Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationThu, 14 May 2009 02:49:13 -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/2009/May/14/t12422910141b5rj2w7f11i62j.htm/, Retrieved Sun, 28 Apr 2024 23:35:42 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=39948, Retrieved Sun, 28 Apr 2024 23:35:42 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact134
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Opgave 5 trimmed ...] [2009-05-14 08:49:13] [c0b80eb26a0ae341c828c46b0228b15b] [Current]
Feedback Forum

Post a new message
Dataseries X:
5.29
5.29
5.29
5.31
5.33
5.34
5.34
5.37
5.41
5.41
5.38
5.44
5.44
5.46
5.46
5.45
5.46
5.46
5.48
5.47
5.48
5.51
5.55
5.58
5.59
5.6
5.6
5.67
5.71
5.7
5.73
5.72
5.75
5.75
5.77
5.83
5.85
5.87
5.86
5.87
5.93
5.97
5.98
5.99
5.99
6.03
6.06
6.07
6.08
6.08
6.1
6.13
6.14
6.14
6.16
6.2
6.19
6.32
6.32
6.33
6.32
6.33
6.38
6.42
6.46
6.47
6.42
6.48
6.47
6.49
6.48
6.51
6.51
6.52
6.57
6.59
6.62
6.63
6.61
6.64




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

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=39948&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=39948&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=39948&T=0

As an alternative you can also use a QR Code:  

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

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







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean5.9250.0481910097188419122.948243553474
Geometric Mean5.90955852796622
Harmonic Mean5.89419258614842
Quadratic Mean5.94046231365876
Winsorized Mean ( 1 / 26 )5.9248750.0481676902549175123.005171488270
Winsorized Mean ( 2 / 26 )5.9246250.0481216627151261123.117628646230
Winsorized Mean ( 3 / 26 )5.9250.0479299330378487123.617948627661
Winsorized Mean ( 4 / 26 )5.9250.0475906862497434124.499150293970
Winsorized Mean ( 5 / 26 )5.9243750.0472737261273324125.320669329992
Winsorized Mean ( 6 / 26 )5.9206250.0466444753502084126.930894935525
Winsorized Mean ( 7 / 26 )5.9223750.0460967762093916128.476988783294
Winsorized Mean ( 8 / 26 )5.9233750.0459460827898764128.920130734304
Winsorized Mean ( 9 / 26 )5.92450.0450891872861619131.395138315528
Winsorized Mean ( 10 / 26 )5.923250.0448918443581172131.944901901296
Winsorized Mean ( 11 / 26 )5.9273750.0443060928711428133.782390093363
Winsorized Mean ( 12 / 26 )5.9258750.0440704606104556134.463650207325
Winsorized Mean ( 13 / 26 )5.92750.043845059476597135.191970788953
Winsorized Mean ( 14 / 26 )5.92750.0433317713123211136.793392480463
Winsorized Mean ( 15 / 26 )5.920.0421855455477887140.332427212389
Winsorized Mean ( 16 / 26 )5.920.0421855455477887140.332427212389
Winsorized Mean ( 17 / 26 )5.91150.0409318281654023144.423063052842
Winsorized Mean ( 18 / 26 )5.90250.0390210507939406151.264506718937
Winsorized Mean ( 19 / 26 )5.9048750.038689364052964152.622694751883
Winsorized Mean ( 20 / 26 )5.9023750.0383431556738007153.935556327540
Winsorized Mean ( 21 / 26 )5.910250.0372584944863907158.628255958083
Winsorized Mean ( 22 / 26 )5.921250.0357878661107294165.454122961100
Winsorized Mean ( 23 / 26 )5.8953750.0299772824058993196.661422479038
Winsorized Mean ( 24 / 26 )5.8953750.0291943204496866201.935681639176
Winsorized Mean ( 25 / 26 )5.8891250.0275986113150461213.384830590712
Winsorized Mean ( 26 / 26 )5.8826250.0267996219921858219.504028889484
Trimmed Mean ( 1 / 26 )5.923974358974360.0478698214429649123.751753827462
Trimmed Mean ( 2 / 26 )5.923026315789470.0475032851077644124.686667508420
Trimmed Mean ( 3 / 26 )5.922162162162160.0470842825759232125.777899506331
Trimmed Mean ( 4 / 26 )5.921111111111110.0466564188763061126.908820987932
Trimmed Mean ( 5 / 26 )5.920.0462484961425248128.004162162511
Trimmed Mean ( 6 / 26 )5.918970588235290.0458363599369404129.132649197675
Trimmed Mean ( 7 / 26 )5.918636363636360.0454851528652137130.122380399052
Trimmed Mean ( 8 / 26 )5.917968750.0451651399361431131.029567457715
