Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationWed, 17 Mar 2010 10:12:13 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Mar/17/t1268842644kfl0rgjbtdjwvxs.htm/, Retrieved Fri, 12 Aug 2022 09:04:34 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=74519, Retrieved Fri, 12 Aug 2022 09:04:34 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP1W52
Estimated Impact134
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [The total generat...] [2010-03-17 16:12:13] [0e6aef37627b8cf9d1bd74110cef2cca] [Current]
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Dataseries X:
227.86
198.24
194.97
184.88
196.79
205.36
226.72
226.05
202.50
194.79
192.43
219.25
217.47
192.34
196.83
186.07
197.31
215.02
242.67
225.17
206.69
197.75
196.43
213.55
222.75
194.03
201.85
189.50
206.07
225.59
247.91
247.64
213.01
203.01
200.26
220.50
237.90
216.94
214.01
196.00
208.37
232.75
257.46
267.69
220.18
210.61
209.59
232.75
232.75
219.82
226.74
208.04
220.12
235.69
257.05
258.69
227.15
219.91
219.30
259.04
237.29
212.88
226.03
211.07
222.91
249.18
266.38
268.53
238.02
224.69
213.75
237.43
248.46
210.82
221.40
209.00
234.37
248.43
271.98
268.11
233.88
223.43
221.38
233.76
243.97
217.76
224.66
210.84
220.35
236.84
266.15
255.20
234.76
221.29
221.26
244.13
245.78
224.62
234.80
211.37
222.39
249.63
282.29
279.13
236.60
223.62
225.86
246.41
261.70
225.01
231.54
214.82
227.70
263.86
278.15
274.64
237.66
227.97
224.75
242.91
253.08
228.13
233.68
217.38
236.38
256.08
292.83
304.71
245.57
234.41
234.12
258.17
268.66
245.31
247.47
226.25
251.67
268.79
288.94
290.16
250.69
240.80




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\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 & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=74519&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=74519&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=74519&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'Gwilym Jenkins' @ 72.249.127.135







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean231.0893661971832.04529311245124112.985940641157
Geometric Mean229.843714260542
Harmonic Mean228.626783472958
Quadratic Mean232.362066055433
Winsorized Mean ( 1 / 47 )231.0140845070422.02421474445881114.125284947870
Winsorized Mean ( 2 / 47 )231.0247887323942.00887048624085115.002331068493
Winsorized Mean ( 3 / 47 )231.0590140845071.99499972351178115.819070730384
Winsorized Mean ( 4 / 47 )230.8742253521131.95791509483149117.918405124704
Winsorized Mean ( 5 / 47 )230.8192957746481.92994140462115119.599121103865
Winsorized Mean ( 6 / 47 )230.811.91833290613162120.318011155549
Winsorized Mean ( 7 / 47 )230.6458450704231.88769927240338122.183574705080
Winsorized Mean ( 8 / 47 )230.5540140845071.85572586075672124.23926343867
Winsorized Mean ( 9 / 47 )230.3790845070421.82098812229339126.513227454168
Winsorized Mean ( 10 / 47 )230.3952816901411.81627995550581126.850093231348
Winsorized Mean ( 11 / 47 )230.3883098591551.81437037175099126.979757521511
Winsorized Mean ( 12 / 47 )230.393380281691.80379401228372127.727101161621
Winsorized Mean ( 13 / 47 )230.3952112676061.79288580331515128.505234879763
Winsorized Mean ( 14 / 47 )230.3143661971831.76778604203349130.284073253713
Winsorized Mean ( 15 / 47 )230.5034507042251.73735516725362132.674915900242
Winsorized Mean ( 16 / 47 )230.4245774647891.67846642556129137.282804085720
Winsorized Mean ( 17 / 47 )230.2438028169011.63314350986915140.981978268002
Winsorized Mean ( 18 / 47 )229.9712676056341.58029687608162145.524091761702
Winsorized Mean ( 19 / 47 )230.2388732394371.53708423004812149.789366606298
Winsorized Mean ( 20 / 47 )230.2656338028171.51609717990737151.880523791282
Winsorized Mean ( 21 / 47 )230.2523239436621.49213052639384154.311114122256
Winsorized Mean ( 22 / 47 )230.3979577464791.46084659541461157.715367561293
Winsorized Mean ( 23 / 47 )230.2942957746481.43487145496639160.498206984013
Winsorized Mean ( 24 / 47 )230.2520422535211.40454076734834163.934039941196
Winsorized Mean ( 25 / 47 )229.9826760563381.34717312776611170.715011542500
Winsorized Mean ( 26 / 47 )229.9112676056341.29621305867081177.371510082914
Winsorized Mean ( 27 / 47 )229.7648591549301.27001130537165180.915601446313
Winsorized Mean ( 28 / 47 )229.5597887323941.24543366309612184.321169030966
Winsorized Mean ( 29 / 47 )229.5148591549301.22996967012637186.602047781672
Winsorized Mean ( 30 / 47 )229.4261267605631.20609658925189190.222017709933
Winsorized Mean ( 31 / 47 )229.7492253521131.17100991033736196.197507231961
Winsorized Mean ( 32 / 47 )229.6613380281691.15481949386862198.87206550247
Winsorized Mean ( 33 / 47 )229.7240845070421.13503265702073202.394251025366
Winsorized Mean ( 34 / 47 )229.7312676056341.12564890378461204.087852645030
Winsorized Mean ( 35 / 47 )229.5340845070421.09024155682667210.53507185613
Winsorized Mean ( 36 / 47 )229.5797183098591.05216642686783218.197152510645
Winsorized Mean ( 37 / 47 )229.5771126760561.04102141076657220.530634914612
Winsorized Mean ( 38 / 47 )230.0213380281690.983653998914351233.843748189954
