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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 computationSun, 19 Oct 2008 11:41:56 -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/2008/Oct/19/t122443816456nwmfwojmbad1v.htm/, Retrieved Sun, 19 May 2024 15:58:10 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=16999, Retrieved Sun, 19 May 2024 15:58:10 +0000
QR Codes:

Original text written by user:Bouwvergunningen volgens effectieve datum van toekenning - woongebouwen - koninkrijk, Aantal woningen + gebouwen
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact186
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
F     [Univariate Data Series] [blog 1e tijdreeks...] [2008-10-13 19:23:31] [7173087adebe3e3a714c80ea2417b3eb]
-   PD  [Univariate Data Series] [tijdreeksen opnie...] [2008-10-19 17:13:12] [7173087adebe3e3a714c80ea2417b3eb]
- RMP       [Central Tendency] [tijdreeks 1 centr...] [2008-10-19 17:41:56] [95d95b0e883740fcbc85e18ec42dcafb] [Current]
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Dataseries X:
5.014
6.153
6.441
5.584
6.427
6.062
5.589
6.216
5.809
4.989
6.706
7.174
6.122
8.075
6.292
6.337
8.576
6.077
5.931
6.288
7.167
6.054
6.468
6.401
6.927
7.914
7.728
8.699
8.522
6.481
7.502
7.778
7.424
6.941
8.574
9.169
7.701
9.035
7.158
8.195
8.124
7.073
7.017
7.390
7.776
6.197
6.889
7.087
6.485
7.654
6.501
6.313
7.826
6.589
6.729
5.684
8.105
6.391
5.901
6.758




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'George Udny Yule' @ 72.249.76.132

\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 & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=16999&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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=16999&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=16999&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'George Udny Yule' @ 72.249.76.132







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean6.936483333333330.12612826735431054.995469919902
Geometric Mean6.86977662580254
Harmonic Mean6.80402022798683
Quadratic Mean7.00381275330326
Winsorized Mean ( 1 / 20 )6.934666666666670.12536750195381355.3147072294818
Winsorized Mean ( 2 / 20 )6.942466666666670.11802062317786658.8241824160158
Winsorized Mean ( 3 / 20 )6.936566666666670.11646207492751459.560734007049
Winsorized Mean ( 4 / 20 )6.942766666666670.11522260049479660.2552505919203
Winsorized Mean ( 5 / 20 )6.948850.11232725802529161.8625445164473
Winsorized Mean ( 6 / 20 )6.925350.10346187055235466.9362535495200
Winsorized Mean ( 7 / 20 )6.920566666666670.10118141777619868.3976052003362
Winsorized Mean ( 8 / 20 )6.934433333333330.098060941407653170.7155492675307
Winsorized Mean ( 9 / 20 )6.931133333333330.096973394530171671.4745870959155
Winsorized Mean ( 10 / 20 )6.90680.09139770546885675.5686367023022
Winsorized Mean ( 11 / 20 )6.898916666666670.087177691425602479.1362624296402
Winsorized Mean ( 12 / 20 )6.895516666666670.08453308612998381.5718079435041
Winsorized Mean ( 13 / 20 )6.904616666666670.083058086990376483.1299746581771
Winsorized Mean ( 14 / 20 )6.897850.080443996819487985.7472312754227
Winsorized Mean ( 15 / 20 )6.90910.076734300921120790.0392642802889
Winsorized Mean ( 16 / 20 )6.897633333333330.07441154065262792.6957468268711
Winsorized Mean ( 17 / 20 )6.860516666666670.0663357641933151103.421084389317
Winsorized Mean ( 18 / 20 )6.844316666666670.0615417018674186111.214289806473
Winsorized Mean ( 19 / 20 )6.850650.0574710087807973119.201840116107
Winsorized Mean ( 20 / 20 )6.781983333333330.0460308634589026147.335566263893
Trimmed Mean ( 1 / 20 )6.931568965517240.11991287952671257.8050414006875
Trimmed Mean ( 2 / 20 )6.928250.11315314082791061.228967656646
Trimmed Mean ( 3 / 20 )6.920351851851850.10977592690643763.0407052518004
Trimmed Mean ( 4 / 20 )6.914115384615380.10631204125602565.0360514474982
Trimmed Mean ( 5 / 20 )6.905520.10242263876024867.4218130247993
