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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 computationFri, 11 Dec 2009 01:24:19 -0700
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/Dec/11/t1260519919pw659b8v4yhv12n.htm/, Retrieved Mon, 29 Apr 2024 02:46:36 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=65871, Retrieved Mon, 29 Apr 2024 02:46:36 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact163
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Central Tendency] [invoer] [2008-12-18 17:20:12] [5e74953d94072114d25d7276793b561e]
-  M D  [Central Tendency] [central tendency ...] [2009-12-06 18:30:17] [1433a524809eda02c3198b3ae6eebb69]
-    D    [Central Tendency] [central tendency ...] [2009-12-11 08:07:42] [1433a524809eda02c3198b3ae6eebb69]
-    D        [Central Tendency] [Univariate EDA Euro] [2009-12-11 08:24:19] [a5c6be3c0aa55fdb2a703a08e16947ef] [Current]
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Dataseries X:
0,5857
0,5858
0,5717
0,5945
0,5961
0,5973
0,6036
0,6096
0,6315
0,6262
0,6121
0,6326
0,6214
0,6274
0,6175
0,6208
0,6225
0,5889
0,6020
0,5932
0,5841
0,6000
0,5947
0,5891
0,6051
0,5960
0,6012
0,5957
0,5959
0,6049
0,6064
0,6137
0,6311
0,6258
0,6010
0,6232
0,6384
0,6014
0,5980
0,5987
0,6237
0,5813
0,5991
0,6160
0,6096
0,6051
0,5857
0,5565
0,5223
0,5091
0,4919
0,4995
0,5069
0,5190
0,5460
0,5648
0,5751
0,5862
0,5877




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\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' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=65871&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' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=65871&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=65871&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' @ 72.249.127.135







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean0.5920389830508470.00443607232576547133.460173679357
Geometric Mean0.591015131680968
Harmonic Mean0.589927070736658
Quadratic Mean0.593002128358143
Winsorized Mean ( 1 / 19 )0.5920694915254240.00437075201079887135.461698596166
Winsorized Mean ( 2 / 19 )0.5922830508474580.00427581181093861138.519438421553
Winsorized Mean ( 3 / 19 )0.5923745762711860.004234376580058139.896526695572
Winsorized Mean ( 4 / 19 )0.5927949152542370.00397431218661608149.156605575812
Winsorized Mean ( 5 / 19 )0.5929728813559320.00387035355596986153.208969873384
Winsorized Mean ( 6 / 19 )0.5953423728813560.00315401018788501188.757276424834
Winsorized Mean ( 7 / 19 )0.5963389830508470.00278996596631848213.744178334100
Winsorized Mean ( 8 / 19 )0.5973966101694920.00251321227139863237.702408574120
Winsorized Mean ( 9 / 19 )0.5983423728813560.00226919142208224263.680871987569
Winsorized Mean ( 10 / 19 )0.598732203389830.00212113083747287282.270283762017
Winsorized Mean ( 11 / 19 )0.5997762711864410.00189095533851136317.181616599476
Winsorized Mean ( 12 / 19 )0.5996745762711860.0016708691103698358.899792059993
Winsorized Mean ( 13 / 19 )0.5996966101694910.00155485695941503385.692462922834
Winsorized Mean ( 14 / 19 )0.5991508474576270.00145851531934706410.795032119273
Winsorized Mean ( 15 / 19 )0.5987694915254240.00138569601421746432.107392517517
Winsorized Mean ( 16 / 19 )0.59820.00125872060322544475.244465266658
Winsorized Mean ( 17 / 19 )0.598632203389830.00118890359708748503.516184875151
Winsorized Mean ( 18 / 19 )0.5980220338983050.000980446074472253609.948929848288
Winsorized Mean ( 19 / 19 )0.5976677966101690.000909677307343014657.01077930133
Trimmed Mean ( 1 / 19 )0.5929824561403510.00415522523570534142.707656625909
Trimmed Mean ( 2 / 19 )0.5939618181818180.00388173092261903153.014680827250
Trimmed Mean ( 3 / 19 )0.5948962264150940.00359992739229327165.252284723478
Trimmed Mean ( 4 / 19 )0.595868627450980.00325373931514951183.133487270046
Trimmed Mean ( 5 / 19 )0.596793877551020.00291980599975722204.395044602499
Trimmed Mean ( 6 / 19 )0.5977531914893620.00250753877410564238.382432073283
Trimmed Mean ( 7 / 19 )0.598280.00226039819500901264.679029261751
