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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 computationMon, 21 Apr 2008 05:12:17 -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/2008/Apr/21/t1208776362gdc4zbnet4y561p.htm/, Retrieved Thu, 16 May 2024 14:21:11 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=10484, Retrieved Thu, 16 May 2024 14:21:11 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact226
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Robuustheid gemid...] [2008-04-21 11:12:17] [d8973bbb712c03ae516525a15d4e5e48] [Current]
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Dataseries X:
7840,00
8292,00
8534,00
8441,00
8602,00
8468,00
8832,00
9006,00
8749,00
8714,00
8193,00
8251,00
8192,00
9056,00
9407,00
9068,00
9431,00
9907,00
10044,00
10838,00
10871,00
11127,00
11303,00
11349,00
11493,00
12694,00
13227,00
12253,00
12234,00
12491,00
13248,00
14042,00
14392,00
14834,00
15542,00
15518,00
16197,00
17325,00
24016,00
23671,00
24998,00
25329,00
25904,00
26548,00
26752,00
26967,00
27034,00
27056,00
27476,00
28497,00
29085,00
28720,00
29067,00
29249,00
29672,00
29761,00
30066,00
30315,00
30571,00
30757,00
30742,00
31310,00
31381,00
31470,00
31226,00
31081,00
31061,00
31114,00
30828,00
30418,00
30195,00
29877,00
29192,00
29876,00
29409,00
28458,00
28340,00
28164,00
28438,00
28053,00




Summary of compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\begin{tabular}{lllllllll}
\hline
Summary of compuational 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 & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=10484&T=0

[TABLE]
[ROW][C]Summary of compuational 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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=10484&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=10484&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 compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean20376.86251037.3585552116519.6430273772047
Geometric Mean17997.6304265605
Harmonic Mean15683.8230505925
Quadratic Mean22365.8094943487
Winsorized Mean ( 1 / 26 )20380.151036.5445234442619.6616252742143
Winsorized Mean ( 2 / 26 )20378.41036.3030685438619.6645176672441
Winsorized Mean ( 3 / 26 )20377.4251035.5608409497519.6776704894627
Winsorized Mean ( 4 / 26 )20373.8751034.5181134312819.6940727624616
Winsorized Mean ( 5 / 26 )20381.1251032.8776659912319.7323707066904
Winsorized Mean ( 6 / 26 )20381.651032.3850524637819.7422947488046
Winsorized Mean ( 7 / 26 )20367.03751028.8961615325319.7950369157403
Winsorized Mean ( 8 / 26 )20366.73751026.9966599146619.8313570968112
Winsorized Mean ( 9 / 26 )20377.651024.9595726976519.88141829474
Winsorized Mean ( 10 / 26 )20360.651021.609640066719.9299705107233
Winsorized Mean ( 11 / 26 )20351.0251017.3224425949120.0044982278088
Winsorized Mean ( 12 / 26 )20361.6751011.6680543261120.1268340073891
Winsorized Mean ( 13 / 26 )20350.31008.0951795090420.1868835539030
Winsorized Mean ( 14 / 26 )20329.8251005.0178490094320.2283223328199
Winsorized Mean ( 15 / 26 )20357.95991.74154913707720.5274751448234
Winsorized Mean ( 16 / 26 )20362.55991.04669270436120.5465092108171
Winsorized Mean ( 17 / 26 )20439.2625974.0971846973820.9827754572043
Winsorized Mean ( 18 / 26 )20450.0625967.46831128292221.1377078313624
Winsorized Mean ( 19 / 26 )20576.175934.68436792872322.0140356531234
Winsorized Mean ( 20 / 26 )20544.425928.83152976645422.1185697746132
