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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 Nov 2011 06:45:06 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Nov/15/t1321357525ybr6njwjcwf4m15.htm/, Retrieved Thu, 28 Mar 2024 08:45:37 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=142767, Retrieved Thu, 28 Mar 2024 08:45:37 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact82
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Central Tendency] [Arabica Price in ...] [2008-01-19 12:03:37] [74be16979710d4c4e7c6647856088456]
- RM D  [Central Tendency] [] [2011-11-14 13:33:25] [e32f7fcc4522d286f7101d32ccf9e2fd]
-    D      [Central Tendency] [mini tutorial] [2011-11-15 11:45:06] [05d3841c0e91f0207133db830e88168b] [Current]
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Dataseries X:
1.324
1.310
1.310
1.310
1.310
1.338
1.338
1.338
1.358
1.358
1.358
1.358
1.351
1.351
1.351
1.351
1.351
1.372
1.372
1.372
1.372
1.386
1.386
1.386
1.386
1.414
1.414
1.414
1.414
1.443
1.443
1.443
1.443
1.443
1.443
1.443
1.443
1.443
1.448
1.448
1.448
1.463
1.463
1.463
1.456
1.456
1.456
1.456
1.456
1.440
1.440
1.440
1.440
1.429
1.429
1.429
1.419
1.419
1.435
1.435
1.435
1.435
1.435
1.465
1.465
1.438
1.438
1.394
1.394
1.394
1.423
1.423
1.423
1.460
1.460
1.460
1.460
1.472
1.472
1.472
1.451
1.451
1.451
1.400
1.421
1.421
1.421
1.421
1.421
1.421
1.450
1.450
1.450
1.450
1.463
1.463
1.463
1.463
1.463
1.463
1.463
1.463
1.459
1.459
1.459
1.459
1.480
1.480
1.480
1.480
1.498
1.498
1.498
1.498
1.498
1.498
1.498
1.498
1.498
1.511
1.511




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

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=142767&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=142767&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=142767&T=0

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

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







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean1.430322314049590.00435129591658894328.711800224068
Geometric Mean1.4295127858565
Harmonic Mean1.42868769695693
Quadratic Mean1.43111633880919
Winsorized Mean ( 1 / 40 )1.430322314049590.00435129591658894328.711800224068
Winsorized Mean ( 2 / 40 )1.430107438016530.0043206181588406330.996025439167
Winsorized Mean ( 3 / 40 )1.430107438016530.0043206181588406330.996025439167
Winsorized Mean ( 4 / 40 )1.430570247933880.00421823449624697339.139573489024
Winsorized Mean ( 5 / 40 )1.431148760330580.00410251990621099348.846268402963
Winsorized Mean ( 6 / 40 )1.431148760330580.00410251990621099348.846268402963
Winsorized Mean ( 7 / 40 )1.431148760330580.00410251990621099348.846268402963
Winsorized Mean ( 8 / 40 )1.432008264462810.00394756429885975362.757426111196
Winsorized Mean ( 9 / 40 )1.432008264462810.00394756429885975362.757426111196
Winsorized Mean ( 10 / 40 )1.432008264462810.00394756429885975362.757426111196
Winsorized Mean ( 11 / 40 )1.430371900826450.00374254322405768382.192486550798
Winsorized Mean ( 12 / 40 )1.430371900826450.00374254322405768382.192486550798
Winsorized Mean ( 13 / 40 )1.431123966942150.00361260363073896396.147519413695
Winsorized Mean ( 14 / 40 )1.431123966942150.00361260363073896396.147519413695
Winsorized Mean ( 15 / 40 )1.430132231404960.00350727190546121407.762007039741
Winsorized Mean ( 16 / 40 )1.430132231404960.00350727190546121407.762007039741
Winsorized Mean ( 17 / 40 )1.432099173553720.00318332009917513449.875956214648
Winsorized Mean ( 18 / 40 )1.431057851239670.00308102916333572464.47397131753
Winsorized Mean ( 19 / 40 )1.431057851239670.00308102916333572464.47397131753
Winsorized Mean ( 20 / 40 )1.430727272727270.00305128343136333468.893599991796
Winsorized Mean ( 21 / 40 )1.433157024793390.00267701182719255535.35700150282
Winsorized Mean ( 22 / 40 )1.433157024793390.00267701182719255535.35700150282
Winsorized Mean ( 23 / 40 )1.433157024793390.00267701182719255535.35700150282
Winsorized Mean ( 24 / 40 )1.433157024793390.00267701182719255535.35700150282
Winsorized Mean ( 25 / 40 )1.434809917355370.002440230819638587.981229401988
Winsorized Mean ( 26 / 40 )1.434809917355370.002440230819638587.981229401988
Winsorized Mean ( 27 / 40 )1.434809917355370.002440230819638587.981229401988
Winsorized Mean ( 28 / 40 )1.436198347107440.00225027148147025638.233368255228
Winsorized Mean ( 29 / 40 )1.439553719008260.00182675819731656788.037366479545
Winsorized Mean ( 30 / 40 )1.439553719008260.00182675819731656788.037366479545
