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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 computationWed, 08 Oct 2014 13:14:34 +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/08/t1412770509uwnycnj0a189dxf.htm/, Retrieved Sat, 11 May 2024 18:42:50 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=239537, Retrieved Sat, 11 May 2024 18:42:50 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact46
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2014-10-08 12:14:34] [4f675b9afdd3602a3170287ae908b245] [Current]
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Dataseries X:
239 050
238 600
236 980
236 050
234 870
233 060
231 370
230 300
228 340
226 760
223 550
221 460
220 560
220 350
219 500
218 800
218 130
217 150
216 430
215 310
213 780
213 040
211 940
212 270
212 540
213 790
214 400
215 520
216 690
217 630
218 710
219 360
219 800
221 110
221 320
225 230
227 340
228 930
230 340
231 270
231 830
232 450
233 220
233 520
234 520
234 860
236 560
238 310
239 690
240 700
241 330
241 580
241 670
241 970
241 690
241 410
242 130
242 130
243 320
242 030
242 740
243 050
243 360
243 940
244 270
244 350
244 260
244 230
245 130
246 740
247 910
249 590
251 610
253 430
255 290
256 710
257 190
257 820
257 460
257 970
259 520
261 340
263 150




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gertrude Mary Cox' @ cox.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 & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=239537&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=239537&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=239537&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'Gertrude Mary Cox' @ cox.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean234429.0361445781528.50625538249153.371329243213
Geometric Mean234020.844813372
Harmonic Mean233613.418636269
Quadratic Mean234837.288692066
Winsorized Mean ( 1 / 27 )234411.2048192771522.94707879402153.91946843281
Winsorized Mean ( 2 / 27 )234373.8554216871512.62285834493154.945334938368
Winsorized Mean ( 3 / 27 )234335.9036144581498.39738107474156.391025888191
Winsorized Mean ( 4 / 27 )234364.3373493981490.91557258337157.194908725318
Winsorized Mean ( 5 / 27 )234343.2530120481486.67747215499157.628845126952
Winsorized Mean ( 6 / 27 )234367.8313253011475.63024929145158.825580756316
Winsorized Mean ( 7 / 27 )234404.0963855421455.55698508327161.040824088472
Winsorized Mean ( 8 / 27 )234287.4698795181427.23984377316164.154238617763
Winsorized Mean ( 9 / 27 )234184.4578313251376.25251107091170.160966790243
Winsorized Mean ( 10 / 27 )233996.5060240961334.95766703702175.283839931388
Winsorized Mean ( 11 / 27 )233789.7590361451283.66124345521182.12730206519
Winsorized Mean ( 12 / 27 )233616.2650602411237.34928628471188.803814452185
Winsorized Mean ( 13 / 27 )233511.3253012051199.82043630438194.621893606392
Winsorized Mean ( 14 / 27 )233337.5903614461149.30503973348203.024943156566
Winsorized Mean ( 15 / 27 )233212.8915662651129.4796537692206.47816964919
Winsorized Mean ( 16 / 27 )233305.4216867471110.96099459326210.003251979305
Winsorized Mean ( 17 / 27 )233332.0481927711106.33356501028210.905693881395
Winsorized Mean ( 18 / 27 )233390.6024096391095.66841901973213.012074052886
Winsorized Mean ( 19 / 27 )233450.1204819281068.75644179716218.431544692607
Winsorized Mean ( 20 / 27 )233360.9638554221044.67020604135223.382424908733
Winsorized Mean ( 21 / 27 )2334901022.81749466246228.281195050397
Winsorized Mean ( 22 / 27 )233474.0963855421006.26283096818232.020988155654
Winsorized Mean ( 23 / 27 )233426.987951807990.638575858735235.632846973944
