Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationTue, 11 Oct 2016 19:12:24 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Oct/11/t1476209664hj4mq9bs56r2ebm.htm/, Retrieved Mon, 29 Apr 2024 06:15:10 +0200
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Mon, 29 Apr 2024 06:15:10 +0200
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact0
Dataseries X:
28886
28549
33348
29017
30924
30435
29431
30290
31286
30622
31742
30391
30740
32086
33947
31312
33239
32362
32170
32665
31412
34891
33919
30706
32846
31368
33130
31665
33139
32201
32230
30287
31918
33853
32232
31484
31902
30260
32823
32018
32100
31952
33274
29491
32751
33643
31226
30976
28880
29325
34923
32642
31487
33832
32724
29545
32338
32743
32231
32536




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Sir Maurice George Kendall' @ kendall.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 & 'Sir Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]'Sir Maurice George Kendall' @ kendall.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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'Sir Maurice George Kendall' @ kendall.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean31772.4166666667194.29427458506163.527292476943
Geometric Mean31737.04170457
Harmonic Mean31701.3388639436
Quadratic Mean31807.4476574801
Winsorized Mean ( 1 / 20 )31777.4192.668954690928164.932643408877
Winsorized Mean ( 2 / 20 )31746.1333333333185.114631559274171.49445760136
Winsorized Mean ( 3 / 20 )31751.2833333333183.146636461796173.365364206165
Winsorized Mean ( 4 / 20 )31767.4166666667177.267838610001179.205753935753
Winsorized Mean ( 5 / 20 )31774.5174.884141631968181.688858140536
Winsorized Mean ( 6 / 20 )31761.6169.863030897063186.983593971354
Winsorized Mean ( 7 / 20 )31733.4833333333162.289941575363195.535736998199
Winsorized Mean ( 8 / 20 )31818.95140.604131194782226.301672145895
Winsorized Mean ( 9 / 20 )31817.75138.929803079166229.020334692833
Winsorized Mean ( 10 / 20 )31801.5833333333136.001556346335233.832495654307
Winsorized Mean ( 11 / 20 )31818.45132.287378546099240.52521374072
Winsorized Mean ( 12 / 20 )31770.45121.613187902264261.241815530177
Winsorized Mean ( 13 / 20 )31805.9833333333113.502727739607280.222193481562
Winsorized Mean ( 14 / 20 )31808.7833333333107.542150694892295.779683852316
Winsorized Mean ( 15 / 20 )31815.2833333333105.773991793468300.785503070123
Winsorized Mean ( 16 / 20 )31859.283333333396.7581850774016329.26706208728
Winsorized Mean ( 17 / 20 )31857.391.8404176622917346.876689053649
Winsorized Mean ( 18 / 20 )31925.479.0381699964276403.923825683755
Winsorized Mean ( 19 / 20 )31910.833333333371.1141168002968448.727127174279
Winsorized Mean ( 20 / 20 )31861.561.466487585067518.355631691254
Trimmed Mean ( 1 / 20 )31773.6724137931185.140074483164171.619637198982
Trimmed Mean ( 2 / 20 )31769.6785714286175.835013628189180.678909825133
Trimmed Mean ( 3 / 20 )31782.7592592593169.433761085732187.582209446306
Trimmed Mean ( 4 / 20 )31794.8653846154162.397609066459195.784073222432
Trimmed Mean ( 5 / 20 )31803.1155.971751105311203.902948929045
Trimmed Mean ( 6 / 20 )31810.25148.658094857517213.982629270803
Trimmed Mean ( 7 / 20 )31820.8260869565140.930007311156225.791701100959
Trimmed Mean ( 8 / 20 )31837.8409090909133.239915956928238.951223290948
Trimmed Mean ( 9 / 20 )31841.2142857143129.852563296957245.210517815481
Trimmed Mean ( 10 / 20 )31845.125125.743502597601253.254636161277
Trimmed Mean ( 11 / 20 )31852120.959611424711263.32756549756
Trimmed Mean ( 12 / 20 )31857.0833333333115.479575429034275.867686688116
Trimmed Mean ( 13 / 20 )31869.8235294118110.890798129434287.398269892625
Trimmed Mean ( 14 / 20 )31879.03125106.864461226999298.312749476961
Trimmed Mean ( 15 / 20 )31889.0666666667102.773603808793310.284601151043
Trimmed Mean ( 16 / 20 )31899.607142857197.1596125742104328.321679118391
Trimmed Mean ( 17 / 20 )31905.423076923192.0227425581796346.712369029335
Trimmed Mean ( 18 / 20 )31912.585.7863667760658371.999668470673
Trimmed Mean ( 19 / 20 )31910.545454545581.3681369526017392.17495508265
Trimmed Mean ( 20 / 20 )31910.577.4179871660463412.184573225319
Median31985
Midrange31736
Midmean - Weighted Average at Xnp31850.9032258065
Midmean - Weighted Average at X(n+1)p31889.0666666667
Midmean - Empirical Distribution Function31850.9032258065
Midmean - Empirical Distribution Function - Averaging31889.0666666667
Midmean - Empirical Distribution Function - Interpolation31889.0666666667
Midmean - Closest Observation31850.9032258065
Midmean - True Basic - Statistics Graphics Toolkit31889.0666666667
Midmean - MS Excel (old versions)31879.03125
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 31772.4166666667 & 194.29427458506 & 163.527292476943 \tabularnewline