Trimmed Mean ( 8 / 19 )0.5986604651162790.00206733852777579289.580277769198
Trimmed Mean ( 9 / 19 )0.5988878048780490.00190759136571761313.949735588552
Trimmed Mean ( 10 / 19 )0.5989794871794870.00177529218475649337.397692798183
Trimmed Mean ( 11 / 19 )0.5990189189189190.00164348672528370364.480533796532
Trimmed Mean ( 12 / 19 )0.5989028571428570.00153637949243600389.814404638575
Trimmed Mean ( 13 / 19 )0.5987878787878790.00145758697941878410.807648011954
Trimmed Mean ( 14 / 19 )0.5986548387096770.00138169164440121433.276730836075
Trimmed Mean ( 15 / 19 )0.598582758620690.00130417167873849458.975431209862
Trimmed Mean ( 16 / 19 )0.5985555555555560.00121421229238472492.957911322071
Trimmed Mean ( 17 / 19 )0.5986080.00112565418016962531.786769458626
Trimmed Mean ( 18 / 19 )0.5986043478260870.00101417772259047590.236143520384
Trimmed Mean ( 19 / 19 )0.5986952380952380.000932647950486402641.93057818119
Median0.5987
Midrange0.56515
Midmean - Weighted Average at Xnp0.597751612903226
Midmean - Weighted Average at X(n+1)p0.59825
Midmean - Empirical Distribution Function0.59825
Midmean - Empirical Distribution Function - Averaging0.59825
Midmean - Empirical Distribution Function - Interpolation0.59858275862069
Midmean - Closest Observation0.597751612903226
Midmean - True Basic - Statistics Graphics Toolkit0.59825
Midmean - MS Excel (old versions)0.59825
Number of observations59

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 0.592038983050847 & 0.00443607232576547 & 133.460173679357 \tabularnewline
Geometric Mean & 0.591015131680968 &  &  \tabularnewline
Harmonic Mean & 0.589927070736658 &  &  \tabularnewline
Quadratic Mean & 0.593002128358143 &  &  \tabularnewline
Winsorized Mean ( 1 / 19 ) & 0.592069491525424 & 0.00437075201079887 & 135.461698596166 \tabularnewline
Winsorized Mean ( 2 / 19 ) & 0.592283050847458 & 0.00427581181093861 & 138.519438421553 \tabularnewline
Winsorized Mean ( 3 / 19 ) & 0.592374576271186 & 0.004234376580058 & 139.896526695572 \tabularnewline
Winsorized Mean ( 4 / 19 ) & 0.592794915254237 & 0.00397431218661608 & 149.156605575812 \tabularnewline
Winsorized Mean ( 5 / 19 ) & 0.592972881355932 & 0.00387035355596986 & 153.208969873384 \tabularnewline
Winsorized Mean ( 6 / 19 ) & 0.595342372881356 & 0.00315401018788501 & 188.757276424834 \tabularnewline
Winsorized Mean ( 7 / 19 ) & 0.596338983050847 & 0.00278996596631848 & 213.744178334100 \tabularnewline
Winsorized Mean ( 8 / 19 ) & 0.597396610169492 & 0.00251321227139863 & 237.702408574120 \tabularnewline
Winsorized Mean ( 9 / 19 ) & 0.598342372881356 & 0.00226919142208224 & 263.680871987569 \tabularnewline
Winsorized Mean ( 10 / 19 ) & 0.59873220338983 & 0.00212113083747287 & 282.270283762017 \tabularnewline
Winsorized Mean ( 11 / 19 ) & 0.599776271186441 & 0.00189095533851136 & 317.181616599476 \tabularnewline
Winsorized Mean ( 12 / 19 ) & 0.599674576271186 & 0.0016708691103698 & 358.899792059993 \tabularnewline
Winsorized Mean ( 13 / 19 ) & 0.599696610169491 & 0.00155485695941503 & 385.692462922834 \tabularnewline
Winsorized Mean ( 14 / 19 ) & 0.599150847457627 & 0.00145851531934706 & 410.795032119273 \tabularnewline
Winsorized Mean ( 15 / 19 ) & 0.598769491525424 & 0.00138569601421746 & 432.107392517517 \tabularnewline
Winsorized Mean ( 16 / 19 ) & 0.5982 & 0.00125872060322544 & 475.244465266658 \tabularnewline
Winsorized Mean ( 17 / 19 ) & 0.59863220338983 & 0.00118890359708748 & 503.516184875151 \tabularnewline
Winsorized Mean ( 18 / 19 ) & 0.598022033898305 & 0.000980446074472253 & 609.948929848288 \tabularnewline
Winsorized Mean ( 19 / 19 ) & 0.597667796610169 & 0.000909677307343014 & 657.01077930133 \tabularnewline
Trimmed Mean ( 1 / 19 ) & 0.592982456140351 & 0.00415522523570534 & 142.707656625909 \tabularnewline
Trimmed Mean ( 2 / 19 ) & 0.593961818181818 & 0.00388173092261903 & 153.014680827250 \tabularnewline
Trimmed Mean ( 3 / 19 ) & 0.594896226415094 & 0.00359992739229327 & 165.252284723478 \tabularnewline
