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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 computationMon, 20 Oct 2008 15:39:59 -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/20/t12245388874tv1vpjdnncmjmf.htm/, Retrieved Sat, 18 May 2024 23:24:18 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=18193, Retrieved Sat, 18 May 2024 23:24:18 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact132
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Central Tendency] [Investigating Ass...] [2007-10-22 10:34:53] [b9964c45117f7aac638ab9056d451faa]
F    D    [Central Tendency] [Q10: voorspelling] [2008-10-20 21:39:59] [d6e9f26c3644bfc30f06303d9993b878] [Current]
Feedback Forum
2008-10-27 17:57:40 [Evelien Blockx] [reply
Dit lijkt mij een correcte redenering, alleen kan je er misschien nog bijzetten voor welke van je reeksen je aan het voorspellen bent.

Post a new message
Dataseries X:
100.3
97.6
89.1
99.1
94.9
96.5
92.6
80.8
89.5
101.4
95.9
92.3
91.2
88.3
80.7
89.9
87.2
86.9
82.8
72.6
81.3
91.2
87.3
83.4
81.7
80.2
74.1
80.6
79.0
79.3
71.2
78.1
68.2
81.0
106.9
123.7
73.7
69.2
72.5
75.7
73.5
70.4
65.7
68.1
62.4
64.7
77.7
85.9
61.0
57.4
75.1
75.9
71.8
72.3
67.3
71.5
67.6
74.2
77.6
76.4
74.2




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=18193&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=18193&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=18193&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 Mean80.9606557377051.5740488995544851.4346509569177
Geometric Mean80.0844940315358
Harmonic Mean79.2431264509305
Quadratic Mean81.8735950949419
Winsorized Mean ( 1 / 20 )80.7442622950821.4556081946525655.4711512285452
Winsorized Mean ( 2 / 20 )80.60983606557381.3959459352700257.745671969725
Winsorized Mean ( 3 / 20 )80.66885245901641.3593323276372159.3444669996445
Winsorized Mean ( 4 / 20 )80.6557377049181.3281762108021660.7266844933215
Winsorized Mean ( 5 / 20 )80.66393442622951.2765776327303263.1876451208901
Winsorized Mean ( 6 / 20 )80.58524590163931.2479794293561264.5725754816457
Winsorized Mean ( 7 / 20 )80.57377049180331.2236242450651165.8484586397809
Winsorized Mean ( 8 / 20 )80.4557377049181.1944784731827867.3563731044373
Winsorized Mean ( 9 / 20 )80.26393442622951.1036180755854572.7279991165882
Winsorized Mean ( 10 / 20 )80.4114754098361.0625520838681575.6776788927876
Winsorized Mean ( 11 / 20 )80.35737704918031.0038816984936380.0466600494463
Winsorized Mean ( 12 / 20 )80.4163934426230.9949879322877280.8214761537118
Winsorized Mean ( 13 / 20 )80.20327868852460.93647101552220885.6441655525243
Winsorized Mean ( 14 / 20 )80.22622950819670.9037260502970488.7727309418907
Winsorized Mean ( 15 / 20 )80.17704918032790.87982981912153191.127906144828
Winsorized Mean ( 16 / 20 )79.99344262295080.84098520435728595.1187276642816
Winsorized Mean ( 17 / 20 )79.96557377049180.75938890173347105.302531532859
Winsorized Mean ( 18 / 20 )79.99508196721310.746303920824318107.188344768249
Winsorized Mean ( 19 / 20 )80.02622950819670.713909048252468112.095833081382
Winsorized Mean ( 20 / 20 )79.73114754098360.657369077258396121.288253888528
Trimmed Mean ( 1 / 20 )80.6355932203391.3971808526319157.7130677595843
Trimmed Mean ( 2 / 20 )80.5192982456141.3250039925141860.7690985842462
Trimmed Mean ( 3 / 20 )80.4690909090911.2765084764385063.0384305269967
Trimmed Mean ( 4 / 20 )80.39245283018871.2340854809477165.1433422330287
Trimmed Mean ( 5 / 20 )80.3137254901961.1933049167648867.303607285832
Trimmed Mean ( 6 / 20 )80.22653061224491.1595865419260569.1854619828461
Trimmed Mean ( 7 / 20 )80.14893617021281.1253650752713071.2203869938744
Trimmed Mean ( 8 / 20 )80.06666666666671.0881547721169173.5802192099051
Trimmed Mean ( 9 / 20 )79.99767441860461.0479716651640176.3357226896823
Trimmed Mean ( 10 / 20 )79.95365853658541.0205038064781078.347241851568
Trimmed Mean ( 11 / 20 )79.88205128205130.99392128028419880.3706016428284
Trimmed Mean ( 12 / 20 )79.81081081081080.9727425069058682.047212128805
Trimmed Mean ( 13 / 20 )79.72285714285710.9443870958429784.4175629821537
Trimmed Mean ( 14 / 20 )79.65454545454550.92052655909838486.5315016359372
Trimmed Mean ( 15 / 20 )79.57419354838710.89418633335077488.9906170341473
Trimmed Mean ( 16 / 20 )79.48965517241380.8614677706631292.272349447532
Trimmed Mean ( 17 / 20 )79.41851851851850.8246390393467596.3070079503283
Trimmed Mean ( 18 / 20 )79.340.79590619212735699.6851146338419
Trimmed Mean ( 19 / 20 )79.24347826086960.75217277068158105.352761160263
Trimmed Mean ( 20 / 20 )79.12380952380950.691613185376003114.404715232248
Median79.3
Midrange90.55
Midmean - Weighted Average at Xnp79.2566666666667
Midmean - Weighted Average at X(n+1)p79.5741935483871
Midmean - Empirical Distribution Function79.5741935483871
Midmean - Empirical Distribution Function - Averaging79.5741935483871
Midmean - Empirical Distribution Function - Interpolation79.5741935483871
Midmean - Closest Observation79.346875
Midmean - True Basic - Statistics Graphics Toolkit79.5741935483871
