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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 computationSat, 25 Oct 2008 08:06:52 -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/25/t1224943957pyak05y3iw8y23m.htm/, Retrieved Sun, 19 May 2024 13:19:00 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=18744, Retrieved Sun, 19 May 2024 13:19:00 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact168
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 17:18:46] [7173087adebe3e3a714c80ea2417b3eb]
- RMP     [Central Tendency] [tijdreeks 2 centr...] [2008-10-19 17:39:42] [7173087adebe3e3a714c80ea2417b3eb]
-    D        [Central Tendency] [assumtion 4 centr...] [2008-10-25 14:06:52] [95d95b0e883740fcbc85e18ec42dcafb] [Current]
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Dataseries X:
-600
1700
700
-100
-200
0
100
700
0
-1000
-1100
-1100
-1200
400
800
-200
100
-900
-1000
-500
-600
-500
300
100
700
2600
700
-100
1000
-100
-600
300
800
1400
1000
100
-300
2200
1600
700
200
-600
-800
200
100
-700
-500
-100
-300
2000
500
0
800
-200
-600
-300
-200
-300
-400
100




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=18744&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=18744&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=18744&T=0

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean113.333333333333106.8413118291381.06076321408874
Geometric MeanNaN
Harmonic Mean0
Quadratic Mean828.45237239888
Winsorized Mean ( 1 / 20 )108.333333333333104.0505001974381.04116110088628
Winsorized Mean ( 2 / 20 )101.666666666667101.8609794460570.998092372757
Winsorized Mean ( 3 / 20 )91.666666666666796.3835225933110.951061594350032
Winsorized Mean ( 4 / 20 )8594.53499038334780.89913797690482
Winsorized Mean ( 5 / 20 )76.666666666666788.56567886429270.86564759227038
Winsorized Mean ( 6 / 20 )46.666666666666777.40372794518150.602899471453322
Winsorized Mean ( 7 / 20 )58.333333333333375.3257208293140.774414538501597
Winsorized Mean ( 8 / 20 )4567.74933026541610.664213208067255
Winsorized Mean ( 9 / 20 )4567.74933026541610.664213208067255
Winsorized Mean ( 10 / 20 )4567.74933026541610.664213208067255
Winsorized Mean ( 11 / 20 )26.666666666666764.39052228161130.414139623686236
Winsorized Mean ( 12 / 20 )26.666666666666764.39052228161130.414139623686236
Winsorized Mean ( 13 / 20 )48.333333333333360.94786447905650.79302751206225
Winsorized Mean ( 14 / 20 )48.333333333333360.94786447905650.79302751206225
Winsorized Mean ( 15 / 20 )48.333333333333360.94786447905650.79302751206225
Winsorized Mean ( 16 / 20 )21.666666666666747.48426243407090.456291528098379
Winsorized Mean ( 17 / 20 )21.666666666666738.55377539213010.56198560183264
Winsorized Mean ( 18 / 20 )-8.3333333333333333.7230048277720-0.247111233885972
Winsorized Mean ( 19 / 20 )-8.3333333333333333.7230048277720-0.247111233885972
Winsorized Mean ( 20 / 20 )-41.666666666666728.7490276589853-1.44932437927667
Trimmed Mean ( 1 / 20 )93.10344827586299.1147162382460.939350399309682
Trimmed Mean ( 2 / 20 )76.785714285714392.93172579171810.82625942466418
Trimmed Mean ( 3 / 20 )62.96296296296386.68506079177930.726341567830267
Trimmed Mean ( 4 / 20 )51.923076923076981.67230186249640.635748910450628
Trimmed Mean ( 5 / 20 )4276.08212533781090.552035051774862
Trimmed Mean ( 6 / 20 )33.333333333333371.231152374210.467960045882987
Trimmed Mean ( 7 / 20 )30.434782608695768.86727171314040.441933909266344
Trimmed Mean ( 8 / 20 )2566.40297568410630.37648915191588
Trimmed Mean ( 9 / 20 )21.428571428571465.33534635243920.327978232685552
Trimmed Mean ( 10 / 20 )17.563.83949223819660.27412498731513
Trimmed Mean ( 11 / 20 )13.157894736842161.7629862216930.213038512898534
Trimmed Mean ( 12 / 20 )11.111111111111159.8646327178320.185603930178318
Trimmed Mean ( 13 / 20 )8.823529411764757.1715445748140.154334284256014
Trimmed Mean ( 14 / 20 )3.12554.34440184689470.0575036230742609
Trimmed Mean ( 15 / 20 )-3.3333333333333350.168299129509-0.0664430206160341
Trimmed Mean ( 16 / 20 )-10.714285714285743.7462880403486-0.244918739263171
Trimmed Mean ( 17 / 20 )-15.384615384615439.8814812209715-0.38575837490523
Trimmed Mean ( 18 / 20 )-20.833333333333337.580429046819-0.554366564239553
Trimmed Mean ( 19 / 20 )-22.727272727272735.996523510481-0.631374102575636
Trimmed Mean ( 20 / 20 )-2533.1464056954342-0.754229590674552
Median0
Midrange700
Midmean - Weighted Average at Xnp47.2222222222222
Midmean - Weighted Average at X(n+1)p47.2222222222222
Midmean - Empirical Distribution Function47.2222222222222
Midmean - Empirical Distribution Function - Averaging47.2222222222222
Midmean - Empirical Distribution Function - Interpolation47.2222222222222
Midmean - Closest Observation47.2222222222222
Midmean - True Basic - Statistics Graphics Toolkit47.2222222222222
Midmean - MS Excel (old versions)47.2222222222222