Geometric Mean & 31737.04170457 &  &  \tabularnewline
Harmonic Mean & 31701.3388639436 &  &  \tabularnewline
Quadratic Mean & 31807.4476574801 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 31777.4 & 192.668954690928 & 164.932643408877 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 31746.1333333333 & 185.114631559274 & 171.49445760136 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 31751.2833333333 & 183.146636461796 & 173.365364206165 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 31767.4166666667 & 177.267838610001 & 179.205753935753 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 31774.5 & 174.884141631968 & 181.688858140536 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 31761.6 & 169.863030897063 & 186.983593971354 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 31733.4833333333 & 162.289941575363 & 195.535736998199 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 31818.95 & 140.604131194782 & 226.301672145895 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 31817.75 & 138.929803079166 & 229.020334692833 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 31801.5833333333 & 136.001556346335 & 233.832495654307 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 31818.45 & 132.287378546099 & 240.52521374072 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 31770.45 & 121.613187902264 & 261.241815530177 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 31805.9833333333 & 113.502727739607 & 280.222193481562 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 31808.7833333333 & 107.542150694892 & 295.779683852316 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 31815.2833333333 & 105.773991793468 & 300.785503070123 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 31859.2833333333 & 96.7581850774016 & 329.26706208728 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 31857.3 & 91.8404176622917 & 346.876689053649 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 31925.4 & 79.0381699964276 & 403.923825683755 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 31910.8333333333 & 71.1141168002968 & 448.727127174279 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 31861.5 & 61.466487585067 & 518.355631691254 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 31773.6724137931 & 185.140074483164 & 171.619637198982 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 31769.6785714286 & 175.835013628189 & 180.678909825133 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 31782.7592592593 & 169.433761085732 & 187.582209446306 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 31794.8653846154 & 162.397609066459 & 195.784073222432 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 31803.1 & 155.971751105311 & 203.902948929045 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 31810.25 & 148.658094857517 & 213.982629270803 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 31820.8260869565 & 140.930007311156 & 225.791701100959 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 31837.8409090909 & 133.239915956928 & 238.951223290948 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 31841.2142857143 & 129.852563296957 & 245.210517815481 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 31845.125 & 125.743502597601 & 253.254636161277 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 31852 & 120.959611424711 & 263.32756549756 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 31857.0833333333 & 115.479575429034 & 275.867686688116 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 31869.8235294118 & 110.890798129434 & 287.398269892625 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 31879.03125 & 106.864461226999 & 298.312749476961 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 31889.0666666667 & 102.773603808793 & 310.284601151043 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 31899.6071428571 & 97.1596125742104 & 328.321679118391 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 31905.4230769231 & 92.0227425581796 & 346.712369029335 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 31912.5 & 85.7863667760658 & 371.999668470673 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 31910.5454545455 & 81.3681369526017 & 392.17495508265 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 31910.5 & 77.4179871660463 & 412.184573225319 \tabularnewline
Median & 31985 &  &  \tabularnewline
Midrange & 31736 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 31850.9032258065 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 31889.0666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 31850.9032258065 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 31889.0666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 31889.0666666667 &  &  \tabularnewline
