Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationThu, 13 Oct 2016 18:07:50 +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/13/t14763785512lgopkk2i2jxew9.htm/, Retrieved Tue, 30 Apr 2024 11:31:58 +0200
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Tue, 30 Apr 2024 11:31:58 +0200
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact0
Dataseries X:
829
721
19
311
264
120
135
435
1456
127
313
1104
585
295
4073
408
224
312
571
1336
586
2279
239
198
320
112
89
407
434
268
354
150
273
728
226
310
554
5725
303
360
129
2466
1042
456
335
866
1417
994
201
224
640
1043
293
2659
436
485
610
31127
2613
432
532




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'George Udny Yule' @ yule.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 & 2 seconds \tabularnewline
R Server & 'George Udny Yule' @ yule.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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ yule.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 time2 seconds
R Server'George Udny Yule' @ yule.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean1254.96721311475513.6883109984112.44305191736908
Geometric Mean483.305352063932
Harmonic Mean267.76910014389
Quadratic Mean4172.22764927527
Winsorized Mean ( 1 / 20 )839.688524590164150.3546509445145.58471932404695
Winsorized Mean ( 2 / 20 )786.27868852459123.3347241048766.37516071999307
Winsorized Mean ( 3 / 20 )717.13114754098495.6195343104857.49983936558817
Winsorized Mean ( 4 / 20 )714.57377049180394.55669204446337.55709358102111
Winsorized Mean ( 5 / 20 )702.68852459016490.56735723901197.75873941795313
Winsorized Mean ( 6 / 20 )684.88524590163984.62949174738758.09274913225249
Winsorized Mean ( 7 / 20 )592.1639344262357.138151917530110.3637222163035
Winsorized Mean ( 8 / 20 )593.34426229508255.073105340341610.7737571474919
Winsorized Mean ( 9 / 20 )581.8360655737752.086950110021411.1704767575137
Winsorized Mean ( 10 / 20 )547.57377049180342.87222379621812.7722269107045
Winsorized Mean ( 11 / 20 )536.57377049180340.536049253473113.2369527956854
Winsorized Mean ( 12 / 20 )536.77049180327940.4446149896713.2717419102735
Winsorized Mean ( 13 / 20 )529.31147540983637.982218596327913.9357703412567
Winsorized Mean ( 14 / 20 )505.67213114754131.429822263140616.0889274814821
Winsorized Mean ( 15 / 20 )497.5573770491829.583931953523216.8185005911604
Winsorized Mean ( 16 / 20 )472.37704918032824.629785201861819.1790973940211
Winsorized Mean ( 17 / 20 )47623.554784415325520.208208727663
Winsorized Mean ( 18 / 20 )452.68852459016419.474623266116423.245046561583
Winsorized Mean ( 19 / 20 )445.8360655737717.664715538115825.2387911150775
Winsorized Mean ( 20 / 20 )440.26229508196716.15403824792727.2540084606067
Trimmed Mean ( 1 / 20 )769.610169491525130.2117122833065.91045272346206
Trimmed Mean ( 2 / 20 )694.614035087719101.18441362386.86483234137493
Trimmed Mean ( 3 / 20 )643.78181818181883.6570709250797.69548600091882
Trimmed Mean ( 4 / 20 )615.64150943396277.15961861494527.97880446385096
Trimmed Mean ( 5 / 20 )586.05882352941268.98507034711098.49544431252371
Trimmed Mean ( 6 / 20 )557.02040816326559.58650381505279.34809684240194
Trimmed Mean ( 7 / 20 )529.3617021276648.908657954177610.8234763387623
Trimmed Mean ( 8 / 20 )517.245.849981549405311.2802662623254
Trimmed Mean ( 9 / 20 )503.69767441860542.37566706660411.8864836658953
Trimmed Mean ( 10 / 20 )490.78048780487838.665506027149212.6929798218669
Trimmed Mean ( 11 / 20 )481.89743589743636.750128202550613.1128096544705
Trimmed Mean ( 12 / 20 )473.70270270270334.849695817838813.5927356490792
Trimmed Mean ( 13 / 20 )464.54285714285732.155879341583714.4465916235142
Trimmed Mean ( 14 / 20 )455.33333333333329.136358711923815.6276677478916
Trimmed Mean ( 15 / 20 )448.25806451612927.231779653576416.4608435518557
Trimmed Mean ( 16 / 20 )441.34482758620725.081555440314917.5963898505597
Trimmed Mean ( 17 / 20 )436.96296296296323.864138330093518.3104437679167
Trimmed Mean ( 18 / 20 )431.3622.271048471053219.3686435805059
Trimmed Mean ( 19 / 20 )428.21739130434821.561929973835819.8598822936521
Trimmed Mean ( 20 / 20 )425.5238095238121.065161833793320.2003579598033
Median432
Midrange15573
Midmean - Weighted Average at Xnp435.566666666667
Midmean - Weighted Average at X(n+1)p448.258064516129
Midmean - Empirical Distribution Function448.258064516129
Midmean - Empirical Distribution Function - Averaging448.258064516129
Midmean - Empirical Distribution Function - Interpolation448.258064516129
Midmean - Closest Observation442.5
Midmean - True Basic - Statistics Graphics Toolkit448.258064516129
Midmean - MS Excel (old versions)448.258064516129
Number of observations61

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 1254.96721311475 & 513.688310998411 & 2.44305191736908 \tabularnewline