Trimmed Mean ( 9 / 26 )5.917096774193550.0447830348019146132.128088245162
Trimmed Mean ( 10 / 26 )5.9160.0444661999484227133.044874688237
Trimmed Mean ( 11 / 26 )5.9150.0440852786849898134.171772901006
Trimmed Mean ( 12 / 26 )5.913392857142860.0436940936197809135.336206046526
Trimmed Mean ( 13 / 26 )5.911851851851850.0432203607792574136.783954258177
Trimmed Mean ( 14 / 26 )5.910.042637409840992138.610671287027
Trimmed Mean ( 15 / 26 )5.9080.0419718078364660140.761151461935
Trimmed Mean ( 16 / 26 )5.906666666666670.0413269841840584142.925180321896
Trimmed Mean ( 17 / 26 )5.905217391304350.0404679620765783145.923270861275
Trimmed Mean ( 18 / 26 )5.904545454545450.0395955431128710149.121466466919
Trimmed Mean ( 19 / 26 )5.90476190476190.0388305202461005152.064970217721
Trimmed Mean ( 20 / 26 )5.904750.0378525944983486155.993270164284
Trimmed Mean ( 21 / 26 )5.9050.0365895887997508161.384705149794
Trimmed Mean ( 22 / 26 )5.904444444444440.0351198502284755168.122711402029
Trimmed Mean ( 23 / 26 )5.902647058823530.0334533725136411176.444005949374
Trimmed Mean ( 24 / 26 )5.90343750.0327367597435676180.330538093648
Trimmed Mean ( 25 / 26 )5.904333333333330.0318534118540431185.359526332307
Trimmed Mean ( 26 / 26 )5.906071428571430.0309605453212808190.761221008336
Median5.9
Midrange5.965
Midmean - Weighted Average at Xnp5.89439024390244
Midmean - Weighted Average at X(n+1)p5.89439024390244
Midmean - Empirical Distribution Function5.89439024390244
Midmean - Empirical Distribution Function - Averaging5.89439024390244
Midmean - Empirical Distribution Function - Interpolation5.89439024390244
Midmean - Closest Observation5.89439024390244
Midmean - True Basic - Statistics Graphics Toolkit5.89439024390244
Midmean - MS Excel (old versions)5.9146511627907
Number of observations80

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 5.925 & 0.0481910097188419 & 122.948243553474 \tabularnewline
Geometric Mean & 5.90955852796622 &  &  \tabularnewline
Harmonic Mean & 5.89419258614842 &  &  \tabularnewline
Quadratic Mean & 5.94046231365876 &  &  \tabularnewline
Winsorized Mean ( 1 / 26 ) & 5.924875 & 0.0481676902549175 & 123.005171488270 \tabularnewline
Winsorized Mean ( 2 / 26 ) & 5.924625 & 0.0481216627151261 & 123.117628646230 \tabularnewline
Winsorized Mean ( 3 / 26 ) & 5.925 & 0.0479299330378487 & 123.617948627661 \tabularnewline
Winsorized Mean ( 4 / 26 ) & 5.925 & 0.0475906862497434 & 124.499150293970 \tabularnewline
Winsorized Mean ( 5 / 26 ) & 5.924375 & 0.0472737261273324 & 125.320669329992 \tabularnewline
Winsorized Mean ( 6 / 26 ) & 5.920625 & 0.0466444753502084 & 126.930894935525 \tabularnewline
Winsorized Mean ( 7 / 26 ) & 5.922375 & 0.0460967762093916 & 128.476988783294 \tabularnewline
Winsorized Mean ( 8 / 26 ) & 5.923375 & 0.0459460827898764 & 128.920130734304 \tabularnewline
Winsorized Mean ( 9 / 26 ) & 5.9245 & 0.0450891872861619 & 131.395138315528 \tabularnewline
Winsorized Mean ( 10 / 26 ) & 5.92325 & 0.0448918443581172 & 131.944901901296 \tabularnewline
Winsorized Mean ( 11 / 26 ) & 5.927375 & 0.0443060928711428 & 133.782390093363 \tabularnewline
Winsorized Mean ( 12 / 26 ) & 5.925875 & 0.0440704606104556 & 134.463650207325 \tabularnewline
Winsorized Mean ( 13 / 26 ) & 5.9275 & 0.043845059476597 & 135.191970788953 \tabularnewline
Winsorized Mean ( 14 / 26 ) & 5.9275 & 0.0433317713123211 & 136.793392480463 \tabularnewline
Winsorized Mean ( 15 / 26 ) & 5.92 & 0.0421855455477887 & 140.332427212389 \tabularnewline
Winsorized Mean ( 16 / 26 ) & 5.92 & 0.0421855455477887 & 140.332427212389 \tabularnewline
Winsorized Mean ( 17 / 26 ) & 5.9115 & 0.0409318281654023 & 144.423063052842 \tabularnewline
Winsorized Mean ( 18 / 26 ) & 5.9025 & 0.0390210507939406 & 151.264506718937 \tabularnewline
Winsorized Mean ( 19 / 26 ) & 5.904875 & 0.038689364052964 & 152.622694751883 \tabularnewline
Winsorized Mean ( 20 / 26 ) & 5.902375 & 0.0383431556738007 & 153.935556327540 \tabularnewline