Midmean - Closest Observation & 31850.9032258065 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 31889.0666666667 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 31879.03125 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]31772.4166666667[/C][C]194.29427458506[/C][C]163.527292476943[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]31737.04170457[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]31701.3388639436[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]31807.4476574801[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]31777.4[/C][C]192.668954690928[/C][C]164.932643408877[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]31746.1333333333[/C][C]185.114631559274[/C][C]171.49445760136[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]31751.2833333333[/C][C]183.146636461796[/C][C]173.365364206165[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]31767.4166666667[/C][C]177.267838610001[/C][C]179.205753935753[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]31774.5[/C][C]174.884141631968[/C][C]181.688858140536[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]31761.6[/C][C]169.863030897063[/C][C]186.983593971354[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]31733.4833333333[/C][C]162.289941575363[/C][C]195.535736998199[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]31818.95[/C][C]140.604131194782[/C][C]226.301672145895[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]31817.75[/C][C]138.929803079166[/C][C]229.020334692833[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]31801.5833333333[/C][C]136.001556346335[/C][C]233.832495654307[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]31818.45[/C][C]132.287378546099[/C][C]240.52521374072[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]31770.45[/C][C]121.613187902264[/C][C]261.241815530177[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]31805.9833333333[/C][C]113.502727739607[/C][C]280.222193481562[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]31808.7833333333[/C][C]107.542150694892[/C][C]295.779683852316[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]31815.2833333333[/C][C]105.773991793468[/C][C]300.785503070123[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]31859.2833333333[/C][C]96.7581850774016[/C][C]329.26706208728[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]31857.3[/C][C]91.8404176622917[/C][C]346.876689053649[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]31925.4[/C][C]79.0381699964276[/C][C]403.923825683755[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]31910.8333333333[/C][C]71.1141168002968[/C][C]448.727127174279[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]31861.5[/C][C]61.466487585067[/C][C]518.355631691254[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]31773.6724137931[/C][C]185.140074483164[/C][C]171.619637198982[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]31769.6785714286[/C][C]175.835013628189[/C][C]180.678909825133[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]31782.7592592593[/C][C]169.433761085732[/C][C]187.582209446306[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]31794.8653846154[/C][C]162.397609066459[/C][C]195.784073222432[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]31803.1[/C][C]155.971751105311[/C][C]203.902948929045[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]31810.25[/C][C]148.658094857517[/C][C]213.982629270803[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]31820.8260869565[/C][C]140.930007311156[/C][C]225.791701100959[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]31837.8409090909[/C][C]133.239915956928[/C][C]238.951223290948[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]31841.2142857143[/C][C]129.852563296957[/C][C]245.210517815481[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]31845.125[/C][C]125.743502597601[/C][C]253.254636161277[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]31852[/C][C]120.959611424711[/C][C]263.32756549756[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]31857.0833333333[/C][C]115.479575429034[/C][C]275.867686688116[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]31869.8235294118[/C][C]110.890798129434[/C][C]287.398269892625[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]31879.03125[/C][C]106.864461226999[/C][C]298.312749476961[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]31889.0666666667[/C][C]102.773603808793[/C][C]310.284601151043[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]31899.6071428571[/C][C]97.1596125742104[/C][C]328.321679118391[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]31905.4230769231[/C][C]92.0227425581796[/C][C]346.712369029335[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]31912.5[/C][C]85.7863667760658[/C][C]371.999668470673[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]31910.5454545455[/C][C]81.3681369526017[/C][C]392.17495508265[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]31910.5[/C][C]77.4179871660463[/C][C]412.184573225319[/C][/ROW]
