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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 computationTue, 15 Dec 2015 19:13:31 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2015/Dec/15/t14502068966zbbdvl42wgfr1h.htm/, Retrieved Sat, 18 May 2024 14:15:31 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=286566, Retrieved Sat, 18 May 2024 14:15:31 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact84
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2015-12-15 19:13:31] [9d441e5437781f0cd4d5053adc3d2c6c] [Current]
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Dataseries X:
63966
60410
59440
59445
57614
55396
53030
50090
48764
61658
63943
64878
60634
57905
57224
60953
60621
57258
54903
53278
53042
63753
69210
71446
68408
65427
64630
66086
65058
62689
60841
57346
56222
68202
70745
73690
68992
65925
65546
67221
65315
62038
58774
55320
53900
65544
67906
70911
66544
63657
61720
62140
60837
58632
54642
51125
51000
60486
62685
66142
61895




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Herman Ole Andreas Wold' @ wold.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 & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=286566&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]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=286566&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=286566&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'Herman Ole Andreas Wold' @ wold.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean61427.9016393443738.53537961466683.1752998365421
Geometric Mean61156.2950520213
Harmonic Mean60879.4879124797
Quadratic Mean61693.7044618777
Winsorized Mean ( 1 / 20 )61412.8524590164723.23901975200484.9136326744023
Winsorized Mean ( 2 / 20 )61425.1475409836711.72587850936486.3045020501884
Winsorized Mean ( 3 / 20 )61423.131147541708.4287938794586.7033238600874
Winsorized Mean ( 4 / 20 )61447.393442623658.97299350065893.2472105058454
Winsorized Mean ( 5 / 20 )61430.5081967213655.29090133141193.745400816504
Winsorized Mean ( 6 / 20 )61396.2786885246639.58414090384595.9940604558469
Winsorized Mean ( 7 / 20 )61444.0163934426620.49224003276399.0246330722819
Winsorized Mean ( 8 / 20 )61502.5081967213594.250052528878103.49600801042
Winsorized Mean ( 9 / 20 )61439.9508196721569.219317469509107.93722021383
Winsorized Mean ( 10 / 20 )61397.3278688525537.982645281116114.125108695226
Winsorized Mean ( 11 / 20 )61338.5409836066524.078323190462117.040790029613
Winsorized Mean ( 12 / 20 )61490.0163934426492.51588279391124.848798874518
Winsorized Mean ( 13 / 20 )61669.2459016393450.488955157596136.894024138872
Winsorized Mean ( 14 / 20 )61590.0655737705435.768360327779141.336708170927
Winsorized Mean ( 15 / 20 )61611.2131147541432.121214851808142.578542772734
Winsorized Mean ( 16 / 20 )61650.8196721311416.003921343039148.197688793644
Winsorized Mean ( 17 / 20 )61700.7049180328398.28112126266154.917473171775
Winsorized Mean ( 18 / 20 )61839.393442623353.486301261607174.941414198841
Winsorized Mean ( 19 / 20 )61827.5573770492338.347880538365182.733691958324
Winsorized Mean ( 20 / 20 )61964.606557377293.993840572154210.768383571523
Trimmed Mean ( 1 / 20 )61434.7118644068701.82905776985887.5351500258803
Trimmed Mean ( 2 / 20 )61458.1052631579675.51950846620890.9790235410089
Trimmed Mean ( 3 / 20 )61476.3818181818650.78222059847194.465367787164
Trimmed Mean ( 4 / 20 )61496.8113207547621.56646478286998.9384318573836
Trimmed Mean ( 5 / 20 )61511.5882352941605.06851090063101.66053451325
Trimmed Mean ( 6 / 20 )61531.7755102041585.345665991462105.120408478606
Trimmed Mean ( 7 / 20 )61561.085106383565.103385324545108.937739013947
Trimmed Mean ( 8 / 20 )61583.7555555556544.76384760011113.046700559986
Trimmed Mean ( 9 / 20 )61598.1627906977525.871251891705117.135444406044
Trimmed Mean ( 10 / 20 )61624.3170731707507.842595451492121.345309796994
Trimmed Mean ( 11 / 20 )61659.8205128205492.155655012575125.285201713765
Trimmed Mean ( 12 / 20 )61707.972972973474.226652717746130.123375856947
Trimmed Mean ( 13 / 20 )61739.6285714286458.584422340059134.630889240381
Trimmed Mean ( 14 / 20 )61749.6363636364448.424292658813137.703593169559
Trimmed Mean ( 15 / 20 )61772.064516129437.17359789901141.298707911448
Trimmed Mean ( 16 / 20 )61794.6206896552420.985828171992146.785512847262
Trimmed Mean ( 17 / 20 )61814.9259259259401.611961824011153.917043818066
Trimmed Mean ( 18 / 20 )61831.32377.894040351701163.620786245939
Trimmed Mean ( 19 / 20 )61830.1304347826358.508103801704172.465084552124
Trimmed Mean ( 20 / 20 )61830.5238095238332.400193535039186.012297862895
Median61720
Midrange61227
Midmean - Weighted Average at Xnp61646.3333333333
Midmean - Weighted Average at X(n+1)p61772.064516129
Midmean - Empirical Distribution Function61772.064516129
Midmean - Empirical Distribution Function - Averaging61772.064516129
Midmean - Empirical Distribution Function - Interpolation61772.064516129
Midmean - Closest Observation61631