Winsorized Mean ( 39 / 47 )229.8180985915490.936839108419591245.312238276691
Winsorized Mean ( 40 / 47 )229.798380281690.929575029604394247.207996087725
Winsorized Mean ( 41 / 47 )229.5760563380280.88885753924905258.282172565004
Winsorized Mean ( 42 / 47 )229.9457746478870.840587126864194273.553766527092
Winsorized Mean ( 43 / 47 )229.3946478873240.779389398184448294.326107619232
Winsorized Mean ( 44 / 47 )228.6943661971830.677583746072507337.514539749173
Winsorized Mean ( 45 / 47 )228.6848591549300.67122960546863340.695430135668
Winsorized Mean ( 46 / 47 )228.6751408450700.657383167921678347.856702154435
Winsorized Mean ( 47 / 47 )228.6188732394370.64819051593376352.703206263511
Trimmed Mean ( 1 / 47 )230.8935714285711.97876495337712116.685698841851
Trimmed Mean ( 2 / 47 )230.7695652173911.92897864005156119.633032956354
Trimmed Mean ( 3 / 47 )230.6363235294121.88324263709207122.467662417382
Trimmed Mean ( 4 / 47 )230.4870149253731.83860510289293125.359716756315
Trimmed Mean ( 5 / 47 )230.3828787878791.80140210167685127.890868215056
Trimmed Mean ( 6 / 47 )230.2875384615381.76790442591550130.260174184634
Trimmed Mean ( 7 / 47 )230.2875384615381.73372487349554132.828190898151
Trimmed Mean ( 8 / 47 )230.1176984126981.70238687398978135.173562442588
Trimmed Mean ( 9 / 47 )230.0552419354841.67376772378291137.447531498297
Trimmed Mean ( 10 / 47 )230.0133606557381.64810329996066139.562465933554
Trimmed Mean ( 11 / 47 )229.9681666666671.62050070064008141.911797122848
Trimmed Mean ( 12 / 47 )229.9222033898311.59025623989552144.581858961885
Trimmed Mean ( 13 / 47 )229.8741379310341.55826537391637147.519249146437
Trimmed Mean ( 14 / 47 )229.8741379310341.52426382339241150.809941430890
Trimmed Mean ( 15 / 47 )229.7798214285711.48987560798026154.227520873418
Trimmed Mean ( 16 / 47 )229.7175454545451.45551319196451157.825807916241
Trimmed Mean ( 17 / 47 )229.6594444444441.42477117261396161.190406472851
Trimmed Mean ( 18 / 47 )229.6133962264151.39611543535527164.465910491123
Trimmed Mean ( 19 / 47 )229.586251.37050463596353167.519499004532
Trimmed Mean ( 20 / 47 )229.5384313725491.34678209454763170.434721624101
Trimmed Mean ( 21 / 47 )229.48681.32250121826909173.52483069948
Trimmed Mean ( 22 / 47 )229.4339795918371.29787759663002176.776284749478
Trimmed Mean ( 23 / 47 )229.3691666666671.27354905975480180.102340706708
Trimmed Mean ( 24 / 47 )229.3084042553191.24898473803532183.595841704220
Trimmed Mean ( 25 / 47 )229.2477173913041.22455227056111187.209417599020
Trimmed Mean ( 26 / 47 )229.2013333333331.20337921208981190.464760426847
Trimmed Mean ( 27 / 47 )229.1572727272731.18489293070863193.399139102151
Trimmed Mean ( 28 / 47 )229.1572727272731.16661091450094196.429906388543
Trimmed Mean ( 29 / 47 )229.0935714285711.14834149961487199.499514304242
Trimmed Mean ( 30 / 47 )229.0684146341461.12895752396703202.902597990777
Trimmed Mean ( 31 / 47 )229.0684146341461.10924090212888206.509166939763
Trimmed Mean ( 32 / 47 )229.0060256410261.09025148308166210.048809100197
Trimmed Mean ( 33 / 47 )228.9677631578951.06997928490661213.992706576444
Trimmed Mean ( 34 / 47 )228.9237837837841.04854179703867218.325854467908
Trimmed Mean ( 35 / 47 )228.8769444444441.02442878161199223.419088327736
Trimmed Mean ( 36 / 47 )228.8388571428571.00064936561882228.690353489946
Trimmed Mean ( 37 / 47 )228.7958823529410.977425019079908234.080239288653
Trimmed Mean ( 38 / 47 )228.7504545454550.951178447880209240.491629152497
Trimmed Mean ( 39 / 47 )228.676250.927329582063379246.596522340178
Trimmed Mean ( 40 / 47 )228.6091935483870.90544160506303252.483641429833
Trimmed Mean ( 41 / 47 )228.5388333333330.8798181659746259.756893153228
Trimmed Mean ( 42 / 47 )228.4768965517240.855095230256145267.194680156599
Trimmed Mean ( 43 / 47 )228.3882142857140.831655917672018274.618636665295
Trimmed Mean ( 44 / 47 )228.3266666666670.813374015204177280.715467175763
Trimmed Mean ( 45 / 47 )228.3038461538460.80699315067556282.906795383239
Trimmed Mean ( 46 / 47 )228.27980.799109529413835285.66772338136
Trimmed Mean ( 47 / 47 )228.2543750.790544122373525288.730721714419
Median226.73
Midrange244.795
Midmean - Weighted Average at Xnp228.63
Midmean - Weighted Average at X(n+1)p228.876944444444
Midmean - Empirical Distribution Function228.876944444444
Midmean - Empirical Distribution Function - Averaging228.876944444444
Midmean - Empirical Distribution Function - Interpolation228.838857142857
Midmean - Closest Observation228.876944444444
Midmean - True Basic - Statistics Graphics Toolkit228.876944444444
Midmean - MS Excel (old versions)228.876944444444
Number of observations142

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 231.089366197183 & 2.04529311245124 & 112.985940641157 \tabularnewline
Geometric Mean & 229.843714260542 &  &  \tabularnewline
Harmonic Mean & 228.626783472958 &  &  \tabularnewline
Quadratic Mean & 232.362066055433 &  &  \tabularnewline
Winsorized Mean ( 1 / 47 ) & 231.014084507042 & 2.02421474445881 & 114.125284947870 \tabularnewline
