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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 computationFri, 10 Oct 2014 11:56:14 +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/10/t1412938875mfv43hynp0g0vah.htm/, Retrieved Sun, 12 May 2024 16:51:38 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=240260, Retrieved Sun, 12 May 2024 16:51:38 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact98
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2014-10-10 10:56:14] [56e8cb9ede54fa5ca6b1344bd59af70d] [Current]
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Dataseries X:
11798
8378
8131
7676
7505
8168
6455
6141
6554
6888
5339
1624
9187
5047
5289
4169
3862
4253
3768
3066
4108
3890
3420
1221
5984
4064
5151
4027
3530
4819
3855
3584
4322
4154
4656
1464
7780
5060
6084
4778
4989
4903
4142
4101
4595
5034
5407
1782
8395
5291
6116
4210
4621
5299
4293
4542
3831
4360
4088
1508
6743
4159
5105
4283
4019
4206
3948
3407
3701
4159
4208
2622




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Sir Maurice George Kendall' @ kendall.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 & 'Sir Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=240260&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]'Sir Maurice George Kendall' @ kendall.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=240260&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=240260&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'Sir Maurice George Kendall' @ kendall.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean4879.38888888889219.23915379188522.2560104091658
Geometric Mean4523.14936883401
Harmonic Mean4109.95906878058
Quadratic Mean5217.38518747125
Winsorized Mean ( 1 / 24 )4846.5204.89124944749723.654011643098
Winsorized Mean ( 2 / 24 )4825.72222222222198.53001474237624.3072677372454
Winsorized Mean ( 3 / 24 )4829.84722222222197.22846338264524.4885912478656
Winsorized Mean ( 4 / 24 )4826.95833333333192.33888898240125.096112174044
Winsorized Mean ( 5 / 24 )4882.72222222222179.99071574715527.1276337890745
Winsorized Mean ( 6 / 24 )4890.47222222222166.55074486507229.3632563828168
Winsorized Mean ( 7 / 24 )4913.51388888889159.30748507733430.8429568548125
Winsorized Mean ( 8 / 24 )4895.95833333333154.53396853932131.6820850432478
Winsorized Mean ( 9 / 24 )4832.58333333333135.18801570110435.7471282367071
Winsorized Mean ( 10 / 24 )4819.94444444444129.91984541231437.0993702243706
Winsorized Mean ( 11 / 24 )4808.94444444444121.64408255389639.5329089872808
Winsorized Mean ( 12 / 24 )4803.61111111111116.92235153870741.0837709633378
Winsorized Mean ( 13 / 24 )4758.29166666667104.56380901400145.5061049471672
Winsorized Mean ( 14 / 24 )4758.09722222222103.08076083817746.1589261035026
Winsorized Mean ( 15 / 24 )4752.88888888889101.66762209116946.7492874440085
Winsorized Mean ( 16 / 24 )4736.8888888888996.835203079157548.9170130104105
Winsorized Mean ( 17 / 24 )4614.3472222222271.911387937316964.1671278302181
Winsorized Mean ( 18 / 24 )4615.0972222222267.026246113913768.8550752846681
Winsorized Mean ( 19 / 24 )4606.6527777777865.169044538711170.6877446245415
Winsorized Mean ( 20 / 24 )4614.7083333333363.565236527496472.597988860423
Winsorized Mean ( 21 / 24 )4621.12562.630973682648673.7833811017415
Winsorized Mean ( 22 / 24 )4582.9305555555655.962723475318881.8925575982156
Winsorized Mean ( 23 / 24 )4570.4722222222253.608627716610685.2562808804387
Winsorized Mean ( 24 / 24 )4566.8055555555650.151065371911691.0609878711233
Trimmed Mean ( 1 / 24 )4832.81428571429195.34413578146124.7400018760785
Trimmed Mean ( 2 / 24 )4818.32352941176183.84456880475526.2086803038978
Trimmed Mean ( 3 / 24 )4814.28787878788174.23527052305827.6309605072227
Trimmed Mean ( 4 / 24 )4808.453125163.17424062156529.4682120577586
Trimmed Mean ( 5 / 24 )4803.08064516129151.58914472588131.6848587928029
Trimmed Mean ( 6 / 24 )4783.96666666667141.67432408683433.7673512649652
Trimmed Mean ( 7 / 24 )4761.93103448276133.70078570466735.6163279773197
Trimmed Mean ( 8 / 24 )4734.08928571429125.77897610126137.6381604657284
Trimmed Mean ( 9 / 24 )4707.11111111111117.15620762806740.1780768293102
Trimmed Mean ( 10 / 24 )4687.80769230769111.75508882451941.9471519517883
Trimmed Mean ( 11 / 24 )4668.78106.25546531922143.9391986659105
Trimmed Mean ( 12 / 24 )4649.66666666667101.30544333203345.8975008028658
Trimmed Mean ( 13 / 24 )4629.5869565217496.051891048521648.1988111424382
Trimmed Mean ( 14 / 24 )4613.3863636363692.430450488428149.9119753204485
Trimmed Mean ( 15 / 24 )4595.6666666666787.943022591956552.2573199239458