Trimmed Mean ( 6 / 20 )6.89468750.098482448648025670.0093021106886
Trimmed Mean ( 7 / 20 )6.888021739130430.09630919656063571.5198754128723
Trimmed Mean ( 8 / 20 )6.881681818181820.094104501831949673.1280829738733
Trimmed Mean ( 9 / 20 )6.87226190476190.091982968551313774.7123300432312
Trimmed Mean ( 10 / 20 )6.862450.089380553081924776.7778869494127
Trimmed Mean ( 11 / 20 )6.855447368421050.087391897842362578.4448849112638
Trimmed Mean ( 12 / 20 )6.848861111111110.085711894238390279.905609040239
Trimmed Mean ( 13 / 20 )6.8420.083950498953310681.500408994653
Trimmed Mean ( 14 / 20 )6.832968750.081669283970807783.6663237116467
Trimmed Mean ( 15 / 20 )6.82370.07901843448528886.3557984215755
Trimmed Mean ( 16 / 20 )6.81150.076041333441322589.5762829469069
Trimmed Mean ( 17 / 20 )6.799076923076920.072193200682973494.178909630758
Trimmed Mean ( 18 / 20 )6.790041666666670.069357519449783297.899142306882
Trimmed Mean ( 19 / 20 )6.781818181818180.0665595341479323101.891010335878
Trimmed Mean ( 20 / 20 )6.770950.0632820118700077106.996440219200
Median6.7435
Midrange7.079
Midmean - Weighted Average at Xnp6.80409677419355
Midmean - Weighted Average at X(n+1)p6.8237
Midmean - Empirical Distribution Function6.80409677419355
Midmean - Empirical Distribution Function - Averaging6.8237
Midmean - Empirical Distribution Function - Interpolation6.8237
Midmean - Closest Observation6.80409677419355
Midmean - True Basic - Statistics Graphics Toolkit6.8237
Midmean - MS Excel (old versions)6.83296875
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 6.93648333333333 & 0.126128267354310 & 54.995469919902 \tabularnewline
Geometric Mean & 6.86977662580254 &  &  \tabularnewline
Harmonic Mean & 6.80402022798683 &  &  \tabularnewline
Quadratic Mean & 7.00381275330326 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 6.93466666666667 & 0.125367501953813 & 55.3147072294818 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 6.94246666666667 & 0.118020623177866 & 58.8241824160158 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 6.93656666666667 & 0.116462074927514 & 59.560734007049 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 6.94276666666667 & 0.115222600494796 & 60.2552505919203 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 6.94885 & 0.112327258025291 & 61.8625445164473 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 6.92535 & 0.103461870552354 & 66.9362535495200 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 6.92056666666667 & 0.101181417776198 & 68.3976052003362 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 6.93443333333333 & 0.0980609414076531 & 70.7155492675307 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 6.93113333333333 & 0.0969733945301716 & 71.4745870959155 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 6.9068 & 0.091397705468856 & 75.5686367023022 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 6.89891666666667 & 0.0871776914256024 & 79.1362624296402 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 6.89551666666667 & 0.084533086129983 & 81.5718079435041 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 6.90461666666667 & 0.0830580869903764 & 83.1299746581771 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 6.89785 & 0.0804439968194879 & 85.7472312754227 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 6.9091 & 0.0767343009211207 & 90.0392642802889 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 6.89763333333333 & 0.074411540652627 & 92.6957468268711 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 6.86051666666667 & 0.0663357641933151 & 103.421084389317 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 6.84431666666667 & 0.0615417018674186 & 111.214289806473 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 6.85065 & 0.0574710087807973 & 119.201840116107 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 6.78198333333333 & 0.0460308634589026 & 147.335566263893 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 