Free Statistics

of Irreproducible Research!

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationSun, 18 Dec 2011 10:09:34 -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/Dec/18/t1324220997vs8xb63ehjt6hty.htm/, Retrieved Sun, 05 May 2024 17:39:45 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=156952, Retrieved Sun, 05 May 2024 17:39:45 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact66
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [paper6] [2011-12-18 15:09:34] [47995d3a8fac585eeb070a274b466f8c] [Current]
Feedback Forum

Post a new message
Dataseries X:
1770
2203
2836
1976
2837
2150
2180
2631
1781
2327
2260
2051
2250
2102
2957
2485
2871
2447
2570
2622
1840
2682
2369
2119
2531
2214
3206
2709
2734
2348
2702
2642
2064
2647
2534
2297
2718
2321
3112
2664
2808
2668
2934
2616
2228
2463
2416
2407
2582
2101
3305
2818
2401
3019
2507
2948
2210
2467
2596
2451




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=156952&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=156952&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=156952&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 Mean2495.0666666666743.817255756968256.94255889747
Geometric Mean2471.97555816001
Harmonic Mean2448.43077648559
Quadratic Mean2517.66455933536
Winsorized Mean ( 1 / 20 )2493.643.277140010144257.6193343510106
Winsorized Mean ( 2 / 20 )2492.4333333333341.912677360680459.4672898580219
Winsorized Mean ( 3 / 20 )2494.5833333333339.134977864655163.7430623305993
Winsorized Mean ( 4 / 20 )2495.4537.159926360511667.1543311412968
Winsorized Mean ( 5 / 20 )2495.7833333333336.785260893742767.8473734505408
Winsorized Mean ( 6 / 20 )2498.0833333333335.778503248835569.8207892029313
Winsorized Mean ( 7 / 20 )2490.8534.305752387794372.6073566859365
Winsorized Mean ( 8 / 20 )2488.5833333333333.041895094714175.3159988614407
Winsorized Mean ( 9 / 20 )2493.0833333333332.153404294433377.5371500480576
Winsorized Mean ( 10 / 20 )2495.0833333333330.727978120268581.1990728308789
Winsorized Mean ( 11 / 20 )2497.4666666666729.680991907324184.1436389479421
Winsorized Mean ( 12 / 20 )2484.0666666666726.960693995437792.1365995655387
Winsorized Mean ( 13 / 20 )2481.4666666666726.274339984471394.4444910179768
Winsorized Mean ( 14 / 20 )2482.6333333333325.396015598637897.7568045542743
Winsorized Mean ( 15 / 20 )2486.3833333333324.2089899217628102.704959660386
Winsorized Mean ( 16 / 20 )2483.7166666666722.9753133502133108.103712398056
Winsorized Mean ( 17 / 20 )2490.2333333333320.700178315598120.300090915492
Winsorized Mean ( 18 / 20 )2496.2333333333319.403715158664128.647184980899
Winsorized Mean ( 19 / 20 )2492.7518.3341647217755135.962016150065
Winsorized Mean ( 20 / 20 )2498.0833333333317.0366386778259146.630058932031
Trimmed Mean ( 1 / 20 )2493.6034482758641.2112138843560.5078864037735
Trimmed Mean ( 2 / 20 )2493.6071428571438.643724634380364.5281262727622
Trimmed Mean ( 3 / 20 )2494.2592592592636.389481985198368.5434120846737
Trimmed Mean ( 4 / 20 )2494.1346153846234.984903325124371.2917395313613
Trimmed Mean ( 5 / 20 )2493.7434.018468093501473.3054761062678
Trimmed Mean ( 6 / 20 )2493.2291666666732.915621757138175.7460753760783
Trimmed Mean ( 7 / 20 )2492.1739130434831.821229269469278.3179647756283
Trimmed Mean ( 8 / 20 )2492.4318181818230.847051553814980.7996775261841
Trimmed Mean ( 9 / 20 )2493.1190476190529.925540627688183.3107437769172
Trimmed Mean ( 10 / 20 )2493.12528.943118120521586.1387839975784
Trimmed Mean ( 11 / 20 )2492.8157894736828.011678504947288.9920177055232
Trimmed Mean ( 12 / 20 )2492.1111111111127.019563100158792.2335828256407
Trimmed Mean ( 13 / 20 )2493.2941176470626.395576028741394.4587879018889
Trimmed Mean ( 14 / 20 )249525.659369162285697.2354380273378
Trimmed Mean ( 15 / 20 )2496.7666666666724.8202125331668100.594088923706
Trimmed Mean ( 16 / 20 )2498.2523.928941598653104.402862521117
Trimmed Mean ( 17 / 20 )2500.3461538461522.9460867994585108.966124625013
Trimmed Mean ( 18 / 20 )2501.8333333333322.2277951949143112.554273214905
Trimmed Mean ( 19 / 20 )2502.6818181818221.5078145834083116.361511695031
Trimmed Mean ( 20 / 20 )2504.2520.6457431575208121.296190739821
Median2496
Midrange2537.5
Midmean - Weighted Average at Xnp2488.09677419355
Midmean - Weighted Average at X(n+1)p2496.76666666667
Midmean - Empirical Distribution Function2488.09677419355
Midmean - Empirical Distribution Function - Averaging2496.76666666667
Midmean - Empirical Distribution Function - Interpolation2496.76666666667
Midmean - Closest Observation2488.09677419355
Midmean - True Basic - Statistics Graphics Toolkit2496.76666666667
Midmean - MS Excel (old versions)2495
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 2495.06666666667 & 43.8172557569682 & 56.94255889747 \tabularnewline
