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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationWed, 06 Jan 2016 15:03:05 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Jan/06/t1452092659neiigk1j1h2ubd1.htm/, Retrieved Fri, 03 May 2024 00:41:26 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=287350, Retrieved Fri, 03 May 2024 00:41:26 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact152
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2016-01-06 15:03:05] [c7db9dbe56b0646da05788291b2eebd0] [Current]
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Dataseries X:
99.1
98.9
98.8
98.8
99.2
99.6
100.5
100.6
100.7
101
101.3
101.5
102.3
103
102.9
103.5
103.8
103.6
103.4
103.4
103.3
103.2
103.2
103.5
104.5
105.7
106.5
107
106.7
107.1
106.1
106.2
106.5
106.8
107
107.2
107.8
107.9
107.9
108.2
108.9
109.1
109.3
109.8
109.8
109.9
109.9
109.9
108.8
108.5
108.8
108.8
108.8
108.9
108.8
108.4
107.7
107.3
107
107.7




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net

\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 & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=287350&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]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=287350&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=287350&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'Gwilym Jenkins' @ jenkins.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean105.4050.447803332791034235.382348190756
Geometric Mean105.348234377314
Harmonic Mean105.290841361614
Quadratic Mean105.461107365069
Winsorized Mean ( 1 / 20 )105.4050.447803332791034235.382348190756
Winsorized Mean ( 2 / 20 )105.4083333333330.446975344475216235.825833877014
Winsorized Mean ( 3 / 20 )105.4133333333330.443690650788347237.582949169732
Winsorized Mean ( 4 / 20 )105.420.442091843105155238.45723834114
Winsorized Mean ( 5 / 20 )105.4116666666670.427561021955103246.541806324281
Winsorized Mean ( 6 / 20 )105.4816666666670.404721370756807260.627864719428
Winsorized Mean ( 7 / 20 )105.470.398828085530482264.449781312954
Winsorized Mean ( 8 / 20 )105.4833333333330.39608370018443266.315764279663
Winsorized Mean ( 9 / 20 )105.5133333333330.384821234208238274.187918840874
Winsorized Mean ( 10 / 20 )105.5633333333330.37503270416086281.477674245857
Winsorized Mean ( 11 / 20 )105.60.368038010810201286.92688499085
Winsorized Mean ( 12 / 20 )105.760.339043186756312311.936662145684
Winsorized Mean ( 13 / 20 )105.890.31739316010131333.624076732468
Winsorized Mean ( 14 / 20 )105.8433333333330.303029586542553349.283825850022
Winsorized Mean ( 15 / 20 )105.8683333333330.291474836028198363.21603187416
Winsorized Mean ( 16 / 20 )105.8150.283748366679388372.918446151136
Winsorized Mean ( 17 / 20 )105.7583333333330.267498261958203395.360824250358
Winsorized Mean ( 18 / 20 )105.7883333333330.262851504410757402.464249046178
Winsorized Mean ( 19 / 20 )105.7566666666670.25857460939782408.998651928577
Winsorized Mean ( 20 / 20 )105.7566666666670.249002151723813424.721898724672
Trimmed Mean ( 1 / 20 )105.4413793103450.442029872569891238.539035150103
Trimmed Mean ( 2 / 20 )105.4803571428570.434654808872162242.676153558629
Trimmed Mean ( 3 / 20 )105.520370370370.425829068682093247.799828924191
Trimmed Mean ( 4 / 20 )105.5615384615380.416180595934665253.643585243244
Trimmed Mean ( 5 / 20 )105.6040.404474564675441261.089347076098
Trimmed Mean ( 6 / 20 )105.6520833333330.394442662546336267.851562128937
Trimmed Mean ( 7 / 20 )105.6891304347830.388546508147878272.011530713739
Trimmed Mean ( 8 / 20 )105.7318181818180.382088020023091276.721102575863
Trimmed Mean ( 9 / 20 )105.776190476190.373929902127531282.877057636634
Trimmed Mean ( 10 / 20 )105.820.365800842549954289.283095310392
Trimmed Mean ( 11 / 20 )105.8605263157890.357176764986796296.381334658493
Trimmed Mean ( 12 / 20 )105.90.34693670801038305.242995494244
Trimmed Mean ( 13 / 20 )105.9205882352940.340749394632375310.846005609398
Trimmed Mean ( 14 / 20 )105.9250.337298326841867314.039506189606
Trimmed Mean ( 15 / 20 )105.9366666666670.335058181028802316.173944302408
Trimmed Mean ( 16 / 20 )105.9464285714290.33355080774213317.632055184038
Trimmed Mean ( 17 / 20 )105.9653846153850.331613412909222319.544929397631
Trimmed Mean ( 18 / 20 )105.9958333333330.331360784956161319.880438922054
Trimmed Mean ( 19 / 20 )106.0272727272730.329710736279941321.576646012675
Trimmed Mean ( 20 / 20 )106.070.325018218112867326.350936928605
Median106.6
Midrange104.35
Midmean - Weighted Average at Xnp105.841935483871
Midmean - Weighted Average at X(n+1)p105.936666666667
Midmean - Empirical Distribution Function105.841935483871
Midmean - Empirical Distribution Function - Averaging105.936666666667
Midmean - Empirical Distribution Function - Interpolation105.936666666667
Midmean - Closest Observation105.841935483871
