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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 14:45:26 -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/t1256071766jta4fufs7cf3asr.htm/, Retrieved Thu, 02 May 2024 21:50:35 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=49158, Retrieved Thu, 02 May 2024 21:50:35 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact85
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] [WS 3 part 2.2 y(t...] [2009-10-20 20:45:26] [51d49d3536f6a59f2486a67bf50b2759] [Current]
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Post a new message
Dataseries X:
-8535
-7919
-8078
-7354
-7311
-7088
-7685
-7537
-7594
-7796
-7838
-8150
-8356
-7727
-8108
-7374
-7635
-7545
-8062
-7836
-7981
-8166
-8249
-8498
-8518
-7711
-8224
-7158
-7802
-7800
-7584
-7553
-7979
-8207
-8091
-8399
-8555
-7523
-8172
-6786
-7136
-7066
-7806
-7636
-7653
-8169
-8130
-8317
-9317
-8799
-8952
-7488
-7609
-7592
-7496
-7719
-7804
-9086
-8890
-8932




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'George Udny Yule' @ 72.249.76.132

\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 & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=49158&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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=49158&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=49158&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'George Udny Yule' @ 72.249.76.132







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean-7934.6833333333368.4565122036502-115.908378588272
Geometric MeanNaN
Harmonic Mean-7900.56841526115
Quadratic Mean7952.08720714254
Winsorized Mean ( 1 / 20 )-7935.566.040795900442-120.16057486592
Winsorized Mean ( 2 / 20 )-7931.7666666666764.6200733477817-122.744624939968
Winsorized Mean ( 3 / 20 )-7933.1666666666763.8340236867273-124.278029309253
Winsorized Mean ( 4 / 20 )-7931.8333333333362.792156328811-126.318855683157
Winsorized Mean ( 5 / 20 )-793758.3643775343467-135.990484869460
Winsorized Mean ( 6 / 20 )-7916.951.9554769193865-152.378545428113
Winsorized Mean ( 7 / 20 )-7916.951.0485959899229-155.085558113348
Winsorized Mean ( 8 / 20 )-7929.8333333333348.020023875796-165.135972315297
Winsorized Mean ( 9 / 20 )-7928.0333333333347.215050546587-167.913265824226
Winsorized Mean ( 10 / 20 )-7916.0333333333343.2650872849897-182.965846831417
Winsorized Mean ( 11 / 20 )-7910.7166666666741.4063171827263-191.050960455059
Winsorized Mean ( 12 / 20 )-7904.5166666666739.7642948866728-198.784278438592
Winsorized Mean ( 13 / 20 )-7891.5166666666736.9921314863319-213.329601447337
Winsorized Mean ( 14 / 20 )-7892.9166666666734.9423034667591-225.884268739617
Winsorized Mean ( 15 / 20 )-7890.6666666666733.9666392220023-232.30637023269
Winsorized Mean ( 16 / 20 )-7881.8666666666732.4421385554184-242.951513606376
Winsorized Mean ( 17 / 20 )-7885.2666666666731.6794580172018-248.907877855265
Winsorized Mean ( 18 / 20 )-7892.1666666666730.4065965065331-259.554424809464
Winsorized Mean ( 19 / 20 )-7887.4166666666729.5933483485452-266.526672607982
Winsorized Mean ( 20 / 20 )-7886.4166666666727.7850027797856-283.837173930545
Trimmed Mean ( 1 / 20 )-7930.655172413863.5658175353528-124.762891124669
Trimmed Mean ( 2 / 20 )-7925.4642857142960.501980027091-130.99512250947
Trimmed Mean ( 3 / 20 )-7921.9629629629657.6700048897631-137.367128338308
Trimmed Mean ( 4 / 20 )-7917.6538461538554.5087957299291-145.254609648375
Trimmed Mean ( 5 / 20 )-7913.450.9349725490397-155.362800919958
Trimmed Mean ( 6 / 20 )-7907.548.0440382350306-164.588579363722
Trimmed Mean ( 7 / 20 )-7905.4565217391346.5295885969009-169.901706852093
Trimmed Mean ( 8 / 20 )-7903.2272727272744.8309352150757-176.289591881402
Trimmed Mean ( 9 / 20 )-7898.4761904761943.451940398384-181.774993661041
Trimmed Mean ( 10 / 20 )-7893.5541.8243572452029-188.730933836535