Geometric Mean & 483.305352063932 &  &  \tabularnewline
Harmonic Mean & 267.76910014389 &  &  \tabularnewline
Quadratic Mean & 4172.22764927527 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 839.688524590164 & 150.354650944514 & 5.58471932404695 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 786.27868852459 & 123.334724104876 & 6.37516071999307 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 717.131147540984 & 95.619534310485 & 7.49983936558817 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 714.573770491803 & 94.5566920444633 & 7.55709358102111 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 702.688524590164 & 90.5673572390119 & 7.75873941795313 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 684.885245901639 & 84.6294917473875 & 8.09274913225249 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 592.16393442623 & 57.1381519175301 & 10.3637222163035 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 593.344262295082 & 55.0731053403416 & 10.7737571474919 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 581.83606557377 & 52.0869501100214 & 11.1704767575137 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 547.573770491803 & 42.872223796218 & 12.7722269107045 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 536.573770491803 & 40.5360492534731 & 13.2369527956854 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 536.770491803279 & 40.44461498967 & 13.2717419102735 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 529.311475409836 & 37.9822185963279 & 13.9357703412567 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 505.672131147541 & 31.4298222631406 & 16.0889274814821 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 497.55737704918 & 29.5839319535232 & 16.8185005911604 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 472.377049180328 & 24.6297852018618 & 19.1790973940211 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 476 & 23.5547844153255 & 20.208208727663 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 452.688524590164 & 19.4746232661164 & 23.245046561583 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 445.83606557377 & 17.6647155381158 & 25.2387911150775 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 440.262295081967 & 16.154038247927 & 27.2540084606067 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 769.610169491525 & 130.211712283306 & 5.91045272346206 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 694.614035087719 & 101.1844136238 & 6.86483234137493 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 643.781818181818 & 83.657070925079 & 7.69548600091882 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 615.641509433962 & 77.1596186149452 & 7.97880446385096 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 586.058823529412 & 68.9850703471109 & 8.49544431252371 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 557.020408163265 & 59.5865038150527 & 9.34809684240194 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 529.36170212766 & 48.9086579541776 & 10.8234763387623 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 517.2 & 45.8499815494053 & 11.2802662623254 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 503.697674418605 & 42.375667066604 & 11.8864836658953 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 490.780487804878 & 38.6655060271492 & 12.6929798218669 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 481.897435897436 & 36.7501282025506 & 13.1128096544705 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 473.702702702703 & 34.8496958178388 & 13.5927356490792 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 464.542857142857 & 32.1558793415837 & 14.4465916235142 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 455.333333333333 & 29.1363587119238 & 15.6276677478916 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 448.258064516129 & 27.2317796535764 & 16.4608435518557 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 441.344827586207 & 25.0815554403149 & 17.5963898505597 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 436.962962962963 & 23.8641383300935 & 18.3104437679167 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 431.36 & 22.2710484710532 & 19.3686435805059 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 428.217391304348 & 21.5619299738358 & 19.8598822936521 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 425.52380952381 & 21.0651618337933 & 20.2003579598033 \tabularnewline
Median & 432 &  &  \tabularnewline
Midrange & 15573 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 435.566666666667 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 448.258064516129 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 448.258064516129 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 448.258064516129 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 448.258064516129 &  &  \tabularnewline