Midmean - True Basic - Statistics Graphics Toolkit61772.064516129
Midmean - MS Excel (old versions)61772.064516129
Number of observations61

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 61427.9016393443 & 738.535379614666 & 83.1752998365421 \tabularnewline
Geometric Mean & 61156.2950520213 &  &  \tabularnewline
Harmonic Mean & 60879.4879124797 &  &  \tabularnewline
Quadratic Mean & 61693.7044618777 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 61412.8524590164 & 723.239019752004 & 84.9136326744023 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 61425.1475409836 & 711.725878509364 & 86.3045020501884 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 61423.131147541 & 708.42879387945 & 86.7033238600874 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 61447.393442623 & 658.972993500658 & 93.2472105058454 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 61430.5081967213 & 655.290901331411 & 93.745400816504 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 61396.2786885246 & 639.584140903845 & 95.9940604558469 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 61444.0163934426 & 620.492240032763 & 99.0246330722819 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 61502.5081967213 & 594.250052528878 & 103.49600801042 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 61439.9508196721 & 569.219317469509 & 107.93722021383 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 61397.3278688525 & 537.982645281116 & 114.125108695226 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 61338.5409836066 & 524.078323190462 & 117.040790029613 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 61490.0163934426 & 492.51588279391 & 124.848798874518 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 61669.2459016393 & 450.488955157596 & 136.894024138872 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 61590.0655737705 & 435.768360327779 & 141.336708170927 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 61611.2131147541 & 432.121214851808 & 142.578542772734 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 61650.8196721311 & 416.003921343039 & 148.197688793644 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 61700.7049180328 & 398.28112126266 & 154.917473171775 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 61839.393442623 & 353.486301261607 & 174.941414198841 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 61827.5573770492 & 338.347880538365 & 182.733691958324 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 61964.606557377 & 293.993840572154 & 210.768383571523 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 61434.7118644068 & 701.829057769858 & 87.5351500258803 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 61458.1052631579 & 675.519508466208 & 90.9790235410089 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 61476.3818181818 & 650.782220598471 & 94.465367787164 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 61496.8113207547 & 621.566464782869 & 98.9384318573836 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 61511.5882352941 & 605.06851090063 & 101.66053451325 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 61531.7755102041 & 585.345665991462 & 105.120408478606 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 61561.085106383 & 565.103385324545 & 108.937739013947 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 61583.7555555556 & 544.76384760011 & 113.046700559986 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 61598.1627906977 & 525.871251891705 & 117.135444406044 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 61624.3170731707 & 507.842595451492 & 121.345309796994 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 61659.8205128205 & 492.155655012575 & 125.285201713765 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 61707.972972973 & 474.226652717746 & 130.123375856947 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 61739.6285714286 & 458.584422340059 & 134.630889240381 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 61749.6363636364 & 448.424292658813 & 137.703593169559 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 61772.064516129 & 437.17359789901 & 141.298707911448 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 61794.6206896552 & 420.985828171992 & 146.785512847262 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 61814.9259259259 & 401.611961824011 & 153.917043818066 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 61831.32 & 377.894040351701 & 163.620786245939 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 61830.1304347826 & 358.508103801704 & 172.465084552124 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 61830.5238095238 & 332.400193535039 & 186.012297862895 \tabularnewline
Median & 61720 &  &  \tabularnewline
Midrange & 61227 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 61646.3333333333 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 61772.064516129 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 61772.064516129 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 61772.064516129 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 61772.064516129 &  &  \tabularnewline