[ROW][C]Median[/C][C]31985[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]31736[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]31850.9032258065[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]31889.0666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]31850.9032258065[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]31889.0666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]31889.0666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]31850.9032258065[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]31889.0666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]31879.03125[/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=&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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 Mean31772.4166666667194.29427458506163.527292476943
Geometric Mean31737.04170457
Harmonic Mean31701.3388639436
Quadratic Mean31807.4476574801
Winsorized Mean ( 1 / 20 )31777.4192.668954690928164.932643408877
Winsorized Mean ( 2 / 20 )31746.1333333333185.114631559274171.49445760136
Winsorized Mean ( 3 / 20 )31751.2833333333183.146636461796173.365364206165
Winsorized Mean ( 4 / 20 )31767.4166666667177.267838610001179.205753935753
Winsorized Mean ( 5 / 20 )31774.5174.884141631968181.688858140536
Winsorized Mean ( 6 / 20 )31761.6169.863030897063186.983593971354
Winsorized Mean ( 7 / 20 )31733.4833333333162.289941575363195.535736998199
Winsorized Mean ( 8 / 20 )31818.95140.604131194782226.301672145895
Winsorized Mean ( 9 / 20 )31817.75138.929803079166229.020334692833
Winsorized Mean ( 10 / 20 )31801.5833333333136.001556346335233.832495654307
Winsorized Mean ( 11 / 20 )31818.45132.287378546099240.52521374072
Winsorized Mean ( 12 / 20 )31770.45121.613187902264261.241815530177
Winsorized Mean ( 13 / 20 )31805.9833333333113.502727739607280.222193481562
Winsorized Mean ( 14 / 20 )31808.7833333333107.542150694892295.779683852316
Winsorized Mean ( 15 / 20 )31815.2833333333105.773991793468300.785503070123
Winsorized Mean ( 16 / 20 )31859.283333333396.7581850774016329.26706208728
Winsorized Mean ( 17 / 20 )31857.391.8404176622917346.876689053649
Winsorized Mean ( 18 / 20 )31925.479.0381699964276403.923825683755
Winsorized Mean ( 19 / 20 )31910.833333333371.1141168002968448.727127174279
Winsorized Mean ( 20 / 20 )31861.561.466487585067518.355631691254
Trimmed Mean ( 1 / 20 )31773.6724137931185.140074483164171.619637198982
Trimmed Mean ( 2 / 20 )31769.6785714286175.835013628189180.678909825133
Trimmed Mean ( 3 / 20 )31782.7592592593169.433761085732187.582209446306
Trimmed Mean ( 4 / 20 )31794.8653846154162.397609066459195.784073222432
Trimmed Mean ( 5 / 20 )31803.1155.971751105311203.902948929045
Trimmed Mean ( 6 / 20 )31810.25148.658094857517213.982629270803
Trimmed Mean ( 7 / 20 )31820.8260869565140.930007311156225.791701100959
Trimmed Mean ( 8 / 20 )31837.8409090909133.239915956928238.951223290948
Trimmed Mean ( 9 / 20 )31841.2142857143129.852563296957245.210517815481
Trimmed Mean ( 10 / 20 )31845.125125.743502597601253.254636161277
Trimmed Mean ( 11 / 20 )31852120.959611424711263.32756549756
Trimmed Mean ( 12 / 20 )31857.0833333333115.479575429034275.867686688116
Trimmed Mean ( 13 / 20 )31869.8235294118110.890798129434287.398269892625
Trimmed Mean ( 14 / 20 )31879.03125106.864461226999298.312749476961
Trimmed Mean ( 15 / 20 )31889.0666666667102.773603808793310.284601151043
Trimmed Mean ( 16 / 20 )31899.607142857197.1596125742104328.321679118391
Trimmed Mean ( 17 / 20 )31905.423076923192.0227425581796346.712369029335
Trimmed Mean ( 18 / 20 )31912.585.7863667760658371.999668470673
Trimmed Mean ( 19 / 20 )31910.545454545581.3681369526017392.17495508265
Trimmed Mean ( 20 / 20 )31910.577.4179871660463412.184573225319
Median31985
Midrange31736
Midmean - Weighted Average at Xnp31850.9032258065
Midmean - Weighted Average at X(n+1)p31889.0666666667
Midmean - Empirical Distribution Function31850.9032258065
Midmean - Empirical Distribution Function - Averaging31889.0666666667
Midmean - Empirical Distribution Function - Interpolation31889.0666666667
Midmean - Closest Observation31850.9032258065
Midmean - True Basic - Statistics Graphics Toolkit31889.0666666667
Midmean - MS Excel (old versions)31879.03125
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')