Winsorized Mean ( 21 / 26 )20596.6625918.24162882448922.4305475306836
Winsorized Mean ( 22 / 26 )20615.6375908.46271114751322.6928824342824
Winsorized Mean ( 23 / 26 )20623.6875906.13740568012422.7600001619185
Winsorized Mean ( 24 / 26 )20562.7875888.35731540849823.1469782972908
Winsorized Mean ( 25 / 26 )20724.6625850.67870631314424.3625029593382
Winsorized Mean ( 26 / 26 )20718.1625848.43390805822924.4193004348644
Trimmed Mean ( 1 / 26 )20395.37179487181041.9741771514719.5737785466319
Trimmed Mean ( 2 / 26 )20411.39473684211047.2310653519719.4908224289373
Trimmed Mean ( 3 / 26 )20429.22972972971052.4083599044519.4118846904490
Trimmed Mean ( 4 / 26 )20448.41666666671057.6266739430519.3342482470027
Trimmed Mean ( 5 / 26 )20469.71428571431062.8866443288719.258605228443
Trimmed Mean ( 6 / 26 )20490.55882352941068.2655435136219.1811473729033
Trimmed Mean ( 7 / 26 )20512.56060606061073.4081113381919.1097499538066
Trimmed Mean ( 8 / 26 )20538.5468751078.8623299793419.0372268122414
Trimmed Mean ( 9 / 26 )20566.25806451611084.2456708427018.9682639438455
Trimmed Mean ( 10 / 26 )20594.21089.4988970988718.9024514433547
Trimmed Mean ( 11 / 26 )20626.41379310341094.7410846260018.8413626589616
Trimmed Mean ( 12 / 26 )20662.17857142861100.0364958842818.7831755116624
Trimmed Mean ( 13 / 26 )20699.27777777781105.5304586397418.7233898586986
Trimmed Mean ( 14 / 26 )20740.57692307691110.7771399837718.672131588322
Trimmed Mean ( 15 / 26 )20787.521115.5274064233618.6347012904412
Trimmed Mean ( 16 / 26 )20835.251121.3078070442118.5812047941788
Trimmed Mean ( 17 / 26 )20886.63043478261126.0262451179318.5489730149186
Trimmed Mean ( 18 / 26 )20934.47727272731132.178347364818.4904412996886
Trimmed Mean ( 19 / 26 )20985.73809523811138.0243124491418.4405006691594
Trimmed Mean ( 20 / 26 )21028.851148.0638051541918.3167955522957
Trimmed Mean ( 21 / 26 )21079.84210526321157.9729158593918.2040890737231
Trimmed Mean ( 22 / 26 )21130.97222222221168.4839264987318.0840931937673
Trimmed Mean ( 23 / 26 )21186.08823529411179.2879905469317.9651521978685
Trimmed Mean ( 24 / 26 )21247.218751188.5675877941417.8763235412070
Trimmed Mean ( 25 / 26 )21323.26666666671198.7688252530017.7876386317990
Trimmed Mean ( 26 / 26 )21391.67857142861214.9979653058217.6063492962675
Median24507
Midrange19655
Midmean - Weighted Average at Xnp20780.2926829268
Midmean - Weighted Average at X(n+1)p21028.85
Midmean - Empirical Distribution Function20780.2926829268
Midmean - Empirical Distribution Function - Averaging21028.85
Midmean - Empirical Distribution Function - Interpolation21028.85
Midmean - Closest Observation20780.2926829268
Midmean - True Basic - Statistics Graphics Toolkit21028.85
Midmean - MS Excel (old versions)20985.7380952381
Number of observations80

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 20376.8625 & 1037.35855521165 & 19.6430273772047 \tabularnewline
Geometric Mean & 17997.6304265605 &  &  \tabularnewline
Harmonic Mean & 15683.8230505925 &  &  \tabularnewline
Quadratic Mean & 22365.8094943487 &  &  \tabularnewline
Winsorized Mean ( 1 / 26 ) & 20380.15 & 1036.54452344426 & 19.6616252742143 \tabularnewline
Winsorized Mean ( 2 / 26 ) & 20378.4 & 1036.30306854386 & 19.6645176672441 \tabularnewline
Winsorized Mean ( 3 / 26 ) & 20377.425 & 1035.56084094975 & 19.6776704894627 \tabularnewline
Winsorized Mean ( 4 / 26 ) & 20373.875 & 1034.51811343128 & 19.6940727624616 \tabularnewline