6.93156896551724 & 0.119912879526712 & 57.8050414006875 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 6.92825 & 0.113153140827910 & 61.228967656646 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 6.92035185185185 & 0.109775926906437 & 63.0407052518004 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 6.91411538461538 & 0.106312041256025 & 65.0360514474982 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 6.90552 & 0.102422638760248 & 67.4218130247993 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 6.8946875 & 0.0984824486480256 & 70.0093021106886 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 6.88802173913043 & 0.096309196560635 & 71.5198754128723 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 6.88168181818182 & 0.0941045018319496 & 73.1280829738733 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 6.8722619047619 & 0.0919829685513137 & 74.7123300432312 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 6.86245 & 0.0893805530819247 & 76.7778869494127 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 6.85544736842105 & 0.0873918978423625 & 78.4448849112638 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 6.84886111111111 & 0.0857118942383902 & 79.905609040239 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 6.842 & 0.0839504989533106 & 81.500408994653 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 6.83296875 & 0.0816692839708077 & 83.6663237116467 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 6.8237 & 0.079018434485288 & 86.3557984215755 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 6.8115 & 0.0760413334413225 & 89.5762829469069 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 6.79907692307692 & 0.0721932006829734 & 94.178909630758 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 6.79004166666667 & 0.0693575194497832 & 97.899142306882 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 6.78181818181818 & 0.0665595341479323 & 101.891010335878 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 6.77095 & 0.0632820118700077 & 106.996440219200 \tabularnewline
Median & 6.7435 &  &  \tabularnewline
Midrange & 7.079 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 6.80409677419355 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 6.8237 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 6.80409677419355 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 6.8237 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 6.8237 &  &  \tabularnewline
Midmean - Closest Observation & 6.80409677419355 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 6.8237 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 6.83296875 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=16999&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]6.93648333333333[/C][C]0.126128267354310[/C][C]54.995469919902[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]6.86977662580254[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]6.80402022798683[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]7.00381275330326[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]6.93466666666667[/C][C]0.125367501953813[/C][C]55.3147072294818[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]6.94246666666667[/C][C]0.118020623177866[/C][C]58.8241824160158[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]6.93656666666667[/C][C]0.116462074927514[/C][C]59.560734007049[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]6.94276666666667[/C][C]0.115222600494796[/C][C]60.2552505919203[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]6.94885[/C][C]0.112327258025291[/C][C]61.8625445164473[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]6.92535[/C][C]0.103461870552354[/C][C]66.9362535495200[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]6.92056666666667[/C][C]0.101181417776198[/C][C]68.3976052003362[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]6.93443333333333[/