Midmean - MS Excel (old versions)79.5741935483871
Number of observations61

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 80.960655737705 & 1.57404889955448 & 51.4346509569177 \tabularnewline
Geometric Mean & 80.0844940315358 &  &  \tabularnewline
Harmonic Mean & 79.2431264509305 &  &  \tabularnewline
Quadratic Mean & 81.8735950949419 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 80.744262295082 & 1.45560819465256 & 55.4711512285452 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 80.6098360655738 & 1.39594593527002 & 57.745671969725 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 80.6688524590164 & 1.35933232763721 & 59.3444669996445 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 80.655737704918 & 1.32817621080216 & 60.7266844933215 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 80.6639344262295 & 1.27657763273032 & 63.1876451208901 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 80.5852459016393 & 1.24797942935612 & 64.5725754816457 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 80.5737704918033 & 1.22362424506511 & 65.8484586397809 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 80.455737704918 & 1.19447847318278 & 67.3563731044373 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 80.2639344262295 & 1.10361807558545 & 72.7279991165882 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 80.411475409836 & 1.06255208386815 & 75.6776788927876 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 80.3573770491803 & 1.00388169849363 & 80.0466600494463 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 80.416393442623 & 0.99498793228772 & 80.8214761537118 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 80.2032786885246 & 0.936471015522208 & 85.6441655525243 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 80.2262295081967 & 0.90372605029704 & 88.7727309418907 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 80.1770491803279 & 0.879829819121531 & 91.127906144828 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 79.9934426229508 & 0.840985204357285 & 95.1187276642816 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 79.9655737704918 & 0.75938890173347 & 105.302531532859 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 79.9950819672131 & 0.746303920824318 & 107.188344768249 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 80.0262295081967 & 0.713909048252468 & 112.095833081382 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 79.7311475409836 & 0.657369077258396 & 121.288253888528 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 80.635593220339 & 1.39718085263191 & 57.7130677595843 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 80.519298245614 & 1.32500399251418 & 60.7690985842462 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 80.469090909091 & 1.27650847643850 & 63.0384305269967 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 80.3924528301887 & 1.23408548094771 & 65.1433422330287 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 80.313725490196 & 1.19330491676488 & 67.303607285832 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 80.2265306122449 & 1.15958654192605 & 69.1854619828461 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 80.1489361702128 & 1.12536507527130 & 71.2203869938744 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 80.0666666666667 & 1.08815477211691 & 73.5802192099051 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 79.9976744186046 & 1.04797166516401 & 76.3357226896823 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 79.9536585365854 & 1.02050380647810 & 78.347241851568 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 79.8820512820513 & 0.993921280284198 & 80.3706016428284 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 79.8108108108108 & 0.97274250690586 & 82.047212128805 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 79.7228571428571 & 0.94438709584297 & 84.4175629821537 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 79.6545454545455 & 0.920526559098384 & 86.5315016359372 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 79.5741935483871 & 0.894186333350774 & 88.9906170341473 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 79.4896551724138 & 0.86146777066312 & 92.272349447532 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 79.4185185185185 & 0.82463903934675 & 96.3070079503283 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 79.34 & 0.795906192127356 & 99.6851146338419 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 79.2434782608696 & 0.75217277068158 & 105.352761160263 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 79.1238095238095 & 0.691613185376003 & 114.404715232248 \tabularnewline
Median & 79.3 &  &  \tabularnewline
Midrange & 90.55 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 79.2566666666667 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 79.5741935483871 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 79.5741935483871 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 79.5741935483871 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 79.5741935483871 &  &  \tabularnewline
