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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationFri, 25 Nov 2011 03:35:35 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Nov/25/t1322210152l282z4s70hhp28g.htm/, Retrieved Mon, 24 Jun 2024 12:27:57 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=147251, Retrieved Mon, 24 Jun 2024 12:27:57 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact183
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
F     [Univariate Data Series] [HPC Retail Sales] [2008-03-02 15:42:48] [74be16979710d4c4e7c6647856088456]
- RMPD  [Central Tendency] [Workshop 8, Robus...] [2010-11-28 19:41:12] [d946de7cca328fbcf207448a112523ab]
-         [Central Tendency] [Workshop 8, Centr...] [2010-11-29 20:08:54] [3635fb7041b1998c5a1332cf9de22bce]
- R  D        [Central Tendency] [] [2011-11-25 08:35:35] [a1e1d0bae7c18896aaea36b6ddc51406] [Current]
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Dataseries X:
9676
8642
9402
9610
9294
9448
10319
9548
9801
9596
8923
9746
9829
9125
9782
9441
9162
9915
10444
10209
9985
9842
9429
10132
9849
9172
10313
9819
9955
10048
10082
10541
10208
10233
9439
9963
10158
9225
10474
9757
10490
10281
10444
10640
10695
10786
9832
9747
10411
9511
10402
9701
10540
10112
10915
11183
10384
10834
9886
10216




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=147251&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' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=147251&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=147251&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' @ jenkins.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean9959.167.3467697898715147.877916506959
Geometric Mean9945.58446764261
Harmonic Mean9931.98306476949
Quadratic Mean9972.52588197527
Winsorized Mean ( 1 / 20 )9959.3166666666764.6820580946502153.973404063505
Winsorized Mean ( 2 / 20 )9963.3562.339759895606159.823361794858
Winsorized Mean ( 3 / 20 )9962.861.3673057473543162.347032816078
Winsorized Mean ( 4 / 20 )9957.459.8960266737238166.244750327792
Winsorized Mean ( 5 / 20 )9957.2333333333357.9964365097915171.68698514179
Winsorized Mean ( 6 / 20 )9954.2333333333354.6599987321039182.111847131947
Winsorized Mean ( 7 / 20 )9966.7166666666752.1902489521499190.968942796279
Winsorized Mean ( 8 / 20 )9963.6550.3238485376309197.99062054146
Winsorized Mean ( 9 / 20 )9962.7549.6323865982186200.730826841955
Winsorized Mean ( 10 / 20 )9958.0833333333348.7133219500056204.422177234254
Winsorized Mean ( 11 / 20 )9959.3666666666748.4831671334691205.419060995944
Winsorized Mean ( 12 / 20 )9965.3666666666745.1698174730222220.620033999883
Winsorized Mean ( 13 / 20 )9971.4333333333343.4980639004601229.238555448162
Winsorized Mean ( 14 / 20 )9978.4333333333340.9827052311126243.479128014177
Winsorized Mean ( 15 / 20 )9965.6833333333337.7727556413115263.832573613825
Winsorized Mean ( 16 / 20 )9981.6833333333334.7983577415169286.843517371639
Winsorized Mean ( 17 / 20 )9979.732.3040402573603308.930397575461
Winsorized Mean ( 18 / 20 )9978.828.123534990093354.820260095867
Winsorized Mean ( 19 / 20 )9973.7333333333327.2611027157854365.859497222689
Winsorized Mean ( 20 / 20 )9974.7333333333326.4425917627927377.222226278468
Trimmed Mean ( 1 / 20 )9960.7068965517262.2796078302896159.935286100298
Trimmed Mean ( 2 / 20 )9962.1964285714359.3129243906258167.959960344594
Trimmed Mean ( 3 / 20 )9961.5555555555557.2321926548104174.055109431812
Trimmed Mean ( 4 / 20 )9961.0769230769255.1138260387432180.736443811297
Trimmed Mean ( 5 / 20 )9962.1853.0467386521797187.800046772351
Trimmed Mean ( 6 / 20 )9963.4166666666751.1015436170697194.972910042164
Trimmed Mean ( 7 / 20 )9965.4130434782649.6817949539111200.584802797946
Trimmed Mean ( 8 / 20 )9965.1590909090948.5615163495855205.206917740619
Trimmed Mean ( 9 / 20 )9965.4285714285747.5828410553666209.433240016773
Trimmed Mean ( 10 / 20 )9965.87546.4305821451049214.640319797297
Trimmed Mean ( 11 / 20 )9967.105263157945.092693996732221.035923555161
Trimmed Mean ( 12 / 20 )9968.2777777777843.2961674155436230.234645993149
Trimmed Mean ( 13 / 20 )9968.7058823529441.7618989290479238.703366896449
Trimmed Mean ( 14 / 20 )9968.312540.0615564027571248.824893366199
Trimmed Mean ( 15 / 20 )9966.8666666666738.366254728807259.782111574813
Trimmed Mean ( 16 / 20 )9967.0357142857136.8979173120277270.124615164573
Trimmed Mean ( 17 / 20 )9964.9230769230835.6209066993366279.749282100915
Trimmed Mean ( 18 / 20 )9962.7534.4490408145637289.202536977115
Trimmed Mean ( 19 / 20 )9960.3181818181834.0273881517716292.714743117879
Trimmed Mean ( 20 / 20 )9958.233.4020642286797298.131275115916
Median9935
Midrange9912.5
Midmean - Weighted Average at Xnp9954.90322580645
Midmean - Weighted Average at X(n+1)p9966.86666666667
Midmean - Empirical Distribution Function9954.90322580645
Midmean - Empirical Distribution Function - Averaging9966.86666666667