Winsorized Mean ( 21 / 26 ) & 5.91025 & 0.0372584944863907 & 158.628255958083 \tabularnewline
Winsorized Mean ( 22 / 26 ) & 5.92125 & 0.0357878661107294 & 165.454122961100 \tabularnewline
Winsorized Mean ( 23 / 26 ) & 5.895375 & 0.0299772824058993 & 196.661422479038 \tabularnewline
Winsorized Mean ( 24 / 26 ) & 5.895375 & 0.0291943204496866 & 201.935681639176 \tabularnewline
Winsorized Mean ( 25 / 26 ) & 5.889125 & 0.0275986113150461 & 213.384830590712 \tabularnewline
Winsorized Mean ( 26 / 26 ) & 5.882625 & 0.0267996219921858 & 219.504028889484 \tabularnewline
Trimmed Mean ( 1 / 26 ) & 5.92397435897436 & 0.0478698214429649 & 123.751753827462 \tabularnewline
Trimmed Mean ( 2 / 26 ) & 5.92302631578947 & 0.0475032851077644 & 124.686667508420 \tabularnewline
Trimmed Mean ( 3 / 26 ) & 5.92216216216216 & 0.0470842825759232 & 125.777899506331 \tabularnewline
Trimmed Mean ( 4 / 26 ) & 5.92111111111111 & 0.0466564188763061 & 126.908820987932 \tabularnewline
Trimmed Mean ( 5 / 26 ) & 5.92 & 0.0462484961425248 & 128.004162162511 \tabularnewline
Trimmed Mean ( 6 / 26 ) & 5.91897058823529 & 0.0458363599369404 & 129.132649197675 \tabularnewline
Trimmed Mean ( 7 / 26 ) & 5.91863636363636 & 0.0454851528652137 & 130.122380399052 \tabularnewline
Trimmed Mean ( 8 / 26 ) & 5.91796875 & 0.0451651399361431 & 131.029567457715 \tabularnewline
Trimmed Mean ( 9 / 26 ) & 5.91709677419355 & 0.0447830348019146 & 132.128088245162 \tabularnewline
Trimmed Mean ( 10 / 26 ) & 5.916 & 0.0444661999484227 & 133.044874688237 \tabularnewline
Trimmed Mean ( 11 / 26 ) & 5.915 & 0.0440852786849898 & 134.171772901006 \tabularnewline
Trimmed Mean ( 12 / 26 ) & 5.91339285714286 & 0.0436940936197809 & 135.336206046526 \tabularnewline
Trimmed Mean ( 13 / 26 ) & 5.91185185185185 & 0.0432203607792574 & 136.783954258177 \tabularnewline
Trimmed Mean ( 14 / 26 ) & 5.91 & 0.042637409840992 & 138.610671287027 \tabularnewline
Trimmed Mean ( 15 / 26 ) & 5.908 & 0.0419718078364660 & 140.761151461935 \tabularnewline
Trimmed Mean ( 16 / 26 ) & 5.90666666666667 & 0.0413269841840584 & 142.925180321896 \tabularnewline
Trimmed Mean ( 17 / 26 ) & 5.90521739130435 & 0.0404679620765783 & 145.923270861275 \tabularnewline
Trimmed Mean ( 18 / 26 ) & 5.90454545454545 & 0.0395955431128710 & 149.121466466919 \tabularnewline
Trimmed Mean ( 19 / 26 ) & 5.9047619047619 & 0.0388305202461005 & 152.064970217721 \tabularnewline
Trimmed Mean ( 20 / 26 ) & 5.90475 & 0.0378525944983486 & 155.993270164284 \tabularnewline
Trimmed Mean ( 21 / 26 ) & 5.905 & 0.0365895887997508 & 161.384705149794 \tabularnewline
Trimmed Mean ( 22 / 26 ) & 5.90444444444444 & 0.0351198502284755 & 168.122711402029 \tabularnewline
Trimmed Mean ( 23 / 26 ) & 5.90264705882353 & 0.0334533725136411 & 176.444005949374 \tabularnewline
Trimmed Mean ( 24 / 26 ) & 5.9034375 & 0.0327367597435676 & 180.330538093648 \tabularnewline
Trimmed Mean ( 25 / 26 ) & 5.90433333333333 & 0.0318534118540431 & 185.359526332307 \tabularnewline
Trimmed Mean ( 26 / 26 ) & 5.90607142857143 & 0.0309605453212808 & 190.761221008336 \tabularnewline
Median & 5.9 &  &  \tabularnewline
Midrange & 5.965 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 5.89439024390244 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 5.89439024390244 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 5.89439024390244 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 5.89439024390244 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 5.89439024390244 &  &  \tabularnewline
Midmean - Closest Observation & 5.89439024390244 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 5.89439024390244 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 5.9146511627907 &  &  \tabularnewline