Winsorized Mean ( 5 / 26 ) & 20381.125 & 1032.87766599123 & 19.7323707066904 \tabularnewline
Winsorized Mean ( 6 / 26 ) & 20381.65 & 1032.38505246378 & 19.7422947488046 \tabularnewline
Winsorized Mean ( 7 / 26 ) & 20367.0375 & 1028.89616153253 & 19.7950369157403 \tabularnewline
Winsorized Mean ( 8 / 26 ) & 20366.7375 & 1026.99665991466 & 19.8313570968112 \tabularnewline
Winsorized Mean ( 9 / 26 ) & 20377.65 & 1024.95957269765 & 19.88141829474 \tabularnewline
Winsorized Mean ( 10 / 26 ) & 20360.65 & 1021.6096400667 & 19.9299705107233 \tabularnewline
Winsorized Mean ( 11 / 26 ) & 20351.025 & 1017.32244259491 & 20.0044982278088 \tabularnewline
Winsorized Mean ( 12 / 26 ) & 20361.675 & 1011.66805432611 & 20.1268340073891 \tabularnewline
Winsorized Mean ( 13 / 26 ) & 20350.3 & 1008.09517950904 & 20.1868835539030 \tabularnewline
Winsorized Mean ( 14 / 26 ) & 20329.825 & 1005.01784900943 & 20.2283223328199 \tabularnewline
Winsorized Mean ( 15 / 26 ) & 20357.95 & 991.741549137077 & 20.5274751448234 \tabularnewline
Winsorized Mean ( 16 / 26 ) & 20362.55 & 991.046692704361 & 20.5465092108171 \tabularnewline
Winsorized Mean ( 17 / 26 ) & 20439.2625 & 974.09718469738 & 20.9827754572043 \tabularnewline
Winsorized Mean ( 18 / 26 ) & 20450.0625 & 967.468311282922 & 21.1377078313624 \tabularnewline
Winsorized Mean ( 19 / 26 ) & 20576.175 & 934.684367928723 & 22.0140356531234 \tabularnewline
Winsorized Mean ( 20 / 26 ) & 20544.425 & 928.831529766454 & 22.1185697746132 \tabularnewline
Winsorized Mean ( 21 / 26 ) & 20596.6625 & 918.241628824489 & 22.4305475306836 \tabularnewline
Winsorized Mean ( 22 / 26 ) & 20615.6375 & 908.462711147513 & 22.6928824342824 \tabularnewline
Winsorized Mean ( 23 / 26 ) & 20623.6875 & 906.137405680124 & 22.7600001619185 \tabularnewline
Winsorized Mean ( 24 / 26 ) & 20562.7875 & 888.357315408498 & 23.1469782972908 \tabularnewline
Winsorized Mean ( 25 / 26 ) & 20724.6625 & 850.678706313144 & 24.3625029593382 \tabularnewline
Winsorized Mean ( 26 / 26 ) & 20718.1625 & 848.433908058229 & 24.4193004348644 \tabularnewline
Trimmed Mean ( 1 / 26 ) & 20395.3717948718 & 1041.97417715147 & 19.5737785466319 \tabularnewline
Trimmed Mean ( 2 / 26 ) & 20411.3947368421 & 1047.23106535197 & 19.4908224289373 \tabularnewline
Trimmed Mean ( 3 / 26 ) & 20429.2297297297 & 1052.40835990445 & 19.4118846904490 \tabularnewline
Trimmed Mean ( 4 / 26 ) & 20448.4166666667 & 1057.62667394305 & 19.3342482470027 \tabularnewline
Trimmed Mean ( 5 / 26 ) & 20469.7142857143 & 1062.88664432887 & 19.258605228443 \tabularnewline
Trimmed Mean ( 6 / 26 ) & 20490.5588235294 & 1068.26554351362 & 19.1811473729033 \tabularnewline
Trimmed Mean ( 7 / 26 ) & 20512.5606060606 & 1073.40811133819 & 19.1097499538066 \tabularnewline
Trimmed Mean ( 8 / 26 ) & 20538.546875 & 1078.86232997934 & 19.0372268122414 \tabularnewline
Trimmed Mean ( 9 / 26 ) & 20566.2580645161 & 1084.24567084270 & 18.9682639438455 \tabularnewline
Trimmed Mean ( 10 / 26 ) & 20594.2 & 1089.49889709887 & 18.9024514433547 \tabularnewline
Trimmed Mean ( 11 / 26 ) & 20626.4137931034 & 1094.74108462600 & 18.8413626589616 \tabularnewline
Trimmed Mean ( 12 / 26 ) & 20662.1785714286 & 1100.03649588428 & 18.7831755116624 \tabularnewline
Trimmed Mean ( 13 / 26 ) & 20699.2777777778 & 1105.53045863974 & 18.7233898586986 \tabularnewline
Trimmed Mean ( 14 / 26 ) & 20740.5769230769 & 1110.77713998377 & 18.672131588322 \tabularnewline
