Free Statistics

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, 08 Dec 2009 13:34:16 -0700
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/Dec/08/t1260304506znyztlb4jborhu0.htm/, Retrieved Sat, 27 Apr 2024 14:03:32 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=64849, Retrieved Sat, 27 Apr 2024 14:03:32 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsbhschhwsstpaper
Estimated Impact218
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [ARIMA Forecasting] [] [2009-12-07 09:54:52] [b98453cac15ba1066b407e146608df68]
- RMPD    [Central Tendency] [Paper] [2009-12-08 20:34:16] [682632737e024f9e62885141c5f654cd] [Current]
Feedback Forum

Post a new message
Dataseries X:
128.6
128.9
129.06
129.23
129.27
129.33
129.35
129.31
129.4
129.49
129.47
129.46
129.45
129.28
129.2
129.25
129.14
129.11
129.02
129.08
128.99
129.11
129.08
129.19
129.23
129.25
129.31
129.33
129.39
129.55
129.43
129.45
129.57
129.76
129.92
130.08
130.41
130.84
131.24
131.49
131.74
132.34
133.5
134.43
136.5
137.41
138.02
138.15
138.24
138.2
138.31
138.65
139.3
139.8
140.52
141.57
141.77
141.66
141.36
141.17




Summary of computational 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 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 & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=64849&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=64849&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=64849&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'Gwilym Jenkins' @ 72.249.127.135







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean132.3610.580466775936489228.025109251872
Geometric Mean132.287572476315
Harmonic Mean132.215818912740
Quadratic Mean132.436074692661
Winsorized Mean ( 1 / 20 )132.3641666666670.579437789647485228.435509439579
Winsorized Mean ( 2 / 20 )132.3641666666670.57832488922343228.875099676938
Winsorized Mean ( 3 / 20 )132.3551666666670.575367899580932230.035715866435
Winsorized Mean ( 4 / 20 )132.3451666666670.571770196601117231.465661297828
Winsorized Mean ( 5 / 20 )132.2926666666670.557747582108968237.190928137131
Winsorized Mean ( 6 / 20 )132.2206666666670.540178557352081244.772149629196
Winsorized Mean ( 7 / 20 )132.1658333333330.526192017306623251.174151234449
Winsorized Mean ( 8 / 20 )132.0791666666670.506701490681776260.664649888738
Winsorized Mean ( 9 / 20 )132.0326666666670.495169939821878266.641118631235
Winsorized Mean ( 10 / 20 )132.0293333333330.491847828349739268.435328415135
Winsorized Mean ( 11 / 20 )132.0238333333330.490100709797363269.381028621484
Winsorized Mean ( 12 / 20 )132.0198333333330.487382811739302270.875029142287
Winsorized Mean ( 13 / 20 )131.9916666666670.481391237498659274.187929453191
Winsorized Mean ( 14 / 20 )131.8540.450962010000040292.383830735516
Winsorized Mean ( 15 / 20 )131.62650.403919904867317325.872774314595
Winsorized Mean ( 16 / 20 )131.0798333333330.292972347055758447.413671121617
Winsorized Mean ( 17 / 20 )130.8191666666670.2423569869711539.778812658148
Winsorized Mean ( 18 / 20 )130.4801666666670.177598940621788734.690005525064
Winsorized Mean ( 19 / 20 )130.2901666666670.144509982777698901.599766066638
Winsorized Mean ( 20 / 20 )130.21350.1296988744076021003.96784933369
Trimmed Mean ( 1 / 20 )132.2636206896550.574079430809146230.392544291709
Trimmed Mean ( 2 / 20 )132.1558928571430.566744335083926233.184320823555
Trimmed Mean ( 3 / 20 )132.0401851851850.557623644882449236.790864944438
Trimmed Mean ( 4 / 20 )131.9190384615380.546888377465541241.217484037409
Trimmed Mean ( 5 / 20 )131.79120.533990341577410246.804463935973
Trimmed Mean ( 6 / 20 )131.6658333333330.521824220537415252.318363447626
Trimmed Mean ( 7 / 20 )131.5452173913040.511127175258727257.362988623561
Trimmed Mean ( 8 / 20 )131.4243181818180.500570224286892262.549212488705
Trimmed Mean ( 9 / 20 )131.3073809523810.491471168383618267.172093500892
Trimmed Mean ( 10 / 20 )131.18650.481464053295139272.474131977579
Trimmed Mean ( 11 / 20 )131.0534210526320.467438356181996280.365141883235
Trimmed Mean ( 12 / 20 )130.9063888888890.447144405632606292.760878230572
Trimmed Mean ( 13 / 20 )130.7426470588240.417669305350112313.029100736115
Trimmed Mean ( 14 / 20 )130.56250.374924454756146348.236820361368
Trimmed Mean ( 15 / 20 )130.3780.321297083852241405.786440501771
Trimmed Mean ( 16 / 20 )130.1996428571430.257608292399382505.4171263062
Trimmed Mean ( 17 / 20 )130.0726923076920.218352261401552595.701145812671
Trimmed Mean ( 18 / 20 )129.9629166666670.182209147989642713.262303789789
Trimmed Mean ( 19 / 20 )129.8845454545450.161931960583214802.093329734002
Trimmed Mean ( 20 / 20 )129.82050.147431473823212880.548071815864
Median129.48
Midrange135.185
Midmean - Weighted Average at Xnp130.341612903226
Midmean - Weighted Average at X(n+1)p130.341612903226
Midmean - Empirical Distribution Function130.341612903226
Midmean - Empirical Distribution Function - Averaging130.341612903226
Midmean - Empirical Distribution Function - Interpolation130.341612903226