Winsorized Mean ( 31 / 40 )1.438785123966940.00174670909032437823.711934595675
Winsorized Mean ( 32 / 40 )1.438785123966940.00174670909032437823.711934595675
Winsorized Mean ( 33 / 40 )1.440148760330580.00159028824063294905.589768907172
Winsorized Mean ( 34 / 40 )1.440148760330580.00159028824063294905.589768907171
Winsorized Mean ( 35 / 40 )1.440438016528930.00149691567940128962.270645134171
Winsorized Mean ( 36 / 40 )1.440438016528930.00149691567940128962.270645134171
Winsorized Mean ( 37 / 40 )1.440438016528930.00149691567940128962.270645134171
Winsorized Mean ( 38 / 40 )1.440438016528930.00149691567940128962.270645134171
Winsorized Mean ( 39 / 40 )1.439471074380170.001399285255377931028.71881830226
Winsorized Mean ( 40 / 40 )1.439471074380170.001399285255377931028.71881830226
Trimmed Mean ( 1 / 40 )1.430655462184870.0042523892087885336.435681669991
Trimmed Mean ( 2 / 40 )1.4310.00414243173057798345.449265810915
Trimmed Mean ( 3 / 40 )1.431469565217390.00403773810715701354.522637978939
Trimmed Mean ( 4 / 40 )1.431955752212390.00392052021119388365.24636402176
Trimmed Mean ( 5 / 40 )1.432333333333330.00382346591705636374.616477406988
Trimmed Mean ( 6 / 40 )1.432596330275230.0037469915277478382.332417798745
Trimmed Mean ( 7 / 40 )1.43286915887850.00366134001503848391.351022574571
Trimmed Mean ( 8 / 40 )1.433152380952380.00356511334202178401.993497390363
Trimmed Mean ( 9 / 40 )1.433320388349510.0034882581205848410.89860291337
Trimmed Mean ( 10 / 40 )1.433495049504950.00340170672836696421.404654772553
Trimmed Mean ( 11 / 40 )1.433676767676770.00330388439398419433.936723175681
Trimmed Mean ( 12 / 40 )1.434051546391750.00322596755292049444.533778739806
Trimmed Mean ( 13 / 40 )1.434442105263160.00313713144159645457.246415066749
Trimmed Mean ( 14 / 40 )1.434774193548390.00305696764779844469.345560324029
Trimmed Mean ( 15 / 40 )1.435120879120880.00296511401790115484.001920484909
Trimmed Mean ( 16 / 40 )1.435573033707870.00287374290322978499.548178820881
Trimmed Mean ( 17 / 40 )1.436045977011490.00276775974352099518.847772236413
Trimmed Mean ( 18 / 40 )1.436376470588240.00269640161037307532.701235996332
Trimmed Mean ( 19 / 40 )1.436807228915660.00262598835101502547.149125151411
Trimmed Mean ( 20 / 40 )1.437259259259260.00254349677753655565.072176207467
Trimmed Mean ( 21 / 40 )1.437759493670890.0024497689939961586.895947003392
Trimmed Mean ( 22 / 40 )1.43810389610390.0023981355551062599.675816090474
Trimmed Mean ( 23 / 40 )1.438466666666670.00233695985874413615.529043549635
Trimmed Mean ( 24 / 40 )1.438849315068490.00226419681722284635.478905421887
Trimmed Mean ( 25 / 40 )1.439253521126760.00217713731428571661.076135015838
Trimmed Mean ( 26 / 40 )1.43956521739130.00211250874692314681.448168907242
Trimmed Mean ( 27 / 40 )1.439895522388060.00203465390698104707.685723575727
Trimmed Mean ( 28 / 40 )1.440246153846150.00194009203405192742.359706945537
Trimmed Mean ( 29 / 40 )1.440523809523810.0018601731942964774.403057704892
Trimmed Mean ( 30 / 40 )1.440590163934430.00183371238741812785.614022034713
Trimmed Mean ( 31 / 40 )1.440590163934430.00180080671731687799.969341563124
Trimmed Mean ( 32 / 40 )1.440789473684210.00177099593246223813.547590524991
Trimmed Mean ( 33 / 40 )1.440927272727270.00173338277813209831.280482825626
Trimmed Mean ( 34 / 40 )1.440981132075470.00171213770039305841.626892360743
Trimmed Mean ( 35 / 40 )1.441039215686270.00168428975764179855.576784901848
Trimmed Mean ( 36 / 40 )1.441081632653060.00166364608971215866.218868042064
Trimmed Mean ( 37 / 40 )1.441127659574470.0016358091071511880.987673484907
Trimmed Mean ( 38 / 40 )1.441177777777780.0015987017741011901.467553939572
Trimmed Mean ( 39 / 40 )1.441232558139530.00154942107193045930.174879023608
Trimmed Mean ( 40 / 40 )1.441365853658540.00150355517615992958.638483317778
Median1.443
Midrange1.4105
Midmean - Weighted Average at Xnp1.4397868852459
Midmean - Weighted Average at X(n+1)p1.44333333333333
Midmean - Empirical Distribution Function1.44333333333333
Midmean - Empirical Distribution Function - Averaging1.44333333333333
Midmean - Empirical Distribution Function - Interpolation1.44333333333333
Midmean - Closest Observation1.44333333333333
Midmean - True Basic - Statistics Graphics Toolkit1.44333333333333
Midmean - MS Excel (old versions)1.44333333333333
Number of observations121

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 1.43032231404959 & 0.00435129591658894 & 328.711800224068 \tabularnewline
Geometric Mean & 1.4295127858565 &  &  \tabularnewline