Winsorized Mean ( 24 / 27 )233854.939759036882.829936866984264.89239885651
Winsorized Mean ( 25 / 27 )234360.963855422812.064799958539288.598845643091
Winsorized Mean ( 26 / 27 )234808.915662651743.847484755698315.668091207929
Winsorized Mean ( 27 / 27 )234978.072289157716.820522864097327.806005539976
Trimmed Mean ( 1 / 27 )234352.0987654321499.48249011106156.288653125969
Trimmed Mean ( 2 / 27 )2342901472.10736611532159.152793738311
Trimmed Mean ( 3 / 27 )234244.8051948051446.4642186484161.94303472898
Trimmed Mean ( 4 / 27 )234211.21422.55225474408164.641544251838
Trimmed Mean ( 5 / 27 )234167.6712328771396.910124711167.632596464517
Trimmed Mean ( 6 / 27 )234126.619718311367.8130548671171.168581031754
Trimmed Mean ( 7 / 27 )234126.619718311336.19803545828175.218503174951
Trimmed Mean ( 8 / 27 )234020.5970149251303.41972505951179.543544198121
Trimmed Mean ( 9 / 27 )2339781270.76705333674184.123438977763
Trimmed Mean ( 10 / 27 )233947.7777777781242.6333146826188.267749635808
Trimmed Mean ( 11 / 27 )233941.1475409841217.0929285111192.213052973013
Trimmed Mean ( 12 / 27 )233960.5084745761195.98518488409195.621577450602
Trimmed Mean ( 13 / 27 )234002.2807017541178.51870134506198.556272747038
Trimmed Mean ( 14 / 27 )234002.2807017541163.2752396292201.158137584312
Trimmed Mean ( 15 / 27 )2341401152.47650930476203.162492345503
Trimmed Mean ( 16 / 27 )234240.5882352941141.11216515807205.273938344918
Trimmed Mean ( 17 / 27 )234339.5918367351128.99856139468207.564119078459
Trimmed Mean ( 18 / 27 )234444.2553191491113.12187536055210.618675734147
Trimmed Mean ( 19 / 27 )234552.2222222221093.61451894595214.474312620034
Trimmed Mean ( 20 / 27 )234664.1860465121072.5852496048218.783715451034
Trimmed Mean ( 21 / 27 )234796.0975609761048.35363832132223.966502312085
Trimmed Mean ( 22 / 27 )234928.4615384621019.97092774726230.328585989537
Trimmed Mean ( 23 / 27 )235076.756756757984.039909074199238.889454166468
Trimmed Mean ( 24 / 27 )235246.857142857936.948181255369251.07776699845
Trimmed Mean ( 25 / 27 )235392.727272727902.317751338277260.875647102812
Trimmed Mean ( 26 / 27 )235503.225806452874.194484783056269.394545385281
Trimmed Mean ( 27 / 27 )235579.655172414853.498087813405276.016617419672
Median234870
Midrange237545
Midmean - Weighted Average at Xnp234457.142857143
Midmean - Weighted Average at X(n+1)p234664.186046512
Midmean - Empirical Distribution Function234664.186046512
Midmean - Empirical Distribution Function - Averaging234664.186046512
Midmean - Empirical Distribution Function - Interpolation234796.097560976
Midmean - Closest Observation234457.142857143
Midmean - True Basic - Statistics Graphics Toolkit234664.186046512
Midmean - MS Excel (old versions)234664.186046512
Number of observations83

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 234429.036144578 & 1528.50625538249 & 153.371329243213 \tabularnewline
Geometric Mean & 234020.844813372 &  &  \tabularnewline
Harmonic Mean & 233613.418636269 &  &  \tabularnewline
Quadratic Mean & 234837.288692066 &  &  \tabularnewline
Winsorized Mean ( 1 / 27 ) & 234411.204819277 & 1522.94707879402 & 153.91946843281 \tabularnewline
Winsorized Mean ( 2 / 27 ) & 234373.855421687 & 1512.62285834493 & 154.945334938368 \tabularnewline
Winsorized Mean ( 3 / 27 ) & 234335.903614458 & 1498.39738107474 & 156.391025888191 \tabularnewline
Winsorized Mean ( 4 / 27 ) & 234364.337349398 & 1490.91557258337 & 157.194908725318 \tabularnewline
Winsorized Mean ( 5 / 27 ) & 234343.253012048 & 1486.67747215499 & 157.628845126952 \tabularnewline
Winsorized Mean ( 6 / 27 ) & 234367.831325301 & 1475.63024929145 & 158.825580756316 \tabularnewline