Midmean - Closest Observation130.341612903226
Midmean - True Basic - Statistics Graphics Toolkit130.341612903226
Midmean - MS Excel (old versions)130.5625
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 132.361 & 0.580466775936489 & 228.025109251872 \tabularnewline
Geometric Mean & 132.287572476315 &  &  \tabularnewline
Harmonic Mean & 132.215818912740 &  &  \tabularnewline
Quadratic Mean & 132.436074692661 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 132.364166666667 & 0.579437789647485 & 228.435509439579 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 132.364166666667 & 0.57832488922343 & 228.875099676938 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 132.355166666667 & 0.575367899580932 & 230.035715866435 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 132.345166666667 & 0.571770196601117 & 231.465661297828 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 132.292666666667 & 0.557747582108968 & 237.190928137131 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 132.220666666667 & 0.540178557352081 & 244.772149629196 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 132.165833333333 & 0.526192017306623 & 251.174151234449 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 132.079166666667 & 0.506701490681776 & 260.664649888738 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 132.032666666667 & 0.495169939821878 & 266.641118631235 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 132.029333333333 & 0.491847828349739 & 268.435328415135 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 132.023833333333 & 0.490100709797363 & 269.381028621484 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 132.019833333333 & 0.487382811739302 & 270.875029142287 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 131.991666666667 & 0.481391237498659 & 274.187929453191 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 131.854 & 0.450962010000040 & 292.383830735516 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 131.6265 & 0.403919904867317 & 325.872774314595 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 131.079833333333 & 0.292972347055758 & 447.413671121617 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 130.819166666667 & 0.2423569869711 & 539.778812658148 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 130.480166666667 & 0.177598940621788 & 734.690005525064 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 130.290166666667 & 0.144509982777698 & 901.599766066638 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 130.2135 & 0.129698874407602 & 1003.96784933369 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 132.263620689655 & 0.574079430809146 & 230.392544291709 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 132.155892857143 & 0.566744335083926 & 233.184320823555 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 132.040185185185 & 0.557623644882449 & 236.790864944438 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 131.919038461538 & 0.546888377465541 & 241.217484037409 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 131.7912 & 0.533990341577410 & 246.804463935973 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 131.665833333333 & 0.521824220537415 & 252.318363447626 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 131.545217391304 & 0.511127175258727 & 257.362988623561 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 131.424318181818 & 0.500570224286892 & 262.549212488705 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 131.307380952381 & 0.491471168383618 & 267.172093500892 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 131.1865 & 0.481464053295139 & 272.474131977579 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 131.053421052632 & 0.467438356181996 & 280.365141883235 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 130.906388888889 & 0.447144405632606 & 292.760878230572 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 130.742647058824 & 0.417669305350112 & 313.029100736115 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 130.5625 & 0.374924454756146 & 348.236820361368 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 130.378 & 0.321297083852241 & 405.786440501771 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 130.199642857143 & 0.257608292399382 & 505.4171263062 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 130.072692307692 & 0.218352261401552 & 595.701145812671 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 129.962916666667 & 0.182209147989642 & 713.262303789789 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 129.884545454545 & 0.161931960583214 & 802.093329734002 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 129.8205 & 0.147431473823212 & 880.548071815864 \tabularnewline
Median & 129.48 &  &  \tabularnewline