Harmonic Mean & 1.42868769695693 &  &  \tabularnewline
Quadratic Mean & 1.43111633880919 &  &  \tabularnewline
Winsorized Mean ( 1 / 40 ) & 1.43032231404959 & 0.00435129591658894 & 328.711800224068 \tabularnewline
Winsorized Mean ( 2 / 40 ) & 1.43010743801653 & 0.0043206181588406 & 330.996025439167 \tabularnewline
Winsorized Mean ( 3 / 40 ) & 1.43010743801653 & 0.0043206181588406 & 330.996025439167 \tabularnewline
Winsorized Mean ( 4 / 40 ) & 1.43057024793388 & 0.00421823449624697 & 339.139573489024 \tabularnewline
Winsorized Mean ( 5 / 40 ) & 1.43114876033058 & 0.00410251990621099 & 348.846268402963 \tabularnewline
Winsorized Mean ( 6 / 40 ) & 1.43114876033058 & 0.00410251990621099 & 348.846268402963 \tabularnewline
Winsorized Mean ( 7 / 40 ) & 1.43114876033058 & 0.00410251990621099 & 348.846268402963 \tabularnewline
Winsorized Mean ( 8 / 40 ) & 1.43200826446281 & 0.00394756429885975 & 362.757426111196 \tabularnewline
Winsorized Mean ( 9 / 40 ) & 1.43200826446281 & 0.00394756429885975 & 362.757426111196 \tabularnewline
Winsorized Mean ( 10 / 40 ) & 1.43200826446281 & 0.00394756429885975 & 362.757426111196 \tabularnewline
Winsorized Mean ( 11 / 40 ) & 1.43037190082645 & 0.00374254322405768 & 382.192486550798 \tabularnewline
Winsorized Mean ( 12 / 40 ) & 1.43037190082645 & 0.00374254322405768 & 382.192486550798 \tabularnewline
Winsorized Mean ( 13 / 40 ) & 1.43112396694215 & 0.00361260363073896 & 396.147519413695 \tabularnewline
Winsorized Mean ( 14 / 40 ) & 1.43112396694215 & 0.00361260363073896 & 396.147519413695 \tabularnewline
Winsorized Mean ( 15 / 40 ) & 1.43013223140496 & 0.00350727190546121 & 407.762007039741 \tabularnewline
Winsorized Mean ( 16 / 40 ) & 1.43013223140496 & 0.00350727190546121 & 407.762007039741 \tabularnewline
Winsorized Mean ( 17 / 40 ) & 1.43209917355372 & 0.00318332009917513 & 449.875956214648 \tabularnewline
Winsorized Mean ( 18 / 40 ) & 1.43105785123967 & 0.00308102916333572 & 464.47397131753 \tabularnewline
Winsorized Mean ( 19 / 40 ) & 1.43105785123967 & 0.00308102916333572 & 464.47397131753 \tabularnewline
Winsorized Mean ( 20 / 40 ) & 1.43072727272727 & 0.00305128343136333 & 468.893599991796 \tabularnewline
Winsorized Mean ( 21 / 40 ) & 1.43315702479339 & 0.00267701182719255 & 535.35700150282 \tabularnewline
Winsorized Mean ( 22 / 40 ) & 1.43315702479339 & 0.00267701182719255 & 535.35700150282 \tabularnewline
Winsorized Mean ( 23 / 40 ) & 1.43315702479339 & 0.00267701182719255 & 535.35700150282 \tabularnewline
Winsorized Mean ( 24 / 40 ) & 1.43315702479339 & 0.00267701182719255 & 535.35700150282 \tabularnewline
Winsorized Mean ( 25 / 40 ) & 1.43480991735537 & 0.002440230819638 & 587.981229401988 \tabularnewline
Winsorized Mean ( 26 / 40 ) & 1.43480991735537 & 0.002440230819638 & 587.981229401988 \tabularnewline
Winsorized Mean ( 27 / 40 ) & 1.43480991735537 & 0.002440230819638 & 587.981229401988 \tabularnewline
Winsorized Mean ( 28 / 40 ) & 1.43619834710744 & 0.00225027148147025 & 638.233368255228 \tabularnewline
Winsorized Mean ( 29 / 40 ) & 1.43955371900826 & 0.00182675819731656 & 788.037366479545 \tabularnewline
Winsorized Mean ( 30 / 40 ) & 1.43955371900826 & 0.00182675819731656 & 788.037366479545 \tabularnewline
Winsorized Mean ( 31 / 40 ) & 1.43878512396694 & 0.00174670909032437 & 823.711934595675 \tabularnewline
Winsorized Mean ( 32 / 40 ) & 1.43878512396694 & 0.00174670909032437 & 823.711934595675 \tabularnewline
Winsorized Mean ( 33 / 40 ) & 1.44014876033058 & 0.00159028824063294 & 905.589768907172 \tabularnewline
Winsorized Mean ( 34 / 40 ) & 1.44014876033058 & 0.00159028824063294 & 905.589768907171 \tabularnewline
Winsorized Mean ( 35 / 40 ) & 1.44043801652893 & 0.00149691567940128 & 962.270645134171 \tabularnewline
Winsorized Mean ( 36 / 40 ) & 1.44043801652893 & 0.00149691567940128 & 962.270645134171 \tabularnewline
Winsorized Mean ( 37 / 40 ) & 1.44043801652893 & 0.00149691567940128 & 962.270645134171 \tabularnewline
Winsorized Mean ( 38 / 40 ) & 1.44043801652893 & 0.00149691567940128 & 962.270645134171 \tabularnewline
Winsorized Mean ( 39 / 40 ) & 1.43947107438017 & 0.00139928525537793 & 1028.71881830226 \tabularnewline
Winsorized Mean ( 40 / 40 ) & 1.43947107438017 & 0.00139928525537793 & 1028.71881830226 \tabularnewline
Trimmed Mean ( 1 / 40 ) & 1.43065546218487 & 0.0042523892087885 & 336.435681669991 \tabularnewline
Trimmed Mean ( 2 / 40 ) & 1.431 & 0.00414243173057798 & 345.449265810915 \tabularnewline
Trimmed Mean ( 3 / 40 ) & 1.43146956521739 & 0.00403773810715701 & 354.522637978939 \tabularnewline
