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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 computationTue, 20 Oct 2009 13:21:07 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Oct/20/t1256066883gx6ezk4xu0ipiuy.htm/, Retrieved Fri, 03 May 2024 01:34:19 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=49062, Retrieved Fri, 03 May 2024 01:34:19 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact138
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Exercise 1.13] [Ex. 1.13 Babies c...] [2009-10-07 19:52:56] [62d80b0d35658f72f0b015f194fffbd1]
-   P   [Exercise 1.13] [Ex. 1.13 Babies c...] [2009-10-07 20:14:54] [62d80b0d35658f72f0b015f194fffbd1]
- R       [Exercise 1.13] [Ex. 1.13 Babies c...] [2009-10-07 20:34:03] [62d80b0d35658f72f0b015f194fffbd1]
F RMPD      [Univariate Data Series] [3e grafiek] [2009-10-12 22:14:27] [df1349bc077b4746949c1672214183f7]
-   PD        [Univariate Data Series] [Y[t] - X[t] = c +...] [2009-10-20 19:10:29] [df1349bc077b4746949c1672214183f7]
-   PD          [Univariate Data Series] [Y[t] / X[t] = c +...] [2009-10-20 19:15:17] [df1349bc077b4746949c1672214183f7]
- RM D              [Central Tendency] [Central Tendency ...] [2009-10-20 19:21:07] [2f1ac16c1440fb5aa417f0550c73728d] [Current]
- RM                  [Harrell-Davis Quantiles] [Harrel Davis 95% ...] [2009-10-20 19:29:53] [df1349bc077b4746949c1672214183f7]
- RM                    [Percentiles] [Percentiles 80% P...] [2009-10-20 19:34:55] [df1349bc077b4746949c1672214183f7]
-   PD                [Central Tendency] [workshop 3 part 3] [2009-10-21 17:22:50] [af8eb90b4bf1bcfcc4325c143dbee260]
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Dataseries X:
23.97
23.81
24.23
25.66
26.79
27.82
28.67
29.44
30.59
30.88
30.88
30.16
30.40
30.97
31.84
31.97
32.02
32.47
33.50
34.99
36.25
37.07
36.72
35.72
33.59
34.82
36.27
37.07
38.43
38.78
39.37
40.66
41.08
39.72
41.85
42.89
42.28
41.86
38.59
39.49
40.76
37.77
38.01
35.66
34.71
34.53
36.50
36.10
33.37
28.99
29.30
28.76
21.63
20.10
18.82
19.42
18.59
17.25
19.36
21.40
21.23




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 seconds
R Server'RServer@AstonUniversity' @ vre.aston.ac.uk

\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 & 4 seconds \tabularnewline
R Server & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=49062&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]4 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=49062&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=49062&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 time4 seconds
R Server'RServer@AstonUniversity' @ vre.aston.ac.uk







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean32.06278688524590.89531321048639235.8118103359910
Geometric Mean31.2184653737359
Harmonic Mean30.2787989554709
Quadratic Mean32.8042291106038
Winsorized Mean ( 1 / 20 )32.07475409836070.88753593343887336.1391047842794
Winsorized Mean ( 2 / 20 )32.06852459016390.88304626233530336.3157922274146
Winsorized Mean ( 3 / 20 )32.09459016393440.87641871164959536.6201562533119
Winsorized Mean ( 4 / 20 )32.04803278688520.86639280518611136.9901880475577
Winsorized Mean ( 5 / 20 )32.07754098360660.8485486695386637.8028298613048
Winsorized Mean ( 6 / 20 )32.17885245901640.82143224573707139.1740799390488
Winsorized Mean ( 7 / 20 )32.09049180327870.7992191348291340.1523066763655
Winsorized Mean ( 8 / 20 )32.09049180327870.7877578136826140.7364944477822
Winsorized Mean ( 9 / 20 )32.39442622950820.7170964345370145.1744349425242
Winsorized Mean ( 10 / 20 )32.32393442622950.69654178079089546.4063108885256
Winsorized Mean ( 11 / 20 )32.33655737704920.68194594137169647.4180655903693
Winsorized Mean ( 12 / 20 )32.58639344262290.62307456565000252.2993478455155
Winsorized Mean ( 13 / 20 )32.73770491803280.56565617361211457.8756255924503
Winsorized Mean ( 14 / 20 )32.91901639344260.5168660661364763.6896452489316
Winsorized Mean ( 15 / 20 )32.95590163934430.45687817947129472.1327984573071
Winsorized Mean ( 16 / 20 )32.97950819672130.45320114752925272.770133916293
Winsorized Mean ( 17 / 20 )32.94606557377050.42880321946229776.8325984471003
Winsorized Mean ( 18 / 20 )32.97262295081970.40539091985858581.33537614094
Winsorized Mean ( 19 / 20 )32.94459016393440.38851437467836584.796322378568