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 113.333333333333 & 106.841311829138 & 1.06076321408874 \tabularnewline
Geometric Mean & NaN &  &  \tabularnewline
Harmonic Mean & 0 &  &  \tabularnewline
Quadratic Mean & 828.45237239888 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 108.333333333333 & 104.050500197438 & 1.04116110088628 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 101.666666666667 & 101.860979446057 & 0.998092372757 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 91.6666666666667 & 96.383522593311 & 0.951061594350032 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 85 & 94.5349903833478 & 0.89913797690482 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 76.6666666666667 & 88.5656788642927 & 0.86564759227038 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 46.6666666666667 & 77.4037279451815 & 0.602899471453322 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 58.3333333333333 & 75.325720829314 & 0.774414538501597 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 45 & 67.7493302654161 & 0.664213208067255 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 45 & 67.7493302654161 & 0.664213208067255 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 45 & 67.7493302654161 & 0.664213208067255 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 26.6666666666667 & 64.3905222816113 & 0.414139623686236 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 26.6666666666667 & 64.3905222816113 & 0.414139623686236 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 48.3333333333333 & 60.9478644790565 & 0.79302751206225 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 48.3333333333333 & 60.9478644790565 & 0.79302751206225 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 48.3333333333333 & 60.9478644790565 & 0.79302751206225 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 21.6666666666667 & 47.4842624340709 & 0.456291528098379 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 21.6666666666667 & 38.5537753921301 & 0.56198560183264 \tabularnewline
Winsorized Mean ( 18 / 20 ) & -8.33333333333333 & 33.7230048277720 & -0.247111233885972 \tabularnewline
Winsorized Mean ( 19 / 20 ) & -8.33333333333333 & 33.7230048277720 & -0.247111233885972 \tabularnewline
Winsorized Mean ( 20 / 20 ) & -41.6666666666667 & 28.7490276589853 & -1.44932437927667 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 93.103448275862 & 99.114716238246 & 0.939350399309682 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 76.7857142857143 & 92.9317257917181 & 0.82625942466418 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 62.962962962963 & 86.6850607917793 & 0.726341567830267 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 51.9230769230769 & 81.6723018624964 & 0.635748910450628 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 42 & 76.0821253378109 & 0.552035051774862 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 33.3333333333333 & 71.23115237421 & 0.467960045882987 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 30.4347826086957 & 68.8672717131404 & 0.441933909266344 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 25 & 66.4029756841063 & 0.37648915191588 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 21.4285714285714 & 65.3353463524392 & 0.327978232685552 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 17.5 & 63.8394922381966 & 0.27412498731513 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 13.1578947368421 & 61.762986221693 & 0.213038512898534 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 11.1111111111111 & 59.864632717832 & 0.185603930178318 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 8.8235294117647 & 57.171544574814 & 0.154334284256014 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 3.125 & 54.3444018468947 & 0.0575036230742609 \tabularnewline
Trimmed Mean ( 15 / 20 ) & -3.33333333333333 & 50.168299129509 & -0.0664430206160341 \tabularnewline
Trimmed Mean ( 16 / 20 ) & -10.7142857142857 & 43.7462880403486 & -0.244918739263171 \tabularnewline
Trimmed Mean ( 17 / 20 ) & -15.3846153846154 & 39.8814812209715 & -0.38575837490523 \tabularnewline
Trimmed Mean ( 18 / 20 ) & -20.8333333333333 & 37.580429046819 & -0.554366564239553 \tabularnewline
Trimmed Mean ( 19 / 20 ) & -22.7272727272727 & 35.996523510481 & -0.631374102575636 \tabularnewline
Trimmed Mean ( 20 / 20 ) & -25 & 33.1464056954342 & -0.754229590674552 \tabularnewline
Median & 0 &  &  \tabularnewline
Midrange & 700 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 47.2222222222222 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 47.2222222222222 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 47.2222222222222 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 47.2222222222222 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 47.2222222222222 &  &  \tabularnewline