Trimmed Mean ( 4 / 40 ) & 1.43195575221239 & 0.00392052021119388 & 365.24636402176 \tabularnewline
Trimmed Mean ( 5 / 40 ) & 1.43233333333333 & 0.00382346591705636 & 374.616477406988 \tabularnewline
Trimmed Mean ( 6 / 40 ) & 1.43259633027523 & 0.0037469915277478 & 382.332417798745 \tabularnewline
Trimmed Mean ( 7 / 40 ) & 1.4328691588785 & 0.00366134001503848 & 391.351022574571 \tabularnewline
Trimmed Mean ( 8 / 40 ) & 1.43315238095238 & 0.00356511334202178 & 401.993497390363 \tabularnewline
Trimmed Mean ( 9 / 40 ) & 1.43332038834951 & 0.0034882581205848 & 410.89860291337 \tabularnewline
Trimmed Mean ( 10 / 40 ) & 1.43349504950495 & 0.00340170672836696 & 421.404654772553 \tabularnewline
Trimmed Mean ( 11 / 40 ) & 1.43367676767677 & 0.00330388439398419 & 433.936723175681 \tabularnewline
Trimmed Mean ( 12 / 40 ) & 1.43405154639175 & 0.00322596755292049 & 444.533778739806 \tabularnewline
Trimmed Mean ( 13 / 40 ) & 1.43444210526316 & 0.00313713144159645 & 457.246415066749 \tabularnewline
Trimmed Mean ( 14 / 40 ) & 1.43477419354839 & 0.00305696764779844 & 469.345560324029 \tabularnewline
Trimmed Mean ( 15 / 40 ) & 1.43512087912088 & 0.00296511401790115 & 484.001920484909 \tabularnewline
Trimmed Mean ( 16 / 40 ) & 1.43557303370787 & 0.00287374290322978 & 499.548178820881 \tabularnewline
Trimmed Mean ( 17 / 40 ) & 1.43604597701149 & 0.00276775974352099 & 518.847772236413 \tabularnewline
Trimmed Mean ( 18 / 40 ) & 1.43637647058824 & 0.00269640161037307 & 532.701235996332 \tabularnewline
Trimmed Mean ( 19 / 40 ) & 1.43680722891566 & 0.00262598835101502 & 547.149125151411 \tabularnewline
Trimmed Mean ( 20 / 40 ) & 1.43725925925926 & 0.00254349677753655 & 565.072176207467 \tabularnewline
Trimmed Mean ( 21 / 40 ) & 1.43775949367089 & 0.0024497689939961 & 586.895947003392 \tabularnewline
Trimmed Mean ( 22 / 40 ) & 1.4381038961039 & 0.0023981355551062 & 599.675816090474 \tabularnewline
Trimmed Mean ( 23 / 40 ) & 1.43846666666667 & 0.00233695985874413 & 615.529043549635 \tabularnewline
Trimmed Mean ( 24 / 40 ) & 1.43884931506849 & 0.00226419681722284 & 635.478905421887 \tabularnewline
Trimmed Mean ( 25 / 40 ) & 1.43925352112676 & 0.00217713731428571 & 661.076135015838 \tabularnewline
Trimmed Mean ( 26 / 40 ) & 1.4395652173913 & 0.00211250874692314 & 681.448168907242 \tabularnewline
Trimmed Mean ( 27 / 40 ) & 1.43989552238806 & 0.00203465390698104 & 707.685723575727 \tabularnewline
Trimmed Mean ( 28 / 40 ) & 1.44024615384615 & 0.00194009203405192 & 742.359706945537 \tabularnewline
Trimmed Mean ( 29 / 40 ) & 1.44052380952381 & 0.0018601731942964 & 774.403057704892 \tabularnewline
Trimmed Mean ( 30 / 40 ) & 1.44059016393443 & 0.00183371238741812 & 785.614022034713 \tabularnewline
Trimmed Mean ( 31 / 40 ) & 1.44059016393443 & 0.00180080671731687 & 799.969341563124 \tabularnewline
Trimmed Mean ( 32 / 40 ) & 1.44078947368421 & 0.00177099593246223 & 813.547590524991 \tabularnewline
Trimmed Mean ( 33 / 40 ) & 1.44092727272727 & 0.00173338277813209 & 831.280482825626 \tabularnewline
Trimmed Mean ( 34 / 40 ) & 1.44098113207547 & 0.00171213770039305 & 841.626892360743 \tabularnewline
Trimmed Mean ( 35 / 40 ) & 1.44103921568627 & 0.00168428975764179 & 855.576784901848 \tabularnewline
Trimmed Mean ( 36 / 40 ) & 1.44108163265306 & 0.00166364608971215 & 866.218868042064 \tabularnewline
Trimmed Mean ( 37 / 40 ) & 1.44112765957447 & 0.0016358091071511 & 880.987673484907 \tabularnewline
Trimmed Mean ( 38 / 40 ) & 1.44117777777778 & 0.0015987017741011 & 901.467553939572 \tabularnewline
Trimmed Mean ( 39 / 40 ) & 1.44123255813953 & 0.00154942107193045 & 930.174879023608 \tabularnewline
Trimmed Mean ( 40 / 40 ) & 1.44136585365854 & 0.00150355517615992 & 958.638483317778 \tabularnewline
Median & 1.443 &  &  \tabularnewline
Midrange & 1.4105 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 1.4397868852459 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 1.44333333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 1.44333333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 1.44333333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 1.44333333333333 &  &  \tabularnewline
Midmean - Closest Observation & 1.44333333333333 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 1.44333333333333 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 1.44333333333333 &  &  \tabularnewline