Midmean - True Basic - Statistics Graphics Toolkit105.936666666667
Midmean - MS Excel (old versions)105.925
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 105.405 & 0.447803332791034 & 235.382348190756 \tabularnewline
Geometric Mean & 105.348234377314 &  &  \tabularnewline
Harmonic Mean & 105.290841361614 &  &  \tabularnewline
Quadratic Mean & 105.461107365069 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 105.405 & 0.447803332791034 & 235.382348190756 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 105.408333333333 & 0.446975344475216 & 235.825833877014 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 105.413333333333 & 0.443690650788347 & 237.582949169732 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 105.42 & 0.442091843105155 & 238.45723834114 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 105.411666666667 & 0.427561021955103 & 246.541806324281 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 105.481666666667 & 0.404721370756807 & 260.627864719428 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 105.47 & 0.398828085530482 & 264.449781312954 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 105.483333333333 & 0.39608370018443 & 266.315764279663 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 105.513333333333 & 0.384821234208238 & 274.187918840874 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 105.563333333333 & 0.37503270416086 & 281.477674245857 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 105.6 & 0.368038010810201 & 286.92688499085 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 105.76 & 0.339043186756312 & 311.936662145684 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 105.89 & 0.31739316010131 & 333.624076732468 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 105.843333333333 & 0.303029586542553 & 349.283825850022 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 105.868333333333 & 0.291474836028198 & 363.21603187416 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 105.815 & 0.283748366679388 & 372.918446151136 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 105.758333333333 & 0.267498261958203 & 395.360824250358 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 105.788333333333 & 0.262851504410757 & 402.464249046178 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 105.756666666667 & 0.25857460939782 & 408.998651928577 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 105.756666666667 & 0.249002151723813 & 424.721898724672 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 105.441379310345 & 0.442029872569891 & 238.539035150103 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 105.480357142857 & 0.434654808872162 & 242.676153558629 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 105.52037037037 & 0.425829068682093 & 247.799828924191 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 105.561538461538 & 0.416180595934665 & 253.643585243244 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 105.604 & 0.404474564675441 & 261.089347076098 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 105.652083333333 & 0.394442662546336 & 267.851562128937 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 105.689130434783 & 0.388546508147878 & 272.011530713739 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 105.731818181818 & 0.382088020023091 & 276.721102575863 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 105.77619047619 & 0.373929902127531 & 282.877057636634 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 105.82 & 0.365800842549954 & 289.283095310392 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 105.860526315789 & 0.357176764986796 & 296.381334658493 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 105.9 & 0.34693670801038 & 305.242995494244 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 105.920588235294 & 0.340749394632375 & 310.846005609398 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 105.925 & 0.337298326841867 & 314.039506189606 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 105.936666666667 & 0.335058181028802 & 316.173944302408 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 105.946428571429 & 0.33355080774213 & 317.632055184038 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 105.965384615385 & 0.331613412909222 & 319.544929397631 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 105.995833333333 & 0.331360784956161 & 319.880438922054 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 106.027272727273 & 0.329710736279941 & 321.576646012675 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 106.07 & 0.325018218112867 & 326.350936928605 \tabularnewline
Median & 106.6 &  &  \tabularnewline