Trimmed Mean ( 11 / 20 )-789040.7574618568527-193.584184111146
Trimmed Mean ( 12 / 20 )-7886.8611111111139.7760227842875-198.281792875144
Trimmed Mean ( 13 / 20 )-7884.2647058823538.8260049580756-203.066597101500
Trimmed Mean ( 14 / 20 )-7883.2187538.2131842213743-206.295782741669
Trimmed Mean ( 15 / 20 )-7881.8333333333337.7962499913677-208.534797370995
Trimmed Mean ( 16 / 20 )-7880.5714285714337.3221152565875-211.150181987085
Trimmed Mean ( 17 / 20 )-7880.3846153846236.9200415419-213.444630240767
Trimmed Mean ( 18 / 20 )-7879.6666666666736.3419581572776-216.820090776775
Trimmed Mean ( 19 / 20 )-7877.7727272727335.6485934598144-220.984110807993
Trimmed Mean ( 20 / 20 )-7876.2534.5844409038455-227.739694329546
Median-7821
Midrange-8051.5
Midmean - Weighted Average at Xnp-7892.87096774194
Midmean - Weighted Average at X(n+1)p-7881.83333333333
Midmean - Empirical Distribution Function-7892.87096774194
Midmean - Empirical Distribution Function - Averaging-7881.83333333333
Midmean - Empirical Distribution Function - Interpolation-7881.83333333333
Midmean - Closest Observation-7892.87096774194
Midmean - True Basic - Statistics Graphics Toolkit-7881.83333333333
Midmean - MS Excel (old versions)-7883.21875
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & -7934.68333333333 & 68.4565122036502 & -115.908378588272 \tabularnewline
Geometric Mean & NaN &  &  \tabularnewline
Harmonic Mean & -7900.56841526115 &  &  \tabularnewline
Quadratic Mean & 7952.08720714254 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & -7935.5 & 66.040795900442 & -120.16057486592 \tabularnewline
Winsorized Mean ( 2 / 20 ) & -7931.76666666667 & 64.6200733477817 & -122.744624939968 \tabularnewline
Winsorized Mean ( 3 / 20 ) & -7933.16666666667 & 63.8340236867273 & -124.278029309253 \tabularnewline
Winsorized Mean ( 4 / 20 ) & -7931.83333333333 & 62.792156328811 & -126.318855683157 \tabularnewline
Winsorized Mean ( 5 / 20 ) & -7937 & 58.3643775343467 & -135.990484869460 \tabularnewline
Winsorized Mean ( 6 / 20 ) & -7916.9 & 51.9554769193865 & -152.378545428113 \tabularnewline
Winsorized Mean ( 7 / 20 ) & -7916.9 & 51.0485959899229 & -155.085558113348 \tabularnewline
Winsorized Mean ( 8 / 20 ) & -7929.83333333333 & 48.020023875796 & -165.135972315297 \tabularnewline
Winsorized Mean ( 9 / 20 ) & -7928.03333333333 & 47.215050546587 & -167.913265824226 \tabularnewline
Winsorized Mean ( 10 / 20 ) & -7916.03333333333 & 43.2650872849897 & -182.965846831417 \tabularnewline
Winsorized Mean ( 11 / 20 ) & -7910.71666666667 & 41.4063171827263 & -191.050960455059 \tabularnewline
Winsorized Mean ( 12 / 20 ) & -7904.51666666667 & 39.7642948866728 & -198.784278438592 \tabularnewline
Winsorized Mean ( 13 / 20 ) & -7891.51666666667 & 36.9921314863319 & -213.329601447337 \tabularnewline
Winsorized Mean ( 14 / 20 ) & -7892.91666666667 & 34.9423034667591 & -225.884268739617 \tabularnewline
Winsorized Mean ( 15 / 20 ) & -7890.66666666667 & 33.9666392220023 & -232.30637023269 \tabularnewline
Winsorized Mean ( 16 / 20 ) & -7881.86666666667 & 32.4421385554184 & -242.951513606376 \tabularnewline
Winsorized Mean ( 17 / 20 ) & -7885.26666666667 & 31.6794580172018 & -248.907877855265 \tabularnewline
Winsorized Mean ( 18 / 20 ) & -7892.16666666667 & 30.4065965065331 & -259.554424809464 \tabularnewline
Winsorized Mean ( 19 / 20 ) & -7887.41666666667 & 29.5933483485452 & -266.526672607982 \tabularnewline
Winsorized Mean ( 20 / 20 ) & -7886.41666666667 & 27.7850027797856 & -283.837173930545 \tabularnewline
Trimmed Mean ( 1 / 20 ) & -7930.6551724138 & 63.5658175353528 & -124.762891124669 \tabularnewline
Trimmed Mean ( 2 / 20 ) & -7925.46428571429 & 60.501980027091 & -130.99512250947 \tabularnewline
Trimmed Mean ( 3 / 20 ) & -7921.96296296296 & 57.6700048897631 & -137.367128338308 \tabularnewline
Trimmed Mean ( 4 / 20 ) & -7917.65384615385 & 54.5087957299291 & -145.254609648375 \tabularnewline