Winsorized Mean ( 2 / 47 ) & 231.024788732394 & 2.00887048624085 & 115.002331068493 \tabularnewline
Winsorized Mean ( 3 / 47 ) & 231.059014084507 & 1.99499972351178 & 115.819070730384 \tabularnewline
Winsorized Mean ( 4 / 47 ) & 230.874225352113 & 1.95791509483149 & 117.918405124704 \tabularnewline
Winsorized Mean ( 5 / 47 ) & 230.819295774648 & 1.92994140462115 & 119.599121103865 \tabularnewline
Winsorized Mean ( 6 / 47 ) & 230.81 & 1.91833290613162 & 120.318011155549 \tabularnewline
Winsorized Mean ( 7 / 47 ) & 230.645845070423 & 1.88769927240338 & 122.183574705080 \tabularnewline
Winsorized Mean ( 8 / 47 ) & 230.554014084507 & 1.85572586075672 & 124.23926343867 \tabularnewline
Winsorized Mean ( 9 / 47 ) & 230.379084507042 & 1.82098812229339 & 126.513227454168 \tabularnewline
Winsorized Mean ( 10 / 47 ) & 230.395281690141 & 1.81627995550581 & 126.850093231348 \tabularnewline
Winsorized Mean ( 11 / 47 ) & 230.388309859155 & 1.81437037175099 & 126.979757521511 \tabularnewline
Winsorized Mean ( 12 / 47 ) & 230.39338028169 & 1.80379401228372 & 127.727101161621 \tabularnewline
Winsorized Mean ( 13 / 47 ) & 230.395211267606 & 1.79288580331515 & 128.505234879763 \tabularnewline
Winsorized Mean ( 14 / 47 ) & 230.314366197183 & 1.76778604203349 & 130.284073253713 \tabularnewline
Winsorized Mean ( 15 / 47 ) & 230.503450704225 & 1.73735516725362 & 132.674915900242 \tabularnewline
Winsorized Mean ( 16 / 47 ) & 230.424577464789 & 1.67846642556129 & 137.282804085720 \tabularnewline
Winsorized Mean ( 17 / 47 ) & 230.243802816901 & 1.63314350986915 & 140.981978268002 \tabularnewline
Winsorized Mean ( 18 / 47 ) & 229.971267605634 & 1.58029687608162 & 145.524091761702 \tabularnewline
Winsorized Mean ( 19 / 47 ) & 230.238873239437 & 1.53708423004812 & 149.789366606298 \tabularnewline
Winsorized Mean ( 20 / 47 ) & 230.265633802817 & 1.51609717990737 & 151.880523791282 \tabularnewline
Winsorized Mean ( 21 / 47 ) & 230.252323943662 & 1.49213052639384 & 154.311114122256 \tabularnewline
Winsorized Mean ( 22 / 47 ) & 230.397957746479 & 1.46084659541461 & 157.715367561293 \tabularnewline
Winsorized Mean ( 23 / 47 ) & 230.294295774648 & 1.43487145496639 & 160.498206984013 \tabularnewline
Winsorized Mean ( 24 / 47 ) & 230.252042253521 & 1.40454076734834 & 163.934039941196 \tabularnewline
Winsorized Mean ( 25 / 47 ) & 229.982676056338 & 1.34717312776611 & 170.715011542500 \tabularnewline
Winsorized Mean ( 26 / 47 ) & 229.911267605634 & 1.29621305867081 & 177.371510082914 \tabularnewline
Winsorized Mean ( 27 / 47 ) & 229.764859154930 & 1.27001130537165 & 180.915601446313 \tabularnewline
Winsorized Mean ( 28 / 47 ) & 229.559788732394 & 1.24543366309612 & 184.321169030966 \tabularnewline
Winsorized Mean ( 29 / 47 ) & 229.514859154930 & 1.22996967012637 & 186.602047781672 \tabularnewline
Winsorized Mean ( 30 / 47 ) & 229.426126760563 & 1.20609658925189 & 190.222017709933 \tabularnewline
Winsorized Mean ( 31 / 47 ) & 229.749225352113 & 1.17100991033736 & 196.197507231961 \tabularnewline
Winsorized Mean ( 32 / 47 ) & 229.661338028169 & 1.15481949386862 & 198.87206550247 \tabularnewline
Winsorized Mean ( 33 / 47 ) & 229.724084507042 & 1.13503265702073 & 202.394251025366 \tabularnewline
Winsorized Mean ( 34 / 47 ) & 229.731267605634 & 1.12564890378461 & 204.087852645030 \tabularnewline
Winsorized Mean ( 35 / 47 ) & 229.534084507042 & 1.09024155682667 & 210.53507185613 \tabularnewline
Winsorized Mean ( 36 / 47 ) & 229.579718309859 & 1.05216642686783 & 218.197152510645 \tabularnewline
Winsorized Mean ( 37 / 47 ) & 229.577112676056 & 1.04102141076657 & 220.530634914612 \tabularnewline
Winsorized Mean ( 38 / 47 ) & 230.021338028169 & 0.983653998914351 & 233.843748189954 \tabularnewline
Winsorized Mean ( 39 / 47 ) & 229.818098591549 & 0.936839108419591 & 245.312238276691 \tabularnewline
Winsorized Mean ( 40 / 47 ) & 229.79838028169 & 0.929575029604394 & 247.207996087725 \tabularnewline
Winsorized Mean ( 41 / 47 ) & 229.576056338028 & 0.88885753924905 & 258.282172565004 \tabularnewline
Winsorized Mean ( 42 / 47 ) & 229.945774647887 & 0.840587126864194 & 273.553766527092 \tabularnewline
Winsorized Mean ( 43 / 47 ) & 229.394647887324 & 0.779389398184448 & 294.326107619232 \tabularnewline
Winsorized Mean ( 44 / 47 ) & 228.694366197183 & 0.677583746072507 & 337.514539749173 \tabularnewline
Winsorized Mean ( 45 / 47 ) & 228.684859154930 & 0.67122960546863 & 340.695430135668 \tabularnewline
Winsorized Mean ( 46 / 47 ) & 228.675140845070 & 0.657383167921678 & 347.856702154435 \tabularnewline
Winsorized Mean ( 47 / 47 ) & 228.618873239437 & 0.64819051593376 & 352.703206263511 \tabularnewline
Trimmed Mean ( 1 / 47 ) & 230.893571428571 & 1.97876495337712 & 116.685698841851 \tabularnewline
Trimmed Mean ( 2 / 47 ) & 230.769565217391 & 1.92897864005156 & 119.633032956354 \tabularnewline
Trimmed Mean ( 3 / 47 ) & 230.636323529412 & 1.88324263709207 & 122.467662417382 \tabularnewline
Trimmed Mean ( 4 / 47 ) & 230.487014925373 & 1.83860510289293 & 125.359716756315 \tabularnewline