Number of observations & 80 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=39948&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]5.925[/C][C]0.0481910097188419[/C][C]122.948243553474[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]5.90955852796622[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]5.89419258614842[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]5.94046231365876[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 26 )[/C][C]5.924875[/C][C]0.0481676902549175[/C][C]123.005171488270[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 26 )[/C][C]5.924625[/C][C]0.0481216627151261[/C][C]123.117628646230[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 26 )[/C][C]5.925[/C][C]0.0479299330378487[/C][C]123.617948627661[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 26 )[/C][C]5.925[/C][C]0.0475906862497434[/C][C]124.499150293970[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 26 )[/C][C]5.924375[/C][C]0.0472737261273324[/C][C]125.320669329992[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 26 )[/C][C]5.920625[/C][C]0.0466444753502084[/C][C]126.930894935525[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 26 )[/C][C]5.922375[/C][C]0.0460967762093916[/C][C]128.476988783294[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 26 )[/C][C]5.923375[/C][C]0.0459460827898764[/C][C]128.920130734304[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 26 )[/C][C]5.9245[/C][C]0.0450891872861619[/C][C]131.395138315528[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 26 )[/C][C]5.92325[/C][C]0.0448918443581172[/C][C]131.944901901296[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 26 )[/C][C]5.927375[/C][C]0.0443060928711428[/C][C]133.782390093363[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 26 )[/C][C]5.925875[/C][C]0.0440704606104556[/C][C]134.463650207325[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 26 )[/C][C]5.9275[/C][C]0.043845059476597[/C][C]135.191970788953[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 26 )[/C][C]5.9275[/C][C]0.0433317713123211[/C][C]136.793392480463[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 26 )[/C][C]5.92[/C][C]0.0421855455477887[/C][C]140.332427212389[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 26 )[/C][C]5.92[/C][C]0.0421855455477887[/C][C]140.332427212389[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 26 )[/C][C]5.9115[/C][C]0.0409318281654023[/C][C]144.423063052842[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 26 )[/C][C]5.9025[/C][C]0.0390210507939406[/C][C]151.264506718937[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 26 )[/C][C]5.904875[/C][C]0.038689364052964[/C][C]152.622694751883[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 26 )[/C][C]5.902375[/C][C]0.0383431556738007[/C][C]153.935556327540[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 26 )[/C][C]5.91025[/C][C]0.0372584944863907[/C][C]158.628255958083[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 26 )[/C][C]5.92125[/C][C]0.0357878661107294[/C][C]165.454122961100[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 26 )[/C][C]5.895375[/C][C]0.0299772824058993[/C][C]196.661422479038[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 26 )[/C][C]5.895375[/C][C]0.0291943204496866[/C][C]201.935681639176[/C][/ROW]
[ROW][C]Winsorized Mean ( 25 / 26 )[/C][C]5.889125[/C][C]0.0275986113150461[/C][C]213.384830590712[/C][/ROW]
[ROW][C]Winsorized Mean ( 26 / 26 )[/C][C]5.882625[/C][C]0.0267996219921858[/C][C]219.504028889484[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 26 )[/C][C]5.92397435897436[/C][C]0.0478698214429649[/C][C]123.751753827462[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 26 )[/C][C]5.92302631578947[/C][C]0.0475032851077644[/C][C]124.686667508420[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 26 )[/C][C]5.92216216216216[/C][C]0.0470842825759232[/C][C]125.777899506331[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 26 )[/C][C]5.92111111111111[/C][C]0.0466564188763061[/C][C]126.908820987932[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 26 )[/C][C]5.92[/C][C]0.0462484961425248[/C][C]128.004162162511[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 26 )[/C][C]5.91897058823529[/C][C]0.0458363599369404[/C][C]129.132649197675[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 26 )[/C][C]5.91863636363636[/C][C]0.0454851528652137[/C][C]130.122380399052[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 26 )[/C][C]5.91796875[/C][C]0.0451651399361431[/C][C]131.029567457715[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 26 )[/C][C]5.91709677419355[/C][C]0.0447830348019146[/C][C]132.128088245162[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 26 )[/C][C]5.916[/C][C]0.0444661999484227[/C][C]133.044874688237[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 26 )[/C][C]5.915[/C][C]0.0440852786849898[/C][C]134.171772901006[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 26 )[/C][C]5.91339285714286[/C][C]0.0436940936197809[/C][C]135.336206046526[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 26 )[/C][C]5.91185185185185[/C][C]0.0432203607792574[/C][C]136.783954258177[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 26 )[/C][C]5.91[/C][C]0.042637409840992[/C][C]138.610671287027[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 26 )[/C][C]5.908[/C][C]0.0419718078364660[/C][C]140.761151461935[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 26 )[/C][C]5.90666666666667[/C][C]0.0413269841840584[/C][C]142.925180321896[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 26 )[/C][C]5.90521739130435[/C][C]0.0404679620765783[/C][C]145.923270861275[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 26 )[/C][C]5.90454545454545[/C][C]0.0395955431128710[/C][C]149.121466466919[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 26 )[/C][C]5.9047619047619[/C][C]0.0388305202461005[/C][C]152.064970217721[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 26 )[/C][C]5.90475[/C][C]0.0378525944983486[/C][C]155.993270164284[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 26 )[/C][C]5.905[/C][C]0.0365895887997508[/C][C]161.384705149794[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 26 )[/C][C]5.90444444444444[/C][C]0.0351198502284755[/C][C]168.122711402029[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 26 )[/C][C]5.90264705882353[/C][C]0.0334533725136411[/C][C]176.444005949374[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 26 )[/C][C]5.9034375[/C][C]0.0327367597435676[/C][C]180.330538093648[/C][/ROW]
[ROW][C]Trimmed Mean ( 25 / 26 )[/C][C]5.90433333333333[/C][C]0.0318534118540431[/C][C]185.359526332307[/C][/ROW]
[ROW][C]Trimmed Mean ( 26 / 26 )[/C][C]5.90607142857143[/C][C]0.0309605453212808[/C][C]190.761221008336[/C][/ROW]
[ROW][C]Median[/C][C]5.9[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]5.965[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]5.89439024390244[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]5.89439024390244[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]5.89439024390244[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]5.89439024390244[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]5.89439024390244[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]5.89439024390244[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]5.89439024390244[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]5.9146511627907[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]80[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=39948&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=39948&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 Mean5.9250.0481910097188419122.948243553474
Geometric Mean5.90955852796622
Harmonic Mean5.89419258614842
Quadratic Mean5.94046231365876
Winsorized Mean ( 1 / 26 )5.9248750.0481676902549175123.005171488270
Winsorized Mean ( 2 / 26 )5.9246250.0481216627151261123.117628646230
Winsorized Mean ( 3 / 26 )5.9250.0479299330378487123.617948627661
Winsorized Mean ( 4 / 26 )5.9250.0475906862497434124.499150293970