Winsorized Mean ( 7 / 27 ) & 234404.096385542 & 1455.55698508327 & 161.040824088472 \tabularnewline
Winsorized Mean ( 8 / 27 ) & 234287.469879518 & 1427.23984377316 & 164.154238617763 \tabularnewline
Winsorized Mean ( 9 / 27 ) & 234184.457831325 & 1376.25251107091 & 170.160966790243 \tabularnewline
Winsorized Mean ( 10 / 27 ) & 233996.506024096 & 1334.95766703702 & 175.283839931388 \tabularnewline
Winsorized Mean ( 11 / 27 ) & 233789.759036145 & 1283.66124345521 & 182.12730206519 \tabularnewline
Winsorized Mean ( 12 / 27 ) & 233616.265060241 & 1237.34928628471 & 188.803814452185 \tabularnewline
Winsorized Mean ( 13 / 27 ) & 233511.325301205 & 1199.82043630438 & 194.621893606392 \tabularnewline
Winsorized Mean ( 14 / 27 ) & 233337.590361446 & 1149.30503973348 & 203.024943156566 \tabularnewline
Winsorized Mean ( 15 / 27 ) & 233212.891566265 & 1129.4796537692 & 206.47816964919 \tabularnewline
Winsorized Mean ( 16 / 27 ) & 233305.421686747 & 1110.96099459326 & 210.003251979305 \tabularnewline
Winsorized Mean ( 17 / 27 ) & 233332.048192771 & 1106.33356501028 & 210.905693881395 \tabularnewline
Winsorized Mean ( 18 / 27 ) & 233390.602409639 & 1095.66841901973 & 213.012074052886 \tabularnewline
Winsorized Mean ( 19 / 27 ) & 233450.120481928 & 1068.75644179716 & 218.431544692607 \tabularnewline
Winsorized Mean ( 20 / 27 ) & 233360.963855422 & 1044.67020604135 & 223.382424908733 \tabularnewline
Winsorized Mean ( 21 / 27 ) & 233490 & 1022.81749466246 & 228.281195050397 \tabularnewline
Winsorized Mean ( 22 / 27 ) & 233474.096385542 & 1006.26283096818 & 232.020988155654 \tabularnewline
Winsorized Mean ( 23 / 27 ) & 233426.987951807 & 990.638575858735 & 235.632846973944 \tabularnewline
Winsorized Mean ( 24 / 27 ) & 233854.939759036 & 882.829936866984 & 264.89239885651 \tabularnewline
Winsorized Mean ( 25 / 27 ) & 234360.963855422 & 812.064799958539 & 288.598845643091 \tabularnewline
Winsorized Mean ( 26 / 27 ) & 234808.915662651 & 743.847484755698 & 315.668091207929 \tabularnewline
Winsorized Mean ( 27 / 27 ) & 234978.072289157 & 716.820522864097 & 327.806005539976 \tabularnewline
Trimmed Mean ( 1 / 27 ) & 234352.098765432 & 1499.48249011106 & 156.288653125969 \tabularnewline
Trimmed Mean ( 2 / 27 ) & 234290 & 1472.10736611532 & 159.152793738311 \tabularnewline
Trimmed Mean ( 3 / 27 ) & 234244.805194805 & 1446.4642186484 & 161.94303472898 \tabularnewline
Trimmed Mean ( 4 / 27 ) & 234211.2 & 1422.55225474408 & 164.641544251838 \tabularnewline
Trimmed Mean ( 5 / 27 ) & 234167.671232877 & 1396.910124711 & 167.632596464517 \tabularnewline
Trimmed Mean ( 6 / 27 ) & 234126.61971831 & 1367.8130548671 & 171.168581031754 \tabularnewline
Trimmed Mean ( 7 / 27 ) & 234126.61971831 & 1336.19803545828 & 175.218503174951 \tabularnewline
Trimmed Mean ( 8 / 27 ) & 234020.597014925 & 1303.41972505951 & 179.543544198121 \tabularnewline
Trimmed Mean ( 9 / 27 ) & 233978 & 1270.76705333674 & 184.123438977763 \tabularnewline
Trimmed Mean ( 10 / 27 ) & 233947.777777778 & 1242.6333146826 & 188.267749635808 \tabularnewline
Trimmed Mean ( 11 / 27 ) & 233941.147540984 & 1217.0929285111 & 192.213052973013 \tabularnewline
Trimmed Mean ( 12 / 27 ) & 233960.508474576 & 1195.98518488409 & 195.621577450602 \tabularnewline
Trimmed Mean ( 13 / 27 ) & 234002.280701754 & 1178.51870134506 & 198.556272747038 \tabularnewline
Trimmed Mean ( 14 / 27 ) & 234002.280701754 & 1163.2752396292 & 201.158137584312 \tabularnewline
Trimmed Mean ( 15 / 27 ) & 234140 & 1152.47650930476 & 203.162492345503 \tabularnewline
Trimmed Mean ( 16 / 27 ) & 234240.588235294 & 1141.11216515807 & 205.273938344918 \tabularnewline