Trimmed Mean ( 5 / 47 ) & 230.382878787879 & 1.80140210167685 & 127.890868215056 \tabularnewline
Trimmed Mean ( 6 / 47 ) & 230.287538461538 & 1.76790442591550 & 130.260174184634 \tabularnewline
Trimmed Mean ( 7 / 47 ) & 230.287538461538 & 1.73372487349554 & 132.828190898151 \tabularnewline
Trimmed Mean ( 8 / 47 ) & 230.117698412698 & 1.70238687398978 & 135.173562442588 \tabularnewline
Trimmed Mean ( 9 / 47 ) & 230.055241935484 & 1.67376772378291 & 137.447531498297 \tabularnewline
Trimmed Mean ( 10 / 47 ) & 230.013360655738 & 1.64810329996066 & 139.562465933554 \tabularnewline
Trimmed Mean ( 11 / 47 ) & 229.968166666667 & 1.62050070064008 & 141.911797122848 \tabularnewline
Trimmed Mean ( 12 / 47 ) & 229.922203389831 & 1.59025623989552 & 144.581858961885 \tabularnewline
Trimmed Mean ( 13 / 47 ) & 229.874137931034 & 1.55826537391637 & 147.519249146437 \tabularnewline
Trimmed Mean ( 14 / 47 ) & 229.874137931034 & 1.52426382339241 & 150.809941430890 \tabularnewline
Trimmed Mean ( 15 / 47 ) & 229.779821428571 & 1.48987560798026 & 154.227520873418 \tabularnewline
Trimmed Mean ( 16 / 47 ) & 229.717545454545 & 1.45551319196451 & 157.825807916241 \tabularnewline
Trimmed Mean ( 17 / 47 ) & 229.659444444444 & 1.42477117261396 & 161.190406472851 \tabularnewline
Trimmed Mean ( 18 / 47 ) & 229.613396226415 & 1.39611543535527 & 164.465910491123 \tabularnewline
Trimmed Mean ( 19 / 47 ) & 229.58625 & 1.37050463596353 & 167.519499004532 \tabularnewline
Trimmed Mean ( 20 / 47 ) & 229.538431372549 & 1.34678209454763 & 170.434721624101 \tabularnewline
Trimmed Mean ( 21 / 47 ) & 229.4868 & 1.32250121826909 & 173.52483069948 \tabularnewline
Trimmed Mean ( 22 / 47 ) & 229.433979591837 & 1.29787759663002 & 176.776284749478 \tabularnewline
Trimmed Mean ( 23 / 47 ) & 229.369166666667 & 1.27354905975480 & 180.102340706708 \tabularnewline
Trimmed Mean ( 24 / 47 ) & 229.308404255319 & 1.24898473803532 & 183.595841704220 \tabularnewline
Trimmed Mean ( 25 / 47 ) & 229.247717391304 & 1.22455227056111 & 187.209417599020 \tabularnewline
Trimmed Mean ( 26 / 47 ) & 229.201333333333 & 1.20337921208981 & 190.464760426847 \tabularnewline
Trimmed Mean ( 27 / 47 ) & 229.157272727273 & 1.18489293070863 & 193.399139102151 \tabularnewline
Trimmed Mean ( 28 / 47 ) & 229.157272727273 & 1.16661091450094 & 196.429906388543 \tabularnewline
Trimmed Mean ( 29 / 47 ) & 229.093571428571 & 1.14834149961487 & 199.499514304242 \tabularnewline
Trimmed Mean ( 30 / 47 ) & 229.068414634146 & 1.12895752396703 & 202.902597990777 \tabularnewline
Trimmed Mean ( 31 / 47 ) & 229.068414634146 & 1.10924090212888 & 206.509166939763 \tabularnewline
Trimmed Mean ( 32 / 47 ) & 229.006025641026 & 1.09025148308166 & 210.048809100197 \tabularnewline
Trimmed Mean ( 33 / 47 ) & 228.967763157895 & 1.06997928490661 & 213.992706576444 \tabularnewline
Trimmed Mean ( 34 / 47 ) & 228.923783783784 & 1.04854179703867 & 218.325854467908 \tabularnewline
Trimmed Mean ( 35 / 47 ) & 228.876944444444 & 1.02442878161199 & 223.419088327736 \tabularnewline
Trimmed Mean ( 36 / 47 ) & 228.838857142857 & 1.00064936561882 & 228.690353489946 \tabularnewline
Trimmed Mean ( 37 / 47 ) & 228.795882352941 & 0.977425019079908 & 234.080239288653 \tabularnewline
Trimmed Mean ( 38 / 47 ) & 228.750454545455 & 0.951178447880209 & 240.491629152497 \tabularnewline
Trimmed Mean ( 39 / 47 ) & 228.67625 & 0.927329582063379 & 246.596522340178 \tabularnewline
Trimmed Mean ( 40 / 47 ) & 228.609193548387 & 0.90544160506303 & 252.483641429833 \tabularnewline
Trimmed Mean ( 41 / 47 ) & 228.538833333333 & 0.8798181659746 & 259.756893153228 \tabularnewline
Trimmed Mean ( 42 / 47 ) & 228.476896551724 & 0.855095230256145 & 267.194680156599 \tabularnewline
Trimmed Mean ( 43 / 47 ) & 228.388214285714 & 0.831655917672018 & 274.618636665295 \tabularnewline
Trimmed Mean ( 44 / 47 ) & 228.326666666667 & 0.813374015204177 & 280.715467175763 \tabularnewline
Trimmed Mean ( 45 / 47 ) & 228.303846153846 & 0.80699315067556 & 282.906795383239 \tabularnewline
Trimmed Mean ( 46 / 47 ) & 228.2798 & 0.799109529413835 & 285.66772338136 \tabularnewline
Trimmed Mean ( 47 / 47 ) & 228.254375 & 0.790544122373525 & 288.730721714419 \tabularnewline
Median & 226.73 &  &  \tabularnewline
Midrange & 244.795 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 228.63 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 228.876944444444 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 228.876944444444 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 228.876944444444 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 228.838857142857 &  &  \tabularnewline
Midmean - Closest Observation & 228.876944444444 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 228.876944444444 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 228.876944444444 &  &  \tabularnewline
