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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationTue, 18 Oct 2011 15:43:13 -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/2011/Oct/18/t1318967116oe6h94a0o2ttjx6.htm/, Retrieved Thu, 16 May 2024 05:36:19 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=132561, Retrieved Thu, 16 May 2024 05:36:19 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDG2011W52a
Estimated Impact56
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2011-10-18 19:43:13] [d06e8713ea83045a022ab0926c74dd0b] [Current]
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Dataseries X:
14097,80
14776,80
16833,30
15385,50
15172,60
16858,90
14143,50
14731,80
16471,60
15214,00
17637,40
17972,40
16896,20
16698,00
19691,60
15930,70
17444,60
17699,40
15189,80
15672,70
17180,80
17664,90
17862,90
16162,30
17463,60
16772,10
19106,90
16721,30
18161,30
18509,90
17802,70
16409,90
17967,70
20286,60
19537,30
18021,90
20194,30
19049,60
20244,70
21473,30
19673,60
21053,20
20159,50
18203,60
21289,50
20432,30
17180,40
15816,80
15076,60
14531,60
15761,30
14345,50
13916,80
15496,80
14285,60
13597,30
16263,10
16773,30
15986,90
16842,60
15911,90
15782,90
18622,80
17422,50
16989,80
18990,50
16849,30
16511,30
18704,50
19111,10
19420,70
18985,10




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' @ yule.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 & 2 seconds \tabularnewline
R Server & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=132561&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' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=132561&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=132561&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' @ yule.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean17237.5180555556228.68515009276775.376639228927
Geometric Mean17130.3847949517
Harmonic Mean17023.969676801
Quadratic Mean17344.8870986404
Winsorized Mean ( 1 / 24 )17239.4027777778227.07665217351775.918869741855
Winsorized Mean ( 2 / 24 )17237.8666666667224.45268472435176.7995566096098
Winsorized Mean ( 3 / 24 )17213.9218.28767809220478.85878007612
Winsorized Mean ( 4 / 24 )17213.7215.09368530602980.0288487107786
Winsorized Mean ( 5 / 24 )17214.95213.71834241035480.5497076472086
Winsorized Mean ( 6 / 24 )17226.2583333333210.01280477160482.024800116676
Winsorized Mean ( 7 / 24 )17242.3388888889205.90770757728483.7381907251689
Winsorized Mean ( 8 / 24 )17195.35195.15880834181288.10952549927
Winsorized Mean ( 9 / 24 )17230.575188.45948682902891.4285361268742
Winsorized Mean ( 10 / 24 )17224.9777777778182.91841412345394.1675438217637
Winsorized Mean ( 11 / 24 )17209.7916666667179.3698584105595.9458396141236
Winsorized Mean ( 12 / 24 )17162.225170.073381551848100.910705975279
Winsorized Mean ( 13 / 24 )17192.4319444444165.063480459732104.156485108398
Winsorized Mean ( 14 / 24 )17202.9319444444159.952842997206107.550023007374
Winsorized Mean ( 15 / 24 )17227.2652777778152.564502908027112.917913075516
Winsorized Mean ( 16 / 24 )17245.7541666667149.579355877619115.295015582074
Winsorized Mean ( 17 / 24 )17184.6013888889138.294412004247124.260996086821
Winsorized Mean ( 18 / 24 )17172.6513888889133.946908627854128.204910175268
Winsorized Mean ( 19 / 24 )17167.9541666667125.884644606875136.378461569164
Winsorized Mean ( 20 / 24 )17088.0930555556112.803030034665151.48611744121
Winsorized Mean ( 21 / 24 )17092.1472222222108.731449121495157.19598478931
Winsorized Mean ( 22 / 24 )17103.147222222295.3175908727335179.433272133977
Winsorized Mean ( 23 / 24 )17119.534722222288.7455829569288192.905766707633
Winsorized Mean ( 24 / 24 )17166.901388888982.0201560567986209.301008608188
Trimmed Mean ( 1 / 24 )17229.01221.1131441084377.9194293015487
Trimmed Mean ( 2 / 24 )17218.0058823529214.01564808348380.4520886044583
Trimmed Mean ( 3 / 24 )17207.1727272727207.22663411345783.0355267839351
Trimmed Mean ( 4 / 24 )17204.65201.94798014961285.1934740186758
Trimmed Mean ( 5 / 24 )17202.0225806452196.75937894185187.4266968779613
Trimmed Mean ( 6 / 24 )17198.92190.89376531801290.0968136457896
Trimmed Mean ( 7 / 24 )17193.2637931034184.80575307173493.0342454567946
Trimmed Mean ( 8 / 24 )17184.25178.42061137922196.3131437963522
Trimmed Mean ( 9 / 24 )17182.4173.31161422546699.1416534707647
Trimmed Mean ( 10 / 24 )17174.9884615385168.529176541647101.911068540076
Trimmed Mean ( 11 / 24 )17167.79163.793870938881104.813384662031
Trimmed Mean ( 12 / 24 )17162.0625158.589801999038108.216684072184
Trimmed Mean ( 13 / 24 )17162.0413043478154.085021971327111.380334602162