Midrange & 135.185 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 130.341612903226 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 130.341612903226 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 130.341612903226 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 130.341612903226 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 130.341612903226 &  &  \tabularnewline
Midmean - Closest Observation & 130.341612903226 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 130.341612903226 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 130.5625 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=64849&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]132.361[/C][C]0.580466775936489[/C][C]228.025109251872[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]132.287572476315[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]132.215818912740[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]132.436074692661[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]132.364166666667[/C][C]0.579437789647485[/C][C]228.435509439579[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]132.364166666667[/C][C]0.57832488922343[/C][C]228.875099676938[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]132.355166666667[/C][C]0.575367899580932[/C][C]230.035715866435[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]132.345166666667[/C][C]0.571770196601117[/C][C]231.465661297828[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]132.292666666667[/C][C]0.557747582108968[/C][C]237.190928137131[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]132.220666666667[/C][C]0.540178557352081[/C][C]244.772149629196[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]132.165833333333[/C][C]0.526192017306623[/C][C]251.174151234449[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]132.079166666667[/C][C]0.506701490681776[/C][C]260.664649888738[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]132.032666666667[/C][C]0.495169939821878[/C][C]266.641118631235[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]132.029333333333[/C][C]0.491847828349739[/C][C]268.435328415135[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]132.023833333333[/C][C]0.490100709797363[/C][C]269.381028621484[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]132.019833333333[/C][C]0.487382811739302[/C][C]270.875029142287[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]131.991666666667[/C][C]0.481391237498659[/C][C]274.187929453191[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]131.854[/C][C]0.450962010000040[/C][C]292.383830735516[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]131.6265[/C][C]0.403919904867317[/C][C]325.872774314595[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]131.079833333333[/C][C]0.292972347055758[/C][C]447.413671121617[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]130.819166666667[/C][C]0.2423569869711[/C][C]539.778812658148[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]130.480166666667[/C][C]0.177598940621788[/C][C]734.690005525064[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]130.290166666667[/C][C]0.144509982777698[/C][C]901.599766066638[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]130.2135[/C][C]0.129698874407602[/C][C]1003.96784933369[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]132.263620689655[/C][C]0.574079430809146[/C][C]230.392544291709[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]132.155892857143[/C][C]0.566744335083926[/C][C]233.184320823555[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]132.040185185185[/C][C]0.557623644882449[/C][C]236.790864944438[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]131.919038461538[/C][C]0.546888377465541[/C][C]241.217484037409[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]131.7912[/C][C]0.533990341577410[/C][C]246.804463935973[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]131.665833333333[/C][C]0.521824220537415[/C][C]252.318363447626[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]131.545217391304[/C][C]0.511127175258727[/C][C]257.362988623561[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]131.424318181818[/C][C]0.500570224286892[/C][C]262.549212488705[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]131.307380952381[/C][C]0.491471168383618[/C][C]267.172093500892[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]131.1865[/C][C]0.481464053295139[/C][C]272.474131977579[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]131.053421052632[/C][C]0.467438356181996[/C][C]280.365141883235[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]130.906388888889[/C][C]0.447144405632606[/C][C]292.760878230572[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]130.742647058824[/C][C]0.417669305350112[/C][C]313.029100736115[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]130.5625[/C][C]0.374924454756146[/C][C]348.236820361368[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]130.378[/C][C]0.321297083852241[/C][C]405.786440501771[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]130.199642857143[/C][C]0.257608292399382[/C][C]505.4171263062[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]130.072692307692[/C][C]0.218352261401552[/C][C]595.701145812671[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]129.962916666667[/C][C]0.182209147989642[/C][C]713.262303789789[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]129.884545454545[/C][C]0.161931960583214[/C][C]802.093329734002[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]129.8205[/C][C]0.147431473823212[/C][C]880.548071815864[/C][/ROW]