Trimmed Mean ( 15 / 26 ) & 20787.52 & 1115.52740642336 & 18.6347012904412 \tabularnewline
Trimmed Mean ( 16 / 26 ) & 20835.25 & 1121.30780704421 & 18.5812047941788 \tabularnewline
Trimmed Mean ( 17 / 26 ) & 20886.6304347826 & 1126.02624511793 & 18.5489730149186 \tabularnewline
Trimmed Mean ( 18 / 26 ) & 20934.4772727273 & 1132.1783473648 & 18.4904412996886 \tabularnewline
Trimmed Mean ( 19 / 26 ) & 20985.7380952381 & 1138.02431244914 & 18.4405006691594 \tabularnewline
Trimmed Mean ( 20 / 26 ) & 21028.85 & 1148.06380515419 & 18.3167955522957 \tabularnewline
Trimmed Mean ( 21 / 26 ) & 21079.8421052632 & 1157.97291585939 & 18.2040890737231 \tabularnewline
Trimmed Mean ( 22 / 26 ) & 21130.9722222222 & 1168.48392649873 & 18.0840931937673 \tabularnewline
Trimmed Mean ( 23 / 26 ) & 21186.0882352941 & 1179.28799054693 & 17.9651521978685 \tabularnewline
Trimmed Mean ( 24 / 26 ) & 21247.21875 & 1188.56758779414 & 17.8763235412070 \tabularnewline
Trimmed Mean ( 25 / 26 ) & 21323.2666666667 & 1198.76882525300 & 17.7876386317990 \tabularnewline
Trimmed Mean ( 26 / 26 ) & 21391.6785714286 & 1214.99796530582 & 17.6063492962675 \tabularnewline
Median & 24507 &  &  \tabularnewline
Midrange & 19655 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 20780.2926829268 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 21028.85 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 20780.2926829268 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 21028.85 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 21028.85 &  &  \tabularnewline
Midmean - Closest Observation & 20780.2926829268 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 21028.85 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 20985.7380952381 &  &  \tabularnewline
Number of observations & 80 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=10484&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]20376.8625[/C][C]1037.35855521165[/C][C]19.6430273772047[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]17997.6304265605[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]15683.8230505925[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]22365.8094943487[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 26 )[/C][C]20380.15[/C][C]1036.54452344426[/C][C]19.6616252742143[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 26 )[/C][C]20378.4[/C][C]1036.30306854386[/C][C]19.6645176672441[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 26 )[/C][C]20377.425[/C][C]1035.56084094975[/C][C]19.6776704894627[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 26 )[/C][C]20373.875[/C][C]1034.51811343128[/C][C]19.6940727624616[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 26 )[/C][C]20381.125[/C][C]1032.87766599123[/C][C]19.7323707066904[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 26 )[/C][C]20381.65[/C][C]1032.38505246378[/C][C]19.7422947488046[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 26 )[/C][C]20367.0375[/C][C]1028.89616153253[/C][C]19.7950369157403[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 26 )[/C][C]20366.7375[/C][C]1026.99665991466[/C][C]19.8313570968112[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 26 )[/C][C]20377.65[/C][C]1024.95957269765[/C][C]19.88141829474[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 26 )[/C][C]20360.65[/C][C]1021.6096400667[/C][C]19.9299705107233[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 26 )[/C][C]20351.025[/C][C]1017.32244259491[/C][C]20.0044982278088[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 26 )[/C][C]20361.675[/C][C]1011.66805432611[/C][C]20.1268340073891[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 26 )[/C][C]20350.3[/C][C]1008.09517950904[/C][C]20.1868835539030[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 26 )[/C][C]20329.825[/C][C]1005.01784900943[/C][C]20.2283223328199[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 26 )[/C][C]20357.95[/C][C]991.741549137077[/C][C]20.5274751448234[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 26 )[/C][C]20362.55[/C][C]991.046692704361[/C][C]20.5465092108171[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 26 )[/C][C]20439.2625[/C][C]974.09718469738[/C][C]20.9827754572043[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 26 )[/C][C]20450.0625[/C][C]967.468311282922[/C][C]21.1377078313624[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 26 )[/C][C]20576.175[/C][C]934.684367928723[/C][C]22.0140356531234[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 26 )[/C][C]20544.425[/C][C]928.831529766454[/C][C]22.1185697746132[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 26 )[/C][C]20596.6625[/C][C]918.241628824489[/C][C]22.4305475306836[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 26 )[/C][C]20615.6375[/C][C]908.462711147513[/C][C]22.6928824342824[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 26 )[/C][C]20623.6875[/C][C]906.137405680124[/C][C]22.7600001619185[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 26 )[/C][C]20562.7875[/C][C]888.357315408498[/C][C]23.1469782972908[/C][/ROW]
[ROW][C]Winsorized Mean ( 25 / 26 )[/C][C]20724.6625[/C][C]850.678706313144[/C][C]24.3625029593382[/C][/ROW]
[ROW][C]Winsorized Mean ( 26 / 26 )[/C][C]20718.1625[/C][C]848.433908058229[/C][C]24.4193004348644[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 26 )[/C][C]20395.3717948718[/C][C]1041.97417715147[/C][C]19.5737785466319[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 26 )[/C][C]20411.3947368421[/C][C]1047.23106535197[/C][C]19.4908224289373[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 26 )[/C][C]20429.2297297297[/C][C]1052.40835990445[/C][C]19.4118846904490[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 26 )[/C][C]20448.4166666667[/C][C]1057.62667394305[/C][C]19.3342482470027[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 26 )[/C][C]20469.7142857143[/C][C]1062.88664432887[/C][C]19.258605228443[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 26 )[/C][C]20490.5588235294[/C][C]1068.26554351362[/C][C]19.1811473729033[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 26 )[/C][C]20512.5606060606[/C][C]1073.40811133819[/C][C]19.1097499538066[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 26 )[/C][C]20538.546875[/C][C]1078.86232997934[/C][C]19.0372268122414[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 26 )[/C][C]20566.2580645161[/C][C]1084.24567084270[/C][C]18.9682639438455[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 26 )[/C][C]20594.2[/C][C]1089.49889709887[/C][C]18.9024514433547[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 26 )[/C][C]20626.4137931034[/C][C]1094.74108462600[/C][C]18.8413626589616[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 26 )[/C][C]20662.1785714286[/C][C]1100.03649588428[/C][C]18.7831755116624[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 26 )[/C][C]20699.2777777778[/C][C]1105.53045863974[/C][C]18.7233898586986[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 26 )[/C][C]20740.5769230769[/C][C]1110.77713998377[/C][C]18.672131588322[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 26 )[/C][C]20787.52[/C][C]1115.52740642336[/C][C]18.6347012904412[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 26 )[/C][C]20835.25[/C][C]1121.30780704421[/C][C]18.5812047941788[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 26 )[/C][C]20886.6304347826[/C][C]1126.02624511793[/C][C]18.5489730149186[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 26 )[/C][C]20934.4772727273[/C][C]1132.1783473648[/C][C]18.4904412996886[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 26 )[/C][C]20985.7380952381[/C][C]1138.02431244914[/C][C]18.4405006691594[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 26 )[/C][C]21028.85[/C][C]1148.06380515419[/C][C]18.3167955522957[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 26 )[/C][C]21079.8421052632[/C][C]1157.97291585939[/C][C]18.2040890737231[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 26 )[/C][C]21130.9722222222[/C][C]1168.48392649873[/C][C]18.0840931937673[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 26 )[/C][C]21186.0882352941[/C][C]1179.28799054693[/C][C]17.9651521978685[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 26 )[/C][C]21247.21875[/C][C]1188.56758779414[/C][C]17.8763235412070[/C][/ROW]
[ROW][C]Trimmed Mean ( 25 / 26 )[/C][C]21323.2666666667[/C][C]1198.76882525300[/C][C]17.7876386317990[/C][/ROW]
[ROW][C]Trimmed Mean ( 26 / 26 )[/C][C]21391.6785714286[/C][C]1214.99796530582[/C][C]17.6063492962675[/C][/ROW]
[ROW][C]Median[/C][C]24507[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]19655[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]20780.2926829268[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]21028.85[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]20780.2926829268[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]21028.85[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]21028.85[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]20780.2926829268[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]21028.85[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]20985.7380952381[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]80[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=10484&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=10484&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 Mean20376.86251037.3585552116519.6430273772047
Geometric Mean17997.6304265605
Harmonic Mean15683.8230505925
Quadratic Mean22365.8094943487
Winsorized Mean ( 1 / 26 )20380.151036.5445234442619.6616252742143
Winsorized Mean ( 2 / 26 )20378.41036.3030685438619.6645176672441
Winsorized Mean ( 3 / 26 )20377.4251035.5608409497519.6776704894627
Winsorized Mean ( 4 / 26 )20373.8751034.5181134312819.6940727624616
Winsorized Mean ( 5 / 26 )20381.1251032.8776659912319.7323707066904
Winsorized Mean ( 6 / 26 )20381.651032.3850524637819.7422947488046
Winsorized Mean ( 7 / 26 )20367.03751028.8961615325319.7950369157403
Winsorized Mean ( 8 / 26 )20366.73751026.9966599146619.8313570968112
Winsorized Mean ( 9 / 26 )20377.651024.9595726976519.88141829474
Winsorized Mean ( 10 / 26 )20360.651021.609640066719.9299705107233
Winsorized Mean ( 11 / 26 )20351.0251017.3224425949120.0044982278088