Midmean - Closest Observation & 61631 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 61772.064516129 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 61772.064516129 &  &  \tabularnewline
Number of observations & 61 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=286566&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]61427.9016393443[/C][C]738.535379614666[/C][C]83.1752998365421[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]61156.2950520213[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]60879.4879124797[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]61693.7044618777[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]61412.8524590164[/C][C]723.239019752004[/C][C]84.9136326744023[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]61425.1475409836[/C][C]711.725878509364[/C][C]86.3045020501884[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]61423.131147541[/C][C]708.42879387945[/C][C]86.7033238600874[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]61447.393442623[/C][C]658.972993500658[/C][C]93.2472105058454[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]61430.5081967213[/C][C]655.290901331411[/C][C]93.745400816504[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]61396.2786885246[/C][C]639.584140903845[/C][C]95.9940604558469[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]61444.0163934426[/C][C]620.492240032763[/C][C]99.0246330722819[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]61502.5081967213[/C][C]594.250052528878[/C][C]103.49600801042[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]61439.9508196721[/C][C]569.219317469509[/C][C]107.93722021383[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]61397.3278688525[/C][C]537.982645281116[/C][C]114.125108695226[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]61338.5409836066[/C][C]524.078323190462[/C][C]117.040790029613[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]61490.0163934426[/C][C]492.51588279391[/C][C]124.848798874518[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]61669.2459016393[/C][C]450.488955157596[/C][C]136.894024138872[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]61590.0655737705[/C][C]435.768360327779[/C][C]141.336708170927[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]61611.2131147541[/C][C]432.121214851808[/C][C]142.578542772734[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]61650.8196721311[/C][C]416.003921343039[/C][C]148.197688793644[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]61700.7049180328[/C][C]398.28112126266[/C][C]154.917473171775[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]61839.393442623[/C][C]353.486301261607[/C][C]174.941414198841[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]61827.5573770492[/C][C]338.347880538365[/C][C]182.733691958324[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]61964.606557377[/C][C]293.993840572154[/C][C]210.768383571523[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]61434.7118644068[/C][C]701.829057769858[/C][C]87.5351500258803[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]61458.1052631579[/C][C]675.519508466208[/C][C]90.9790235410089[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]61476.3818181818[/C][C]650.782220598471[/C][C]94.465367787164[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]61496.8113207547[/C][C]621.566464782869[/C][C]98.9384318573836[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]61511.5882352941[/C][C]605.06851090063[/C][C]101.66053451325[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]61531.7755102041[/C][C]585.345665991462[/C][C]105.120408478606[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]61561.085106383[/C][C]565.103385324545[/C][C]108.937739013947[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]61583.7555555556[/C][C]544.76384760011[/C][C]113.046700559986[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]61598.1627906977[/C][C]525.871251891705[/C][C]117.135444406044[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]61624.3170731707[/C][C]507.842595451492[/C][C]121.345309796994[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]61659.8205128205[/C][C]492.155655012575[/C][C]125.285201713765[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]61707.972972973[/C][C]474.226652717746[/C][C]130.123375856947[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]61739.6285714286[/C][C]458.584422340059[/C][C]134.630889240381[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]61749.6363636364[/C][C]448.424292658813[/C][C]137.703593169559[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]61772.064516129[/C][C]437.17359789901[/C][C]141.298707911448[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]61794.6206896552[/C][C]420.985828171992[/C][C]146.785512847262[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]61814.9259259259[/C][C]401.611961824011[/C][C]153.917043818066[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]61831.32[/C][C]377.894040351701[/C][C]163.620786245939[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]61830.1304347826[/C][C]358.508103801704[/C][C]172.465084552124[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]61830.5238095238[/C][C]332.400193535039[/C][C]186.012297862895[/C][/ROW]