Winsorized Mean ( 20 / 20 )33.17409836065570.35298232722902893.9823209311301
Trimmed Mean ( 1 / 20 )32.13033898305080.87113719339026836.8832133753891
Trimmed Mean ( 2 / 20 )32.18982456140350.85075694186829737.8366875158413
Trimmed Mean ( 3 / 20 )32.25709090909090.82833164330162238.9422415163549
Trimmed Mean ( 4 / 20 )32.31943396226410.8034872928881240.2239515774948
Trimmed Mean ( 5 / 20 )32.40058823529410.77605646710687841.7502973154554
Trimmed Mean ( 6 / 20 )32.48102040816330.74752171292936243.4516079551426
Trimmed Mean ( 7 / 20 )32.54638297872340.7199384176518845.2071763094339
Trimmed Mean ( 8 / 20 )32.63466666666670.6906795511843747.2500837916876
Trimmed Mean ( 9 / 20 )32.73116279069770.65551457552576649.932013738131
Trimmed Mean ( 10 / 20 )32.78682926829270.63064460238328351.9893917182312
Trimmed Mean ( 11 / 20 )32.85923076923080.60273201496554454.5171485060558
Trimmed Mean ( 12 / 20 )32.93756756756760.56874108980980957.9131139945984
Trimmed Mean ( 13 / 20 )32.98857142857140.5404918617158261.0343536419725
Trimmed Mean ( 14 / 20 )33.02424242424240.51855477894771563.6851568338785
Trimmed Mean ( 15 / 20 )33.03903225806450.50197916994840365.8175363361402
Trimmed Mean ( 16 / 20 )33.05068965517240.49505334614133766.7618750843398
Trimmed Mean ( 17 / 20 )33.06074074074070.48398215394270668.3098343015649
Trimmed Mean ( 18 / 20 )33.07720.47340557664649569.87074430832
Trimmed Mean ( 19 / 20 )33.09260869565220.46301863022271871.4714409649871
Trimmed Mean ( 20 / 20 )33.11523809523810.4499505893760173.5974990968724
Median33.37
Midrange30.07
Midmean - Weighted Average at Xnp33.0390322580645
Midmean - Weighted Average at X(n+1)p33.0390322580645
Midmean - Empirical Distribution Function33.0390322580645
Midmean - Empirical Distribution Function - Averaging33.0390322580645
Midmean - Empirical Distribution Function - Interpolation33.0390322580645
Midmean - Closest Observation32.8759375
Midmean - True Basic - Statistics Graphics Toolkit33.0390322580645
Midmean - MS Excel (old versions)33.0390322580645
Number of observations61

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 32.0627868852459 & 0.895313210486392 & 35.8118103359910 \tabularnewline
Geometric Mean & 31.2184653737359 &  &  \tabularnewline
Harmonic Mean & 30.2787989554709 &  &  \tabularnewline
Quadratic Mean & 32.8042291106038 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 32.0747540983607 & 0.887535933438873 & 36.1391047842794 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 32.0685245901639 & 0.883046262335303 & 36.3157922274146 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 32.0945901639344 & 0.876418711649595 & 36.6201562533119 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 32.0480327868852 & 0.866392805186111 & 36.9901880475577 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 32.0775409836066 & 0.84854866953866 & 37.8028298613048 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 32.1788524590164 & 0.821432245737071 & 39.1740799390488 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 32.0904918032787 & 0.79921913482913 & 40.1523066763655 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 32.0904918032787 & 0.78775781368261 & 40.7364944477822 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 32.3944262295082 & 0.71709643453701 & 45.1744349425242 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 32.3239344262295 & 0.696541780790895 & 46.4063108885256 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 32.3365573770492 & 0.681945941371696 & 47.4180655903693 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 32.5863934426229 & 0.623074565650002 & 52.2993478455155 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 32.7377049180328 & 0.565656173612114 & 57.8756255924503 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 32.9190163934426 & 0.51686606613647 & 63.6896452489316 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 32.9559016393443 & 0.456878179471294 & 72.1327984573071 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 32.9795081967213 & 0.453201147529252 & 72.770133916293 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 32.9460655737705 & 0.428803219462297 & 76.8325984471003 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 32.9726229508197 & 