean ( 22 / 24 )26319.2916666667676.06767222853638.9299662560551
Winsorized Mean ( 23 / 24 )26296.9305555556669.67285601777739.2683238080318
Winsorized Mean ( 24 / 24 )26436.2638888889628.84858669592242.0391560833261
Trimmed Mean ( 1 / 24 )27556.48571428571109.8273838033124.8295240471103
Trimmed Mean ( 2 / 24 )27501.30882352941104.597523677324.8971306145746
Trimmed Mean ( 3 / 24 )27442.1969696971097.987825693224.9931705320791
Trimmed Mean ( 4 / 24 )27392.343751092.4062405779925.0752355053434
Trimmed Mean ( 5 / 24 )27337.54838709681085.8333294736325.1765603845933
Trimmed Mean ( 6 / 24 )27288.151079.1619310128825.2864275654978
Trimmed Mean ( 7 / 24 )27233.2241379311071.3099494966725.4204902612226
Trimmed Mean ( 8 / 24 )27175.10714285711062.2969241158925.5814608194163
Trimmed Mean ( 9 / 24 )27113.92592592591051.2825307049425.7912836311897
Trimmed Mean ( 10 / 24 )27038.34615384621039.3443162668126.0148111945851
Trimmed Mean ( 11 / 24 )26945.921026.6047256498126.2476095489858
Trimmed Mean ( 12 / 24 )26850.22916666671011.1795738302626.553373764227
Trimmed Mean ( 13 / 24 )26749.4782608696995.0622322873926.8822164010581
Trimmed Mean ( 14 / 24 )26633.1818181818974.72259092131227.3238581584613
Trimmed Mean ( 15 / 24 )26514.6428571429950.69713269796227.8896842592736
Trimmed Mean ( 16 / 24 )26390.65920.73308971710128.6626496807111
Trimmed Mean ( 17 / 24 )26260.3684210526883.76793828215729.7140994638217
Trimmed Mean ( 18 / 24 )26207.0833333333875.99232834848329.9170237971625
Trimmed Mean ( 19 / 24 )26179.7647058824872.75251473514129.9967794579512
Trimmed Mean ( 20 / 24 )26149.09375868.47644841432130.1091570159945
Trimmed Mean ( 21 / 24 )26108.7333333333861.91247379906430.2916295180803
Trimmed Mean ( 22 / 24 )26099.75860.33387856449130.3367688408932
Trimmed Mean ( 23 / 24 )26072.1153846154858.10475840105530.3833711785921
Trimmed Mean ( 24 / 24 )26042.7916666667850.80824739629830.6094725178847
Median25090.5
Midrange29592
Midmean - Weighted Average at Xnp26017.1081081081
Midmean - Weighted Average at X(n+1)p26207.0833333333
Midmean - Empirical Distribution Function26017.1081081081
Midmean - Empirical Distribution Function - Averaging26207.0833333333
Midmean - Empirical Distribution Function - Interpolation26207.0833333333
Midmean - Closest Observation26017.1081081081
Midmean - True Basic - Statistics Graphics Toolkit26207.0833333333
Midmean - MS Excel (old versions)26260.3684210526
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')