Midmean - Closest Observation & 47.2222222222222 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 47.2222222222222 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 47.2222222222222 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=18744&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]113.333333333333[/C][C]106.841311829138[/C][C]1.06076321408874[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]NaN[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]0[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]828.45237239888[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]108.333333333333[/C][C]104.050500197438[/C][C]1.04116110088628[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]101.666666666667[/C][C]101.860979446057[/C][C]0.998092372757[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]91.6666666666667[/C][C]96.383522593311[/C][C]0.951061594350032[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]85[/C][C]94.5349903833478[/C][C]0.89913797690482[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]76.6666666666667[/C][C]88.5656788642927[/C][C]0.86564759227038[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]46.6666666666667[/C][C]77.4037279451815[/C][C]0.602899471453322[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]58.3333333333333[/C][C]75.325720829314[/C][C]0.774414538501597[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]45[/C][C]67.7493302654161[/C][C]0.664213208067255[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]45[/C][C]67.7493302654161[/C][C]0.664213208067255[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]45[/C][C]67.7493302654161[/C][C]0.664213208067255[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]26.6666666666667[/C][C]64.3905222816113[/C][C]0.414139623686236[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]26.6666666666667[/C][C]64.3905222816113[/C][C]0.414139623686236[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]48.3333333333333[/C][C]60.9478644790565[/C][C]0.79302751206225[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]48.3333333333333[/C][C]60.9478644790565[/C][C]0.79302751206225[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]48.3333333333333[/C][C]60.9478644790565[/C][C]0.79302751206225[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]21.6666666666667[/C][C]47.4842624340709[/C][C]0.456291528098379[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]21.6666666666667[/C][C]38.5537753921301[/C][C]0.56198560183264[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]-8.33333333333333[/C][C]33.7230048277720[/C][C]-0.247111233885972[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]-8.33333333333333[/C][C]33.7230048277720[/C][C]-0.247111233885972[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]-41.6666666666667[/C][C]28.7490276589853[/C][C]-1.44932437927667[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]93.103448275862[/C][C]99.114716238246[/C][C]0.939350399309682[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]76.7857142857143[/C][C]92.9317257917181[/C][C]0.82625942466418[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]62.962962962963[/C][C]86.6850607917793[/C][C]0.726341567830267[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]51.9230769230769[/C][C]81.6723018624964[/C][C]0.635748910450628[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]42[/C][C]76.0821253378109[/C][C]0.552035051774862[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]33.3333333333333[/C][C]71.23115237421[/C][C]0.467960045882987[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]30.4347826086957[/C][C]68.8672717131404[/C][C]0.441933909266344[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]25[/C][C]66.4029756841063[/C][C]0.37648915191588[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]21.4285714285714[/C][C]65.3353463524392[/C][C]0.327978232685552[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]17.5[/C][C]63.8394922381966[/C][C]0.27412498731513[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]13.1578947368421[/C][C]61.762986221693[/C][C]0.213038512898534[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]11.1111111111111[/C][C]59.864632717832[/C][C]0.185603930178318[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]8.8235294117647[/C][C]57.171544574814[/C][C]0.154334284256014[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]3.125[/C][C]54.3444018468947[/C][C]0.0575036230742609[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]-3.33333333333333[/C][C]50.168299129509[/C][C]-0.0664430206160341[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]-10.7142857142857[/C][C]43.7462880403486[/C][C]-0.244918739263171[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]-15.3846153846154[/C][C]39.8814812209715[/C][C]-0.38575837490523[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]-20.8333333333333[/C][C]37.580429046819[/C][C]-0.554366564239553[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]-22.7272727272727[/C][C]35.996523510481[/C][C]-0.631374102575636[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]-25[/C][C]33.1464056954342[/C][C]-0.754229590674552[/C][/ROW]