0.405390919858585 & 81.33537614094 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 32.9445901639344 & 0.388514374678365 & 84.796322378568 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 33.1740983606557 & 0.352982327229028 & 93.9823209311301 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 32.1303389830508 & 0.871137193390268 & 36.8832133753891 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 32.1898245614035 & 0.850756941868297 & 37.8366875158413 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 32.2570909090909 & 0.828331643301622 & 38.9422415163549 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 32.3194339622641 & 0.80348729288812 & 40.2239515774948 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 32.4005882352941 & 0.776056467106878 & 41.7502973154554 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 32.4810204081633 & 0.747521712929362 & 43.4516079551426 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 32.5463829787234 & 0.71993841765188 & 45.2071763094339 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 32.6346666666667 & 0.69067955118437 & 47.2500837916876 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 32.7311627906977 & 0.655514575525766 & 49.932013738131 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 32.7868292682927 & 0.630644602383283 & 51.9893917182312 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 32.8592307692308 & 0.602732014965544 & 54.5171485060558 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 32.9375675675676 & 0.568741089809809 & 57.9131139945984 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 32.9885714285714 & 0.54049186171582 & 61.0343536419725 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 33.0242424242424 & 0.518554778947715 & 63.6851568338785 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 33.0390322580645 & 0.501979169948403 & 65.8175363361402 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 33.0506896551724 & 0.495053346141337 & 66.7618750843398 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 33.0607407407407 & 0.483982153942706 & 68.3098343015649 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 33.0772 & 0.473405576646495 & 69.87074430832 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 33.0926086956522 & 0.463018630222718 & 71.4714409649871 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 33.1152380952381 & 0.44995058937601 & 73.5974990968724 \tabularnewline
Median & 33.37 &  &  \tabularnewline
Midrange & 30.07 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 33.0390322580645 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 33.0390322580645 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 33.0390322580645 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 33.0390322580645 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 33.0390322580645 &  &  \tabularnewline
Midmean - Closest Observation & 32.8759375 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 33.0390322580645 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 33.0390322580645 &  &  \tabularnewline
Number of observations & 61 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=49062&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]32.0627868852459[/C][C]0.895313210486392[/C][C]35.8118103359910[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]31.2184653737359[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]30.2787989554709[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]32.8042291106038[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]32.0747540983607[/C][C]0.887535933438873[/C][C]36.1391047842794[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]32.0685245901639[/C][C]0.883046262335303[/C][C]36.3157922274146[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]32.0945901639344[/C][C]0.876418711649595[/C][C]36.6201562533119[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]32.0480327868852[/C][C]0.866392805186111[/C][C]36.9901880475577[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]32.0775409836066[/C][C]0.84854866953866[/C][C]37.8028298613048[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]32.1788524590164[/C][C]0.821432245737071[/C][C]39.1740799390488[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]32.0904