Trimmed Mean ( 17 / 27 ) & 234339.591836735 & 1128.99856139468 & 207.564119078459 \tabularnewline
Trimmed Mean ( 18 / 27 ) & 234444.255319149 & 1113.12187536055 & 210.618675734147 \tabularnewline
Trimmed Mean ( 19 / 27 ) & 234552.222222222 & 1093.61451894595 & 214.474312620034 \tabularnewline
Trimmed Mean ( 20 / 27 ) & 234664.186046512 & 1072.5852496048 & 218.783715451034 \tabularnewline
Trimmed Mean ( 21 / 27 ) & 234796.097560976 & 1048.35363832132 & 223.966502312085 \tabularnewline
Trimmed Mean ( 22 / 27 ) & 234928.461538462 & 1019.97092774726 & 230.328585989537 \tabularnewline
Trimmed Mean ( 23 / 27 ) & 235076.756756757 & 984.039909074199 & 238.889454166468 \tabularnewline
Trimmed Mean ( 24 / 27 ) & 235246.857142857 & 936.948181255369 & 251.07776699845 \tabularnewline
Trimmed Mean ( 25 / 27 ) & 235392.727272727 & 902.317751338277 & 260.875647102812 \tabularnewline
Trimmed Mean ( 26 / 27 ) & 235503.225806452 & 874.194484783056 & 269.394545385281 \tabularnewline
Trimmed Mean ( 27 / 27 ) & 235579.655172414 & 853.498087813405 & 276.016617419672 \tabularnewline
Median & 234870 &  &  \tabularnewline
Midrange & 237545 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 234457.142857143 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 234664.186046512 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 234664.186046512 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 234664.186046512 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 234796.097560976 &  &  \tabularnewline
Midmean - Closest Observation & 234457.142857143 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 234664.186046512 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 234664.186046512 &  &  \tabularnewline
Number of observations & 83 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=239537&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]234429.036144578[/C][C]1528.50625538249[/C][C]153.371329243213[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]234020.844813372[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]233613.418636269[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]234837.288692066[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 27 )[/C][C]234411.204819277[/C][C]1522.94707879402[/C][C]153.91946843281[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 27 )[/C][C]234373.855421687[/C][C]1512.62285834493[/C][C]154.945334938368[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 27 )[/C][C]234335.903614458[/C][C]1498.39738107474[/C][C]156.391025888191[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 27 )[/C][C]234364.337349398[/C][C]1490.91557258337[/C][C]157.194908725318[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 27 )[/C][C]234343.253012048[/C][C]1486.67747215499[/C][C]157.628845126952[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 27 )[/C][C]234367.831325301[/C][C]1475.63024929145[/C][C]158.825580756316[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 27 )[/C][C]234404.096385542[/C][C]1455.55698508327[/C][C]161.040824088472[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 27 )[/C][C]234287.469879518[/C][C]1427.23984377316[/C][C]164.154238617763[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 27 )[/C][C]234184.457831325[/C][C]1376.25251107091[/C][C]170.160966790243[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 27 )[/C][C]233996.506024096[/C][C]1334.95766703702[/C][C]175.283839931388[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 27 )[/C][C]233789.759036145[/C][C]1283.66124345521[/C][C]182.12730206519[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 27 )[/C][C]233616.265060241[/C][C]1237.34928628471[/C][C]188.803814452185[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 27 )[/C][C]233511.325301205[/C][C]1199.82043630438[/C][C]194.621893606392[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 27 )[/C][C]233337.590361446[/C][C]1149.30503973348[/C][C]203.024943156566[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 27 )[/C][C]233212.891566265[/C][C]1129.4796537692[/C][C]206.47816964919[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 27 )[/C][C]233305.421686747[/C][C]1110.96099459326[/C][C]210.003251979305[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 27 )[/C][C]233332.048192771[/C][C]1106.33356501028[/C][C]210.905693881395[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 27 )[/C][C]233390.602409639[/C][C]1095.66841901973[/C][C]213.012074052886[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 27 )[/C][C]233450.120481928[/C][C]1068.75644179716[/C][C]218.431544692607[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 27 )[/C][C]233360.963855422[/C][C]1044.67020604135[/C][C]223.382424908733[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 27 )[/C][C]233490[/C][C]1022.81749466246[/C][C]228.281195050397[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 27 )[/C][C]233474.096385542[/C][C]1006.26283096818[/C][C]232.020988155654[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 27 )[/C][C]233426.987951807[/C][C]990.638575858735[/C][C]235.632846973944[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 27 )[/C][C]233854.939759036[/C][C]882.829936866984[/C][C]264.89239885651[/C][/ROW]
[ROW][C]Winsorized Mean ( 25 / 27 )[/C][C]234360.963855422[/C][C]812.064799958539[/C][C]288.598845643091[/C][/ROW]
[ROW][C]Winsorized Mean ( 26 / 27 )[/C][C]234808.915662651[/C][C]743.847484755698[/C][C]315.668091207929[/C][/ROW]
[ROW][C]Winsorized Mean ( 27 / 27 )[/C][C]234978.072289157[/C][C]716.820522864097[/C][C]327.806005539976[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 27 )[/C][C]234352.098765432[/C][C]1499.48249011106[/C][C]156.288653125969[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 27 )[/C][C]234290[/C][C]1472.10736611532[/C][C]159.152793738311[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 27 )[/C][C]234244.805194805[/C][C]1446.4642186484[/C][C]161.94303472898[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 27 )[/C][C]234211.2[/C][C]1422.55225474408[/C][C]164.641544251838[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 27 )[/C][C]234167.671232877[/C][C]1396.910124711[/C][C]167.632596464517[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 27 )[/C][C]234126.61971831[/C][C]1367.8130548671[/C][C]171.168581031754[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 27 )[/C][C]234126.61971831[/C][C]1336.19803545828[/C][C]175.218503174951[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 27 )[/C][C]234020.597014925[/C][C]1303.41972505951[/C][C]179.543544198121[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 27 )[/C][C]233978[/C][C]1270.76705333674[/C][C]184.123438977763[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 27 )[/C][C]233947.777777778[/C][C]1242.6333146826[/C][C]188.267749635808[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 27 )[/C][C]233941.147540984[/C][C]1217.0929285111[/C][C]192.213052973013[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 27 )[/C][C]233960.508474576[/C][C]1195.98518488409[/C][C]195.621577450602[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 27 )[/C][C]234002.280701754[/C][C]1178.51870134506[/C][C]198.556272747038[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 27 )[/C][C]234002.280701754[/C][C]1163.2752396292[/C][C]201.158137584312[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 27 )[/C][C]234140[/C][C]1152.47650930476[/C][C]203.162492345503[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 27 )[/C][C]234240.588235294[/C][C]1141.11216515807[/C][C]205.273938344918[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 27 )[/C][C]234339.591836735[/C][C]1128.99856139468[/C][C]207.564119078459[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 27 )[/C][C]234444.255319149[/C][C]1113.12187536055[/C][C]210.618675734147[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 27 )[/C][C]234552.222222222[/C][C]1093.61451894595[/C][C]214.474312620034[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 27 )[/C][C]234664.186046512[/C][C]1072.5852496048[/C][C]218.783715451034[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 27 )[/C][C]234796.097560976[/C][C]1048.35363832132[/C][C]223.966502312085[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 27 )[/C][C]234928.461538462[/C][C]1019.97092774726[/C][C]230.328585989537[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 27 )[/C][C]235076.756756757[/C][C]984.039909074199[/C][C]238.889454166468[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 27 )[/C][C]235246.857142857[/C][C]936.948181255369[/C][C]251.07776699845[/C][/ROW]
[ROW][C]Trimmed Mean ( 25 / 27 )[/C][C]235392.727272727[/C][C]902.317751338277[/C][C]260.875647102812[/C][/ROW]
[ROW][C]Trimmed Mean ( 26 / 27 )[/C][C]235503.225806452[/C][C]874.194484783056[/C][C]269.394545385281[/C][/ROW]
[ROW][C]Trimmed Mean ( 27 / 27 )[/C][C]235579.655172414[/C][C]853.498087813405[/C][C]276.016617419672[/C][/ROW]
[ROW][C]Median[/C][C]234870[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]237545[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]234457.142857143[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]234664.186046512[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]234664.186046512[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]234664.186046512[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]234796.097560976[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]234457.142857143[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]234664.186046512[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]234664.186046512[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]83[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=239537&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=239537&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 Mean234429.0361445781528.50625538249153.371329243213
Geometric Mean234020.844813372
Harmonic Mean233613.418636269
Quadratic Mean234837.288692066
Winsorized Mean ( 1 / 27 )234411.2048192771522.94707879402153.91946843281
Winsorized Mean ( 2 / 27 )234373.8554216871512.62285834493154.945334938368
Winsorized Mean ( 3 / 27 )234335.9036144581498.39738107474156.391025888191
Winsorized Mean ( 4 / 27 )234364.3373493981490.91557258337157.194908725318
Winsorized Mean ( 5 / 27 )234343.2530120481486.67747215499157.628845126952
Winsorized Mean ( 6 / 27 )234367.8313253011475.63024929145158.825580756316
Winsorized Mean ( 7 / 27 )234404.0963855421455.55698508327161.040824088472
Winsorized Mean ( 8 / 27 )234287.4698795181427.23984377316164.154238617763
Winsorized Mean ( 9 / 27 )234184.4578313251376.25251107091170.160966790243
Winsorized Mean ( 10 / 27 )233996.5060240961334.95766703702175.283839931388
Winsorized Mean ( 11 / 27 )233789.7590361451283.66124345521182.12730206519
Winsorized Mean ( 12 / 27 )233616.2650602411237.34928628471188.803814452185