Midmean - Empirical Distribution Function - Interpolation9966.86666666667
Midmean - Closest Observation9954.90322580645
Midmean - True Basic - Statistics Graphics Toolkit9966.86666666667
Midmean - MS Excel (old versions)9968.3125
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 9959.1 & 67.3467697898715 & 147.877916506959 \tabularnewline
Geometric Mean & 9945.58446764261 &  &  \tabularnewline
Harmonic Mean & 9931.98306476949 &  &  \tabularnewline
Quadratic Mean & 9972.52588197527 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 9959.31666666667 & 64.6820580946502 & 153.973404063505 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 9963.35 & 62.339759895606 & 159.823361794858 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 9962.8 & 61.3673057473543 & 162.347032816078 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 9957.4 & 59.8960266737238 & 166.244750327792 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 9957.23333333333 & 57.9964365097915 & 171.68698514179 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 9954.23333333333 & 54.6599987321039 & 182.111847131947 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 9966.71666666667 & 52.1902489521499 & 190.968942796279 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 9963.65 & 50.3238485376309 & 197.99062054146 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 9962.75 & 49.6323865982186 & 200.730826841955 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 9958.08333333333 & 48.7133219500056 & 204.422177234254 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 9959.36666666667 & 48.4831671334691 & 205.419060995944 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 9965.36666666667 & 45.1698174730222 & 220.620033999883 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 9971.43333333333 & 43.4980639004601 & 229.238555448162 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 9978.43333333333 & 40.9827052311126 & 243.479128014177 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 9965.68333333333 & 37.7727556413115 & 263.832573613825 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 9981.68333333333 & 34.7983577415169 & 286.843517371639 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 9979.7 & 32.3040402573603 & 308.930397575461 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 9978.8 & 28.123534990093 & 354.820260095867 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 9973.73333333333 & 27.2611027157854 & 365.859497222689 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 9974.73333333333 & 26.4425917627927 & 377.222226278468 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 9960.70689655172 & 62.2796078302896 & 159.935286100298 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 9962.19642857143 & 59.3129243906258 & 167.959960344594 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 9961.55555555555 & 57.2321926548104 & 174.055109431812 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 9961.07692307692 & 55.1138260387432 & 180.736443811297 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 9962.18 & 53.0467386521797 & 187.800046772351 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 9963.41666666667 & 51.1015436170697 & 194.972910042164 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 9965.41304347826 & 49.6817949539111 & 200.584802797946 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 9965.15909090909 & 48.5615163495855 & 205.206917740619 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 9965.42857142857 & 47.5828410553666 & 209.433240016773 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 9965.875 & 46.4305821451049 & 214.640319797297 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 9967.1052631579 & 45.092693996732 & 221.035923555161 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 9968.27777777778 & 43.2961674155436 & 230.234645993149 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 9968.70588235294 & 41.7618989290479 & 238.703366896449 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 9968.3125 & 40.0615564027571 & 248.824893366199 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 9966.86666666667 & 38.366254728807 & 259.782111574813 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 9967.03571428571 & 36.8979173120277 & 270.124615164573 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 9964.92307692308 & 35.6209066993366 & 279.749282100915 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 9962.75 & 34.4490408145637 & 289.202536977115 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 9960.31818181818 & 34.0273881517716 & 292.714743117879 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 9958.2 & 33.4020642286797 & 298.131275115916 \tabularnewline
Median & 9935 &  &  \tabularnewline