Midmean - Closest Observation & 79.346875 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 79.5741935483871 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 79.5741935483871 &  &  \tabularnewline
Number of observations & 61 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=18193&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]80.960655737705[/C][C]1.57404889955448[/C][C]51.4346509569177[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]80.0844940315358[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]79.2431264509305[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]81.8735950949419[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]80.744262295082[/C][C]1.45560819465256[/C][C]55.4711512285452[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]80.6098360655738[/C][C]1.39594593527002[/C][C]57.745671969725[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]80.6688524590164[/C][C]1.35933232763721[/C][C]59.3444669996445[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]80.655737704918[/C][C]1.32817621080216[/C][C]60.7266844933215[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]80.6639344262295[/C][C]1.27657763273032[/C][C]63.1876451208901[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]80.5852459016393[/C][C]1.24797942935612[/C][C]64.5725754816457[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]80.5737704918033[/C][C]1.22362424506511[/C][C]65.8484586397809[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]80.455737704918[/C][C]1.19447847318278[/C][C]67.3563731044373[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]80.2639344262295[/C][C]1.10361807558545[/C][C]72.7279991165882[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]80.411475409836[/C][C]1.06255208386815[/C][C]75.6776788927876[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]80.3573770491803[/C][C]1.00388169849363[/C][C]80.0466600494463[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]80.416393442623[/C][C]0.99498793228772[/C][C]80.8214761537118[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]80.2032786885246[/C][C]0.936471015522208[/C][C]85.6441655525243[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]80.2262295081967[/C][C]0.90372605029704[/C][C]88.7727309418907[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]80.1770491803279[/C][C]0.879829819121531[/C][C]91.127906144828[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]79.9934426229508[/C][C]0.840985204357285[/C][C]95.1187276642816[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]79.9655737704918[/C][C]0.75938890173347[/C][C]105.302531532859[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]79.9950819672131[/C][C]0.746303920824318[/C][C]107.188344768249[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]80.0262295081967[/C][C]0.713909048252468[/C][C]112.095833081382[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]79.7311475409836[/C][C]0.657369077258396[/C][C]121.288253888528[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]80.635593220339[/C][C]1.39718085263191[/C][C]57.7130677595843[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]80.519298245614[/C][C]1.32500399251418[/C][C]60.7690985842462[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]80.469090909091[/C][C]1.27650847643850[/C][C]63.0384305269967[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]80.3924528301887[/C][C]1.23408548094771[/C][C]65.1433422330287[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]80.313725490196[/C][C]1.19330491676488[/C][C]67.303607285832[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]80.2265306122449[/C][C]1.15958654192605[/C][C]69.1854619828461[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]80.1489361702128[/C][C]1.12536507527130[/C][C]71.2203869938744[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]80.0666666666667[/C][C]1.08815477211691[/C][C]73.5802192099051[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]79.9976744186046[/C][C]1.04797166516401[/C][C]76.3357226896823[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]79.9536585365854[/C][C]1.02050380647810[/C][C]78.347241851568[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]79.8820512820513[/C][C]0.993921280284198[/C][C]80.3706016428284[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]79.8108108108108[/C][C]0.97274250690586[/C][C]82.047212128805[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]79.7228571428571[/C][C]0.94438709584297[/C][C]84.4175629821537[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]79.6545454545455[/C][C]0.920526559098384[/C][C]86.5315016359372[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]79.5741935483871[/C][C]0.894186333350774[/C][C]88.9906170341473[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]79.4896551724138[/C][C]0.86146777066312[/C][C]92.272349447532[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]79.4185185185185[/C][C]0.82463903934675[/C][C]96.3070079503283[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]79.34[/C][C]0.795906192127356[/C][C]99.6851146338419[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]79.2434782608696[/C][C]0.75217277068158[/C][C]105.352761160263[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]79.1238095238095[/C][C]0.691613185376003[/C][C]114.404715232248[/C][/ROW]