918032787[/C][C]0.79921913482913[/C][C]40.1523066763655[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]32.0904918032787[/C][C]0.78775781368261[/C][C]40.7364944477822[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]32.3944262295082[/C][C]0.71709643453701[/C][C]45.1744349425242[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]32.3239344262295[/C][C]0.696541780790895[/C][C]46.4063108885256[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]32.3365573770492[/C][C]0.681945941371696[/C][C]47.4180655903693[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]32.5863934426229[/C][C]0.623074565650002[/C][C]52.2993478455155[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]32.7377049180328[/C][C]0.565656173612114[/C][C]57.8756255924503[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]32.9190163934426[/C][C]0.51686606613647[/C][C]63.6896452489316[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]32.9559016393443[/C][C]0.456878179471294[/C][C]72.1327984573071[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]32.9795081967213[/C][C]0.453201147529252[/C][C]72.770133916293[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]32.9460655737705[/C][C]0.428803219462297[/C][C]76.8325984471003[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]32.9726229508197[/C][C]0.405390919858585[/C][C]81.33537614094[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]32.9445901639344[/C][C]0.388514374678365[/C][C]84.796322378568[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]33.1740983606557[/C][C]0.352982327229028[/C][C]93.9823209311301[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]32.1303389830508[/C][C]0.871137193390268[/C][C]36.8832133753891[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]32.1898245614035[/C][C]0.850756941868297[/C][C]37.8366875158413[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]32.2570909090909[/C][C]0.828331643301622[/C][C]38.9422415163549[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]32.3194339622641[/C][C]0.80348729288812[/C][C]40.2239515774948[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]32.4005882352941[/C][C]0.776056467106878[/C][C]41.7502973154554[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]32.4810204081633[/C][C]0.747521712929362[/C][C]43.4516079551426[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]32.5463829787234[/C][C]0.71993841765188[/C][C]45.2071763094339[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]32.6346666666667[/C][C]0.69067955118437[/C][C]47.2500837916876[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]32.7311627906977[/C][C]0.655514575525766[/C][C]49.932013738131[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]32.7868292682927[/C][C]0.630644602383283[/C][C]51.9893917182312[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]32.8592307692308[/C][C]0.602732014965544[/C][C]54.5171485060558[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]32.9375675675676[/C][C]0.568741089809809[/C][C]57.9131139945984[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]32.9885714285714[/C][C]0.54049186171582[/C][C]61.0343536419725[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]33.0242424242424[/C][C]0.518554778947715[/C][C]63.6851568338785[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]33.0390322580645[/C][C]0.501979169948403[/C][C]65.8175363361402[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]33.0506896551724[/C][C]0.495053346141337[/C][C]66.7618750843398[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]33.0607407407407[/C][C]0.483982153942706[/C][C]68.3098343015649[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]33.0772[/C][C]0.473405576646495[/C][C]69.87074430832[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]33.0926086956522[/C][C]0.463018630222718[/C][C]71.4714409649871[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]33.1152380952381[/C][C]0.44995058937601[/C][C]73.5974990968724[/C][/ROW]