Midmean - Closest Observation & 442.5 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 448.258064516129 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 448.258064516129 &  &  \tabularnewline
Number of observations & 61 &  &  \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]1254.96721311475[/C][C]513.688310998411[/C][C]2.44305191736908[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]483.305352063932[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]267.76910014389[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]4172.22764927527[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]839.688524590164[/C][C]150.354650944514[/C][C]5.58471932404695[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]786.27868852459[/C][C]123.334724104876[/C][C]6.37516071999307[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]717.131147540984[/C][C]95.619534310485[/C][C]7.49983936558817[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]714.573770491803[/C][C]94.5566920444633[/C][C]7.55709358102111[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]702.688524590164[/C][C]90.5673572390119[/C][C]7.75873941795313[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]684.885245901639[/C][C]84.6294917473875[/C][C]8.09274913225249[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]592.16393442623[/C][C]57.1381519175301[/C][C]10.3637222163035[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]593.344262295082[/C][C]55.0731053403416[/C][C]10.7737571474919[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]581.83606557377[/C][C]52.0869501100214[/C][C]11.1704767575137[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]547.573770491803[/C][C]42.872223796218[/C][C]12.7722269107045[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]536.573770491803[/C][C]40.5360492534731[/C][C]13.2369527956854[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]536.770491803279[/C][C]40.44461498967[/C][C]13.2717419102735[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]529.311475409836[/C][C]37.9822185963279[/C][C]13.9357703412567[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]505.672131147541[/C][C]31.4298222631406[/C][C]16.0889274814821[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]497.55737704918[/C][C]29.5839319535232[/C][C]16.8185005911604[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]472.377049180328[/C][C]24.6297852018618[/C][C]19.1790973940211[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]476[/C][C]23.5547844153255[/C][C]20.208208727663[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]452.688524590164[/C][C]19.4746232661164[/C][C]23.245046561583[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]445.83606557377[/C][C]17.6647155381158[/C][C]25.2387911150775[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]440.262295081967[/C][C]16.154038247927[/C][C]27.2540084606067[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]769.610169491525[/C][C]130.211712283306[/C][C]5.91045272346206[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]694.614035087719[/C][C]101.1844136238[/C][C]6.86483234137493[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]643.781818181818[/C][C]83.657070925079[/C][C]7.69548600091882[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]615.641509433962[/C][C]77.1596186149452[/C][C]7.97880446385096[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]586.058823529412[/C][C]68.9850703471109[/C][C]8.49544431252371[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]557.020408163265[/C][C]59.5865038150527[/C][C]9.34809684240194[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]529.36170212766[/C][C]48.9086579541776[/C][C]10.8234763387623[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]517.2[/C][C]45.8499815494053[/C][C]11.2802662623254[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]503.697674418605[/C][C]42.375667066604[/C][C]11.8864836658953[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]490.780487804878[/C][C]38.6655060271492[/C][C]12.6929798218669[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]481.897435897436[/C][C]36.7501282025506[/C][C]13.1128096544705[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]473.702702702703[/C][C]34.8496958178388[/C][C]13.5927356490792[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]464.542857142857[/C][C]32.1558793415837[/C][C]14.4465916235142[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]455.333333333333[/C][C]29.1363587119238[/C][C]15.6276677478916[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]448.258064516129[/C][C]27.2317796535764[/C][C]16.4608435518557[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]441.344827586207[/C][C]25.0815554403149[/C][C]17.5963898505597[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]436.962962962963[/C][C]23.8641383300935[/C][C]18.3104437679167[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]431.36[/C][C]22.2710484710532[/C][C]19.3686435805059[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]428.217391304348[/C][C]21.5619299738358[/C][C]19.8598822936521[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]425.52380952381[/C][C]21.0651618337933[/C][C]20.2003579598033[/C][/ROW]