C][C]0.0980609414076531[/C][C]70.7155492675307[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]6.93113333333333[/C][C]0.0969733945301716[/C][C]71.4745870959155[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]6.9068[/C][C]0.091397705468856[/C][C]75.5686367023022[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]6.89891666666667[/C][C]0.0871776914256024[/C][C]79.1362624296402[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]6.89551666666667[/C][C]0.084533086129983[/C][C]81.5718079435041[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]6.90461666666667[/C][C]0.0830580869903764[/C][C]83.1299746581771[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]6.89785[/C][C]0.0804439968194879[/C][C]85.7472312754227[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]6.9091[/C][C]0.0767343009211207[/C][C]90.0392642802889[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]6.89763333333333[/C][C]0.074411540652627[/C][C]92.6957468268711[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]6.86051666666667[/C][C]0.0663357641933151[/C][C]103.421084389317[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]6.84431666666667[/C][C]0.0615417018674186[/C][C]111.214289806473[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]6.85065[/C][C]0.0574710087807973[/C][C]119.201840116107[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]6.78198333333333[/C][C]0.0460308634589026[/C][C]147.335566263893[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]6.93156896551724[/C][C]0.119912879526712[/C][C]57.8050414006875[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]6.92825[/C][C]0.113153140827910[/C][C]61.228967656646[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]6.92035185185185[/C][C]0.109775926906437[/C][C]63.0407052518004[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]6.91411538461538[/C][C]0.106312041256025[/C][C]65.0360514474982[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]6.90552[/C][C]0.102422638760248[/C][C]67.4218130247993[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]6.8946875[/C][C]0.0984824486480256[/C][C]70.0093021106886[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]6.88802173913043[/C][C]0.096309196560635[/C][C]71.5198754128723[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]6.88168181818182[/C][C]0.0941045018319496[/C][C]73.1280829738733[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]6.8722619047619[/C][C]0.0919829685513137[/C][C]74.7123300432312[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]6.86245[/C][C]0.0893805530819247[/C][C]76.7778869494127[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]6.85544736842105[/C][C]0.0873918978423625[/C][C]78.4448849112638[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]6.84886111111111[/C][C]0.0857118942383902[/C][C]79.905609040239[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]6.842[/C][C]0.0839504989533106[/C][C]81.500408994653[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]6.83296875[/C][C]0.0816692839708077[/C][C]83.6663237116467[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]6.8237[/C][C]0.079018434485288[/C][C]86.3557984215755[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]6.8115[/C][C]0.0760413334413225[/C][C]89.5762829469069[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]6.79907692307692[/C][C]0.0721932006829734[/C][C]94.178909630758[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]6.79004166666667[/C][C]0.0693575194497832[/C][C]97.899142306882[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]6.78181818181818[/C][C]0.0665595341479323[/C][C]101.891010335878[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]6.77095[/C][C]0.0632820118700077[/C][C]106.996440219200[/C][/ROW]