Trimmed Mean ( 16 / 24 )4576.882.237400250737555.6535102769005
Trimmed Mean ( 17 / 24 )4557.8421052631675.829697323553860.1062943165333
Trimmed Mean ( 18 / 24 )4551.1944444444474.483052503433861.1037583916774
Trimmed Mean ( 19 / 24 )4543.6764705882473.639432306023161.7016770540286
Trimmed Mean ( 20 / 24 )4536.2187572.714473289408162.3839869120081
Trimmed Mean ( 21 / 24 )4526.871.516807766450663.297008652609
Trimmed Mean ( 22 / 24 )4515.2569.698132656242664.7829407750365
Trimmed Mean ( 23 / 24 )4506.7307692307769.002242052588665.3128164414725
Trimmed Mean ( 24 / 24 )4498.4166666666768.316715459037665.846500910365
Median4341
Midrange6509.5
Midmean - Weighted Average at Xnp4534.89189189189
Midmean - Weighted Average at X(n+1)p4551.19444444444
Midmean - Empirical Distribution Function4534.89189189189
Midmean - Empirical Distribution Function - Averaging4551.19444444444
Midmean - Empirical Distribution Function - Interpolation4551.19444444444
Midmean - Closest Observation4534.89189189189
Midmean - True Basic - Statistics Graphics Toolkit4551.19444444444
Midmean - MS Excel (old versions)4557.84210526316
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 4879.38888888889 & 219.239153791885 & 22.2560104091658 \tabularnewline
Geometric Mean & 4523.14936883401 &  &  \tabularnewline
Harmonic Mean & 4109.95906878058 &  &  \tabularnewline
Quadratic Mean & 5217.38518747125 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 4846.5 & 204.891249447497 & 23.654011643098 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 4825.72222222222 & 198.530014742376 & 24.3072677372454 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 4829.84722222222 & 197.228463382645 & 24.4885912478656 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 4826.95833333333 & 192.338888982401 & 25.096112174044 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 4882.72222222222 & 179.990715747155 & 27.1276337890745 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 4890.47222222222 & 166.550744865072 & 29.3632563828168 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 4913.51388888889 & 159.307485077334 & 30.8429568548125 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 4895.95833333333 & 154.533968539321 & 31.6820850432478 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 4832.58333333333 & 135.188015701104 & 35.7471282367071 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 4819.94444444444 & 129.919845412314 & 37.0993702243706 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 4808.94444444444 & 121.644082553896 & 39.5329089872808 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 4803.61111111111 & 116.922351538707 & 41.0837709633378 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 4758.29166666667 & 104.563809014001 & 45.5061049471672 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 4758.09722222222 & 103.080760838177 & 46.1589261035026 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 4752.88888888889 & 101.667622091169 & 46.7492874440085 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 4736.88888888889 & 96.8352030791575 & 48.9170130104105 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 4614.34722222222 & 71.9113879373169 & 64.1671278302181 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 4615.09722222222 & 67.0262461139137 & 68.8550752846681 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 4606.65277777778 & 65.1690445387111 & 70.6877446245415 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 4614.70833333333 & 63.5652365274964 & 72.597988860423 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 4621.125 & 62.6309736826486 & 73.7833811017415 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 4582.93055555556 & 55.9627234753188 & 81.8925575982156 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 4570.47222222222 & 53.6086277166106 & 85.2562808804387 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 4566.80555555556 & 50.1510653719116 & 91.0609878711233 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 4832.81428571429 & 195.344135781461 & 24.7400018760785 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 4818.32352941176 & 183.844568804755 & 26.2086803038978 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 4814.28787878788 & 174.235270523058 & 27.6309605072227 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 4808.453125 & 163.174240621565 & 29.4682120577586 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 4803.08064516129 & 151.589144725881 & 31.6848587928029 