Trimmed Mean ( 14 / 24 )17158.2159090909149.359314154016114.878780786297
Trimmed Mean ( 15 / 24 )17152.7404761905144.323942719282118.848890579115
Trimmed Mean ( 16 / 24 )17143.7975139.36014175084123.017939596037
Trimmed Mean ( 17 / 24 )17131.7236842105133.318287924889128.502427917935
Trimmed Mean ( 18 / 24 )17125.5027777778128.160275986943133.62567024686
Trimmed Mean ( 19 / 24 )17119.9558823529122.146295149454140.159436366085
Trimmed Mean ( 20 / 24 )17114.271875115.99649529209147.541284173325
Trimmed Mean ( 21 / 24 )17117.4133333333111.209501034338153.920422033437
Trimmed Mean ( 22 / 24 )17120.5071428571105.357437960308162.499273656475
Trimmed Mean ( 23 / 24 )17122.6923076923101.230500712761169.145585442451
Trimmed Mean ( 24 / 24 )17123.104166666797.0585800027166176.420303760754
Median16943
Midrange17535.3
Midmean - Weighted Average at Xnp17089.2162162162
Midmean - Weighted Average at X(n+1)p17125.5027777778
Midmean - Empirical Distribution Function17089.2162162162
Midmean - Empirical Distribution Function - Averaging17125.5027777778
Midmean - Empirical Distribution Function - Interpolation17125.5027777778
Midmean - Closest Observation17089.2162162162
Midmean - True Basic - Statistics Graphics Toolkit17125.5027777778
Midmean - MS Excel (old versions)17131.7236842105
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 17237.5180555556 & 228.685150092767 & 75.376639228927 \tabularnewline
Geometric Mean & 17130.3847949517 &  &  \tabularnewline
Harmonic Mean & 17023.969676801 &  &  \tabularnewline
Quadratic Mean & 17344.8870986404 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 17239.4027777778 & 227.076652173517 & 75.918869741855 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 17237.8666666667 & 224.452684724351 & 76.7995566096098 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 17213.9 & 218.287678092204 & 78.85878007612 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 17213.7 & 215.093685306029 & 80.0288487107786 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 17214.95 & 213.718342410354 & 80.5497076472086 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 17226.2583333333 & 210.012804771604 & 82.024800116676 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 17242.3388888889 & 205.907707577284 & 83.7381907251689 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 17195.35 & 195.158808341812 & 88.10952549927 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 17230.575 & 188.459486829028 & 91.4285361268742 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 17224.9777777778 & 182.918414123453 & 94.1675438217637 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 17209.7916666667 & 179.36985841055 & 95.9458396141236 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 17162.225 & 170.073381551848 & 100.910705975279 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 17192.4319444444 & 165.063480459732 & 104.156485108398 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 17202.9319444444 & 159.952842997206 & 107.550023007374 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 17227.2652777778 & 152.564502908027 & 112.917913075516 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 17245.7541666667 & 149.579355877619 & 115.295015582074 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 17184.6013888889 & 138.294412004247 & 124.260996086821 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 17172.6513888889 & 133.946908627854 & 128.204910175268 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 17167.9541666667 & 125.884644606875 & 136.378461569164 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 17088.0930555556 & 112.803030034665 & 151.48611744121 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 17092.1472222222 & 108.731449121495 & 157.19598478931 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 17103.1472222222 & 95.3175908727335 & 179.433272133977 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 17119.5347222222 & 88.7455829569288 & 192.905766707633 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 17166.9013888889 & 82.0201560567986 & 209.301008608188 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 17229.01 & 221.11314410843 & 77.9194293015487 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 17218.0058823529 & 214.015648083483 & 80.4520886044583 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 17207.1727272727 & 207.226634113457 & 83.0355267839351 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 17204.65 & 201.947980149612 & 85.1934740186758 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 17202.0225806452 & 196.759378941851 & 87.4266968779613 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 17198.92 & 190.893765318012 & 90.0968136457896 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 17193.2637931034 & 184.805753071734 & 93.0342454567946 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 17184.25 & 178.420611379221 & 96.3131437963522 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 17182.4 & 173.311614225466 & 99.1416534707647 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 17174.9884615385 & 168.529176541647 & 101.911068540076 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 17167.79 & 163.793870938881 & 104.813384662031 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 17162.0625 & 158.589801999038 & 108.216684072184 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 17162.0413043478 & 154.085021971327 & 111.380334602162 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 17158.2159090909 & 149.359314154016 & 114.878780786297 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 17152.7404761905 & 144.323942719282 & 118.848890579115 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 17143.7975 & 139.36014175084 & 123.017939596037 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 17131.7236842105 & 133.318287924889 & 128.502427917935 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 17125.5027777778 & 128.160275986943 & 133.62567024686 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 17119.9558823529 & 122.146295149454 & 140.159436366085 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 17114.271875 & 115.99649529209 & 147.541284173325 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 17117.4133333333 & 111.209501034338 & 153.920422033437 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 17120.5071428571 & 105.357437960308 & 162.499273656475 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 17122.6923076923 & 101.230500712761 & 169.145585442451 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 17123.1041666667 & 97.0585800027166 & 176.420303760754 \tabularnewline
Median & 16943 &  &  \tabularnewline
Midrange & 17535.3 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 17089.2162162162 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 17125.5027777778 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 17089.2162162162 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 17125.5027777778 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 17125.5027777778 &  &  \tabularnewline
Midmean - Closest Observation & 17089.2162162162 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 17125.5027777778 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 17131.7236842105 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=132561&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]17237.5180555556[/C][C]228.685150092767[/C][C]75.376639228927[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]17130.3847949517[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]17023.969676801[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]17344.8870986404[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]17239.4027777778[/C][C]227.076652173517[/C][C]75.918869741855[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]17237.8666666667[/C][C]224.452684724351[/C][C]76.7995566096098[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]17213.9[/C][C]218.287678092204[/C][C]78.85878007612[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]17213.7[/C][C]215.093685306029[/C][C]80.0288487107786[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]17214.95[/C][C]213.718342410354[/C][C]80.5497076472086[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]17226.2583333333[/C][C]210.012804771604[/C][C]82.024800116676[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]17242.3388888889[/C][C]205.907707577284[/C][C]83.7381907251689[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]17195.35[/C][C]195.158808341812[/C][C]88.10952549927[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]17230.575[/C][C]188.459486829028[/C][C]91.4285361268742[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]17224.9777777778[/C][C]182.918414123453[/C][C]94.1675438217637[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]17209.7916666667[/C][C]179.36985841055[/C][C]95.9458396141236[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]17162.225[/C][C]170.073381551848[/C][C]100.910705975279[