Number of observations & 142 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=74519&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]231.089366197183[/C][C]2.04529311245124[/C][C]112.985940641157[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]229.843714260542[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]228.626783472958[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]232.362066055433[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 47 )[/C][C]231.014084507042[/C][C]2.02421474445881[/C][C]114.125284947870[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 47 )[/C][C]231.024788732394[/C][C]2.00887048624085[/C][C]115.002331068493[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 47 )[/C][C]231.059014084507[/C][C]1.99499972351178[/C][C]115.819070730384[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 47 )[/C][C]230.874225352113[/C][C]1.95791509483149[/C][C]117.918405124704[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 47 )[/C][C]230.819295774648[/C][C]1.92994140462115[/C][C]119.599121103865[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 47 )[/C][C]230.81[/C][C]1.91833290613162[/C][C]120.318011155549[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 47 )[/C][C]230.645845070423[/C][C]1.88769927240338[/C][C]122.183574705080[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 47 )[/C][C]230.554014084507[/C][C]1.85572586075672[/C][C]124.23926343867[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 47 )[/C][C]230.379084507042[/C][C]1.82098812229339[/C][C]126.513227454168[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 47 )[/C][C]230.395281690141[/C][C]1.81627995550581[/C][C]126.850093231348[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 47 )[/C][C]230.388309859155[/C][C]1.81437037175099[/C][C]126.979757521511[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 47 )[/C][C]230.39338028169[/C][C]1.80379401228372[/C][C]127.727101161621[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 47 )[/C][C]230.395211267606[/C][C]1.79288580331515[/C][C]128.505234879763[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 47 )[/C][C]230.314366197183[/C][C]1.76778604203349[/C][C]130.284073253713[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 47 )[/C][C]230.503450704225[/C][C]1.73735516725362[/C][C]132.674915900242[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 47 )[/C][C]230.424577464789[/C][C]1.67846642556129[/C][C]137.282804085720[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 47 )[/C][C]230.243802816901[/C][C]1.63314350986915[/C][C]140.981978268002[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 47 )[/C][C]229.971267605634[/C][C]1.58029687608162[/C][C]145.524091761702[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 47 )[/C][C]230.238873239437[/C][C]1.53708423004812[/C][C]149.789366606298[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 47 )[/C][C]230.265633802817[/C][C]1.51609717990737[/C][C]151.880523791282[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 47 )[/C][C]230.252323943662[/C][C]1.49213052639384[/C][C]154.311114122256[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 47 )[/C][C]230.397957746479[/C][C]1.46084659541461[/C][C]157.715367561293[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 47 )[/C][C]230.294295774648[/C][C]1.43487145496639[/C][C]160.498206984013[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 47 )[/C][C]230.252042253521[/C][C]1.40454076734834[/C][C]163.934039941196[/C][/ROW]
[ROW][C]Winsorized Mean ( 25 / 47 )[/C][C]229.982676056338[/C][C]1.34717312776611[/C][C]170.715011542500[/C][/ROW]
[ROW][C]Winsorized Mean ( 26 / 47 )[/C][C]229.911267605634[/C][C]1.29621305867081[/C][C]177.371510082914[/C][/ROW]
[ROW][C]Winsorized Mean ( 27 / 47 )[/C][C]229.764859154930[/C][C]1.27001130537165[/C][C]180.915601446313[/C][/ROW]
[ROW][C]Winsorized Mean ( 28 / 47 )[/C][C]229.559788732394[/C][C]1.24543366309612[/C][C]184.321169030966[/C][/ROW]
[ROW][C]Winsorized Mean ( 29 / 47 )[/C][C]229.514859154930[/C][C]1.22996967012637[/C][C]186.602047781672[/C][/ROW]
[ROW][C]Winsorized Mean ( 30 / 47 )[/C][C]229.426126760563[/C][C]1.20609658925189[/C][C]190.222017709933[/C][/ROW]
[ROW][C]Winsorized Mean ( 31 / 47 )[/C][C]229.749225352113[/C][C]1.17100991033736[/C][C]196.197507231961[/C][/ROW]
[ROW][C]Winsorized Mean ( 32 / 47 )[/C][C]229.661338028169[/C][C]1.15481949386862[/C][C]198.87206550247[/C][/ROW]
[ROW][C]Winsorized Mean ( 33 / 47 )[/C][C]229.724084507042[/C][C]1.13503265702073[/C][C]202.394251025366[/C][/ROW]
[ROW][C]Winsorized Mean ( 34 / 47 )[/C][C]229.731267605634[/C][C]1.12564890378461[/C][C]204.087852645030[/C][/ROW]
[ROW][C]Winsorized Mean ( 35 / 47 )[/C][C]229.534084507042[/C][C]1.09024155682667[/C][C]210.53507185613[/C][/ROW]
[ROW][C]Winsorized Mean ( 36 / 47 )[/C][C]229.579718309859[/C][C]1.05216642686783[/C][C]218.197152510645[/C][/ROW]
[ROW][C]Winsorized Mean ( 37 / 47 )[/C][C]229.577112676056[/C][C]1.04102141076657[/C][C]220.530634914612[/C][/ROW]
[ROW][C]Winsorized Mean ( 38 / 47 )[/C][C]230.021338028169[/C][C]0.983653998914351[/C][C]233.843748189954[/C][/ROW]
[ROW][C]Winsorized Mean ( 39 / 47 )[/C][C]229.818098591549[/C][C]0.936839108419591[/C][C]245.312238276691[/C][/ROW]