Geometric Mean & 2471.97555816001 &  &  \tabularnewline
Harmonic Mean & 2448.43077648559 &  &  \tabularnewline
Quadratic Mean & 2517.66455933536 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 2493.6 & 43.2771400101442 & 57.6193343510106 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 2492.43333333333 & 41.9126773606804 & 59.4672898580219 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 2494.58333333333 & 39.1349778646551 & 63.7430623305993 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 2495.45 & 37.1599263605116 & 67.1543311412968 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 2495.78333333333 & 36.7852608937427 & 67.8473734505408 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 2498.08333333333 & 35.7785032488355 & 69.8207892029313 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 2490.85 & 34.3057523877943 & 72.6073566859365 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 2488.58333333333 & 33.0418950947141 & 75.3159988614407 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 2493.08333333333 & 32.1534042944333 & 77.5371500480576 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 2495.08333333333 & 30.7279781202685 & 81.1990728308789 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 2497.46666666667 & 29.6809919073241 & 84.1436389479421 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 2484.06666666667 & 26.9606939954377 & 92.1365995655387 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 2481.46666666667 & 26.2743399844713 & 94.4444910179768 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 2482.63333333333 & 25.3960155986378 & 97.7568045542743 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 2486.38333333333 & 24.2089899217628 & 102.704959660386 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 2483.71666666667 & 22.9753133502133 & 108.103712398056 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 2490.23333333333 & 20.700178315598 & 120.300090915492 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 2496.23333333333 & 19.403715158664 & 128.647184980899 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 2492.75 & 18.3341647217755 & 135.962016150065 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 2498.08333333333 & 17.0366386778259 & 146.630058932031 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 2493.60344827586 & 41.21121388435 & 60.5078864037735 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 2493.60714285714 & 38.6437246343803 & 64.5281262727622 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 2494.25925925926 & 36.3894819851983 & 68.5434120846737 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 2494.13461538462 & 34.9849033251243 & 71.2917395313613 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 2493.74 & 34.0184680935014 & 73.3054761062678 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 2493.22916666667 & 32.9156217571381 & 75.7460753760783 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 2492.17391304348 & 31.8212292694692 & 78.3179647756283 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 2492.43181818182 & 30.8470515538149 & 80.7996775261841 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 2493.11904761905 & 29.9255406276881 & 83.3107437769172 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 2493.125 & 28.9431181205215 & 86.1387839975784 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 2492.81578947368 & 28.0116785049472 & 88.9920177055232 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 2492.11111111111 & 27.0195631001587 & 92.2335828256407 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 2493.29411764706 & 26.3955760287413 & 94.4587879018889 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 2495 & 25.6593691622856 & 97.2354380273378 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 2496.76666666667 & 24.8202125331668 & 100.594088923706 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 2498.25 & 23.928941598653 & 104.402862521117 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 2500.34615384615 & 22.9460867994585 & 108.966124625013 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 2501.83333333333 & 22.2277951949143 & 112.554273214905 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 2502.68181818182 & 21.5078145834083 & 116.361511695031 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 2504.25 & 20.6457431575208 & 121.296190739821 \tabularnewline
Median & 2496 &  &  \tabularnewline
Midrange & 2537.5 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 2488.09677419355 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 2496.76666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 2488.09677419355 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 2496.76666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 2496.76666666667 &  &  \tabularnewline