Number of observations & 121 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=142767&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]1.43032231404959[/C][C]0.00435129591658894[/C][C]328.711800224068[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]1.4295127858565[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]1.42868769695693[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]1.43111633880919[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 40 )[/C][C]1.43032231404959[/C][C]0.00435129591658894[/C][C]328.711800224068[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 40 )[/C][C]1.43010743801653[/C][C]0.0043206181588406[/C][C]330.996025439167[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 40 )[/C][C]1.43010743801653[/C][C]0.0043206181588406[/C][C]330.996025439167[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 40 )[/C][C]1.43057024793388[/C][C]0.00421823449624697[/C][C]339.139573489024[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 40 )[/C][C]1.43114876033058[/C][C]0.00410251990621099[/C][C]348.846268402963[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 40 )[/C][C]1.43114876033058[/C][C]0.00410251990621099[/C][C]348.846268402963[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 40 )[/C][C]1.43114876033058[/C][C]0.00410251990621099[/C][C]348.846268402963[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 40 )[/C][C]1.43200826446281[/C][C]0.00394756429885975[/C][C]362.757426111196[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 40 )[/C][C]1.43200826446281[/C][C]0.00394756429885975[/C][C]362.757426111196[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 40 )[/C][C]1.43200826446281[/C][C]0.00394756429885975[/C][C]362.757426111196[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 40 )[/C][C]1.43037190082645[/C][C]0.00374254322405768[/C][C]382.192486550798[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 40 )[/C][C]1.43037190082645[/C][C]0.00374254322405768[/C][C]382.192486550798[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 40 )[/C][C]1.43112396694215[/C][C]0.00361260363073896[/C][C]396.147519413695[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 40 )[/C][C]1.43112396694215[/C][C]0.00361260363073896[/C][C]396.147519413695[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 40 )[/C][C]1.43013223140496[/C][C]0.00350727190546121[/C][C]407.762007039741[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 40 )[/C][C]1.43013223140496[/C][C]0.00350727190546121[/C][C]407.762007039741[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 40 )[/C][C]1.43209917355372[/C][C]0.00318332009917513[/C][C]449.875956214648[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 40 )[/C][C]1.43105785123967[/C][C]0.00308102916333572[/C][C]464.47397131753[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 40 )[/C][C]1.43105785123967[/C][C]0.00308102916333572[/C][C]464.47397131753[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 40 )[/C][C]1.43072727272727[/C][C]0.00305128343136333[/C][C]468.893599991796[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 40 )[/C][C]1.43315702479339[/C][C]0.00267701182719255[/C][C]535.35700150282[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 40 )[/C][C]1.43315702479339[/C][C]0.00267701182719255[/C][C]535.35700150282[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 40 )[/C][C]1.43315702479339[/C][C]0.00267701182719255[/C][C]535.35700150282[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 40 )[/C][C]1.43315702479339[/C][C]0.00267701182719255[/C][C]535.35700150282[/C][/ROW]
[ROW][C]Winsorized Mean ( 25 / 40 )[/C][C]1.43480991735537[/C][C]0.002440230819638[/C][C]587.981229401988[/C][/ROW]
[ROW][C]Winsorized Mean ( 26 / 40 )[/C][C]1.43480991735537[/C][C]0.002440230819638[/C][C]587.981229401988[/C][/ROW]
[ROW][C]Winsorized Mean ( 27 / 40 )[/C][C]1.43480991735537[/C][C]0.002440230819638[/C][C]587.981229401988[/C][/ROW]
[ROW][C]Winsorized Mean ( 28 / 40 )[/C][C]1.43619834710744[/C][C]0.00225027148147025[/C][C]638.233368255228[/C][/ROW]
[ROW][C]Winsorized Mean ( 29 / 40 )[/C][C]1.43955371900826[/C][C]0.00182675819731656[/C][C]788.037366479545[/C][/ROW]
[ROW][C]Winsorized Mean ( 30 / 40 )[/C][C]1.43955371900826[/C][C]0.00182675819731656[/C][C]788.037366479545[/C][/ROW]
[ROW][C]Winsorized Mean ( 31 / 40 )[/C][C]1.43878512396694[/C][C]0.00174670909032437[/C][C]823.711934595675[/C][/ROW]
[ROW][C]Winsorized Mean ( 32 / 40 )[/C][C]1.43878512396694[/C][C]0.00174670909032437[/C][C]823.711934595675[/C][/ROW]
[ROW][C]Winsorized Mean ( 33 / 40 )[/C][C]1.44014876033058[/C][C]0.00159028824063294[/C][C]905.589768907172[/C][/ROW]
