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of Irreproducible Research!

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationTue, 20 Oct 2009 09:26:17 -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/2009/Oct/20/t1256052423ftshlc6xf5fgank.htm/, Retrieved Fri, 03 May 2024 00:30:29 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=48728, Retrieved Fri, 03 May 2024 00:30:29 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact109
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Bivariate Data Series] [Bivariate dataset] [2008-01-05 23:51:08] [74be16979710d4c4e7c6647856088456]
F RMPD  [Univariate Explorative Data Analysis] [Colombia Coffee] [2008-01-07 14:21:11] [74be16979710d4c4e7c6647856088456]
F RMPD    [Univariate Data Series] [] [2009-10-14 08:30:28] [74be16979710d4c4e7c6647856088456]
- RMPD        [Central Tendency] [] [2009-10-20 15:26:17] [244731fa3e7e6c85774b8c0902c58f85] [Current]
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Post a new message
Dataseries X:
3071
3388
2652
3190
2885
3295
3818
3226
3953
3810
2877
3515
3708
3450
3360
4110
4385
3729
4309
3506
3690
3911
2952
3324
3417
3498
2770
2907
3179
3014
3483
3016
2617
3534
2849
3129
2578
3626
2813
2591
2890
3369
2926
3016
2878
3198
2560
2573
3121
2658
2869
3076
2168
2341
2570
2626
2490
2756




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'RServer@AstonUniversity' @ vre.aston.ac.uk

\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 & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=48728&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]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=48728&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=48728&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'RServer@AstonUniversity' @ vre.aston.ac.uk







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean3158.9655172413864.870800748769848.6962621206936
Geometric Mean3121.73851710474
Harmonic Mean3085.24018208051
Quadratic Mean3196.70638691418
Winsorized Mean ( 1 / 19 )3160.6379310344863.70941621632949.6102164914265
Winsorized Mean ( 2 / 19 )3158.9137931034560.596751516091552.1300847664185
Winsorized Mean ( 3 / 19 )3154.4137931034557.8138899995554.5615213425009
Winsorized Mean ( 4 / 19 )3152.2068965517257.000603676559955.3012896922703
Winsorized Mean ( 5 / 19 )3144.4482758620755.157686139270157.0083427343654
Winsorized Mean ( 6 / 19 )3144.1379310344854.887160540343257.2836688959976
Winsorized Mean ( 7 / 19 )3135.9310344827652.593752099202259.6255431361462
Winsorized Mean ( 8 / 19 )3136.6206896551751.380464223310761.0469511529272
Winsorized Mean ( 9 / 19 )3135.2241379310350.592102393792561.9706236662685
Winsorized Mean ( 10 / 19 )3128.6724137931047.732076341554765.5465392162155
Winsorized Mean ( 11 / 19 )3112.3620689655244.479878457384669.972360017742
Winsorized Mean ( 12 / 19 )3128.7068965517240.355146081479277.5293165891333
Winsorized Mean ( 13 / 19 )3129.827586206939.512364440728479.2113463850507
Winsorized Mean ( 14 / 19 )3138.2758620689737.570516824830183.5302819149642
Winsorized Mean ( 15 / 19 )3143.7068965517235.534523558953588.4690881344212
Winsorized Mean ( 16 / 19 )3140.1206896551733.230328547606394.4956257401003
Winsorized Mean ( 17 / 19 )3132.7931034482831.333170108924999.9832794625505
Winsorized Mean ( 18 / 19 )3124.1034482758629.8746087881517104.573869751054
Winsorized Mean ( 19 / 19 )3120.172413793128.5857212454651109.151432178333
Trimmed Mean ( 1 / 19 )3154.7678571428660.908218108587551.7954383679148
Trimmed Mean ( 2 / 19 )3148.4629629629657.399994843905154.8512760589085
Trimmed Mean ( 3 / 19 )3142.6346153846255.162272809529356.9707239264029
Trimmed Mean ( 4 / 19 )3138.0853.728401184825458.4063536379022
Trimmed Mean ( 5 / 19 )3133.812552.218178543821360.0138225305986
Trimmed Mean ( 6 / 19 )3131.1304347826150.926522883849861.4832950979965