[ROW][C]Median[/C][C]129.48[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]135.185[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]130.341612903226[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]130.341612903226[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]130.341612903226[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]130.341612903226[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]130.341612903226[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]130.341612903226[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]130.341612903226[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]130.5625[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]60[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=64849&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=64849&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 Mean132.3610.580466775936489228.025109251872
Geometric Mean132.287572476315
Harmonic Mean132.215818912740
Quadratic Mean132.436074692661
Winsorized Mean ( 1 / 20 )132.3641666666670.579437789647485228.435509439579
Winsorized Mean ( 2 / 20 )132.3641666666670.57832488922343228.875099676938
Winsorized Mean ( 3 / 20 )132.3551666666670.575367899580932230.035715866435
Winsorized Mean ( 4 / 20 )132.3451666666670.571770196601117231.465661297828
Winsorized Mean ( 5 / 20 )132.2926666666670.557747582108968237.190928137131
Winsorized Mean ( 6 / 20 )132.2206666666670.540178557352081244.772149629196
Winsorized Mean ( 7 / 20 )132.1658333333330.526192017306623251.174151234449
Winsorized Mean ( 8 / 20 )132.0791666666670.506701490681776260.664649888738
Winsorized Mean ( 9 / 20 )132.0326666666670.495169939821878266.641118631235
Winsorized Mean ( 10 / 20 )132.0293333333330.491847828349739268.435328415135
Winsorized Mean ( 11 / 20 )132.0238333333330.490100709797363269.381028621484
Winsorized Mean ( 12 / 20 )132.0198333333330.487382811739302270.875029142287
Winsorized Mean ( 13 / 20 )131.9916666666670.481391237498659274.187929453191
Winsorized Mean ( 14 / 20 )131.8540.450962010000040292.383830735516
Winsorized Mean ( 15 / 20 )131.62650.403919904867317325.872774314595
Winsorized Mean ( 16 / 20 )131.0798333333330.292972347055758447.413671121617
Winsorized Mean ( 17 / 20 )130.8191666666670.2423569869711539.778812658148
Winsorized Mean ( 18 / 20 )130.4801666666670.177598940621788734.690005525064
Winsorized Mean ( 19 / 20 )130.2901666666670.144509982777698901.599766066638
Winsorized Mean ( 20 / 20 )130.21350.1296988744076021003.96784933369
Trimmed Mean ( 1 / 20 )132.2636206896550.574079430809146230.392544291709
Trimmed Mean ( 2 / 20 )132.1558928571430.566744335083926233.184320823555
Trimmed Mean ( 3 / 20 )132.0401851851850.557623644882449236.790864944438
Trimmed Mean ( 4 / 20 )131.9190384615380.546888377465541241.217484037409
Trimmed Mean ( 5 / 20 )131.79120.533990341577410246.804463935973
Trimmed Mean ( 6 / 20 )131.6658333333330.521824220537415252.318363447626
Trimmed Mean ( 7 / 20 )131.5452173913040.511127175258727257.362988623561
Trimmed Mean ( 8 / 20 )131.4243181818180.500570224286892262.549212488705
Trimmed Mean ( 9 / 20 )131.3073809523810.491471168383618267.172093500892
Trimmed Mean ( 10 / 20 )131.18650.481464053295139272.474131977579
Trimmed Mean ( 11 / 20 )131.0534210526320.467438356181996280.365141883235
Trimmed Mean ( 12 / 20 )130.9063888888890.447144405632606292.760878230572
Trimmed Mean ( 13 / 20 )130.7426470588240.417669305350112313.029100736115
Trimmed Mean ( 14 / 20 )130.56250.374924454756146348.236820361368
Trimmed Mean ( 15 / 20 )130.3780.321297083852241405.786440501771
Trimmed Mean ( 16 / 20 )130.1996428571430.257608292399382505.4171263062
Trimmed Mean ( 17 / 20 )130.0726923076920.218352261401552595.701145812671
Trimmed Mean ( 18 / 20 )129.9629166666670.182209147989642713.262303789789
Trimmed Mean ( 19 / 20 )129.8845454545450.161931960583214802.093329734002
Trimmed Mean ( 20 / 20 )129.82050.147431473823212880.548071815864
Median129.48
Midrange135.185
Midmean - Weighted Average at Xnp130.341612903226
Midmean - Weighted Average at X(n+1)p130.341612903226
Midmean - Empirical Distribution Function130.341612903226
Midmean - Empirical Distribution Function - Averaging130.341612903226
Midmean - Empirical Distribution Function - Interpolation130.341612903226
Midmean - Closest Observation130.341612903226
Midmean - True Basic - Statistics Graphics Toolkit130.341612903226
Midmean - MS Excel (old versions)130.5625
Number of observations60



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')