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 4783.96666666667 & 141.674324086834 & 33.7673512649652 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 4761.93103448276 & 133.700785704667 & 35.6163279773197 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 4734.08928571429 & 125.778976101261 & 37.6381604657284 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 4707.11111111111 & 117.156207628067 & 40.1780768293102 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 4687.80769230769 & 111.755088824519 & 41.9471519517883 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 4668.78 & 106.255465319221 & 43.9391986659105 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 4649.66666666667 & 101.305443332033 & 45.8975008028658 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 4629.58695652174 & 96.0518910485216 & 48.1988111424382 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 4613.38636363636 & 92.4304504884281 & 49.9119753204485 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 4595.66666666667 & 87.9430225919565 & 52.2573199239458 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 4576.8 & 82.2374002507375 & 55.6535102769005 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 4557.84210526316 & 75.8296973235538 & 60.1062943165333 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 4551.19444444444 & 74.4830525034338 & 61.1037583916774 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 4543.67647058824 & 73.6394323060231 & 61.7016770540286 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 4536.21875 & 72.7144732894081 & 62.3839869120081 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 4526.8 & 71.5168077664506 & 63.297008652609 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 4515.25 & 69.6981326562426 & 64.7829407750365 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 4506.73076923077 & 69.0022420525886 & 65.3128164414725 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 4498.41666666667 & 68.3167154590376 & 65.846500910365 \tabularnewline
Median & 4341 &  &  \tabularnewline
Midrange & 6509.5 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 4534.89189189189 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 4551.19444444444 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 4534.89189189189 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 4551.19444444444 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 4551.19444444444 &  &  \tabularnewline
Midmean - Closest Observation & 4534.89189189189 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 4551.19444444444 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 4557.84210526316 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=240260&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]4879.38888888889[/C][C]219.239153791885[/C][C]22.2560104091658[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]4523.14936883401[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]4109.95906878058[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]5217.38518747125[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]4846.5[/C][C]204.891249447497[/C][C]23.654011643098[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]4825.72222222222[/C][C]198.530014742376[/C][C]24.3072677372454[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]4829.84722222222[/C][C]197.228463382645[/C][C]24.4885912478656[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]4826.95833333333[/C][C]192.338888982401[/C][C]25.096112174044[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]4882.72222222222[/C][C]179.990715747155[/C][C]27.1276337890745[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]4890.47222222222[/C][C]166.550744865072[/C][C]29.3632563828168[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]4913.51388888889[/C][C]159.307485077334[/C][C]30.8429568548125[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]4895.95833333333[/C][C]154.533968539321[/C][C]31.6820850432478[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]4832.58333333333[/C][C]135.188015701104[/C][C]35.7471282367071[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]4819.94444444444[/C][C]129.919845412314[/C][C]37.0993702243706[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]4808.94444444444[/C][C]121.644082553896[/C][C]39.5329089872808[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]4803.61111111111[/C][C]116.922351538707[/C][C]41.0837709633378[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]4758.29166666667[/C][C]104.563809014001