Midmean - Closest Observation & 2488.09677419355 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 2496.76666666667 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 2495 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=156952&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]2495.06666666667[/C][C]43.8172557569682[/C][C]56.94255889747[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]2471.97555816001[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]2448.43077648559[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]2517.66455933536[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]2493.6[/C][C]43.2771400101442[/C][C]57.6193343510106[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]2492.43333333333[/C][C]41.9126773606804[/C][C]59.4672898580219[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]2494.58333333333[/C][C]39.1349778646551[/C][C]63.7430623305993[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]2495.45[/C][C]37.1599263605116[/C][C]67.1543311412968[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]2495.78333333333[/C][C]36.7852608937427[/C][C]67.8473734505408[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]2498.08333333333[/C][C]35.7785032488355[/C][C]69.8207892029313[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]2490.85[/C][C]34.3057523877943[/C][C]72.6073566859365[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]2488.58333333333[/C][C]33.0418950947141[/C][C]75.3159988614407[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]2493.08333333333[/C][C]32.1534042944333[/C][C]77.5371500480576[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]2495.08333333333[/C][C]30.7279781202685[/C][C]81.1990728308789[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]2497.46666666667[/C][C]29.6809919073241[/C][C]84.1436389479421[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]2484.06666666667[/C][C]26.9606939954377[/C][C]92.1365995655387[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]2481.46666666667[/C][C]26.2743399844713[/C][C]94.4444910179768[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]2482.63333333333[/C][C]25.3960155986378[/C][C]97.7568045542743[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]2486.38333333333[/C][C]24.2089899217628[/C][C]102.704959660386[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]2483.71666666667[/C][C]22.9753133502133[/C][C]108.103712398056[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]2490.23333333333[/C][C]20.700178315598[/C][C]120.300090915492[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]2496.23333333333[/C][C]19.403715158664[/C][C]128.647184980899[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]2492.75[/C][C]18.3341647217755[/C][C]135.962016150065[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]2498.08333333333[/C][C]17.0366386778259[/C][C]146.630058932031[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]2493.60344827586[/C][C]41.21121388435[/C][C]60.5078864037735[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]2493.60714285714[/C][C]38.6437246343803[/C][C]64.5281262727622[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]2494.25925925926[/C][C]36.3894819851983[/C][C]68.5434120846737[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]2494.13461538462[/C][C]34.9849033251243[/C][C]71.2917395313613[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]2493.74[/C][C]34.0184680935014[/C][C]73.3054761062678[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]2493.22916666667[/C][C]32.9156217571381[/C][C]75.7460753760783[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]2492.17391304348[/C][C]31.8212292694692[/C][C]78.3179647756283[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]2492.43181818182[/C][C]30.8470515538149[/C][C]80.7996775261841[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]2493.11904761905[/C][C]29.9255406276881[/C][C]83.3107437769172[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]2493.125[/C][C]28.9431181205215[/C][C]86.1387839975784[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]2492.81578947368[/C][C]28.0116785049472[/C][C]88.9920177055232[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]2492.11111111111[/C][C]27.0195631001587[/C][C]92.2335828256407[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]2493.29411764706[/C][C]26.3955760287413[/C][C]94.4587879018889[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]2495[/C][C]25.6593691622856[/C][C]97.2354380273378[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]2496.76666666667[/C][C]24.8202125331668[/C][C]100.594088923706[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]2498.25[/C][C]23.928941598653[/C][C]104.402862521117[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]2500.34615384615[/C][C]22.9460867994585[/C][C]108.966124625013[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]2501.83333333333[/C][C]22.2277951949143[/C][C]112.554273214905[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]2502.68181818182[/C][C]21.5078145834083[/C][C]116.361511695031[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]2504.25[/C][C]20.6457431575208[/C][C]121.296190739821[/C][/ROW]