Winsorized Mean ( 12 / 26 )20361.6751011.6680543261120.1268340073891
Winsorized Mean ( 13 / 26 )20350.31008.0951795090420.1868835539030
Winsorized Mean ( 14 / 26 )20329.8251005.0178490094320.2283223328199
Winsorized Mean ( 15 / 26 )20357.95991.74154913707720.5274751448234
Winsorized Mean ( 16 / 26 )20362.55991.04669270436120.5465092108171
Winsorized Mean ( 17 / 26 )20439.2625974.0971846973820.9827754572043
Winsorized Mean ( 18 / 26 )20450.0625967.46831128292221.1377078313624
Winsorized Mean ( 19 / 26 )20576.175934.68436792872322.0140356531234
Winsorized Mean ( 20 / 26 )20544.425928.83152976645422.1185697746132
Winsorized Mean ( 21 / 26 )20596.6625918.24162882448922.4305475306836
Winsorized Mean ( 22 / 26 )20615.6375908.46271114751322.6928824342824
Winsorized Mean ( 23 / 26 )20623.6875906.13740568012422.7600001619185
Winsorized Mean ( 24 / 26 )20562.7875888.35731540849823.1469782972908
Winsorized Mean ( 25 / 26 )20724.6625850.67870631314424.3625029593382
Winsorized Mean ( 26 / 26 )20718.1625848.43390805822924.4193004348644
Trimmed Mean ( 1 / 26 )20395.37179487181041.9741771514719.5737785466319
Trimmed Mean ( 2 / 26 )20411.39473684211047.2310653519719.4908224289373
Trimmed Mean ( 3 / 26 )20429.22972972971052.4083599044519.4118846904490
Trimmed Mean ( 4 / 26 )20448.41666666671057.6266739430519.3342482470027
Trimmed Mean ( 5 / 26 )20469.71428571431062.8866443288719.258605228443
Trimmed Mean ( 6 / 26 )20490.55882352941068.2655435136219.1811473729033
Trimmed Mean ( 7 / 26 )20512.56060606061073.4081113381919.1097499538066
Trimmed Mean ( 8 / 26 )20538.5468751078.8623299793419.0372268122414
Trimmed Mean ( 9 / 26 )20566.25806451611084.2456708427018.9682639438455
Trimmed Mean ( 10 / 26 )20594.21089.4988970988718.9024514433547
Trimmed Mean ( 11 / 26 )20626.41379310341094.7410846260018.8413626589616
Trimmed Mean ( 12 / 26 )20662.17857142861100.0364958842818.7831755116624
Trimmed Mean ( 13 / 26 )20699.27777777781105.5304586397418.7233898586986
Trimmed Mean ( 14 / 26 )20740.57692307691110.7771399837718.672131588322
Trimmed Mean ( 15 / 26 )20787.521115.5274064233618.6347012904412
Trimmed Mean ( 16 / 26 )20835.251121.3078070442118.5812047941788
Trimmed Mean ( 17 / 26 )20886.63043478261126.0262451179318.5489730149186
Trimmed Mean ( 18 / 26 )20934.47727272731132.178347364818.4904412996886
Trimmed Mean ( 19 / 26 )20985.73809523811138.0243124491418.4405006691594
Trimmed Mean ( 20 / 26 )21028.851148.0638051541918.3167955522957
Trimmed Mean ( 21 / 26 )21079.84210526321157.9729158593918.2040890737231
Trimmed Mean ( 22 / 26 )21130.97222222221168.4839264987318.0840931937673
Trimmed Mean ( 23 / 26 )21186.08823529411179.2879905469317.9651521978685
Trimmed Mean ( 24 / 26 )21247.218751188.5675877941417.8763235412070
Trimmed Mean ( 25 / 26 )21323.26666666671198.7688252530017.7876386317990
Trimmed Mean ( 26 / 26 )21391.67857142861214.9979653058217.6063492962675
Median24507
Midrange19655
Midmean - Weighted Average at Xnp20780.2926829268
Midmean - Weighted Average at X(n+1)p21028.85
Midmean - Empirical Distribution Function20780.2926829268
Midmean - Empirical Distribution Function - Averaging21028.85
Midmean - Empirical Distribution Function - Interpolation21028.85
Midmean - Closest Observation20780.2926829268
Midmean - True Basic - Statistics Graphics Toolkit21028.85
Midmean - MS Excel (old versions)20985.7380952381
Number of observations80



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')