[ROW][C]Median[/C][C]432[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]15573[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]435.566666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]448.258064516129[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]448.258064516129[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]448.258064516129[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]448.258064516129[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]442.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]448.258064516129[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]448.258064516129[/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=&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 Mean1254.96721311475513.6883109984112.44305191736908
Geometric Mean483.305352063932
Harmonic Mean267.76910014389
Quadratic Mean4172.22764927527
Winsorized Mean ( 1 / 20 )839.688524590164150.3546509445145.58471932404695
Winsorized Mean ( 2 / 20 )786.27868852459123.3347241048766.37516071999307
Winsorized Mean ( 3 / 20 )717.13114754098495.6195343104857.49983936558817
Winsorized Mean ( 4 / 20 )714.57377049180394.55669204446337.55709358102111
Winsorized Mean ( 5 / 20 )702.68852459016490.56735723901197.75873941795313
Winsorized Mean ( 6 / 20 )684.88524590163984.62949174738758.09274913225249
Winsorized Mean ( 7 / 20 )592.1639344262357.138151917530110.3637222163035
Winsorized Mean ( 8 / 20 )593.34426229508255.073105340341610.7737571474919
Winsorized Mean ( 9 / 20 )581.8360655737752.086950110021411.1704767575137
Winsorized Mean ( 10 / 20 )547.57377049180342.87222379621812.7722269107045
Winsorized Mean ( 11 / 20 )536.57377049180340.536049253473113.2369527956854
Winsorized Mean ( 12 / 20 )536.77049180327940.4446149896713.2717419102735
Winsorized Mean ( 13 / 20 )529.31147540983637.982218596327913.9357703412567
Winsorized Mean ( 14 / 20 )505.67213114754131.429822263140616.0889274814821
Winsorized Mean ( 15 / 20 )497.5573770491829.583931953523216.8185005911604
Winsorized Mean ( 16 / 20 )472.37704918032824.629785201861819.1790973940211
Winsorized Mean ( 17 / 20 )47623.554784415325520.208208727663
Winsorized Mean ( 18 / 20 )452.68852459016419.474623266116423.245046561583
Winsorized Mean ( 19 / 20 )445.8360655737717.664715538115825.2387911150775
Winsorized Mean ( 20 / 20 )440.26229508196716.15403824792727.2540084606067
Trimmed Mean ( 1 / 20 )769.610169491525130.2117122833065.91045272346206
Trimmed Mean ( 2 / 20 )694.614035087719101.18441362386.86483234137493
Trimmed Mean ( 3 / 20 )643.78181818181883.6570709250797.69548600091882
Trimmed Mean ( 4 / 20 )615.64150943396277.15961861494527.97880446385096
Trimmed Mean ( 5 / 20 )586.05882352941268.98507034711098.49544431252371
Trimmed Mean ( 6 / 20 )557.02040816326559.58650381505279.34809684240194
Trimmed Mean ( 7 / 20 )529.3617021276648.908657954177610.8234763387623
Trimmed Mean ( 8 / 20 )517.245.849981549405311.2802662623254
Trimmed Mean ( 9 / 20 )503.69767441860542.37566706660411.8864836658953
Trimmed Mean ( 10 / 20 )490.78048780487838.665506027149212.6929798218669
Trimmed Mean ( 11 / 20 )481.89743589743636.750128202550613.1128096544705
Trimmed Mean ( 12 / 20 )473.70270270270334.849695817838813.5927356490792
Trimmed Mean ( 13 / 20 )464.54285714285732.155879341583714.4465916235142
Trimmed Mean ( 14 / 20 )455.33333333333329.136358711923815.6276677478916
Trimmed Mean ( 15 / 20 )448.25806451612927.231779653576416.4608435518557
Trimmed Mean ( 16 / 20 )441.34482758620725.081555440314917.5963898505597
Trimmed Mean ( 17 / 20 )436.96296296296323.864138330093518.3104437679167
Trimmed Mean ( 18 / 20 )431.3622.271048471053219.3686435805059
Trimmed Mean ( 19 / 20 )428.21739130434821.561929973835819.8598822936521
Trimmed Mean ( 20 / 20 )425.5238095238121.065161833793320.2003579598033
Median432
Midrange15573
Midmean - Weighted Average at Xnp435.566666666667
Midmean - Weighted Average at X(n+1)p448.258064516129
Midmean - Empirical Distribution Function448.258064516129
Midmean - Empirical Distribution Function - Averaging448.258064516129
Midmean - Empirical Distribution Function - Interpolation448.258064516129
Midmean - Closest Observation442.5
Midmean - True Basic - Statistics Graphics Toolkit448.258064516129
Midmean - MS Excel (old versions)448.258064516129
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')