Winsorized Mean ( 5 / 26 )5.9243750.0472737261273324125.320669329992
Winsorized Mean ( 6 / 26 )5.9206250.0466444753502084126.930894935525
Winsorized Mean ( 7 / 26 )5.9223750.0460967762093916128.476988783294
Winsorized Mean ( 8 / 26 )5.9233750.0459460827898764128.920130734304
Winsorized Mean ( 9 / 26 )5.92450.0450891872861619131.395138315528
Winsorized Mean ( 10 / 26 )5.923250.0448918443581172131.944901901296
Winsorized Mean ( 11 / 26 )5.9273750.0443060928711428133.782390093363
Winsorized Mean ( 12 / 26 )5.9258750.0440704606104556134.463650207325
Winsorized Mean ( 13 / 26 )5.92750.043845059476597135.191970788953
Winsorized Mean ( 14 / 26 )5.92750.0433317713123211136.793392480463
Winsorized Mean ( 15 / 26 )5.920.0421855455477887140.332427212389
Winsorized Mean ( 16 / 26 )5.920.0421855455477887140.332427212389
Winsorized Mean ( 17 / 26 )5.91150.0409318281654023144.423063052842
Winsorized Mean ( 18 / 26 )5.90250.0390210507939406151.264506718937
Winsorized Mean ( 19 / 26 )5.9048750.038689364052964152.622694751883
Winsorized Mean ( 20 / 26 )5.9023750.0383431556738007153.935556327540
Winsorized Mean ( 21 / 26 )5.910250.0372584944863907158.628255958083
Winsorized Mean ( 22 / 26 )5.921250.0357878661107294165.454122961100
Winsorized Mean ( 23 / 26 )5.8953750.0299772824058993196.661422479038
Winsorized Mean ( 24 / 26 )5.8953750.0291943204496866201.935681639176
Winsorized Mean ( 25 / 26 )5.8891250.0275986113150461213.384830590712
Winsorized Mean ( 26 / 26 )5.8826250.0267996219921858219.504028889484
Trimmed Mean ( 1 / 26 )5.923974358974360.0478698214429649123.751753827462
Trimmed Mean ( 2 / 26 )5.923026315789470.0475032851077644124.686667508420
Trimmed Mean ( 3 / 26 )5.922162162162160.0470842825759232125.777899506331
Trimmed Mean ( 4 / 26 )5.921111111111110.0466564188763061126.908820987932
Trimmed Mean ( 5 / 26 )5.920.0462484961425248128.004162162511
Trimmed Mean ( 6 / 26 )5.918970588235290.0458363599369404129.132649197675
Trimmed Mean ( 7 / 26 )5.918636363636360.0454851528652137130.122380399052
Trimmed Mean ( 8 / 26 )5.917968750.0451651399361431131.029567457715
Trimmed Mean ( 9 / 26 )5.917096774193550.0447830348019146132.128088245162
Trimmed Mean ( 10 / 26 )5.9160.0444661999484227133.044874688237
Trimmed Mean ( 11 / 26 )5.9150.0440852786849898134.171772901006
Trimmed Mean ( 12 / 26 )5.913392857142860.0436940936197809135.336206046526
Trimmed Mean ( 13 / 26 )5.911851851851850.0432203607792574136.783954258177
Trimmed Mean ( 14 / 26 )5.910.042637409840992138.610671287027
Trimmed Mean ( 15 / 26 )5.9080.0419718078364660140.761151461935
Trimmed Mean ( 16 / 26 )5.906666666666670.0413269841840584142.925180321896
Trimmed Mean ( 17 / 26 )5.905217391304350.0404679620765783145.923270861275
Trimmed Mean ( 18 / 26 )5.904545454545450.0395955431128710149.121466466919
Trimmed Mean ( 19 / 26 )5.90476190476190.0388305202461005152.064970217721
Trimmed Mean ( 20 / 26 )5.904750.0378525944983486155.993270164284
Trimmed Mean ( 21 / 26 )5.9050.0365895887997508161.384705149794
Trimmed Mean ( 22 / 26 )5.904444444444440.0351198502284755168.122711402029
Trimmed Mean ( 23 / 26 )5.902647058823530.0334533725136411176.444005949374
Trimmed Mean ( 24 / 26 )5.90343750.0327367597435676180.330538093648
Trimmed Mean ( 25 / 26 )5.904333333333330.0318534118540431185.359526332307
Trimmed Mean ( 26 / 26 )5.906071428571430.0309605453212808190.761221008336
Median5.9
Midrange5.965
Midmean - Weighted Average at Xnp5.89439024390244
Midmean - Weighted Average at X(n+1)p5.89439024390244
Midmean - Empirical Distribution Function5.89439024390244
Midmean - Empirical Distribution Function - Averaging5.89439024390244
Midmean - Empirical Distribution Function - Interpolation5.89439024390244
Midmean - Closest Observation5.89439024390244
Midmean - True Basic - Statistics Graphics Toolkit5.89439024390244
Midmean - MS Excel (old versions)5.9146511627907
Number of observations80



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')