Trimmed Mean ( 5 / 20 ) & -7913.4 & 50.9349725490397 & -155.362800919958 \tabularnewline
Trimmed Mean ( 6 / 20 ) & -7907.5 & 48.0440382350306 & -164.588579363722 \tabularnewline
Trimmed Mean ( 7 / 20 ) & -7905.45652173913 & 46.5295885969009 & -169.901706852093 \tabularnewline
Trimmed Mean ( 8 / 20 ) & -7903.22727272727 & 44.8309352150757 & -176.289591881402 \tabularnewline
Trimmed Mean ( 9 / 20 ) & -7898.47619047619 & 43.451940398384 & -181.774993661041 \tabularnewline
Trimmed Mean ( 10 / 20 ) & -7893.55 & 41.8243572452029 & -188.730933836535 \tabularnewline
Trimmed Mean ( 11 / 20 ) & -7890 & 40.7574618568527 & -193.584184111146 \tabularnewline
Trimmed Mean ( 12 / 20 ) & -7886.86111111111 & 39.7760227842875 & -198.281792875144 \tabularnewline
Trimmed Mean ( 13 / 20 ) & -7884.26470588235 & 38.8260049580756 & -203.066597101500 \tabularnewline
Trimmed Mean ( 14 / 20 ) & -7883.21875 & 38.2131842213743 & -206.295782741669 \tabularnewline
Trimmed Mean ( 15 / 20 ) & -7881.83333333333 & 37.7962499913677 & -208.534797370995 \tabularnewline
Trimmed Mean ( 16 / 20 ) & -7880.57142857143 & 37.3221152565875 & -211.150181987085 \tabularnewline
Trimmed Mean ( 17 / 20 ) & -7880.38461538462 & 36.9200415419 & -213.444630240767 \tabularnewline
Trimmed Mean ( 18 / 20 ) & -7879.66666666667 & 36.3419581572776 & -216.820090776775 \tabularnewline
Trimmed Mean ( 19 / 20 ) & -7877.77272727273 & 35.6485934598144 & -220.984110807993 \tabularnewline
Trimmed Mean ( 20 / 20 ) & -7876.25 & 34.5844409038455 & -227.739694329546 \tabularnewline
Median & -7821 &  &  \tabularnewline
Midrange & -8051.5 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & -7892.87096774194 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & -7881.83333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function & -7892.87096774194 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & -7881.83333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & -7881.83333333333 &  &  \tabularnewline
Midmean - Closest Observation & -7892.87096774194 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & -7881.83333333333 &  &  \tabularnewline
Midmean - MS Excel (old versions) & -7883.21875 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=49158&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]-7934.68333333333[/C][C]68.4565122036502[/C][C]-115.908378588272[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]NaN[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]-7900.56841526115[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]7952.08720714254[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]-7935.5[/C][C]66.040795900442[/C][C]-120.16057486592[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]-7931.76666666667[/C][C]64.6200733477817[/C][C]-122.744624939968[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]-7933.16666666667[/C][C]63.8340236867273[/C][C]-124.278029309253[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]-7931.83333333333[/C][C]62.792156328811[/C][C]-126.318855683157[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]-7937[/C][C]58.3643775343467[/C][C]-135.990484869460[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]-7916.9[/C][C]51.9554769193865[/C][C]-152.378545428113[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]-7916.9[/C][C]51.0485959899229[/C][C]-155.085558113348[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]-7929.83333333333[/C][C]48.020023875796[/C][C]-165.135972315297[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]-7928.03333333333[/C][C]47.215050546587[/C][C]-167.913265824226[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]-7916.03333333333[/C][C]43.2650872849897[/C][C]-182.965846831417[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]-7910.71666666667[/C][C]41.4063171827263[/C][C]-191.050960455059[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]-7904.51666