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]17192.4319444444[/C][C]165.063480459732[/C][C]104.156485108398[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]17202.9319444444[/C][C]159.952842997206[/C][C]107.550023007374[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]17227.2652777778[/C][C]152.564502908027[/C][C]112.917913075516[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]17245.7541666667[/C][C]149.579355877619[/C][C]115.295015582074[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]17184.6013888889[/C][C]138.294412004247[/C][C]124.260996086821[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]17172.6513888889[/C][C]133.946908627854[/C][C]128.204910175268[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]17167.9541666667[/C][C]125.884644606875[/C][C]136.378461569164[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]17088.0930555556[/C][C]112.803030034665[/C][C]151.48611744121[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]17092.1472222222[/C][C]108.731449121495[/C][C]157.19598478931[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]17103.1472222222[/C][C]95.3175908727335[/C][C]179.433272133977[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]17119.5347222222[/C][C]88.7455829569288[/C][C]192.905766707633[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]17166.9013888889[/C][C]82.0201560567986[/C][C]209.301008608188[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]17229.01[/C][C]221.11314410843[/C][C]77.9194293015487[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]17218.0058823529[/C][C]214.015648083483[/C][C]80.4520886044583[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]17207.1727272727[/C][C]207.226634113457[/C][C]83.0355267839351[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]17204.65[/C][C]201.947980149612[/C][C]85.1934740186758[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]17202.0225806452[/C][C]196.759378941851[/C][C]87.4266968779613[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]17198.92[/C][C]190.893765318012[/C][C]90.0968136457896[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]17193.2637931034[/C][C]184.805753071734[/C][C]93.0342454567946[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]17184.25[/C][C]178.420611379221[/C][C]96.3131437963522[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]17182.4[/C][C]173.311614225466[/C][C]99.1416534707647[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]17174.9884615385[/C][C]168.529176541647[/C][C]101.911068540076[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]17167.79[/C][C]163.793870938881[/C][C]104.813384662031[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]17162.0625[/C][C]158.589801999038[/C][C]108.216684072184[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]17162.0413043478[/C][C]154.085021971327[/C][C]111.380334602162[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]17158.2159090909[/C][C]149.359314154016[/C][C]114.878780786297[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]17152.7404761905[/C][C]144.323942719282[/C][C]118.848890579115[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]17143.7975[/C][C]139.36014175084[/C][C]123.017939596037[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]17131.7236842105[/C][C]133.318287924889[/C][C]128.502427917935[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]17125.5027777778[/C][C]128.160275986943[/C][C]133.62567024686[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]17119.9558823529[/C][C]122.146295149454[/C][C]140.159436366085[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]17114.271875[/C][C]115.99649529209[/C][C]147.541284173325[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]17117.4133333333[/C][C]111.209501034338[/C][C]153.920422033437[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]17120.5071428571[/C][C]105.357437960308[/C][C]162.499273656475[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]17122.6923076923[/C][C]101.230500712761[/C][C]169.145585442451[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]17123.1041666667[/C][C]97.0585800027166[/C][C]176.420303760754[/C][/ROW]