Trimmed Mean ( 7 / 19 )3128.2727272727349.31556242495963.4337838493247
Trimmed Mean ( 8 / 19 )3126.7619047619047.904761904761965.2703777335984
Trimmed Mean ( 9 / 19 )3124.97546.367656824115867.3955773062636
Trimmed Mean ( 10 / 19 )3123.2368421052644.510877955225670.1679451312327
Trimmed Mean ( 11 / 19 )3122.3611111111142.824209752394872.9111203490802
Trimmed Mean ( 12 / 19 )3123.9117647058841.426983371258575.407657292112
Trimmed Mean ( 13 / 19 )3123.187540.625711842398776.8771144765644
Trimmed Mean ( 14 / 19 )3122.239.623643237949278.7963888441672
Trimmed Mean ( 15 / 19 )3119.8214285714338.643330860967980.7337607567011
Trimmed Mean ( 16 / 19 )3116.2692307692337.690421459868182.6806681927758
Trimmed Mean ( 17 / 19 )3112.6666666666736.873740050529384.4141837090915
Trimmed Mean ( 18 / 19 )3109.5454545454536.102531195975786.1309540227494
Trimmed Mean ( 19 / 19 )3107.235.202691284676188.2659787251147
Median3098.5
Midrange3276.5
Midmean - Weighted Average at Xnp3109.24137931034
Midmean - Weighted Average at X(n+1)p3122.2
Midmean - Empirical Distribution Function3122.2
Midmean - Empirical Distribution Function - Averaging3122.2
Midmean - Empirical Distribution Function - Interpolation3119.82142857143
Midmean - Closest Observation3122.2
Midmean - True Basic - Statistics Graphics Toolkit3122.2
Midmean - MS Excel (old versions)3122.2
Number of observations58

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 3158.96551724138 & 64.8708007487698 & 48.6962621206936 \tabularnewline
Geometric Mean & 3121.73851710474 &  &  \tabularnewline
Harmonic Mean & 3085.24018208051 &  &  \tabularnewline
Quadratic Mean & 3196.70638691418 &  &  \tabularnewline
Winsorized Mean ( 1 / 19 ) & 3160.63793103448 & 63.709416216329 & 49.6102164914265 \tabularnewline
Winsorized Mean ( 2 / 19 ) & 3158.91379310345 & 60.5967515160915 & 52.1300847664185 \tabularnewline
Winsorized Mean ( 3 / 19 ) & 3154.41379310345 & 57.81388999955 & 54.5615213425009 \tabularnewline
Winsorized Mean ( 4 / 19 ) & 3152.20689655172 & 57.0006036765599 & 55.3012896922703 \tabularnewline
Winsorized Mean ( 5 / 19 ) & 3144.44827586207 & 55.1576861392701 & 57.0083427343654 \tabularnewline
Winsorized Mean ( 6 / 19 ) & 3144.13793103448 & 54.8871605403432 & 57.2836688959976 \tabularnewline
Winsorized Mean ( 7 / 19 ) & 3135.93103448276 & 52.5937520992022 & 59.6255431361462 \tabularnewline
Winsorized Mean ( 8 / 19 ) & 3136.62068965517 & 51.3804642233107 & 61.0469511529272 \tabularnewline
Winsorized Mean ( 9 / 19 ) & 3135.22413793103 & 50.5921023937925 & 61.9706236662685 \tabularnewline
Winsorized Mean ( 10 / 19 ) & 3128.67241379310 & 47.7320763415547 & 65.5465392162155 \tabularnewline
Winsorized Mean ( 11 / 19 ) & 3112.36206896552 & 44.4798784573846 & 69.972360017742 \tabularnewline
Winsorized Mean ( 12 / 19 ) & 3128.70689655172 & 40.3551460814792 & 77.5293165891333 \tabularnewline
Winsorized Mean ( 13 / 19 ) & 3129.8275862069 & 39.5123644407284 & 79.2113463850507 \tabularnewline
Winsorized Mean ( 14 / 19 ) & 3138.27586206897 & 37.5705168248301 & 83.5302819149642 \tabularnewline
Winsorized Mean ( 15 / 19 ) & 3143.70689655172 & 35.5345235589535 & 88.4690881344212 \tabularnewline
Winsorized Mean ( 16 / 19 ) & 3140.12068965517 & 33.2303285476063 & 94.4956257401003 \tabularnewline
Winsorized Mean ( 17 / 19 ) & 3132.79310344828 & 31.3331701089249 & 99.9832794625505 \tabularnewline
Winsorized Mean ( 18 / 19 ) & 3124.10344827586 & 29.8746087881517 & 104.573869751054 \tabularnewline
Winsorized Mean ( 19 / 19 ) & 3120.1724137931 & 28.5857212454651 & 109.151432178333 \tabularnewline
Trimmed Mean ( 1 / 19 ) & 3154.76785714286 & 60.9082181085875 & 51.7954383679148 \tabularnewline
Trimmed Mean ( 2 / 19 ) & 3148.46296296296 & 57.3999948439051 & 54.8512760589085 \tabularnewline
Trimmed Mean ( 3 / 19 ) & 3142.63461538462 & 55.1622728095293 & 56.9707239264029 \tabularnewline