[ROW][C]Winsorized Mean ( 34 / 40 )[/C][C]1.44014876033058[/C][C]0.00159028824063294[/C][C]905.589768907171[/C][/ROW]
[ROW][C]Winsorized Mean ( 35 / 40 )[/C][C]1.44043801652893[/C][C]0.00149691567940128[/C][C]962.270645134171[/C][/ROW]
[ROW][C]Winsorized Mean ( 36 / 40 )[/C][C]1.44043801652893[/C][C]0.00149691567940128[/C][C]962.270645134171[/C][/ROW]
[ROW][C]Winsorized Mean ( 37 / 40 )[/C][C]1.44043801652893[/C][C]0.00149691567940128[/C][C]962.270645134171[/C][/ROW]
[ROW][C]Winsorized Mean ( 38 / 40 )[/C][C]1.44043801652893[/C][C]0.00149691567940128[/C][C]962.270645134171[/C][/ROW]
[ROW][C]Winsorized Mean ( 39 / 40 )[/C][C]1.43947107438017[/C][C]0.00139928525537793[/C][C]1028.71881830226[/C][/ROW]
[ROW][C]Winsorized Mean ( 40 / 40 )[/C][C]1.43947107438017[/C][C]0.00139928525537793[/C][C]1028.71881830226[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 40 )[/C][C]1.43065546218487[/C][C]0.0042523892087885[/C][C]336.435681669991[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 40 )[/C][C]1.431[/C][C]0.00414243173057798[/C][C]345.449265810915[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 40 )[/C][C]1.43146956521739[/C][C]0.00403773810715701[/C][C]354.522637978939[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 40 )[/C][C]1.43195575221239[/C][C]0.00392052021119388[/C][C]365.24636402176[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 40 )[/C][C]1.43233333333333[/C][C]0.00382346591705636[/C][C]374.616477406988[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 40 )[/C][C]1.43259633027523[/C][C]0.0037469915277478[/C][C]382.332417798745[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 40 )[/C][C]1.4328691588785[/C][C]0.00366134001503848[/C][C]391.351022574571[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 40 )[/C][C]1.43315238095238[/C][C]0.00356511334202178[/C][C]401.993497390363[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 40 )[/C][C]1.43332038834951[/C][C]0.0034882581205848[/C][C]410.89860291337[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 40 )[/C][C]1.43349504950495[/C][C]0.00340170672836696[/C][C]421.404654772553[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 40 )[/C][C]1.43367676767677[/C][C]0.00330388439398419[/C][C]433.936723175681[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 40 )[/C][C]1.43405154639175[/C][C]0.00322596755292049[/C][C]444.533778739806[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 40 )[/C][C]1.43444210526316[/C][C]0.00313713144159645[/C][C]457.246415066749[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 40 )[/C][C]1.43477419354839[/C][C]0.00305696764779844[/C][C]469.345560324029[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 40 )[/C][C]1.43512087912088[/C][C]0.00296511401790115[/C][C]484.001920484909[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 40 )[/C][C]1.43557303370787[/C][C]0.00287374290322978[/C][C]499.548178820881[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 40 )[/C][C]1.43604597701149[/C][C]0.00276775974352099[/C][C]518.847772236413[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 40 )[/C][C]1.43637647058824[/C][C]0.00269640161037307[/C][C]532.701235996332[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 40 )[/C][C]1.43680722891566[/C][C]0.00262598835101502[/C][C]547.149125151411[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 40 )[/C][C]1.43725925925926[/C][C]0.00254349677753655[/C][C]565.072176207467[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 40 )[/C][C]1.43775949367089[/C][C]0.0024497689939961[/C][C]586.895947003392[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 40 )[/C][C]1.4381038961039[/C][C]0.0023981355551062[/C][C]599.675816090474[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 40 )[/C][C]1.43846666666667[/C][C]0.00233695985874413[/C][C]615.529043549635[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 40 )[/C][C]1.43884931506849[/C][C]0.00226419681722284[/C][C]635.478905421887[/C][/ROW]
[ROW][C]Trimmed Mean ( 25 / 40 )[/C][C]1.43925352112676[/C][C]0.00217713731428571[/C][C]661.076135015838[/C][/ROW]
[ROW][C]Trimmed Mean ( 26 / 40 )[/C][C]1.4395652173913[/C][C]0.00211250874692314[/C][C]681.448168907242[/C][/ROW]
[ROW][C]Trimmed Mean ( 27 / 40 )[/C][C]1.43989552238806[/C][C]0.00203465390698104[/C][C]707.685723575727[/C][/ROW]
[ROW][C]Trimmed Mean ( 28 / 40 )[/C][C]1.44024615384615[/C][C]0.00194009203405192[/C][C]742.359706945537[/C][/ROW]
[ROW][C]Trimmed Mean ( 29 / 40 )[/C][C]1.44052380952381[/C][C]0.0018601731942964[/C][C]774.403057704892[/C][/ROW]