[ROW][C]Median[/C][C]33.37[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]30.07[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]33.0390322580645[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]33.0390322580645[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]33.0390322580645[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]33.0390322580645[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]33.0390322580645[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]32.8759375[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]33.0390322580645[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]33.0390322580645[/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=49062&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=49062&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 Mean32.06278688524590.89531321048639235.8118103359910
Geometric Mean31.2184653737359
Harmonic Mean30.2787989554709
Quadratic Mean32.8042291106038
Winsorized Mean ( 1 / 20 )32.07475409836070.88753593343887336.1391047842794
Winsorized Mean ( 2 / 20 )32.06852459016390.88304626233530336.3157922274146
Winsorized Mean ( 3 / 20 )32.09459016393440.87641871164959536.6201562533119
Winsorized Mean ( 4 / 20 )32.04803278688520.86639280518611136.9901880475577
Winsorized Mean ( 5 / 20 )32.07754098360660.8485486695386637.8028298613048
Winsorized Mean ( 6 / 20 )32.17885245901640.82143224573707139.1740799390488
Winsorized Mean ( 7 / 20 )32.09049180327870.7992191348291340.1523066763655
Winsorized Mean ( 8 / 20 )32.09049180327870.7877578136826140.7364944477822
Winsorized Mean ( 9 / 20 )32.39442622950820.7170964345370145.1744349425242
Winsorized Mean ( 10 / 20 )32.32393442622950.69654178079089546.4063108885256
Winsorized Mean ( 11 / 20 )32.33655737704920.68194594137169647.4180655903693
Winsorized Mean ( 12 / 20 )32.58639344262290.62307456565000252.2993478455155
Winsorized Mean ( 13 / 20 )32.73770491803280.56565617361211457.8756255924503
Winsorized Mean ( 14 / 20 )32.91901639344260.5168660661364763.6896452489316
Winsorized Mean ( 15 / 20 )32.95590163934430.45687817947129472.1327984573071
Winsorized Mean ( 16 / 20 )32.97950819672130.45320114752925272.770133916293
Winsorized Mean ( 17 / 20 )32.94606557377050.42880321946229776.8325984471003
Winsorized Mean ( 18 / 20 )32.97262295081970.40539091985858581.33537614094
Winsorized Mean ( 19 / 20 )32.94459016393440.38851437467836584.796322378568
Winsorized Mean ( 20 / 20 )33.17409836065570.35298232722902893.9823209311301
Trimmed Mean ( 1 / 20 )32.13033898305080.87113719339026836.8832133753891
Trimmed Mean ( 2 / 20 )32.18982456140350.85075694186829737.8366875158413
Trimmed Mean ( 3 / 20 )32.25709090909090.82833164330162238.9422415163549
Trimmed Mean ( 4 / 20 )32.31943396226410.8034872928881240.2239515774948
Trimmed Mean ( 5 / 20 )32.40058823529410.77605646710687841.7502973154554
Trimmed Mean ( 6 / 20 )32.48102040816330.74752171292936243.4516079551426
Trimmed Mean ( 7 / 20 )32.54638297872340.7199384176518845.2071763094339
Trimmed Mean ( 8 / 20 )32.63466666666670.6906795511843747.2500837916876
Trimmed Mean ( 9 / 20 )32.73116279069770.65551457552576649.932013738131
Trimmed Mean ( 10 / 20 )32.78682926829270.63064460238328351.9893917182312
Trimmed Mean ( 11 / 20 )32.85923076923080.60273201496554454.5171485060558
Trimmed Mean ( 12 / 20 )32.93756756756760.56874108980980957.9131139945984
Trimmed Mean ( 13 / 20 )32.98857142857140.5404918617158261.0343536419725
Trimmed Mean ( 14 / 20 )33.02424242424240.51855477894771563.6851568338785
Trimmed Mean ( 15 / 20 )33.03903225806450.50197916994840365.8175363361402
Trimmed Mean ( 16 / 20 )33.05068965517240.49505334614133766.7618750843398
Trimmed Mean ( 17 / 20 )33.06074074074070.48398215394270668.3098343015649
Trimmed Mean ( 18 / 20 )33.07720.47340557664649569.87074430832
Trimmed Mean ( 19 / 20 )33.09260869565220.46301863022271871.4714409649871
Trimmed Mean ( 20 / 20 )33.11523809523810.4499505893760173.5974990968724
Median33.37
Midrange30.07
Midmean - Weighted Average at Xnp33.0390322580645
Midmean - Weighted Average at X(n+1)p33.0390322580645
Midmean - Empirical Distribution Function33.0390322580645
Midmean - Empirical Distribution Function - Averaging33.0390322580645
Midmean - Empirical Distribution Function - Interpolation33.0390322580645
Midmean - Closest Observation32.8759375
Midmean - True Basic - Statistics Graphics Toolkit33.0390322580645
Midmean - MS Excel (old versions)33.0390322580645
Number of observations61



Parameters (Session):
par1 = Y[t] / X[t] = c + e[t] ; par3 = Y[t] - X[t] = c + e[t] ;
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')