[ROW][C]Median[/C][C]6.7435[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]7.079[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]6.80409677419355[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]6.8237[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]6.80409677419355[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]6.8237[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]6.8237[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]6.80409677419355[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]6.8237[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]6.83296875[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]60[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=16999&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=16999&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 Mean6.936483333333330.12612826735431054.995469919902
Geometric Mean6.86977662580254
Harmonic Mean6.80402022798683
Quadratic Mean7.00381275330326
Winsorized Mean ( 1 / 20 )6.934666666666670.12536750195381355.3147072294818
Winsorized Mean ( 2 / 20 )6.942466666666670.11802062317786658.8241824160158
Winsorized Mean ( 3 / 20 )6.936566666666670.11646207492751459.560734007049
Winsorized Mean ( 4 / 20 )6.942766666666670.11522260049479660.2552505919203
Winsorized Mean ( 5 / 20 )6.948850.11232725802529161.8625445164473
Winsorized Mean ( 6 / 20 )6.925350.10346187055235466.9362535495200
Winsorized Mean ( 7 / 20 )6.920566666666670.10118141777619868.3976052003362
Winsorized Mean ( 8 / 20 )6.934433333333330.098060941407653170.7155492675307
Winsorized Mean ( 9 / 20 )6.931133333333330.096973394530171671.4745870959155
Winsorized Mean ( 10 / 20 )6.90680.09139770546885675.5686367023022
Winsorized Mean ( 11 / 20 )6.898916666666670.087177691425602479.1362624296402
Winsorized Mean ( 12 / 20 )6.895516666666670.08453308612998381.5718079435041
Winsorized Mean ( 13 / 20 )6.904616666666670.083058086990376483.1299746581771
Winsorized Mean ( 14 / 20 )6.897850.080443996819487985.7472312754227
Winsorized Mean ( 15 / 20 )6.90910.076734300921120790.0392642802889
Winsorized Mean ( 16 / 20 )6.897633333333330.07441154065262792.6957468268711
Winsorized Mean ( 17 / 20 )6.860516666666670.0663357641933151103.421084389317
Winsorized Mean ( 18 / 20 )6.844316666666670.0615417018674186111.214289806473
Winsorized Mean ( 19 / 20 )6.850650.0574710087807973119.201840116107
Winsorized Mean ( 20 / 20 )6.781983333333330.0460308634589026147.335566263893
Trimmed Mean ( 1 / 20 )6.931568965517240.11991287952671257.8050414006875
Trimmed Mean ( 2 / 20 )6.928250.11315314082791061.228967656646
Trimmed Mean ( 3 / 20 )6.920351851851850.10977592690643763.0407052518004
Trimmed Mean ( 4 / 20 )6.914115384615380.10631204125602565.0360514474982
Trimmed Mean ( 5 / 20 )6.905520.10242263876024867.4218130247993
Trimmed Mean ( 6 / 20 )6.89468750.098482448648025670.0093021106886
Trimmed Mean ( 7 / 20 )6.888021739130430.09630919656063571.5198754128723
Trimmed Mean ( 8 / 20 )6.881681818181820.094104501831949673.1280829738733
Trimmed Mean ( 9 / 20 )6.87226190476190.091982968551313774.7123300432312
Trimmed Mean ( 10 / 20 )6.862450.089380553081924776.7778869494127
Trimmed Mean ( 11 / 20 )6.855447368421050.087391897842362578.4448849112638
Trimmed Mean ( 12 / 20 )6.848861111111110.085711894238390279.905609040239
Trimmed Mean ( 13 / 20 )6.8420.083950498953310681.500408994653
Trimmed Mean ( 14 / 20 )6.832968750.081669283970807783.6663237116467
Trimmed Mean ( 15 / 20 )6.82370.07901843448528886.3557984215755
Trimmed Mean ( 16 / 20 )6.81150.076041333441322589.5762829469069
Trimmed Mean ( 17 / 20 )6.799076923076920.072193200682973494.178909630758
Trimmed Mean ( 18 / 20 )6.790041666666670.069357519449783297.899142306882
Trimmed Mean ( 19 / 20 )6.781818181818180.0665595341479323101.891010335878
Trimmed Mean ( 20 / 20 )6.770950.0632820118700077106.996440219200
Median6.7435
Midrange7.079
Midmean - Weighted Average at Xnp6.80409677419355
Midmean - Weighted Average at X(n+1)p6.8237
Midmean - Empirical Distribution Function6.80409677419355
Midmean - Empirical Distribution Function - Averaging6.8237
Midmean - Empirical Distribution Function - Interpolation6.8237