666667[/C][C]39.7642948866728[/C][C]-198.784278438592[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]-7891.51666666667[/C][C]36.9921314863319[/C][C]-213.329601447337[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]-7892.91666666667[/C][C]34.9423034667591[/C][C]-225.884268739617[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]-7890.66666666667[/C][C]33.9666392220023[/C][C]-232.30637023269[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]-7881.86666666667[/C][C]32.4421385554184[/C][C]-242.951513606376[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]-7885.26666666667[/C][C]31.6794580172018[/C][C]-248.907877855265[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]-7892.16666666667[/C][C]30.4065965065331[/C][C]-259.554424809464[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]-7887.41666666667[/C][C]29.5933483485452[/C][C]-266.526672607982[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]-7886.41666666667[/C][C]27.7850027797856[/C][C]-283.837173930545[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]-7930.6551724138[/C][C]63.5658175353528[/C][C]-124.762891124669[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]-7925.46428571429[/C][C]60.501980027091[/C][C]-130.99512250947[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]-7921.96296296296[/C][C]57.6700048897631[/C][C]-137.367128338308[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]-7917.65384615385[/C][C]54.5087957299291[/C][C]-145.254609648375[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]-7913.4[/C][C]50.9349725490397[/C][C]-155.362800919958[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]-7907.5[/C][C]48.0440382350306[/C][C]-164.588579363722[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]-7905.45652173913[/C][C]46.5295885969009[/C][C]-169.901706852093[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]-7903.22727272727[/C][C]44.8309352150757[/C][C]-176.289591881402[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]-7898.47619047619[/C][C]43.451940398384[/C][C]-181.774993661041[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]-7893.55[/C][C]41.8243572452029[/C][C]-188.730933836535[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]-7890[/C][C]40.7574618568527[/C][C]-193.584184111146[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]-7886.86111111111[/C][C]39.7760227842875[/C][C]-198.281792875144[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]-7884.26470588235[/C][C]38.8260049580756[/C][C]-203.066597101500[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]-7883.21875[/C][C]38.2131842213743[/C][C]-206.295782741669[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]-7881.83333333333[/C][C]37.7962499913677[/C][C]-208.534797370995[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]-7880.57142857143[/C][C]37.3221152565875[/C][C]-211.150181987085[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]-7880.38461538462[/C][C]36.9200415419[/C][C]-213.444630240767[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]-7879.66666666667[/C][C]36.3419581572776[/C][C]-216.820090776775[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]-7877.77272727273[/C][C]35.6485934598144[/C][C]-220.984110807993[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]-7876.25[/C][C]34.5844409038455[/C][C]-227.739694329546[/C][/ROW]
[ROW][C]Median[/C][C]-7821[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]-8051.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]-7892.87096774194[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]-7881.83333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]-7892.87096774194[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]-7881.83333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]-7881.83333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]-7892.87096774194[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]-7881.83333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]-7883.21875[/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=49158&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=49158&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 Mean-7934.6833333333368.4565122036502-115.908378588272