[ROW][C]Median[/C][C]61720[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]61227[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]61646.3333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]61772.064516129[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]61772.064516129[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]61772.064516129[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]61772.064516129[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]61631[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]61772.064516129[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]61772.064516129[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]61[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=286566&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=286566&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 Mean61427.9016393443738.53537961466683.1752998365421
Geometric Mean61156.2950520213
Harmonic Mean60879.4879124797
Quadratic Mean61693.7044618777
Winsorized Mean ( 1 / 20 )61412.8524590164723.23901975200484.9136326744023
Winsorized Mean ( 2 / 20 )61425.1475409836711.72587850936486.3045020501884
Winsorized Mean ( 3 / 20 )61423.131147541708.4287938794586.7033238600874
Winsorized Mean ( 4 / 20 )61447.393442623658.97299350065893.2472105058454
Winsorized Mean ( 5 / 20 )61430.5081967213655.29090133141193.745400816504
Winsorized Mean ( 6 / 20 )61396.2786885246639.58414090384595.9940604558469
Winsorized Mean ( 7 / 20 )61444.0163934426620.49224003276399.0246330722819
Winsorized Mean ( 8 / 20 )61502.5081967213594.250052528878103.49600801042
Winsorized Mean ( 9 / 20 )61439.9508196721569.219317469509107.93722021383
Winsorized Mean ( 10 / 20 )61397.3278688525537.982645281116114.125108695226
Winsorized Mean ( 11 / 20 )61338.5409836066524.078323190462117.040790029613
Winsorized Mean ( 12 / 20 )61490.0163934426492.51588279391124.848798874518
Winsorized Mean ( 13 / 20 )61669.2459016393450.488955157596136.894024138872
Winsorized Mean ( 14 / 20 )61590.0655737705435.768360327779141.336708170927
Winsorized Mean ( 15 / 20 )61611.2131147541432.121214851808142.578542772734
Winsorized Mean ( 16 / 20 )61650.8196721311416.003921343039148.197688793644
Winsorized Mean ( 17 / 20 )61700.7049180328398.28112126266154.917473171775
Winsorized Mean ( 18 / 20 )61839.393442623353.486301261607174.941414198841
Winsorized Mean ( 19 / 20 )61827.5573770492338.347880538365182.733691958324
Winsorized Mean ( 20 / 20 )61964.606557377293.993840572154210.768383571523
Trimmed Mean ( 1 / 20 )61434.7118644068701.82905776985887.5351500258803
Trimmed Mean ( 2 / 20 )61458.1052631579675.51950846620890.9790235410089
Trimmed Mean ( 3 / 20 )61476.3818181818650.78222059847194.465367787164
Trimmed Mean ( 4 / 20 )61496.8113207547621.56646478286998.9384318573836
Trimmed Mean ( 5 / 20 )61511.5882352941605.06851090063101.66053451325
Trimmed Mean ( 6 / 20 )61531.7755102041585.345665991462105.120408478606
Trimmed Mean ( 7 / 20 )61561.085106383565.103385324545108.937739013947
Trimmed Mean ( 8 / 20 )61583.7555555556544.76384760011113.046700559986
Trimmed Mean ( 9 / 20 )61598.1627906977525.871251891705117.135444406044
Trimmed Mean ( 10 / 20 )61624.3170731707507.842595451492121.345309796994
Trimmed Mean ( 11 / 20 )61659.8205128205492.155655012575125.285201713765
Trimmed Mean ( 12 / 20 )61707.972972973474.226652717746130.123375856947
Trimmed Mean ( 13 / 20 )61739.6285714286458.584422340059134.630889240381
Trimmed Mean ( 14 / 20 )61749.6363636364448.424292658813137.703593169559
Trimmed Mean ( 15 / 20 )61772.064516129437.17359789901141.298707911448
Trimmed Mean ( 16 / 20 )61794.6206896552420.985828171992146.785512847262
Trimmed Mean ( 17 / 20 )61814.9259259259401.611961824011153.917043818066
Trimmed Mean ( 18 / 20 )61831.32377.894040351701163.620786245939
Trimmed Mean ( 19 / 20 )61830.1304347826358.508103801704172.465084552124
Trimmed Mean ( 20 / 20 )61830.5238095238332.400193535039186.012297862895
Median61720
Midrange61227
Midmean - Weighted Average at Xnp61646.3333333333
Midmean - Weighted Average at X(n+1)p61772.064516129
Midmean - Empirical Distribution Function61772.064516129
Midmean - Empirical Distribution Function - Averaging61772.064516129
Midmean - Empirical Distribution Function - Interpolation61772.064516129
Midmean - Closest Observation61631
Midmean - True Basic - Statistics Graphics Toolkit61772.064516129
Midmean - MS Excel (old versions)61772.064516129
Number of observations61



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')