Midmean - Closest Observation6.80409677419355
Midmean - True Basic - Statistics Graphics Toolkit6.8237
Midmean - MS Excel (old versions)6.83296875
Number of observations60



Parameters (Session):
Parameters (R input):
R code (references can be found in the software module):
geomean <- function(x) {
return(exp(mean(log(x))))
}
harmean <- function(x) {
return(1/mean(1/x))
}
quamean <- function(x) {
return(sqrt(mean(x*x)))
}
winmean <- function(x) {
x <-sort(x[!is.na(x)])
n<-length(x)
denom <- 3
nodenom <- n/denom
if (nodenom>40) denom <- n/40
sqrtn = sqrt(n)
roundnodenom = floor(nodenom)
win <- array(NA,dim=c(roundnodenom,2))
for (j in 1:roundnodenom) {
win[j,1] <- (j*x[j+1]+sum(x[(j+1):(n-j)])+j*x[n-j])/n
win[j,2] <- sd(c(rep(x[j+1],j),x[(j+1):(n-j)],rep(x[n-j],j)))/sqrtn
}
return(win)
}
trimean <- function(x) {
x <-sort(x[!is.na(x)])
n<-length(x)
denom <- 3
nodenom <- n/denom
if (nodenom>40) denom <- n/40
sqrtn = sqrt(n)
roundnodenom = floor(nodenom)
tri <- array(NA,dim=c(roundnodenom,2))
for (j in 1:roundnodenom) {
tri[j,1] <- mean(x,trim=j/n)
tri[j,2] <- sd(x[(j+1):(n-j)]) / sqrt(n-j*2)
}
return(tri)
}
midrange <- function(x) {
return((max(x)+min(x))/2)
}
q1 <- function(data,n,p,i,f) {
np <- n*p;
i <<- floor(np)
f <<- np - i
qvalue <- (1-f)*data[i] + f*data[i+1]
}
q2 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
qvalue <- (1-f)*data[i] + f*data[i+1]
}
q3 <- function(data,n,p,i,f) {
np <- n*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
qvalue <- data[i+1]
}
}
q4 <- function(data,n,p,i,f) {
np <- n*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- (data[i]+data[i+1])/2
} else {
qvalue <- data[i+1]
}
}
q5 <- function(data,n,p,i,f) {
np <- (n-1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i+1]
} else {
qvalue <- data[i+1] + f*(data[i+2]-data[i+1])
}
}
q6 <- function(data,n,p,i,f) {
np <- n*p+0.5
i <<- floor(np)
f <<- np - i
qvalue <- data[i]
}
q7 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
qvalue <- f*data[i] + (1-f)*data[i+1]
}
}
q8 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
if (f == 0.5) {
qvalue <- (data[i]+data[i+1])/2
} else {
if (f < 0.5) {
qvalue <- data[i]
} else {
qvalue <- data[i+1]
}
}
}
}
midmean <- function(x,def) {
x <-sort(x[!is.na(x)])
n<-length(x)
if (def==1) {
qvalue1 <- q1(x,n,0.25,i,f)
qvalue3 <- q1(x,n,0.75,i,f)
}
if (def==2) {
qvalue1 <- q2(x,n,0.25,i,f)
qvalue3 <- q2(x,n,0.75,i,f)
}
if (def==3) {
qvalue1 <- q3(x,n,0.25,i,f)
qvalue3 <- q3(x,n,0.75,i,f)
}
if (def==4) {
qvalue1 <- q4(x,n,0.25,i,f)
qvalue3 <- q4(x,n,0.75,i,f)
}
if (def==5) {
qvalue1 <- q5(x,n,0.25,i,f)
qvalue3 <- q5(x,n,0.75,i,f)
}
if (def==6) {
qvalue1 <- q6(x,n,0.25,i,f)
qvalue3 <- q6(x,n,0.75,i,f)
}
if (def==7) {
qvalue1 <- q7(x,n,0.25,i,f)
qvalue3 <- q7(x,n,0.75,i,f)
}
if (def==8) {
qvalue1 <- q8(x,n,0.25,i,f)
qvalue3 <- q8(x,n,0.75,i,f)
}
midm <- 0
myn <- 0
roundno4 <- round(n/4)
round3no4 <- round(3*n/4)
for (i in 1:n) {
if ((x[i]>=qvalue1) & (x[i]<=qvalue3)){
midm = midm + x[i]
myn = myn + 1
}
}
midm = midm / myn
return(midm)
}
(arm <- mean(x))
sqrtn <- sqrt(length(x))
(armse <- sd(x) / sqrtn)
(armose <- arm / armse)
(geo <- geomean(x))
(har <- harmean(x))
(qua <- quamean(x))
(win <- winmean(x))
(tri <- trimean(x))
(midr <- midrange(x))
midm <- array(NA,dim=8)
for (j in 1:8) midm[j] <- midmean(x,j)
midm
bitmap(file='test1.png')
lb <- win[,1] - 2*win[,2]
ub <- win[,1] + 2*win[,2]
if ((ylimmin == '') | (ylimmax == '')) plot(win[,1],type='b',main=main, xlab='j', pch=19, ylab='Winsorized Mean(j/n)', ylim=c(min(lb),max(ub))) else plot(win[,1],type='l',main=main, xlab='j', pch=19, ylab='Winsorized Mean(j/n)', ylim=c(ylimmin,ylimmax))
lines(ub,lty=3)
lines(lb,lty=3)
grid()
dev.off()
bitmap(file='test2.png')
lb <- tri[,1] - 2*tri[,2]
ub <- tri[,1] + 2*tri[,2]
if ((ylimmin == '') | (ylimmax == '')) plot(tri[,1],type='b',main=main, xlab='j', pch=19, ylab='Trimmed Mean(j/n)', ylim=c(min(lb),max(ub))) else plot(tri[,1],type='l',main=main, xlab='j', pch=19, ylab='Trimmed Mean(j/n)', ylim=c(ylimmin,ylimmax))