[ROW][C]Winsorized Mean ( 40 / 47 )[/C][C]229.79838028169[/C][C]0.929575029604394[/C][C]247.207996087725[/C][/ROW]
[ROW][C]Winsorized Mean ( 41 / 47 )[/C][C]229.576056338028[/C][C]0.88885753924905[/C][C]258.282172565004[/C][/ROW]
[ROW][C]Winsorized Mean ( 42 / 47 )[/C][C]229.945774647887[/C][C]0.840587126864194[/C][C]273.553766527092[/C][/ROW]
[ROW][C]Winsorized Mean ( 43 / 47 )[/C][C]229.394647887324[/C][C]0.779389398184448[/C][C]294.326107619232[/C][/ROW]
[ROW][C]Winsorized Mean ( 44 / 47 )[/C][C]228.694366197183[/C][C]0.677583746072507[/C][C]337.514539749173[/C][/ROW]
[ROW][C]Winsorized Mean ( 45 / 47 )[/C][C]228.684859154930[/C][C]0.67122960546863[/C][C]340.695430135668[/C][/ROW]
[ROW][C]Winsorized Mean ( 46 / 47 )[/C][C]228.675140845070[/C][C]0.657383167921678[/C][C]347.856702154435[/C][/ROW]
[ROW][C]Winsorized Mean ( 47 / 47 )[/C][C]228.618873239437[/C][C]0.64819051593376[/C][C]352.703206263511[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 47 )[/C][C]230.893571428571[/C][C]1.97876495337712[/C][C]116.685698841851[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 47 )[/C][C]230.769565217391[/C][C]1.92897864005156[/C][C]119.633032956354[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 47 )[/C][C]230.636323529412[/C][C]1.88324263709207[/C][C]122.467662417382[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 47 )[/C][C]230.487014925373[/C][C]1.83860510289293[/C][C]125.359716756315[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 47 )[/C][C]230.382878787879[/C][C]1.80140210167685[/C][C]127.890868215056[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 47 )[/C][C]230.287538461538[/C][C]1.76790442591550[/C][C]130.260174184634[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 47 )[/C][C]230.287538461538[/C][C]1.73372487349554[/C][C]132.828190898151[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 47 )[/C][C]230.117698412698[/C][C]1.70238687398978[/C][C]135.173562442588[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 47 )[/C][C]230.055241935484[/C][C]1.67376772378291[/C][C]137.447531498297[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 47 )[/C][C]230.013360655738[/C][C]1.64810329996066[/C][C]139.562465933554[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 47 )[/C][C]229.968166666667[/C][C]1.62050070064008[/C][C]141.911797122848[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 47 )[/C][C]229.922203389831[/C][C]1.59025623989552[/C][C]144.581858961885[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 47 )[/C][C]229.874137931034[/C][C]1.55826537391637[/C][C]147.519249146437[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 47 )[/C][C]229.874137931034[/C][C]1.52426382339241[/C][C]150.809941430890[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 47 )[/C][C]229.779821428571[/C][C]1.48987560798026[/C][C]154.227520873418[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 47 )[/C][C]229.717545454545[/C][C]1.45551319196451[/C][C]157.825807916241[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 47 )[/C][C]229.659444444444[/C][C]1.42477117261396[/C][C]161.190406472851[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 47 )[/C][C]229.613396226415[/C][C]1.39611543535527[/C][C]164.465910491123[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 47 )[/C][C]229.58625[/C][C]1.37050463596353[/C][C]167.519499004532[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 47 )[/C][C]229.538431372549[/C][C]1.34678209454763[/C][C]170.434721624101[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 47 )[/C][C]229.4868[/C][C]1.32250121826909[/C][C]173.52483069948[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 47 )[/C][C]229.433979591837[/C][C]1.29787759663002[/C][C]176.776284749478[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 47 )[/C][C]229.369166666667[/C][C]1.27354905975480[/C][C]180.102340706708[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 47 )[/C][C]229.308404255319[/C][C]1.24898473803532[/C][C]183.595841704220[/C][/ROW]
[ROW][C]Trimmed Mean ( 25 / 47 )[/C][C]229.247717391304[/C][C]1.22455227056111[/C][C]187.209417599020[/C][/ROW]
[ROW][C]Trimmed Mean ( 26 / 47 )[/C][C]229.201333333333[/C][C]1.20337921208981[/C][C]190.464760426847[/C][/ROW]
[ROW][C]Trimmed Mean ( 27 / 47 )[/C][C]229.157272727273[/C][C]1.18489293070863[/C][C]193.399139102151[/C][/ROW]
[ROW][C]Trimmed Mean ( 28 / 47 )[/C][C]229.157272727273[/C][C]1.16661091450094[/C][C]196.429906388543[/C][/ROW]
[ROW][C]Trimmed Mean ( 29 / 47 )[/C][C]229.093571428571[/C][C]1.14834149961487[/C][C]199.499514304242[/C][/ROW]
[ROW][C]Trimmed Mean ( 30 / 47 )[/C][C]229.068414634146[/C][C]1.12895752396703[/C][C]202.902597990777[/C][/ROW]
[ROW][C]Trimmed Mean ( 31 / 47 )[/C][C]229.068414634146[/C][C]1.10924090212888[/C][C]206.509166939763[/C][/ROW]
[ROW][C]Trimmed Mean ( 32 / 47 )[/C][C]229.006025641026[/C][C]1.09025148308166[/C][C]210.048809100197[/C][/ROW]
[ROW][C]Trimmed Mean ( 33 / 47 )[/C][C]228.967763157895[/C][C]1.06997928490661[/C][C]213.992706576444[/C][/ROW]