[ROW][C]Median[/C][C]16943[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]17535.3[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]17089.2162162162[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]17125.5027777778[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]17089.2162162162[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]17125.5027777778[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]17125.5027777778[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]17089.2162162162[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]17125.5027777778[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]17131.7236842105[/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=132561&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=132561&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 Mean17237.5180555556228.68515009276775.376639228927
Geometric Mean17130.3847949517
Harmonic Mean17023.969676801
Quadratic Mean17344.8870986404
Winsorized Mean ( 1 / 24 )17239.4027777778227.07665217351775.918869741855
Winsorized Mean ( 2 / 24 )17237.8666666667224.45268472435176.7995566096098
Winsorized Mean ( 3 / 24 )17213.9218.28767809220478.85878007612
Winsorized Mean ( 4 / 24 )17213.7215.09368530602980.0288487107786
Winsorized Mean ( 5 / 24 )17214.95213.71834241035480.5497076472086
Winsorized Mean ( 6 / 24 )17226.2583333333210.01280477160482.024800116676
Winsorized Mean ( 7 / 24 )17242.3388888889205.90770757728483.7381907251689
Winsorized Mean ( 8 / 24 )17195.35195.15880834181288.10952549927
Winsorized Mean ( 9 / 24 )17230.575188.45948682902891.4285361268742
Winsorized Mean ( 10 / 24 )17224.9777777778182.91841412345394.1675438217637
Winsorized Mean ( 11 / 24 )17209.7916666667179.3698584105595.9458396141236
Winsorized Mean ( 12 / 24 )17162.225170.073381551848100.910705975279
Winsorized Mean ( 13 / 24 )17192.4319444444165.063480459732104.156485108398
Winsorized Mean ( 14 / 24 )17202.9319444444159.952842997206107.550023007374
Winsorized Mean ( 15 / 24 )17227.2652777778152.564502908027112.917913075516
Winsorized Mean ( 16 / 24 )17245.7541666667149.579355877619115.295015582074
Winsorized Mean ( 17 / 24 )17184.6013888889138.294412004247124.260996086821
Winsorized Mean ( 18 / 24 )17172.6513888889133.946908627854128.204910175268
Winsorized Mean ( 19 / 24 )17167.9541666667125.884644606875136.378461569164
Winsorized Mean ( 20 / 24 )17088.0930555556112.803030034665151.48611744121
Winsorized Mean ( 21 / 24 )17092.1472222222108.731449121495157.19598478931
Winsorized Mean ( 22 / 24 )17103.147222222295.3175908727335179.433272133977
Winsorized Mean ( 23 / 24 )17119.534722222288.7455829569288192.905766707633
Winsorized Mean ( 24 / 24 )17166.901388888982.0201560567986209.301008608188
Trimmed Mean ( 1 / 24 )17229.01221.1131441084377.9194293015487
Trimmed Mean ( 2 / 24 )17218.0058823529214.01564808348380.4520886044583
Trimmed Mean ( 3 / 24 )17207.1727272727207.22663411345783.0355267839351
Trimmed Mean ( 4 / 24 )17204.65201.94798014961285.1934740186758
Trimmed Mean ( 5 / 24 )17202.0225806452196.75937894185187.4266968779613
Trimmed Mean ( 6 / 24 )17198.92190.89376531801290.0968136457896
Trimmed Mean ( 7 / 24 )17193.2637931034184.80575307173493.0342454567946
Trimmed Mean ( 8 / 24 )17184.25178.42061137922196.3131437963522
Trimmed Mean ( 9 / 24 )17182.4173.31161422546699.1416534707647
Trimmed Mean ( 10 / 24 )17174.9884615385168.529176541647101.911068540076
Trimmed Mean ( 11 / 24 )17167.79163.793870938881104.813384662031
Trimmed Mean ( 12 / 24 )17162.0625158.589801999038108.216684072184
Trimmed Mean ( 13 / 24 )17162.0413043478154.085021971327111.380334602162
Trimmed Mean ( 14 / 24 )17158.2159090909149.359314154016114.878780786297
Trimmed Mean ( 15 / 24 )17152.7404761905144.323942719282118.848890579115
Trimmed Mean ( 16 / 24 )17143.7975139.36014175084123.017939596037
Trimmed Mean ( 17 / 24 )17131.7236842105133.318287924889128.502427917935
Trimmed Mean ( 18 / 24 )17125.5027777778128.160275986943133.62567024686
Trimmed Mean ( 19 / 24 )17119.9558823529122.146295149454140.159436366085
Trimmed Mean ( 20 / 24 )17114.271875115.99649529209147.541284173325
Trimmed Mean ( 21 / 24 )17117.4133333333111.209501034338153.920422033437
Trimmed Mean ( 22 / 24 )17120.5071428571105.357437960308162.499273656475
Trimmed Mean ( 23 / 24 )17122.6923076923101.230500712761169.145585442451
Trimmed Mean ( 24 / 24 )17123.104166666797.0585800027166176.420303760754
Median16943
Midrange17535.3
Midmean - Weighted Average at Xnp17089.2162162162
Midmean - Weighted Average at X(n+1)p17125.5027777778
Midmean - Empirical Distribution Function17089.2162162162
Midmean - Empirical Distribution Function - Averaging17125.5027777778
Midmean - Empirical Distribution Function - Interpolation17125.5027777778
Midmean - Closest Observation17089.2162162162
Midmean - True Basic - Statistics Graphics Toolkit17125.5027777778
Midmean - MS Excel (old versions)17131.7236842105
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')