lines(ub,lty=3)
lines(lb,lty=3)
grid()
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Central Tendency - Ungrouped Data',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Measure',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.element(a,'S.E.',header=TRUE)
a<-table.element(a,'Value/S.E.',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('arithmetic_mean.htm', 'Arithmetic Mean', 'click to view the definition of the Arithmetic Mean'),header=TRUE)
a<-table.element(a,arm)
a<-table.element(a,hyperlink('arithmetic_mean_standard_error.htm', armse, 'click to view the definition of the Standard Error of the Arithmetic Mean'))
a<-table.element(a,armose)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('geometric_mean.htm', 'Geometric Mean', 'click to view the definition of the Geometric Mean'),header=TRUE)
a<-table.element(a,geo)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('harmonic_mean.htm', 'Harmonic Mean', 'click to view the definition of the Harmonic Mean'),header=TRUE)
a<-table.element(a,har)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('quadratic_mean.htm', 'Quadratic Mean', 'click to view the definition of the Quadratic Mean'),header=TRUE)
a<-table.element(a,qua)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
for (j in 1:length(win[,1])) {
a<-table.row.start(a)
mylabel <- paste('Winsorized Mean (',j)
mylabel <- paste(mylabel,'/')
mylabel <- paste(mylabel,length(win[,1]))
mylabel <- paste(mylabel,')')
a<-table.element(a,hyperlink('winsorized_mean.htm', mylabel, 'click to view the definition of the Winsorized Mean'),header=TRUE)
a<-table.element(a,win[j,1])
a<-table.element(a,win[j,2])
a<-table.element(a,win[j,1]/win[j,2])
a<-table.row.end(a)
}
for (j in 1:length(tri[,1])) {
a<-table.row.start(a)
mylabel <- paste('Trimmed Mean (',j)
mylabel <- paste(mylabel,'/')
mylabel <- paste(mylabel,length(tri[,1]))
mylabel <- paste(mylabel,')')
a<-table.element(a,hyperlink('arithmetic_mean.htm', mylabel, 'click to view the definition of the Trimmed Mean'),header=TRUE)
a<-table.element(a,tri[j,1])
a<-table.element(a,tri[j,2])
a<-table.element(a,tri[j,1]/tri[j,2])
a<-table.row.end(a)
}
a<-table.row.start(a)
a<-table.element(a,hyperlink('median_1.htm', 'Median', 'click to view the definition of the Median'),header=TRUE)
a<-table.element(a,median(x))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('midrange.htm', 'Midrange', 'click to view the definition of the Midrange'),header=TRUE)
a<-table.element(a,midr)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_1.htm','Weighted Average at Xnp',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[1])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_2.htm','Weighted Average at X(n+1)p',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[2])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_3.htm','Empirical Distribution Function',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[3])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_4.htm','Empirical Distribution Function - Averaging',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[4])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_5.htm','Empirical Distribution Function - Interpolation',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[5])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_6.htm','Closest Observation',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[6])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_7.htm','True Basic - Statistics Graphics Toolkit',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[7])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_8.htm','MS Excel (old versions)',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[8])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Number of observations',header=TRUE)
a<-table.element(a,length(x))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')