[ROW][C]Trimmed Mean ( 30 / 40 )[/C][C]1.44059016393443[/C][C]0.00183371238741812[/C][C]785.614022034713[/C][/ROW]
[ROW][C]Trimmed Mean ( 31 / 40 )[/C][C]1.44059016393443[/C][C]0.00180080671731687[/C][C]799.969341563124[/C][/ROW]
[ROW][C]Trimmed Mean ( 32 / 40 )[/C][C]1.44078947368421[/C][C]0.00177099593246223[/C][C]813.547590524991[/C][/ROW]
[ROW][C]Trimmed Mean ( 33 / 40 )[/C][C]1.44092727272727[/C][C]0.00173338277813209[/C][C]831.280482825626[/C][/ROW]
[ROW][C]Trimmed Mean ( 34 / 40 )[/C][C]1.44098113207547[/C][C]0.00171213770039305[/C][C]841.626892360743[/C][/ROW]
[ROW][C]Trimmed Mean ( 35 / 40 )[/C][C]1.44103921568627[/C][C]0.00168428975764179[/C][C]855.576784901848[/C][/ROW]
[ROW][C]Trimmed Mean ( 36 / 40 )[/C][C]1.44108163265306[/C][C]0.00166364608971215[/C][C]866.218868042064[/C][/ROW]
[ROW][C]Trimmed Mean ( 37 / 40 )[/C][C]1.44112765957447[/C][C]0.0016358091071511[/C][C]880.987673484907[/C][/ROW]
[ROW][C]Trimmed Mean ( 38 / 40 )[/C][C]1.44117777777778[/C][C]0.0015987017741011[/C][C]901.467553939572[/C][/ROW]
[ROW][C]Trimmed Mean ( 39 / 40 )[/C][C]1.44123255813953[/C][C]0.00154942107193045[/C][C]930.174879023608[/C][/ROW]
[ROW][C]Trimmed Mean ( 40 / 40 )[/C][C]1.44136585365854[/C][C]0.00150355517615992[/C][C]958.638483317778[/C][/ROW]
[ROW][C]Median[/C][C]1.443[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]1.4105[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]1.4397868852459[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]1.44333333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]1.44333333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]1.44333333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]1.44333333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]1.44333333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]1.44333333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]1.44333333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]121[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=142767&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=142767&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 Mean1.430322314049590.00435129591658894328.711800224068
Geometric Mean1.4295127858565
Harmonic Mean1.42868769695693
Quadratic Mean1.43111633880919
Winsorized Mean ( 1 / 40 )1.430322314049590.00435129591658894328.711800224068
Winsorized Mean ( 2 / 40 )1.430107438016530.0043206181588406330.996025439167
Winsorized Mean ( 3 / 40 )1.430107438016530.0043206181588406330.996025439167
Winsorized Mean ( 4 / 40 )1.430570247933880.00421823449624697339.139573489024
Winsorized Mean ( 5 / 40 )1.431148760330580.00410251990621099348.846268402963
Winsorized Mean ( 6 / 40 )1.431148760330580.00410251990621099348.846268402963
Winsorized Mean ( 7 / 40 )1.431148760330580.00410251990621099348.846268402963
Winsorized Mean ( 8 / 40 )1.432008264462810.00394756429885975362.757426111196
Winsorized Mean ( 9 / 40 )1.432008264462810.00394756429885975362.757426111196
Winsorized Mean ( 10 / 40 )1.432008264462810.00394756429885975362.757426111196
Winsorized Mean ( 11 / 40 )1.430371900826450.00374254322405768382.192486550798
Winsorized Mean ( 12 / 40 )1.430371900826450.00374254322405768382.192486550798
Winsorized Mean ( 13 / 40 )1.431123966942150.00361260363073896396.147519413695
Winsorized Mean ( 14 / 40 )1.431123966942150.00361260363073896396.147519413695
Winsorized Mean ( 15 / 40 )1.430132231404960.00350727190546121407.762007039741
Winsorized Mean ( 16 / 40 )1.430132231404960.00350727190546121407.762007039741
Winsorized Mean ( 17 / 40 )1.432099173553720.00318332009917513449.875956214648
Winsorized Mean ( 18 / 40 )1.431057851239670.00308102916333572464.47397131753
Winsorized Mean ( 19 / 40 )1.431057851239670.00308102916333572464.47397131753
Winsorized Mean ( 20 / 40 )1.430727272727270.00305128343136333468.893599991796
Winsorized Mean ( 21 / 40 )1.433157024793390.00267701182719255535.35700150282
Winsorized Mean ( 22 / 40 )1.433157024793390.00267701182719255535.35700150282
Winsorized Mean ( 23 / 40 )1.433157024793390.00267701182719255535.35700150282
Winsorized Mean ( 24 / 40 )1.433157024793390.00267701182719255535.35700150282
Winsorized Mean ( 25 / 40 )1.434809917355370.002440230819638587.981229401988
Winsorized Mean ( 26 / 40 )1.434809917355370.002440230819638587.981229401988
Winsorized Mean ( 27 / 40 )1.434809917355370.002440230819638587.981229401988
Winsorized Mean ( 28 / 40 )1.436198347107440.00225027148147025638.233368255228