[/C][C]45.5061049471672[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]4758.09722222222[/C][C]103.080760838177[/C][C]46.1589261035026[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]4752.88888888889[/C][C]101.667622091169[/C][C]46.7492874440085[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]4736.88888888889[/C][C]96.8352030791575[/C][C]48.9170130104105[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]4614.34722222222[/C][C]71.9113879373169[/C][C]64.1671278302181[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]4615.09722222222[/C][C]67.0262461139137[/C][C]68.8550752846681[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]4606.65277777778[/C][C]65.1690445387111[/C][C]70.6877446245415[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]4614.70833333333[/C][C]63.5652365274964[/C][C]72.597988860423[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]4621.125[/C][C]62.6309736826486[/C][C]73.7833811017415[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]4582.93055555556[/C][C]55.9627234753188[/C][C]81.8925575982156[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]4570.47222222222[/C][C]53.6086277166106[/C][C]85.2562808804387[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]4566.80555555556[/C][C]50.1510653719116[/C][C]91.0609878711233[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]4832.81428571429[/C][C]195.344135781461[/C][C]24.7400018760785[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]4818.32352941176[/C][C]183.844568804755[/C][C]26.2086803038978[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]4814.28787878788[/C][C]174.235270523058[/C][C]27.6309605072227[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]4808.453125[/C][C]163.174240621565[/C][C]29.4682120577586[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]4803.08064516129[/C][C]151.589144725881[/C][C]31.6848587928029[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]4783.96666666667[/C][C]141.674324086834[/C][C]33.7673512649652[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]4761.93103448276[/C][C]133.700785704667[/C][C]35.6163279773197[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]4734.08928571429[/C][C]125.778976101261[/C][C]37.6381604657284[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]4707.11111111111[/C][C]117.156207628067[/C][C]40.1780768293102[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]4687.80769230769[/C][C]111.755088824519[/C][C]41.9471519517883[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]4668.78[/C][C]106.255465319221[/C][C]43.9391986659105[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]4649.66666666667[/C][C]101.305443332033[/C][C]45.8975008028658[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]4629.58695652174[/C][C]96.0518910485216[/C][C]48.1988111424382[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]4613.38636363636[/C][C]92.4304504884281[/C][C]49.9119753204485[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]4595.66666666667[/C][C]87.9430225919565[/C][C]52.2573199239458[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]4576.8[/C][C]82.2374002507375[/C][C]55.6535102769005[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]4557.84210526316[/C][C]75.8296973235538[/C][C]60.1062943165333[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]4551.19444444444[/C][C]74.4830525034338[/C][C]61.1037583916774[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]4543.67647058824[/C][C]73.6394323060231[/C][C]61.7016770540286[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]4536.21875[/C][C]72.7144732894081[/C][C]62.3839869120081[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]4526.8[/C][C]71.5168077664506[/C][C]63.297008652609[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]4515.25[/C][C]69.6981326562426[/C][C]64.7829407750365[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]4506.73076923077[/C][C]69.0022420525886[/C][C]65.3128164414725[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]4498.41666666667[/C][C]68.3167154590376[/C][C]65.846500910365[/C][/ROW]
[ROW][C]Median[/C][C]4341[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]6509.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]4534.89189189189[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]4551.19444444444[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]4534.89189189189[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]4551.19444444444[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]4551.19444444444[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]4534.89189189189[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]4551.19444444444[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]4557.84210526316[/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=240260&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=240260&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 Mean4879.38888888889219.23915379188522.2560104091658