Geometric MeanNaN
Harmonic Mean-7900.56841526115
Quadratic Mean7952.08720714254
Winsorized Mean ( 1 / 20 )-7935.566.040795900442-120.16057486592
Winsorized Mean ( 2 / 20 )-7931.7666666666764.6200733477817-122.744624939968
Winsorized Mean ( 3 / 20 )-7933.1666666666763.8340236867273-124.278029309253
Winsorized Mean ( 4 / 20 )-7931.8333333333362.792156328811-126.318855683157
Winsorized Mean ( 5 / 20 )-793758.3643775343467-135.990484869460
Winsorized Mean ( 6 / 20 )-7916.951.9554769193865-152.378545428113
Winsorized Mean ( 7 / 20 )-7916.951.0485959899229-155.085558113348
Winsorized Mean ( 8 / 20 )-7929.8333333333348.020023875796-165.135972315297
Winsorized Mean ( 9 / 20 )-7928.0333333333347.215050546587-167.913265824226
Winsorized Mean ( 10 / 20 )-7916.0333333333343.2650872849897-182.965846831417
Winsorized Mean ( 11 / 20 )-7910.7166666666741.4063171827263-191.050960455059
Winsorized Mean ( 12 / 20 )-7904.5166666666739.7642948866728-198.784278438592
Winsorized Mean ( 13 / 20 )-7891.5166666666736.9921314863319-213.329601447337
Winsorized Mean ( 14 / 20 )-7892.9166666666734.9423034667591-225.884268739617
Winsorized Mean ( 15 / 20 )-7890.6666666666733.9666392220023-232.30637023269
Winsorized Mean ( 16 / 20 )-7881.8666666666732.4421385554184-242.951513606376
Winsorized Mean ( 17 / 20 )-7885.2666666666731.6794580172018-248.907877855265
Winsorized Mean ( 18 / 20 )-7892.1666666666730.4065965065331-259.554424809464
Winsorized Mean ( 19 / 20 )-7887.4166666666729.5933483485452-266.526672607982
Winsorized Mean ( 20 / 20 )-7886.4166666666727.7850027797856-283.837173930545
Trimmed Mean ( 1 / 20 )-7930.655172413863.5658175353528-124.762891124669
Trimmed Mean ( 2 / 20 )-7925.4642857142960.501980027091-130.99512250947
Trimmed Mean ( 3 / 20 )-7921.9629629629657.6700048897631-137.367128338308
Trimmed Mean ( 4 / 20 )-7917.6538461538554.5087957299291-145.254609648375
Trimmed Mean ( 5 / 20 )-7913.450.9349725490397-155.362800919958
Trimmed Mean ( 6 / 20 )-7907.548.0440382350306-164.588579363722
Trimmed Mean ( 7 / 20 )-7905.4565217391346.5295885969009-169.901706852093
Trimmed Mean ( 8 / 20 )-7903.2272727272744.8309352150757-176.289591881402
Trimmed Mean ( 9 / 20 )-7898.4761904761943.451940398384-181.774993661041
Trimmed Mean ( 10 / 20 )-7893.5541.8243572452029-188.730933836535
Trimmed Mean ( 11 / 20 )-789040.7574618568527-193.584184111146
Trimmed Mean ( 12 / 20 )-7886.8611111111139.7760227842875-198.281792875144
Trimmed Mean ( 13 / 20 )-7884.2647058823538.8260049580756-203.066597101500
Trimmed Mean ( 14 / 20 )-7883.2187538.2131842213743-206.295782741669
Trimmed Mean ( 15 / 20 )-7881.8333333333337.7962499913677-208.534797370995
Trimmed Mean ( 16 / 20 )-7880.5714285714337.3221152565875-211.150181987085
Trimmed Mean ( 17 / 20 )-7880.3846153846236.9200415419-213.444630240767
Trimmed Mean ( 18 / 20 )-7879.6666666666736.3419581572776-216.820090776775
Trimmed Mean ( 19 / 20 )-7877.7727272727335.6485934598144-220.984110807993
Trimmed Mean ( 20 / 20 )-7876.2534.5844409038455-227.739694329546
Median-7821
Midrange-8051.5
Midmean - Weighted Average at Xnp-7892.87096774194
Midmean - Weighted Average at X(n+1)p-7881.83333333333
Midmean - Empirical Distribution Function-7892.87096774194
Midmean - Empirical Distribution Function - Averaging-7881.83333333333
Midmean - Empirical Distribution Function - Interpolation-7881.83333333333
Midmean - Closest Observation-7892.87096774194
Midmean - True Basic - Statistics Graphics Toolkit-7881.83333333333
Midmean - MS Excel (old versions)-7883.21875
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')