Trimmed Mean ( 4 / 19 ) & 3138.08 & 53.7284011848254 & 58.4063536379022 \tabularnewline
Trimmed Mean ( 5 / 19 ) & 3133.8125 & 52.2181785438213 & 60.0138225305986 \tabularnewline
Trimmed Mean ( 6 / 19 ) & 3131.13043478261 & 50.9265228838498 & 61.4832950979965 \tabularnewline
Trimmed Mean ( 7 / 19 ) & 3128.27272727273 & 49.315562424959 & 63.4337838493247 \tabularnewline
Trimmed Mean ( 8 / 19 ) & 3126.76190476190 & 47.9047619047619 & 65.2703777335984 \tabularnewline
Trimmed Mean ( 9 / 19 ) & 3124.975 & 46.3676568241158 & 67.3955773062636 \tabularnewline
Trimmed Mean ( 10 / 19 ) & 3123.23684210526 & 44.5108779552256 & 70.1679451312327 \tabularnewline
Trimmed Mean ( 11 / 19 ) & 3122.36111111111 & 42.8242097523948 & 72.9111203490802 \tabularnewline
Trimmed Mean ( 12 / 19 ) & 3123.91176470588 & 41.4269833712585 & 75.407657292112 \tabularnewline
Trimmed Mean ( 13 / 19 ) & 3123.1875 & 40.6257118423987 & 76.8771144765644 \tabularnewline
Trimmed Mean ( 14 / 19 ) & 3122.2 & 39.6236432379492 & 78.7963888441672 \tabularnewline
Trimmed Mean ( 15 / 19 ) & 3119.82142857143 & 38.6433308609679 & 80.7337607567011 \tabularnewline
Trimmed Mean ( 16 / 19 ) & 3116.26923076923 & 37.6904214598681 & 82.6806681927758 \tabularnewline
Trimmed Mean ( 17 / 19 ) & 3112.66666666667 & 36.8737400505293 & 84.4141837090915 \tabularnewline
Trimmed Mean ( 18 / 19 ) & 3109.54545454545 & 36.1025311959757 & 86.1309540227494 \tabularnewline
Trimmed Mean ( 19 / 19 ) & 3107.2 & 35.2026912846761 & 88.2659787251147 \tabularnewline
Median & 3098.5 &  &  \tabularnewline
Midrange & 3276.5 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 3109.24137931034 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 3122.2 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 3122.2 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 3122.2 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 3119.82142857143 &  &  \tabularnewline
Midmean - Closest Observation & 3122.2 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 3122.2 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 3122.2 &  &  \tabularnewline
Number of observations & 58 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=48728&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]3158.96551724138[/C][C]64.8708007487698[/C][C]48.6962621206936[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]3121.73851710474[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]3085.24018208051[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]3196.70638691418[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 19 )[/C][C]3160.63793103448[/C][C]63.709416216329[/C][C]49.6102164914265[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 19 )[/C][C]3158.91379310345[/C][C]60.5967515160915[/C][C]52.1300847664185[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 19 )[/C][C]3154.41379310345[/C][C]57.81388999955[/C][C]54.5615213425009[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 19 )[/C][C]3152.20689655172[/C][C]57.0006036765599[/C][C]55.3012896922703[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 19 )[/C][C]3144.44827586207[/C][C]55.1576861392701[/C][C]57.0083427343654[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 19 )[/C][C]3144.13793103448[/C][C]54.8871605403432[/C][C]57.2836688959976[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 19 )[/C][C]3135.93103448276[/C][C]52.5937520992022[/C][C]59.6255431361462[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 19 )[/C][C]3136.62068965517[/C][C]51.3804642233107[/C][C]61.0469511529272[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 19 )[/C][C]3135.22413793103[/C][C]50.5921023937925[/C][C]61.9706236662685[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 19 )[/C][C]3128.67241379310[/C][C]47.7320763415547[/C][C]65.5465392162155[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 19 )[/C][C]3112.36206896552[/C][C]44.4798784573846[/C][C]69.972360017742[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 19 )[/C][C]3128.70689655172[/C][C]40.3551460814792[/C][C]77.5293165891333[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 19 )[/C][C]3129.8275862069[/C][C]39.5123644407284[/C][C]79.2113463850507[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 19 )[/C][C]3138.27586206897[/C][C]37.5705168248301[/C][C]83.5302819149642[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 19 )[/C][C]3143.70689655172[/C][C]35.5345235589535[/C][C]88.4690881344212[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 19 )[/C][C]3140.12068965517[/C][C]33.2303285476063[/C][C]94.4956257401003[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 19 )[/C][C]3132.79310344828[/C][C]31.3331701089249[/C][C]99.9832794625505[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 19 )[/C][C]3124.10344827586[/C][C]29.8746087881517[/C][C]104.573869751054[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 19 )[/C][C]3120.1724137931[/C][C]28.5857212454651[/C][C]109.151432178333[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 19 )[/C][C]3154.76785714286[/C][C]60.9082181085875[/C][C]51.7954383679148[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 19 )[/C][C]3148.46296296296[/C][C]57.3999948439051[/C][C]54.8512760589085[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 19 )[/C][C]3142.63461538462[/C][C]55.1622728095293[/C][C]56.9707239264029[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 19 )[/C][C]3138.08[/C][C]53.7284011848254[/C][C]58.4063536379022[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 19 )[/C][C]3133.8125[/C][C]52.2181785438213[/C][C]60.0138225305986[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 19 )[/C][C]3131.13043478261[/C][C]50.9265228838498[/C][C]61.4832950979965[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 19 )[/C][C]3128.27272727273[/C][C]49.315562424959[/C][C]63.4337838493247[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 19 )[/C][C]3126.76190476190[/C][C]47.9047619047619[/C][C]65.2703777335984[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 19 )[/C][C]3124.975[/C][C]46.3676568241158[/C][C]67.3955773062636[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 19 )[/C][C]3123.23684210526[/C][C]44.5108779552256[/C][C]70.1679451312327[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 19 )[/C][C]3122.36111111111[/C][C]42.8242097523948[/C][C]72.9111203490802[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 19 )[/C][C]3123.91176470588[/C][C]41.4269833712585[/C][C]75.407657292112[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 19 )[/C][C]3123.1875[/C][C]40.6257118423987[/C][C]76.8771144765644[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 19 )[/C][C]3122.2[/C][C]39.6236432379492[/C][C]78.7963888441672[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 19 )[/C][C]3119.82142857143[/C][C]38.6433308609679[/C][C]80.7337607567011[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 19 )[/C][C]3116.26923076923[/C][C]37.6904214598681[/C][C]82.6806681927758[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 19 )[/C][C]3112.66666666667[/C][C]36.8737400505293[/C][C]84.4141837090915[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 19 )[/C][C]3109.54545454545[/C][C]36.1025311959757[/C][C]86.1309540227494[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 19 )[/C][C]3107.2[/C][C]35.2026912846761[/C][C]88.2659787251147[/C][/ROW]