[ROW][C]Median[/C][C]79.3[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]90.55[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]79.2566666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]79.5741935483871[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]79.5741935483871[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]79.5741935483871[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]79.5741935483871[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]79.346875[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]79.5741935483871[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]79.5741935483871[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]61[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=18193&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=18193&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 Mean80.9606557377051.5740488995544851.4346509569177
Geometric Mean80.0844940315358
Harmonic Mean79.2431264509305
Quadratic Mean81.8735950949419
Winsorized Mean ( 1 / 20 )80.7442622950821.4556081946525655.4711512285452
Winsorized Mean ( 2 / 20 )80.60983606557381.3959459352700257.745671969725
Winsorized Mean ( 3 / 20 )80.66885245901641.3593323276372159.3444669996445
Winsorized Mean ( 4 / 20 )80.6557377049181.3281762108021660.7266844933215
Winsorized Mean ( 5 / 20 )80.66393442622951.2765776327303263.1876451208901
Winsorized Mean ( 6 / 20 )80.58524590163931.2479794293561264.5725754816457
Winsorized Mean ( 7 / 20 )80.57377049180331.2236242450651165.8484586397809
Winsorized Mean ( 8 / 20 )80.4557377049181.1944784731827867.3563731044373
Winsorized Mean ( 9 / 20 )80.26393442622951.1036180755854572.7279991165882
Winsorized Mean ( 10 / 20 )80.4114754098361.0625520838681575.6776788927876
Winsorized Mean ( 11 / 20 )80.35737704918031.0038816984936380.0466600494463
Winsorized Mean ( 12 / 20 )80.4163934426230.9949879322877280.8214761537118
Winsorized Mean ( 13 / 20 )80.20327868852460.93647101552220885.6441655525243
Winsorized Mean ( 14 / 20 )80.22622950819670.9037260502970488.7727309418907
Winsorized Mean ( 15 / 20 )80.17704918032790.87982981912153191.127906144828
Winsorized Mean ( 16 / 20 )79.99344262295080.84098520435728595.1187276642816
Winsorized Mean ( 17 / 20 )79.96557377049180.75938890173347105.302531532859
Winsorized Mean ( 18 / 20 )79.99508196721310.746303920824318107.188344768249
Winsorized Mean ( 19 / 20 )80.02622950819670.713909048252468112.095833081382
Winsorized Mean ( 20 / 20 )79.73114754098360.657369077258396121.288253888528
Trimmed Mean ( 1 / 20 )80.6355932203391.3971808526319157.7130677595843
Trimmed Mean ( 2 / 20 )80.5192982456141.3250039925141860.7690985842462
Trimmed Mean ( 3 / 20 )80.4690909090911.2765084764385063.0384305269967
Trimmed Mean ( 4 / 20 )80.39245283018871.2340854809477165.1433422330287
Trimmed Mean ( 5 / 20 )80.3137254901961.1933049167648867.303607285832
Trimmed Mean ( 6 / 20 )80.22653061224491.1595865419260569.1854619828461
Trimmed Mean ( 7 / 20 )80.14893617021281.1253650752713071.2203869938744
Trimmed Mean ( 8 / 20 )80.06666666666671.0881547721169173.5802192099051
Trimmed Mean ( 9 / 20 )79.99767441860461.0479716651640176.3357226896823
Trimmed Mean ( 10 / 20 )79.95365853658541.0205038064781078.347241851568
Trimmed Mean ( 11 / 20 )79.88205128205130.99392128028419880.3706016428284
Trimmed Mean ( 12 / 20 )79.81081081081080.9727425069058682.047212128805
Trimmed Mean ( 13 / 20 )79.72285714285710.9443870958429784.4175629821537
Trimmed Mean ( 14 / 20 )79.65454545454550.92052655909838486.5315016359372
Trimmed Mean ( 15 / 20 )79.57419354838710.89418633335077488.9906170341473
Trimmed Mean ( 16 / 20 )79.48965517241380.8614677706631292.272349447532
Trimmed Mean ( 17 / 20 )79.41851851851850.8246390393467596.3070079503283
Trimmed Mean ( 18 / 20 )79.340.79590619212735699.6851146338419
Trimmed Mean ( 19 / 20 )79.24347826086960.75217277068158105.352761160263
Trimmed Mean ( 20 / 20 )79.12380952380950.691613185376003114.404715232248
Median79.3
Midrange90.55
Midmean - Weighted Average at Xnp79.2566666666667
Midmean - Weighted Average at X(n+1)p79.5741935483871
Midmean - Empirical Distribution Function79.5741935483871
Midmean - Empirical Distribution Function - Averaging79.5741935483871
Midmean - Empirical Distribution Function - Interpolation79.5741935483871
Midmean - Closest Observation79.346875
Midmean - True Basic - Statistics Graphics Toolkit79.5741935483871
Midmean - MS Excel (old versions)79.5741935483871
Number of observations61



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')