Geometric Mean4523.14936883401
Harmonic Mean4109.95906878058
Quadratic Mean5217.38518747125
Winsorized Mean ( 1 / 24 )4846.5204.89124944749723.654011643098
Winsorized Mean ( 2 / 24 )4825.72222222222198.53001474237624.3072677372454
Winsorized Mean ( 3 / 24 )4829.84722222222197.22846338264524.4885912478656
Winsorized Mean ( 4 / 24 )4826.95833333333192.33888898240125.096112174044
Winsorized Mean ( 5 / 24 )4882.72222222222179.99071574715527.1276337890745
Winsorized Mean ( 6 / 24 )4890.47222222222166.55074486507229.3632563828168
Winsorized Mean ( 7 / 24 )4913.51388888889159.30748507733430.8429568548125
Winsorized Mean ( 8 / 24 )4895.95833333333154.53396853932131.6820850432478
Winsorized Mean ( 9 / 24 )4832.58333333333135.18801570110435.7471282367071
Winsorized Mean ( 10 / 24 )4819.94444444444129.91984541231437.0993702243706
Winsorized Mean ( 11 / 24 )4808.94444444444121.64408255389639.5329089872808
Winsorized Mean ( 12 / 24 )4803.61111111111116.92235153870741.0837709633378
Winsorized Mean ( 13 / 24 )4758.29166666667104.56380901400145.5061049471672
Winsorized Mean ( 14 / 24 )4758.09722222222103.08076083817746.1589261035026
Winsorized Mean ( 15 / 24 )4752.88888888889101.66762209116946.7492874440085
Winsorized Mean ( 16 / 24 )4736.8888888888996.835203079157548.9170130104105
Winsorized Mean ( 17 / 24 )4614.3472222222271.911387937316964.1671278302181
Winsorized Mean ( 18 / 24 )4615.0972222222267.026246113913768.8550752846681
Winsorized Mean ( 19 / 24 )4606.6527777777865.169044538711170.6877446245415
Winsorized Mean ( 20 / 24 )4614.7083333333363.565236527496472.597988860423
Winsorized Mean ( 21 / 24 )4621.12562.630973682648673.7833811017415
Winsorized Mean ( 22 / 24 )4582.9305555555655.962723475318881.8925575982156
Winsorized Mean ( 23 / 24 )4570.4722222222253.608627716610685.2562808804387
Winsorized Mean ( 24 / 24 )4566.8055555555650.151065371911691.0609878711233
Trimmed Mean ( 1 / 24 )4832.81428571429195.34413578146124.7400018760785
Trimmed Mean ( 2 / 24 )4818.32352941176183.84456880475526.2086803038978
Trimmed Mean ( 3 / 24 )4814.28787878788174.23527052305827.6309605072227
Trimmed Mean ( 4 / 24 )4808.453125163.17424062156529.4682120577586
Trimmed Mean ( 5 / 24 )4803.08064516129151.58914472588131.6848587928029
Trimmed Mean ( 6 / 24 )4783.96666666667141.67432408683433.7673512649652
Trimmed Mean ( 7 / 24 )4761.93103448276133.70078570466735.6163279773197
Trimmed Mean ( 8 / 24 )4734.08928571429125.77897610126137.6381604657284
Trimmed Mean ( 9 / 24 )4707.11111111111117.15620762806740.1780768293102
Trimmed Mean ( 10 / 24 )4687.80769230769111.75508882451941.9471519517883
Trimmed Mean ( 11 / 24 )4668.78106.25546531922143.9391986659105
Trimmed Mean ( 12 / 24 )4649.66666666667101.30544333203345.8975008028658
Trimmed Mean ( 13 / 24 )4629.5869565217496.051891048521648.1988111424382
Trimmed Mean ( 14 / 24 )4613.3863636363692.430450488428149.9119753204485
Trimmed Mean ( 15 / 24 )4595.6666666666787.943022591956552.2573199239458
Trimmed Mean ( 16 / 24 )4576.882.237400250737555.6535102769005
Trimmed Mean ( 17 / 24 )4557.8421052631675.829697323553860.1062943165333
Trimmed Mean ( 18 / 24 )4551.1944444444474.483052503433861.1037583916774
Trimmed Mean ( 19 / 24 )4543.6764705882473.639432306023161.7016770540286
Trimmed Mean ( 20 / 24 )4536.2187572.714473289408162.3839869120081
Trimmed Mean ( 21 / 24 )4526.871.516807766450663.297008652609
Trimmed Mean ( 22 / 24 )4515.2569.698132656242664.7829407750365
Trimmed Mean ( 23 / 24 )4506.7307692307769.002242052588665.3128164414725
Trimmed Mean ( 24 / 24 )4498.4166666666768.316715459037665.846500910365
Median4341
Midrange6509.5
Midmean - Weighted Average at Xnp4534.89189189189
Midmean - Weighted Average at X(n+1)p4551.19444444444
Midmean - Empirical Distribution Function4534.89189189189
Midmean - Empirical Distribution Function - Averaging4551.19444444444
Midmean - Empirical Distribution Function - Interpolation4551.19444444444
Midmean - Closest Observation4534.89189189189
Midmean - True Basic - Statistics Graphics Toolkit4551.19444444444
Midmean - MS Excel (old versions)4557.84210526316
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')