[ROW][C]Trimmed Mean ( 34 / 47 )[/C][C]228.923783783784[/C][C]1.04854179703867[/C][C]218.325854467908[/C][/ROW]
[ROW][C]Trimmed Mean ( 35 / 47 )[/C][C]228.876944444444[/C][C]1.02442878161199[/C][C]223.419088327736[/C][/ROW]
[ROW][C]Trimmed Mean ( 36 / 47 )[/C][C]228.838857142857[/C][C]1.00064936561882[/C][C]228.690353489946[/C][/ROW]
[ROW][C]Trimmed Mean ( 37 / 47 )[/C][C]228.795882352941[/C][C]0.977425019079908[/C][C]234.080239288653[/C][/ROW]
[ROW][C]Trimmed Mean ( 38 / 47 )[/C][C]228.750454545455[/C][C]0.951178447880209[/C][C]240.491629152497[/C][/ROW]
[ROW][C]Trimmed Mean ( 39 / 47 )[/C][C]228.67625[/C][C]0.927329582063379[/C][C]246.596522340178[/C][/ROW]
[ROW][C]Trimmed Mean ( 40 / 47 )[/C][C]228.609193548387[/C][C]0.90544160506303[/C][C]252.483641429833[/C][/ROW]
[ROW][C]Trimmed Mean ( 41 / 47 )[/C][C]228.538833333333[/C][C]0.8798181659746[/C][C]259.756893153228[/C][/ROW]
[ROW][C]Trimmed Mean ( 42 / 47 )[/C][C]228.476896551724[/C][C]0.855095230256145[/C][C]267.194680156599[/C][/ROW]
[ROW][C]Trimmed Mean ( 43 / 47 )[/C][C]228.388214285714[/C][C]0.831655917672018[/C][C]274.618636665295[/C][/ROW]
[ROW][C]Trimmed Mean ( 44 / 47 )[/C][C]228.326666666667[/C][C]0.813374015204177[/C][C]280.715467175763[/C][/ROW]
[ROW][C]Trimmed Mean ( 45 / 47 )[/C][C]228.303846153846[/C][C]0.80699315067556[/C][C]282.906795383239[/C][/ROW]
[ROW][C]Trimmed Mean ( 46 / 47 )[/C][C]228.2798[/C][C]0.799109529413835[/C][C]285.66772338136[/C][/ROW]
[ROW][C]Trimmed Mean ( 47 / 47 )[/C][C]228.254375[/C][C]0.790544122373525[/C][C]288.730721714419[/C][/ROW]
[ROW][C]Median[/C][C]226.73[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]244.795[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]228.63[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]228.876944444444[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]228.876944444444[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]228.876944444444[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]228.838857142857[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]228.876944444444[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]228.876944444444[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]228.876944444444[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]142[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=74519&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=74519&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 Mean231.0893661971832.04529311245124112.985940641157
Geometric Mean229.843714260542
Harmonic Mean228.626783472958
Quadratic Mean232.362066055433
Winsorized Mean ( 1 / 47 )231.0140845070422.02421474445881114.125284947870
Winsorized Mean ( 2 / 47 )231.0247887323942.00887048624085115.002331068493
Winsorized Mean ( 3 / 47 )231.0590140845071.99499972351178115.819070730384
Winsorized Mean ( 4 / 47 )230.8742253521131.95791509483149117.918405124704
Winsorized Mean ( 5 / 47 )230.8192957746481.92994140462115119.599121103865
Winsorized Mean ( 6 / 47 )230.811.91833290613162120.318011155549
Winsorized Mean ( 7 / 47 )230.6458450704231.88769927240338122.183574705080
Winsorized Mean ( 8 / 47 )230.5540140845071.85572586075672124.23926343867
Winsorized Mean ( 9 / 47 )230.3790845070421.82098812229339126.513227454168
Winsorized Mean ( 10 / 47 )230.3952816901411.81627995550581126.850093231348
Winsorized Mean ( 11 / 47 )230.3883098591551.81437037175099126.979757521511
Winsorized Mean ( 12 / 47 )230.393380281691.80379401228372127.727101161621
Winsorized Mean ( 13 / 47 )230.3952112676061.79288580331515128.505234879763
Winsorized Mean ( 14 / 47 )230.3143661971831.76778604203349130.284073253713
Winsorized Mean ( 15 / 47 )230.5034507042251.73735516725362132.674915900242
Winsorized Mean ( 16 / 47 )230.4245774647891.67846642556129137.282804085720
Winsorized Mean ( 17 / 47 )230.2438028169011.63314350986915140.981978268002
Winsorized Mean ( 18 / 47 )229.9712676056341.58029687608162145.524091761702
Winsorized Mean ( 19 / 47 )230.2388732394371.53708423004812149.789366606298
Winsorized Mean ( 20 / 47 )230.2656338028171.51609717990737151.880523791282
Winsorized Mean ( 21 / 47 )230.2523239436621.49213052639384154.311114122256
Winsorized Mean ( 22 / 47 )230.3979577464791.46084659541461157.715367561293
Winsorized Mean ( 23 / 47 )230.2942957746481.43487145496639160.498206984013
Winsorized Mean ( 24 / 47 )230.2520422535211.40454076734834163.934039941196
Winsorized Mean ( 25 / 47 )229.9826760563381.34717312776611170.715011542500
Winsorized Mean ( 26 / 47 )229.9112676056341.29621305867081177.371510082914
Winsorized Mean ( 27 / 47 )229.7648591549301.27001130537165180.915601446313
Winsorized Mean ( 28 / 47 )229.5597887323941.24543366309612184.321169030966
Winsorized Mean ( 29 / 47 )229.5148591549301.22996967012637186.602047781672
Winsorized Mean ( 30 / 47 )229.4261267605631.20609658925189190.222017709933
Winsorized Mean ( 31 / 47 )229.7492253521131.17100991033736196.197507231961
Winsorized Mean ( 32 / 47 )229.6613380281691.15481949386862198.87206550247
Winsorized Mean ( 33 / 47 )229.7240845070421.13503265702073202.394251025366