[ROW][C]Median[/C][C]2496[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]2537.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]2488.09677419355[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]2496.76666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]2488.09677419355[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]2496.76666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]2496.76666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]2488.09677419355[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]2496.76666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]2495[/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=156952&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=156952&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 Mean2495.0666666666743.817255756968256.94255889747
Geometric Mean2471.97555816001
Harmonic Mean2448.43077648559
Quadratic Mean2517.66455933536
Winsorized Mean ( 1 / 20 )2493.643.277140010144257.6193343510106
Winsorized Mean ( 2 / 20 )2492.4333333333341.912677360680459.4672898580219
Winsorized Mean ( 3 / 20 )2494.5833333333339.134977864655163.7430623305993
Winsorized Mean ( 4 / 20 )2495.4537.159926360511667.1543311412968
Winsorized Mean ( 5 / 20 )2495.7833333333336.785260893742767.8473734505408
Winsorized Mean ( 6 / 20 )2498.0833333333335.778503248835569.8207892029313
Winsorized Mean ( 7 / 20 )2490.8534.305752387794372.6073566859365
Winsorized Mean ( 8 / 20 )2488.5833333333333.041895094714175.3159988614407
Winsorized Mean ( 9 / 20 )2493.0833333333332.153404294433377.5371500480576
Winsorized Mean ( 10 / 20 )2495.0833333333330.727978120268581.1990728308789
Winsorized Mean ( 11 / 20 )2497.4666666666729.680991907324184.1436389479421
Winsorized Mean ( 12 / 20 )2484.0666666666726.960693995437792.1365995655387
Winsorized Mean ( 13 / 20 )2481.4666666666726.274339984471394.4444910179768
Winsorized Mean ( 14 / 20 )2482.6333333333325.396015598637897.7568045542743
Winsorized Mean ( 15 / 20 )2486.3833333333324.2089899217628102.704959660386
Winsorized Mean ( 16 / 20 )2483.7166666666722.9753133502133108.103712398056
Winsorized Mean ( 17 / 20 )2490.2333333333320.700178315598120.300090915492
Winsorized Mean ( 18 / 20 )2496.2333333333319.403715158664128.647184980899
Winsorized Mean ( 19 / 20 )2492.7518.3341647217755135.962016150065
Winsorized Mean ( 20 / 20 )2498.0833333333317.0366386778259146.630058932031
Trimmed Mean ( 1 / 20 )2493.6034482758641.2112138843560.5078864037735
Trimmed Mean ( 2 / 20 )2493.6071428571438.643724634380364.5281262727622
Trimmed Mean ( 3 / 20 )2494.2592592592636.389481985198368.5434120846737
Trimmed Mean ( 4 / 20 )2494.1346153846234.984903325124371.2917395313613
Trimmed Mean ( 5 / 20 )2493.7434.018468093501473.3054761062678
Trimmed Mean ( 6 / 20 )2493.2291666666732.915621757138175.7460753760783
Trimmed Mean ( 7 / 20 )2492.1739130434831.821229269469278.3179647756283
Trimmed Mean ( 8 / 20 )2492.4318181818230.847051553814980.7996775261841
Trimmed Mean ( 9 / 20 )2493.1190476190529.925540627688183.3107437769172
Trimmed Mean ( 10 / 20 )2493.12528.943118120521586.1387839975784
Trimmed Mean ( 11 / 20 )2492.8157894736828.011678504947288.9920177055232
Trimmed Mean ( 12 / 20 )2492.1111111111127.019563100158792.2335828256407
Trimmed Mean ( 13 / 20 )2493.2941176470626.395576028741394.4587879018889
Trimmed Mean ( 14 / 20 )249525.659369162285697.2354380273378
Trimmed Mean ( 15 / 20 )2496.7666666666724.8202125331668100.594088923706
Trimmed Mean ( 16 / 20 )2498.2523.928941598653104.402862521117
Trimmed Mean ( 17 / 20 )2500.3461538461522.9460867994585108.966124625013
Trimmed Mean ( 18 / 20 )2501.8333333333322.2277951949143112.554273214905
Trimmed Mean ( 19 / 20 )2502.6818181818221.5078145834083116.361511695031
Trimmed Mean ( 20 / 20 )2504.2520.6457431575208121.296190739821
Median2496
Midrange2537.5
Midmean - Weighted Average at Xnp2488.09677419355
Midmean - Weighted Average at X(n+1)p2496.76666666667
Midmean - Empirical Distribution Function2488.09677419355
Midmean - Empirical Distribution Function - Averaging2496.76666666667
Midmean - Empirical Distribution Function - Interpolation2496.76666666667
Midmean - Closest Observation2488.09677419355
Midmean - True Basic - Statistics Graphics Toolkit2496.76666666667
Midmean - MS Excel (old versions)2495
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')