Trimmed Mean ( 4 / 19 ) & 0.59586862745098 & 0.00325373931514951 & 183.133487270046 \tabularnewline
Trimmed Mean ( 5 / 19 ) & 0.59679387755102 & 0.00291980599975722 & 204.395044602499 \tabularnewline
Trimmed Mean ( 6 / 19 ) & 0.597753191489362 & 0.00250753877410564 & 238.382432073283 \tabularnewline
Trimmed Mean ( 7 / 19 ) & 0.59828 & 0.00226039819500901 & 264.679029261751 \tabularnewline
Trimmed Mean ( 8 / 19 ) & 0.598660465116279 & 0.00206733852777579 & 289.580277769198 \tabularnewline
Trimmed Mean ( 9 / 19 ) & 0.598887804878049 & 0.00190759136571761 & 313.949735588552 \tabularnewline
Trimmed Mean ( 10 / 19 ) & 0.598979487179487 & 0.00177529218475649 & 337.397692798183 \tabularnewline
Trimmed Mean ( 11 / 19 ) & 0.599018918918919 & 0.00164348672528370 & 364.480533796532 \tabularnewline
Trimmed Mean ( 12 / 19 ) & 0.598902857142857 & 0.00153637949243600 & 389.814404638575 \tabularnewline
Trimmed Mean ( 13 / 19 ) & 0.598787878787879 & 0.00145758697941878 & 410.807648011954 \tabularnewline
Trimmed Mean ( 14 / 19 ) & 0.598654838709677 & 0.00138169164440121 & 433.276730836075 \tabularnewline
Trimmed Mean ( 15 / 19 ) & 0.59858275862069 & 0.00130417167873849 & 458.975431209862 \tabularnewline
Trimmed Mean ( 16 / 19 ) & 0.598555555555556 & 0.00121421229238472 & 492.957911322071 \tabularnewline
Trimmed Mean ( 17 / 19 ) & 0.598608 & 0.00112565418016962 & 531.786769458626 \tabularnewline
Trimmed Mean ( 18 / 19 ) & 0.598604347826087 & 0.00101417772259047 & 590.236143520384 \tabularnewline
Trimmed Mean ( 19 / 19 ) & 0.598695238095238 & 0.000932647950486402 & 641.93057818119 \tabularnewline
Median & 0.5987 &  &  \tabularnewline
Midrange & 0.56515 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 0.597751612903226 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 0.59825 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 0.59825 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 0.59825 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 0.59858275862069 &  &  \tabularnewline
Midmean - Closest Observation & 0.597751612903226 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 0.59825 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 0.59825 &  &  \tabularnewline
Number of observations & 59 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=65871&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]0.592038983050847[/C][C]0.00443607232576547[/C][C]133.460173679357[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]0.591015131680968[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]0.589927070736658[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]0.593002128358143[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 19 )[/C][C]0.592069491525424[/C][C]0.00437075201079887[/C][C]135.461698596166[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 19 )[/C][C]0.592283050847458[/C][C]0.00427581181093861[/C][C]138.519438421553[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 19 )[/C][C]0.592374576271186[/C][C]0.004234376580058[/C][C]139.896526695572[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 19 )[/C][C]0.592794915254237[/C][C]0.00397431218661608[/C][C]149.156605575812[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 19 )[/C][C]0.592972881355932[/C][C]0.00387035355596986[/C][C]153.208969873384[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 19 )[/C][C]0.595342372881356[/C][C]0.00315401018788501[/C][C]188.757276424834[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 19 )[/C][C]0.596338983050847[/C][C]0.00278996596631848[/C][C]213.744178334100[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 19 )[/C][C]0.597396610169492[/C][C]0.00251321227139863[/C][C]237.702408574120[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 19 )[/C][C]0.598342372881356[/C][C]0.00226919142208224[/C][C]263.680871987569[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 19 )[/C][C]0.59873220338983[/C][C]0.00212113083747287[/C][C]282.270283762017[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 19 )[/C][C]0.599776271186441[/C][C]0.00189095533851136[/C][C]317.181616599476[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 19 )[/C][C]0.599674576271186[/C][C]0.0016708691103698[/C][C]358.899792059993[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 19 )[/C][C]0.599696610169491[/C][C]0.00155485695941503[/C][C]385.692462922834[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 19 )[/C][C]0.599150847457627[/C][C]0.00145851531934706[/C][C]410.795032119273[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 19 )[/C][C]0.598769491525424[/C][C]0.00138569601421746[/C][C]432.107392517517[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 19 )[/C][C]0.5982[/C][C]0.00125872060322544[/C][C]475.244465266658[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 19 )[/C][C]0.59863220338983[/C][C]0.00118890359708748[/C][C]503.516184875151[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 19 )[/C][C]0.598022033898305[/C][C]0.000980446074472253[/C][C]609.948929848288[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 19 )[/C][C]0.597667796610169[/C][C]0.000909677307343014[/C][C]657.01077930133[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 19 )[/C][C]0.592982456140351[/C][C]0.00415522523570534[/C][C]142.707656625909[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 19 )[/C][C]0.593961818181818[/C][C]0.00388173092261903[/C][C]153.014680827250[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 19 )[/C][C]0.594896226415094[/C][C]0.00359992739229327[/C][C]165.252284723478[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 19 )[/C][C]0.59586862745098[/C][C]0.00325373931514951[/C][C]183.133487270046[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 19 )[/C][C]0.59679387755102[/C][C]0.00291980599975722[/C][C]204.395044602499[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 19 )[/C][C]0.597753191489362[/C][C]0.00250753877410564[/C][C]238.382432073283[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 19 )[/C][C]0.59828[/C][C]0.00226039819500901[/C][C]264.679029261751[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 19 )[/C][C]0.598660465116279[/C][C]0.00206733852777579[/C][C]289.580277769198[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 19 )[/C][C]0.598887804878049[/C][C]0.00190759136571761[/C][C]313.949735588552[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 19 )[/C][C]0.598979487179487[/C][C]0.00177529218475649[/C][C]337.397692798183[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 19 )[/C][C]0.599018918918919[/C][C]0.00164348672528370[/C][C]364.480533796532[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 19 )[/C][C]0.598902857142857[/C][C]0.00153637949243600[/C][C]389.814404638575[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 19 )[/C][C]0.598787878787879[/C][C]0.00145758697941878[/C][C]410.807648011954[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 19 )[/C][C]0.598654838709677[/C][C]0.00138169164440121[/C][C]433.276730836075[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 19 )[/C][C]0.59858275862069[/C][C]0.00130417167873849[/C][C]458.975431209862[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 19 )[/C][C]0.598555555555556[/C][C]0.00121421229238472[/C][C]492.957911322071[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 19 )[/C][C]0.598608[/C][C]0.00112565418016962[/C][C]531.786769458626[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 19 )[/C][C]0.598604347826087[/C][C]0.00101417772259047[/C][C]590.236143520384[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 19 )[/C][C]0.598695238095238[/C][C]0.000932647950486402[/C][C]641.93057818119[/C][/ROW]