Winsorized Mean ( 34 / 47 )229.7312676056341.12564890378461204.087852645030
Winsorized Mean ( 35 / 47 )229.5340845070421.09024155682667210.53507185613
Winsorized Mean ( 36 / 47 )229.5797183098591.05216642686783218.197152510645
Winsorized Mean ( 37 / 47 )229.5771126760561.04102141076657220.530634914612
Winsorized Mean ( 38 / 47 )230.0213380281690.983653998914351233.843748189954
Winsorized Mean ( 39 / 47 )229.8180985915490.936839108419591245.312238276691
Winsorized Mean ( 40 / 47 )229.798380281690.929575029604394247.207996087725
Winsorized Mean ( 41 / 47 )229.5760563380280.88885753924905258.282172565004
Winsorized Mean ( 42 / 47 )229.9457746478870.840587126864194273.553766527092
Winsorized Mean ( 43 / 47 )229.3946478873240.779389398184448294.326107619232
Winsorized Mean ( 44 / 47 )228.6943661971830.677583746072507337.514539749173
Winsorized Mean ( 45 / 47 )228.6848591549300.67122960546863340.695430135668
Winsorized Mean ( 46 / 47 )228.6751408450700.657383167921678347.856702154435
Winsorized Mean ( 47 / 47 )228.6188732394370.64819051593376352.703206263511
Trimmed Mean ( 1 / 47 )230.8935714285711.97876495337712116.685698841851
Trimmed Mean ( 2 / 47 )230.7695652173911.92897864005156119.633032956354
Trimmed Mean ( 3 / 47 )230.6363235294121.88324263709207122.467662417382
Trimmed Mean ( 4 / 47 )230.4870149253731.83860510289293125.359716756315
Trimmed Mean ( 5 / 47 )230.3828787878791.80140210167685127.890868215056
Trimmed Mean ( 6 / 47 )230.2875384615381.76790442591550130.260174184634
Trimmed Mean ( 7 / 47 )230.2875384615381.73372487349554132.828190898151
Trimmed Mean ( 8 / 47 )230.1176984126981.70238687398978135.173562442588
Trimmed Mean ( 9 / 47 )230.0552419354841.67376772378291137.447531498297
Trimmed Mean ( 10 / 47 )230.0133606557381.64810329996066139.562465933554
Trimmed Mean ( 11 / 47 )229.9681666666671.62050070064008141.911797122848
Trimmed Mean ( 12 / 47 )229.9222033898311.59025623989552144.581858961885
Trimmed Mean ( 13 / 47 )229.8741379310341.55826537391637147.519249146437
Trimmed Mean ( 14 / 47 )229.8741379310341.52426382339241150.809941430890
Trimmed Mean ( 15 / 47 )229.7798214285711.48987560798026154.227520873418
Trimmed Mean ( 16 / 47 )229.7175454545451.45551319196451157.825807916241
Trimmed Mean ( 17 / 47 )229.6594444444441.42477117261396161.190406472851
Trimmed Mean ( 18 / 47 )229.6133962264151.39611543535527164.465910491123
Trimmed Mean ( 19 / 47 )229.586251.37050463596353167.519499004532
Trimmed Mean ( 20 / 47 )229.5384313725491.34678209454763170.434721624101
Trimmed Mean ( 21 / 47 )229.48681.32250121826909173.52483069948
Trimmed Mean ( 22 / 47 )229.4339795918371.29787759663002176.776284749478
Trimmed Mean ( 23 / 47 )229.3691666666671.27354905975480180.102340706708
Trimmed Mean ( 24 / 47 )229.3084042553191.24898473803532183.595841704220
Trimmed Mean ( 25 / 47 )229.2477173913041.22455227056111187.209417599020
Trimmed Mean ( 26 / 47 )229.2013333333331.20337921208981190.464760426847
Trimmed Mean ( 27 / 47 )229.1572727272731.18489293070863193.399139102151
Trimmed Mean ( 28 / 47 )229.1572727272731.16661091450094196.429906388543
Trimmed Mean ( 29 / 47 )229.0935714285711.14834149961487199.499514304242
Trimmed Mean ( 30 / 47 )229.0684146341461.12895752396703202.902597990777
Trimmed Mean ( 31 / 47 )229.0684146341461.10924090212888206.509166939763
Trimmed Mean ( 32 / 47 )229.0060256410261.09025148308166210.048809100197
Trimmed Mean ( 33 / 47 )228.9677631578951.06997928490661213.992706576444
Trimmed Mean ( 34 / 47 )228.9237837837841.04854179703867218.325854467908
Trimmed Mean ( 35 / 47 )228.8769444444441.02442878161199223.419088327736
Trimmed Mean ( 36 / 47 )228.8388571428571.00064936561882228.690353489946
Trimmed Mean ( 37 / 47 )228.7958823529410.977425019079908234.080239288653
Trimmed Mean ( 38 / 47 )228.7504545454550.951178447880209240.491629152497
Trimmed Mean ( 39 / 47 )228.676250.927329582063379246.596522340178
Trimmed Mean ( 40 / 47 )228.6091935483870.90544160506303252.483641429833
Trimmed Mean ( 41 / 47 )228.5388333333330.8798181659746259.756893153228
Trimmed Mean ( 42 / 47 )228.4768965517240.855095230256145267.194680156599
Trimmed Mean ( 43 / 47 )228.3882142857140.831655917672018274.618636665295
Trimmed Mean ( 44 / 47 )228.3266666666670.813374015204177280.715467175763
Trimmed Mean ( 45 / 47 )228.3038461538460.80699315067556282.906795383239
Trimmed Mean ( 46 / 47 )228.27980.799109529413835285.66772338136
Trimmed Mean ( 47 / 47 )228.2543750.790544122373525288.730721714419
Median226.73
Midrange244.795
Midmean - Weighted Average at Xnp228.63
Midmean - Weighted Average at X(n+1)p228.876944444444
Midmean - Empirical Distribution Function228.876944444444
Midmean - Empirical Distribution Function - Averaging228.876944444444
Midmean - Empirical Distribution Function - Interpolation228.838857142857
Midmean - Closest Observation228.876944444444
Midmean - True Basic - Statistics Graphics Toolkit228.876944444444
Midmean - MS Excel (old versions)228.876944444444
Number of observations142



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')