Midrange & 9912.5 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 9954.90322580645 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 9966.86666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 9954.90322580645 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 9966.86666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 9966.86666666667 &  &  \tabularnewline
Midmean - Closest Observation & 9954.90322580645 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 9966.86666666667 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 9968.3125 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=147251&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]9959.1[/C][C]67.3467697898715[/C][C]147.877916506959[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]9945.58446764261[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]9931.98306476949[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]9972.52588197527[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]9959.31666666667[/C][C]64.6820580946502[/C][C]153.973404063505[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]9963.35[/C][C]62.339759895606[/C][C]159.823361794858[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]9962.8[/C][C]61.3673057473543[/C][C]162.347032816078[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]9957.4[/C][C]59.8960266737238[/C][C]166.244750327792[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]9957.23333333333[/C][C]57.9964365097915[/C][C]171.68698514179[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]9954.23333333333[/C][C]54.6599987321039[/C][C]182.111847131947[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]9966.71666666667[/C][C]52.1902489521499[/C][C]190.968942796279[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]9963.65[/C][C]50.3238485376309[/C][C]197.99062054146[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]9962.75[/C][C]49.6323865982186[/C][C]200.730826841955[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]9958.08333333333[/C][C]48.7133219500056[/C][C]204.422177234254[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]9959.36666666667[/C][C]48.4831671334691[/C][C]205.419060995944[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]9965.36666666667[/C][C]45.1698174730222[/C][C]220.620033999883[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]9971.43333333333[/C][C]43.4980639004601[/C][C]229.238555448162[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]9978.43333333333[/C][C]40.9827052311126[/C][C]243.479128014177[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]9965.68333333333[/C][C]37.7727556413115[/C][C]263.832573613825[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]9981.68333333333[/C][C]34.7983577415169[/C][C]286.843517371639[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]9979.7[/C][C]32.3040402573603[/C][C]308.930397575461[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]9978.8[/C][C]28.123534990093[/C][C]354.820260095867[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]9973.73333333333[/C][C]27.2611027157854[/C][C]365.859497222689[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]9974.73333333333[/C][C]26.4425917627927[/C][C]377.222226278468[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]9960.70689655172[/C][C]62.2796078302896[/C][C]159.935286100298[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]9962.19642857143[/C][C]59.3129243906258[/C][C]167.959960344594[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]9961.55555555555[/C][C]57.2321926548104[/C][C]174.055109431812[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]9961.07692307692[/C][C]55.1138260387432[/C][C]180.736443811297[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]9962.18[/C][C]53.0467386521797[/C][C]187.800046772351[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]9963.41666666667[/C][C]51.1015436170697[/C][C]194.972910042164[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]9965.41304347826[/C][C]49.6817949539111[/C][C]200.584802797946[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]9965.15909090909[/C][C]48.5615163495855[/C][C]205.206917740619[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]9965.42857142857[/C][C]47.5828410553666[/C][C]209.433240016773[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]9965.875[/C][C]46.4305821451049[/C][C]214.640319797297[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]9967.1052631579[/C][C]45.092693996732[/C][C]221.035923555161[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]9968.27777777778[/C][C]43.2961674155436[/C][C]230.234645993149[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]9968.70588235294[/C][C]41.7618989290479[/C][C]238.703366896449[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]9968.3125[/C][C]40.0615564027571[/C][C]248.824893366199[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]9966.86666666667[/C][C]38.366254728807[/C][C]259.782111574813[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]9967.03571428571[/C][C]36.8979173120277[/C][C]270.124615164573[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]9964.92307692308[/C][C]35.6209066993366[/C][C]279.749282100915[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]9962.75[/C][C]34.4490408145637[/C][C]289.202536977115[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]9960.31818181818[/C][C]34.0273881517716[/C][C]292.714743117879[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]9958.2[/C][C]33.4020642286797[/C][C]298.131275115916[/C][/ROW]