[ROW][C]Median[/C][C]3098.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]3276.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]3109.24137931034[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]3122.2[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]3122.2[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]3122.2[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]3119.82142857143[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]3122.2[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]3122.2[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]3122.2[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]58[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=48728&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=48728&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 Mean3158.9655172413864.870800748769848.6962621206936
Geometric Mean3121.73851710474
Harmonic Mean3085.24018208051
Quadratic Mean3196.70638691418
Winsorized Mean ( 1 / 19 )3160.6379310344863.70941621632949.6102164914265
Winsorized Mean ( 2 / 19 )3158.9137931034560.596751516091552.1300847664185
Winsorized Mean ( 3 / 19 )3154.4137931034557.8138899995554.5615213425009
Winsorized Mean ( 4 / 19 )3152.2068965517257.000603676559955.3012896922703
Winsorized Mean ( 5 / 19 )3144.4482758620755.157686139270157.0083427343654
Winsorized Mean ( 6 / 19 )3144.1379310344854.887160540343257.2836688959976
Winsorized Mean ( 7 / 19 )3135.9310344827652.593752099202259.6255431361462
Winsorized Mean ( 8 / 19 )3136.6206896551751.380464223310761.0469511529272
Winsorized Mean ( 9 / 19 )3135.2241379310350.592102393792561.9706236662685
Winsorized Mean ( 10 / 19 )3128.6724137931047.732076341554765.5465392162155
Winsorized Mean ( 11 / 19 )3112.3620689655244.479878457384669.972360017742
Winsorized Mean ( 12 / 19 )3128.7068965517240.355146081479277.5293165891333
Winsorized Mean ( 13 / 19 )3129.827586206939.512364440728479.2113463850507
Winsorized Mean ( 14 / 19 )3138.2758620689737.570516824830183.5302819149642
Winsorized Mean ( 15 / 19 )3143.7068965517235.534523558953588.4690881344212
Winsorized Mean ( 16 / 19 )3140.1206896551733.230328547606394.4956257401003
Winsorized Mean ( 17 / 19 )3132.7931034482831.333170108924999.9832794625505
Winsorized Mean ( 18 / 19 )3124.1034482758629.8746087881517104.573869751054
Winsorized Mean ( 19 / 19 )3120.172413793128.5857212454651109.151432178333
Trimmed Mean ( 1 / 19 )3154.7678571428660.908218108587551.7954383679148
Trimmed Mean ( 2 / 19 )3148.4629629629657.399994843905154.8512760589085
Trimmed Mean ( 3 / 19 )3142.6346153846255.162272809529356.9707239264029
Trimmed Mean ( 4 / 19 )3138.0853.728401184825458.4063536379022
Trimmed Mean ( 5 / 19 )3133.812552.218178543821360.0138225305986
Trimmed Mean ( 6 / 19 )3131.1304347826150.926522883849861.4832950979965
Trimmed Mean ( 7 / 19 )3128.2727272727349.31556242495963.4337838493247
Trimmed Mean ( 8 / 19 )3126.7619047619047.904761904761965.2703777335984
Trimmed Mean ( 9 / 19 )3124.97546.367656824115867.3955773062636
Trimmed Mean ( 10 / 19 )3123.2368421052644.510877955225670.1679451312327
Trimmed Mean ( 11 / 19 )3122.3611111111142.824209752394872.9111203490802
Trimmed Mean ( 12 / 19 )3123.9117647058841.426983371258575.407657292112
Trimmed Mean ( 13 / 19 )3123.187540.625711842398776.8771144765644
Trimmed Mean ( 14 / 19 )3122.239.623643237949278.7963888441672
Trimmed Mean ( 15 / 19 )3119.8214285714338.643330860967980.7337607567011
Trimmed Mean ( 16 / 19 )3116.2692307692337.690421459868182.6806681927758
Trimmed Mean ( 17 / 19 )3112.6666666666736.873740050529384.4141837090915
Trimmed Mean ( 18 / 19 )3109.5454545454536.102531195975786.1309540227494
Trimmed Mean ( 19 / 19 )3107.235.202691284676188.2659787251147
Median3098.5
Midrange3276.5
Midmean - Weighted Average at Xnp3109.24137931034
Midmean - Weighted Average at X(n+1)p3122.2
Midmean - Empirical Distribution Function3122.2
Midmean - Empirical Distribution Function - Averaging3122.2
Midmean - Empirical Distribution Function - Interpolation3119.82142857143
Midmean - Closest Observation3122.2
Midmean - True Basic - Statistics Graphics Toolkit3122.2
Midmean - MS Excel (old versions)3122.2
Number of observations58



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')