Winsorized Mean ( 29 / 40 )1.439553719008260.00182675819731656788.037366479545
Winsorized Mean ( 30 / 40 )1.439553719008260.00182675819731656788.037366479545
Winsorized Mean ( 31 / 40 )1.438785123966940.00174670909032437823.711934595675
Winsorized Mean ( 32 / 40 )1.438785123966940.00174670909032437823.711934595675
Winsorized Mean ( 33 / 40 )1.440148760330580.00159028824063294905.589768907172
Winsorized Mean ( 34 / 40 )1.440148760330580.00159028824063294905.589768907171
Winsorized Mean ( 35 / 40 )1.440438016528930.00149691567940128962.270645134171
Winsorized Mean ( 36 / 40 )1.440438016528930.00149691567940128962.270645134171
Winsorized Mean ( 37 / 40 )1.440438016528930.00149691567940128962.270645134171
Winsorized Mean ( 38 / 40 )1.440438016528930.00149691567940128962.270645134171
Winsorized Mean ( 39 / 40 )1.439471074380170.001399285255377931028.71881830226
Winsorized Mean ( 40 / 40 )1.439471074380170.001399285255377931028.71881830226
Trimmed Mean ( 1 / 40 )1.430655462184870.0042523892087885336.435681669991
Trimmed Mean ( 2 / 40 )1.4310.00414243173057798345.449265810915
Trimmed Mean ( 3 / 40 )1.431469565217390.00403773810715701354.522637978939
Trimmed Mean ( 4 / 40 )1.431955752212390.00392052021119388365.24636402176
Trimmed Mean ( 5 / 40 )1.432333333333330.00382346591705636374.616477406988
Trimmed Mean ( 6 / 40 )1.432596330275230.0037469915277478382.332417798745
Trimmed Mean ( 7 / 40 )1.43286915887850.00366134001503848391.351022574571
Trimmed Mean ( 8 / 40 )1.433152380952380.00356511334202178401.993497390363
Trimmed Mean ( 9 / 40 )1.433320388349510.0034882581205848410.89860291337
Trimmed Mean ( 10 / 40 )1.433495049504950.00340170672836696421.404654772553
Trimmed Mean ( 11 / 40 )1.433676767676770.00330388439398419433.936723175681
Trimmed Mean ( 12 / 40 )1.434051546391750.00322596755292049444.533778739806
Trimmed Mean ( 13 / 40 )1.434442105263160.00313713144159645457.246415066749
Trimmed Mean ( 14 / 40 )1.434774193548390.00305696764779844469.345560324029
Trimmed Mean ( 15 / 40 )1.435120879120880.00296511401790115484.001920484909
Trimmed Mean ( 16 / 40 )1.435573033707870.00287374290322978499.548178820881
Trimmed Mean ( 17 / 40 )1.436045977011490.00276775974352099518.847772236413
Trimmed Mean ( 18 / 40 )1.436376470588240.00269640161037307532.701235996332
Trimmed Mean ( 19 / 40 )1.436807228915660.00262598835101502547.149125151411
Trimmed Mean ( 20 / 40 )1.437259259259260.00254349677753655565.072176207467
Trimmed Mean ( 21 / 40 )1.437759493670890.0024497689939961586.895947003392
Trimmed Mean ( 22 / 40 )1.43810389610390.0023981355551062599.675816090474
Trimmed Mean ( 23 / 40 )1.438466666666670.00233695985874413615.529043549635
Trimmed Mean ( 24 / 40 )1.438849315068490.00226419681722284635.478905421887
Trimmed Mean ( 25 / 40 )1.439253521126760.00217713731428571661.076135015838
Trimmed Mean ( 26 / 40 )1.43956521739130.00211250874692314681.448168907242
Trimmed Mean ( 27 / 40 )1.439895522388060.00203465390698104707.685723575727
Trimmed Mean ( 28 / 40 )1.440246153846150.00194009203405192742.359706945537
Trimmed Mean ( 29 / 40 )1.440523809523810.0018601731942964774.403057704892
Trimmed Mean ( 30 / 40 )1.440590163934430.00183371238741812785.614022034713
Trimmed Mean ( 31 / 40 )1.440590163934430.00180080671731687799.969341563124
Trimmed Mean ( 32 / 40 )1.440789473684210.00177099593246223813.547590524991
Trimmed Mean ( 33 / 40 )1.440927272727270.00173338277813209831.280482825626
Trimmed Mean ( 34 / 40 )1.440981132075470.00171213770039305841.626892360743
Trimmed Mean ( 35 / 40 )1.441039215686270.00168428975764179855.576784901848
Trimmed Mean ( 36 / 40 )1.441081632653060.00166364608971215866.218868042064
Trimmed Mean ( 37 / 40 )1.441127659574470.0016358091071511880.987673484907
Trimmed Mean ( 38 / 40 )1.441177777777780.0015987017741011901.467553939572
Trimmed Mean ( 39 / 40 )1.441232558139530.00154942107193045930.174879023608
Trimmed Mean ( 40 / 40 )1.441365853658540.00150355517615992958.638483317778
Median1.443
Midrange1.4105
Midmean - Weighted Average at Xnp1.4397868852459
Midmean - Weighted Average at X(n+1)p1.44333333333333
Midmean - Empirical Distribution Function1.44333333333333
Midmean - Empirical Distribution Function - Averaging1.44333333333333
Midmean - Empirical Distribution Function - Interpolation1.44333333333333
Midmean - Closest Observation1.44333333333333
Midmean - True Basic - Statistics Graphics Toolkit1.44333333333333
Midmean - MS Excel (old versions)1.44333333333333
Number of observations121



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')