[ROW][C]Median[/C][C]9935[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]9912.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]9954.90322580645[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]9966.86666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]9954.90322580645[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]9966.86666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]9966.86666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]9954.90322580645[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]9966.86666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]9968.3125[/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=147251&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=147251&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 Mean9959.167.3467697898715147.877916506959
Geometric Mean9945.58446764261
Harmonic Mean9931.98306476949
Quadratic Mean9972.52588197527
Winsorized Mean ( 1 / 20 )9959.3166666666764.6820580946502153.973404063505
Winsorized Mean ( 2 / 20 )9963.3562.339759895606159.823361794858
Winsorized Mean ( 3 / 20 )9962.861.3673057473543162.347032816078
Winsorized Mean ( 4 / 20 )9957.459.8960266737238166.244750327792
Winsorized Mean ( 5 / 20 )9957.2333333333357.9964365097915171.68698514179
Winsorized Mean ( 6 / 20 )9954.2333333333354.6599987321039182.111847131947
Winsorized Mean ( 7 / 20 )9966.7166666666752.1902489521499190.968942796279
Winsorized Mean ( 8 / 20 )9963.6550.3238485376309197.99062054146
Winsorized Mean ( 9 / 20 )9962.7549.6323865982186200.730826841955
Winsorized Mean ( 10 / 20 )9958.0833333333348.7133219500056204.422177234254
Winsorized Mean ( 11 / 20 )9959.3666666666748.4831671334691205.419060995944
Winsorized Mean ( 12 / 20 )9965.3666666666745.1698174730222220.620033999883
Winsorized Mean ( 13 / 20 )9971.4333333333343.4980639004601229.238555448162
Winsorized Mean ( 14 / 20 )9978.4333333333340.9827052311126243.479128014177
Winsorized Mean ( 15 / 20 )9965.6833333333337.7727556413115263.832573613825
Winsorized Mean ( 16 / 20 )9981.6833333333334.7983577415169286.843517371639
Winsorized Mean ( 17 / 20 )9979.732.3040402573603308.930397575461
Winsorized Mean ( 18 / 20 )9978.828.123534990093354.820260095867
Winsorized Mean ( 19 / 20 )9973.7333333333327.2611027157854365.859497222689
Winsorized Mean ( 20 / 20 )9974.7333333333326.4425917627927377.222226278468
Trimmed Mean ( 1 / 20 )9960.7068965517262.2796078302896159.935286100298
Trimmed Mean ( 2 / 20 )9962.1964285714359.3129243906258167.959960344594
Trimmed Mean ( 3 / 20 )9961.5555555555557.2321926548104174.055109431812
Trimmed Mean ( 4 / 20 )9961.0769230769255.1138260387432180.736443811297
Trimmed Mean ( 5 / 20 )9962.1853.0467386521797187.800046772351
Trimmed Mean ( 6 / 20 )9963.4166666666751.1015436170697194.972910042164
Trimmed Mean ( 7 / 20 )9965.4130434782649.6817949539111200.584802797946
Trimmed Mean ( 8 / 20 )9965.1590909090948.5615163495855205.206917740619
Trimmed Mean ( 9 / 20 )9965.4285714285747.5828410553666209.433240016773
Trimmed Mean ( 10 / 20 )9965.87546.4305821451049214.640319797297
Trimmed Mean ( 11 / 20 )9967.105263157945.092693996732221.035923555161
Trimmed Mean ( 12 / 20 )9968.2777777777843.2961674155436230.234645993149
Trimmed Mean ( 13 / 20 )9968.7058823529441.7618989290479238.703366896449
Trimmed Mean ( 14 / 20 )9968.312540.0615564027571248.824893366199
Trimmed Mean ( 15 / 20 )9966.8666666666738.366254728807259.782111574813
Trimmed Mean ( 16 / 20 )9967.0357142857136.8979173120277270.124615164573
Trimmed Mean ( 17 / 20 )9964.9230769230835.6209066993366279.749282100915
Trimmed Mean ( 18 / 20 )9962.7534.4490408145637289.202536977115
Trimmed Mean ( 19 / 20 )9960.3181818181834.0273881517716292.714743117879
Trimmed Mean ( 20 / 20 )9958.233.4020642286797298.131275115916
Median9935
Midrange9912.5
Midmean - Weighted Average at Xnp9954.90322580645
Midmean - Weighted Average at X(n+1)p9966.86666666667
Midmean - Empirical Distribution Function9954.90322580645
Midmean - Empirical Distribution Function - Averaging9966.86666666667
Midmean - Empirical Distribution Function - Interpolation9966.86666666667
Midmean - Closest Observation9954.90322580645
Midmean - True Basic - Statistics Graphics Toolkit9966.86666666667
Midmean - MS Excel (old versions)9968.3125
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')