[ROW][C]Median[/C][C]0.5987[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]0.56515[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]0.597751612903226[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]0.59825[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]0.59825[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]0.59825[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]0.59858275862069[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]0.597751612903226[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]0.59825[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]0.59825[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]59[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=65871&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=65871&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 Mean0.5920389830508470.00443607232576547133.460173679357
Geometric Mean0.591015131680968
Harmonic Mean0.589927070736658
Quadratic Mean0.593002128358143
Winsorized Mean ( 1 / 19 )0.5920694915254240.00437075201079887135.461698596166
Winsorized Mean ( 2 / 19 )0.5922830508474580.00427581181093861138.519438421553
Winsorized Mean ( 3 / 19 )0.5923745762711860.004234376580058139.896526695572
Winsorized Mean ( 4 / 19 )0.5927949152542370.00397431218661608149.156605575812
Winsorized Mean ( 5 / 19 )0.5929728813559320.00387035355596986153.208969873384
Winsorized Mean ( 6 / 19 )0.5953423728813560.00315401018788501188.757276424834
Winsorized Mean ( 7 / 19 )0.5963389830508470.00278996596631848213.744178334100
Winsorized Mean ( 8 / 19 )0.5973966101694920.00251321227139863237.702408574120
Winsorized Mean ( 9 / 19 )0.5983423728813560.00226919142208224263.680871987569
Winsorized Mean ( 10 / 19 )0.598732203389830.00212113083747287282.270283762017
Winsorized Mean ( 11 / 19 )0.5997762711864410.00189095533851136317.181616599476
Winsorized Mean ( 12 / 19 )0.5996745762711860.0016708691103698358.899792059993
Winsorized Mean ( 13 / 19 )0.5996966101694910.00155485695941503385.692462922834
Winsorized Mean ( 14 / 19 )0.5991508474576270.00145851531934706410.795032119273
Winsorized Mean ( 15 / 19 )0.5987694915254240.00138569601421746432.107392517517
Winsorized Mean ( 16 / 19 )0.59820.00125872060322544475.244465266658
Winsorized Mean ( 17 / 19 )0.598632203389830.00118890359708748503.516184875151
Winsorized Mean ( 18 / 19 )0.5980220338983050.000980446074472253609.948929848288
Winsorized Mean ( 19 / 19 )0.5976677966101690.000909677307343014657.01077930133
Trimmed Mean ( 1 / 19 )0.5929824561403510.00415522523570534142.707656625909
Trimmed Mean ( 2 / 19 )0.5939618181818180.00388173092261903153.014680827250
Trimmed Mean ( 3 / 19 )0.5948962264150940.00359992739229327165.252284723478
Trimmed Mean ( 4 / 19 )0.595868627450980.00325373931514951183.133487270046
Trimmed Mean ( 5 / 19 )0.596793877551020.00291980599975722204.395044602499
Trimmed Mean ( 6 / 19 )0.5977531914893620.00250753877410564238.382432073283
Trimmed Mean ( 7 / 19 )0.598280.00226039819500901264.679029261751
Trimmed Mean ( 8 / 19 )0.5986604651162790.00206733852777579289.580277769198
Trimmed Mean ( 9 / 19 )0.5988878048780490.00190759136571761313.949735588552
Trimmed Mean ( 10 / 19 )0.5989794871794870.00177529218475649337.397692798183
Trimmed Mean ( 11 / 19 )0.5990189189189190.00164348672528370364.480533796532
Trimmed Mean ( 12 / 19 )0.5989028571428570.00153637949243600389.814404638575
Trimmed Mean ( 13 / 19 )0.5987878787878790.00145758697941878410.807648011954
Trimmed Mean ( 14 / 19 )0.5986548387096770.00138169164440121433.276730836075
Trimmed Mean ( 15 / 19 )0.598582758620690.00130417167873849458.975431209862
Trimmed Mean ( 16 / 19 )0.5985555555555560.00121421229238472492.957911322071
Trimmed Mean ( 17 / 19 )0.5986080.00112565418016962531.786769458626
Trimmed Mean ( 18 / 19 )0.5986043478260870.00101417772259047590.236143520384
Trimmed Mean ( 19 / 19 )0.5986952380952380.000932647950486402641.93057818119
Median0.5987
Midrange0.56515
Midmean - Weighted Average at Xnp0.597751612903226
Midmean - Weighted Average at X(n+1)p0.59825
Midmean - Empirical Distribution Function0.59825
Midmean - Empirical Distribution Function - Averaging0.59825
Midmean - Empirical Distribution Function - Interpolation0.59858275862069
Midmean - Closest Observation0.597751612903226
Midmean - True Basic - Statistics Graphics Toolkit0.59825
Midmean - MS Excel (old versions)0.59825
Number of observations59



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')