Midrange & 104.35 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 105.841935483871 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 105.936666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 105.841935483871 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 105.936666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 105.936666666667 &  &  \tabularnewline
Midmean - Closest Observation & 105.841935483871 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 105.936666666667 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 105.925 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=287350&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]105.405[/C][C]0.447803332791034[/C][C]235.382348190756[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]105.348234377314[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]105.290841361614[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]105.461107365069[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]105.405[/C][C]0.447803332791034[/C][C]235.382348190756[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]105.408333333333[/C][C]0.446975344475216[/C][C]235.825833877014[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]105.413333333333[/C][C]0.443690650788347[/C][C]237.582949169732[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]105.42[/C][C]0.442091843105155[/C][C]238.45723834114[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]105.411666666667[/C][C]0.427561021955103[/C][C]246.541806324281[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]105.481666666667[/C][C]0.404721370756807[/C][C]260.627864719428[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]105.47[/C][C]0.398828085530482[/C][C]264.449781312954[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]105.483333333333[/C][C]0.39608370018443[/C][C]266.315764279663[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]105.513333333333[/C][C]0.384821234208238[/C][C]274.187918840874[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]105.563333333333[/C][C]0.37503270416086[/C][C]281.477674245857[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]105.6[/C][C]0.368038010810201[/C][C]286.92688499085[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]105.76[/C][C]0.339043186756312[/C][C]311.936662145684[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]105.89[/C][C]0.31739316010131[/C][C]333.624076732468[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]105.843333333333[/C][C]0.303029586542553[/C][C]349.283825850022[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]105.868333333333[/C][C]0.291474836028198[/C][C]363.21603187416[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]105.815[/C][C]0.283748366679388[/C][C]372.918446151136[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]105.758333333333[/C][C]0.267498261958203[/C][C]395.360824250358[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]105.788333333333[/C][C]0.262851504410757[/C][C]402.464249046178[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]105.756666666667[/C][C]0.25857460939782[/C][C]408.998651928577[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]105.756666666667[/C][C]0.249002151723813[/C][C]424.721898724672[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]105.441379310345[/C][C]0.442029872569891[/C][C]238.539035150103[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]105.480357142857[/C][C]0.434654808872162[/C][C]242.676153558629[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]105.52037037037[/C][C]0.425829068682093[/C][C]247.799828924191[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]105.561538461538[/C][C]0.416180595934665[/C][C]253.643585243244[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]105.604[/C][C]0.404474564675441[/C][C]261.089347076098[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]105.652083333333[/C][C]0.394442662546336[/C][C]267.851562128937[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]105.689130434783[/C][C]0.388546508147878[/C][C]272.011530713739[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]105.731818181818[/C][C]0.382088020023091[/C][C]276.721102575863[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]105.77619047619[/C][C]0.373929902127531[/C][C]282.877057636634[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]105.82[/C][C]0.365800842549954[/C][C]289.283095310392[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]105.860526315789[/C][C]0.357176764986796[/C][C]296.381334658493[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]105.9[/C][C]0.34693670801038[/C][C]305.242995494244[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]105.920588235294[/C][C]0.340749394632375[/C][C]310.846005609398[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]105.925[/C][C]0.337298326841867[/C][C]314.039506189606[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]105.936666666667[/C][C]0.335058181028802[/C][C]316.173944302408[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]105.946428571429[/C][C]0.33355080774213[/C][C]317.632055184038[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]105.965384615385[/C][C]0.331613412909222[/C][C]319.544929397631[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]105.995833333333[/C][C]0.331360784956161[/C][C]319.880438922054[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]106.027272727273[/C][C]0.329710736279941[/C][C]321.576646012675[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]106.07[/C][C]0.325018218112867[/C][C]326.350936928605[/C][/ROW]