Winsorized Mean ( 13 / 27 )233511.3253012051199.82043630438194.621893606392
Winsorized Mean ( 14 / 27 )233337.5903614461149.30503973348203.024943156566
Winsorized Mean ( 15 / 27 )233212.8915662651129.4796537692206.47816964919
Winsorized Mean ( 16 / 27 )233305.4216867471110.96099459326210.003251979305
Winsorized Mean ( 17 / 27 )233332.0481927711106.33356501028210.905693881395
Winsorized Mean ( 18 / 27 )233390.6024096391095.66841901973213.012074052886
Winsorized Mean ( 19 / 27 )233450.1204819281068.75644179716218.431544692607
Winsorized Mean ( 20 / 27 )233360.9638554221044.67020604135223.382424908733
Winsorized Mean ( 21 / 27 )2334901022.81749466246228.281195050397
Winsorized Mean ( 22 / 27 )233474.0963855421006.26283096818232.020988155654
Winsorized Mean ( 23 / 27 )233426.987951807990.638575858735235.632846973944
Winsorized Mean ( 24 / 27 )233854.939759036882.829936866984264.89239885651
Winsorized Mean ( 25 / 27 )234360.963855422812.064799958539288.598845643091
Winsorized Mean ( 26 / 27 )234808.915662651743.847484755698315.668091207929
Winsorized Mean ( 27 / 27 )234978.072289157716.820522864097327.806005539976
Trimmed Mean ( 1 / 27 )234352.0987654321499.48249011106156.288653125969
Trimmed Mean ( 2 / 27 )2342901472.10736611532159.152793738311
Trimmed Mean ( 3 / 27 )234244.8051948051446.4642186484161.94303472898
Trimmed Mean ( 4 / 27 )234211.21422.55225474408164.641544251838
Trimmed Mean ( 5 / 27 )234167.6712328771396.910124711167.632596464517
Trimmed Mean ( 6 / 27 )234126.619718311367.8130548671171.168581031754
Trimmed Mean ( 7 / 27 )234126.619718311336.19803545828175.218503174951
Trimmed Mean ( 8 / 27 )234020.5970149251303.41972505951179.543544198121
Trimmed Mean ( 9 / 27 )2339781270.76705333674184.123438977763
Trimmed Mean ( 10 / 27 )233947.7777777781242.6333146826188.267749635808
Trimmed Mean ( 11 / 27 )233941.1475409841217.0929285111192.213052973013
Trimmed Mean ( 12 / 27 )233960.5084745761195.98518488409195.621577450602
Trimmed Mean ( 13 / 27 )234002.2807017541178.51870134506198.556272747038
Trimmed Mean ( 14 / 27 )234002.2807017541163.2752396292201.158137584312
Trimmed Mean ( 15 / 27 )2341401152.47650930476203.162492345503
Trimmed Mean ( 16 / 27 )234240.5882352941141.11216515807205.273938344918
Trimmed Mean ( 17 / 27 )234339.5918367351128.99856139468207.564119078459
Trimmed Mean ( 18 / 27 )234444.2553191491113.12187536055210.618675734147
Trimmed Mean ( 19 / 27 )234552.2222222221093.61451894595214.474312620034
Trimmed Mean ( 20 / 27 )234664.1860465121072.5852496048218.783715451034
Trimmed Mean ( 21 / 27 )234796.0975609761048.35363832132223.966502312085
Trimmed Mean ( 22 / 27 )234928.4615384621019.97092774726230.328585989537
Trimmed Mean ( 23 / 27 )235076.756756757984.039909074199238.889454166468
Trimmed Mean ( 24 / 27 )235246.857142857936.948181255369251.07776699845
Trimmed Mean ( 25 / 27 )235392.727272727902.317751338277260.875647102812
Trimmed Mean ( 26 / 27 )235503.225806452874.194484783056269.394545385281
Trimmed Mean ( 27 / 27 )235579.655172414853.498087813405276.016617419672
Median234870
Midrange237545
Midmean - Weighted Average at Xnp234457.142857143
Midmean - Weighted Average at X(n+1)p234664.186046512
Midmean - Empirical Distribution Function234664.186046512
Midmean - Empirical Distribution Function - Averaging234664.186046512
Midmean - Empirical Distribution Function - Interpolation234796.097560976
Midmean - Closest Observation234457.142857143
Midmean - True Basic - Statistics Graphics Toolkit234664.186046512
Midmean - MS Excel (old versions)234664.186046512
Number of observations83



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')