[ROW][C]Median[/C][C]0[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]700[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]47.2222222222222[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]47.2222222222222[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]47.2222222222222[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]47.2222222222222[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]47.2222222222222[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]47.2222222222222[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]47.2222222222222[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]47.2222222222222[/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=18744&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=18744&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 Mean113.333333333333106.8413118291381.06076321408874
Geometric MeanNaN
Harmonic Mean0
Quadratic Mean828.45237239888
Winsorized Mean ( 1 / 20 )108.333333333333104.0505001974381.04116110088628
Winsorized Mean ( 2 / 20 )101.666666666667101.8609794460570.998092372757
Winsorized Mean ( 3 / 20 )91.666666666666796.3835225933110.951061594350032
Winsorized Mean ( 4 / 20 )8594.53499038334780.89913797690482
Winsorized Mean ( 5 / 20 )76.666666666666788.56567886429270.86564759227038
Winsorized Mean ( 6 / 20 )46.666666666666777.40372794518150.602899471453322
Winsorized Mean ( 7 / 20 )58.333333333333375.3257208293140.774414538501597
Winsorized Mean ( 8 / 20 )4567.74933026541610.664213208067255
Winsorized Mean ( 9 / 20 )4567.74933026541610.664213208067255
Winsorized Mean ( 10 / 20 )4567.74933026541610.664213208067255
Winsorized Mean ( 11 / 20 )26.666666666666764.39052228161130.414139623686236
Winsorized Mean ( 12 / 20 )26.666666666666764.39052228161130.414139623686236
Winsorized Mean ( 13 / 20 )48.333333333333360.94786447905650.79302751206225
Winsorized Mean ( 14 / 20 )48.333333333333360.94786447905650.79302751206225
Winsorized Mean ( 15 / 20 )48.333333333333360.94786447905650.79302751206225
Winsorized Mean ( 16 / 20 )21.666666666666747.48426243407090.456291528098379
Winsorized Mean ( 17 / 20 )21.666666666666738.55377539213010.56198560183264
Winsorized Mean ( 18 / 20 )-8.3333333333333333.7230048277720-0.247111233885972
Winsorized Mean ( 19 / 20 )-8.3333333333333333.7230048277720-0.247111233885972
Winsorized Mean ( 20 / 20 )-41.666666666666728.7490276589853-1.44932437927667
Trimmed Mean ( 1 / 20 )93.10344827586299.1147162382460.939350399309682
Trimmed Mean ( 2 / 20 )76.785714285714392.93172579171810.82625942466418
Trimmed Mean ( 3 / 20 )62.96296296296386.68506079177930.726341567830267
Trimmed Mean ( 4 / 20 )51.923076923076981.67230186249640.635748910450628
Trimmed Mean ( 5 / 20 )4276.08212533781090.552035051774862
Trimmed Mean ( 6 / 20 )33.333333333333371.231152374210.467960045882987
Trimmed Mean ( 7 / 20 )30.434782608695768.86727171314040.441933909266344
Trimmed Mean ( 8 / 20 )2566.40297568410630.37648915191588
Trimmed Mean ( 9 / 20 )21.428571428571465.33534635243920.327978232685552
Trimmed Mean ( 10 / 20 )17.563.83949223819660.27412498731513
Trimmed Mean ( 11 / 20 )13.157894736842161.7629862216930.213038512898534
Trimmed Mean ( 12 / 20 )11.111111111111159.8646327178320.185603930178318
Trimmed Mean ( 13 / 20 )8.823529411764757.1715445748140.154334284256014
Trimmed Mean ( 14 / 20 )3.12554.34440184689470.0575036230742609
Trimmed Mean ( 15 / 20 )-3.3333333333333350.168299129509-0.0664430206160341
Trimmed Mean ( 16 / 20 )-10.714285714285743.7462880403486-0.244918739263171
Trimmed Mean ( 17 / 20 )-15.384615384615439.8814812209715-0.38575837490523
Trimmed Mean ( 18 / 20 )-20.833333333333337.580429046819-0.554366564239553
Trimmed Mean ( 19 / 20 )-22.727272727272735.996523510481-0.631374102575636
Trimmed Mean ( 20 / 20 )-2533.1464056954342-0.754229590674552
Median0
Midrange700
Midmean - Weighted Average at Xnp47.2222222222222
Midmean - Weighted Average at X(n+1)p47.2222222222222
Midmean - Empirical Distribution Function47.2222222222222
Midmean - Empirical Distribution Function - Averaging47.2222222222222
Midmean - Empirical Distribution Function - Interpolation47.2222222222222
Midmean - Closest Observation47.2222222222222
Midmean - True Basic - Statistics Graphics Toolkit47.2222222222222
Midmean - MS Excel (old versions)47.2222222222222
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')