[ROW][C]Median[/C][C]106.6[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]104.35[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]105.841935483871[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]105.936666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]105.841935483871[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]105.936666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]105.936666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]105.841935483871[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]105.936666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]105.925[/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=287350&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=287350&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 Mean105.4050.447803332791034235.382348190756
Geometric Mean105.348234377314
Harmonic Mean105.290841361614
Quadratic Mean105.461107365069
Winsorized Mean ( 1 / 20 )105.4050.447803332791034235.382348190756
Winsorized Mean ( 2 / 20 )105.4083333333330.446975344475216235.825833877014
Winsorized Mean ( 3 / 20 )105.4133333333330.443690650788347237.582949169732
Winsorized Mean ( 4 / 20 )105.420.442091843105155238.45723834114
Winsorized Mean ( 5 / 20 )105.4116666666670.427561021955103246.541806324281
Winsorized Mean ( 6 / 20 )105.4816666666670.404721370756807260.627864719428
Winsorized Mean ( 7 / 20 )105.470.398828085530482264.449781312954
Winsorized Mean ( 8 / 20 )105.4833333333330.39608370018443266.315764279663
Winsorized Mean ( 9 / 20 )105.5133333333330.384821234208238274.187918840874
Winsorized Mean ( 10 / 20 )105.5633333333330.37503270416086281.477674245857
Winsorized Mean ( 11 / 20 )105.60.368038010810201286.92688499085
Winsorized Mean ( 12 / 20 )105.760.339043186756312311.936662145684
Winsorized Mean ( 13 / 20 )105.890.31739316010131333.624076732468
Winsorized Mean ( 14 / 20 )105.8433333333330.303029586542553349.283825850022
Winsorized Mean ( 15 / 20 )105.8683333333330.291474836028198363.21603187416
Winsorized Mean ( 16 / 20 )105.8150.283748366679388372.918446151136
Winsorized Mean ( 17 / 20 )105.7583333333330.267498261958203395.360824250358
Winsorized Mean ( 18 / 20 )105.7883333333330.262851504410757402.464249046178
Winsorized Mean ( 19 / 20 )105.7566666666670.25857460939782408.998651928577
Winsorized Mean ( 20 / 20 )105.7566666666670.249002151723813424.721898724672
Trimmed Mean ( 1 / 20 )105.4413793103450.442029872569891238.539035150103
Trimmed Mean ( 2 / 20 )105.4803571428570.434654808872162242.676153558629
Trimmed Mean ( 3 / 20 )105.520370370370.425829068682093247.799828924191
Trimmed Mean ( 4 / 20 )105.5615384615380.416180595934665253.643585243244
Trimmed Mean ( 5 / 20 )105.6040.404474564675441261.089347076098
Trimmed Mean ( 6 / 20 )105.6520833333330.394442662546336267.851562128937
Trimmed Mean ( 7 / 20 )105.6891304347830.388546508147878272.011530713739
Trimmed Mean ( 8 / 20 )105.7318181818180.382088020023091276.721102575863
Trimmed Mean ( 9 / 20 )105.776190476190.373929902127531282.877057636634
Trimmed Mean ( 10 / 20 )105.820.365800842549954289.283095310392
Trimmed Mean ( 11 / 20 )105.8605263157890.357176764986796296.381334658493
Trimmed Mean ( 12 / 20 )105.90.34693670801038305.242995494244
Trimmed Mean ( 13 / 20 )105.9205882352940.340749394632375310.846005609398
Trimmed Mean ( 14 / 20 )105.9250.337298326841867314.039506189606
Trimmed Mean ( 15 / 20 )105.9366666666670.335058181028802316.173944302408
Trimmed Mean ( 16 / 20 )105.9464285714290.33355080774213317.632055184038
Trimmed Mean ( 17 / 20 )105.9653846153850.331613412909222319.544929397631
Trimmed Mean ( 18 / 20 )105.9958333333330.331360784956161319.880438922054
Trimmed Mean ( 19 / 20 )106.0272727272730.329710736279941321.576646012675
Trimmed Mean ( 20 / 20 )106.070.325018218112867326.350936928605
Median106.6
Midrange104.35
Midmean - Weighted Average at Xnp105.841935483871
Midmean - Weighted Average at X(n+1)p105.936666666667
Midmean - Empirical Distribution Function105.841935483871
Midmean - Empirical Distribution Function - Averaging105.936666666667
Midmean - Empirical Distribution Function - Interpolation105.936666666667
Midmean - Closest Observation105.841935483871
Midmean - True Basic - Statistics Graphics Toolkit105.936666666667
Midmean - MS Excel (old versions)105.925
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')