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Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationThu, 18 Dec 2014 12:49:33 +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/2014/Dec/18/t1418906995s3mkf9talsakhy5.htm/, Retrieved Sun, 19 May 2024 19:19:50 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=270872, Retrieved Sun, 19 May 2024 19:19:50 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact63

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [robuustheid decte...] [2014-12-18 12:49:33] [a4db37450d58660d7913ff50f679bb50] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
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1
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Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Sir Ronald Aylmer Fisher' @ fisher.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 & 1 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=270872&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]'Sir Ronald Aylmer Fisher' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=270872&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=270872&T=0

As an alternative you can also use a QR Code:  
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'Sir Ronald Aylmer Fisher' @ fisher.wessa.net






Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean0.4285714285714290.2768729319334451.54789933988364
Geometric MeanNaN
Harmonic Mean0
Quadratic Mean2.22182536138823
Winsorized Mean ( 1 / 21 )0.3968253968253970.2682553316513711.47928242239419
Winsorized Mean ( 2 / 21 )0.3968253968253970.2682553316513711.47928242239419
Winsorized Mean ( 3 / 21 )0.3968253968253970.2682553316513711.47928242239419
Winsorized Mean ( 4 / 21 )0.3968253968253970.2400500060334571.6530947171486
Winsorized Mean ( 5 / 21 )0.3968253968253970.2400500060334571.6530947171486
Winsorized Mean ( 6 / 21 )0.3968253968253970.2400500060334571.6530947171486
Winsorized Mean ( 7 / 21 )0.3968253968253970.2400500060334571.6530947171486
Winsorized Mean ( 8 / 21 )0.5238095238095240.2133020604684192.45571713024815
Winsorized Mean ( 9 / 21 )0.3809523809523810.18989927994222.00607596336507
Winsorized Mean ( 10 / 21 )0.3809523809523810.18989927994222.00607596336507
Winsorized Mean ( 11 / 21 )0.3809523809523810.18989927994222.00607596336507
Winsorized Mean ( 12 / 21 )0.5714285714285710.1546584789702843.6947768737488
Winsorized Mean ( 13 / 21 )0.5714285714285710.1546584789702843.6947768737488
Winsorized Mean ( 14 / 21 )0.5714285714285710.1546584789702843.6947768737488
Winsorized Mean ( 15 / 21 )0.5714285714285710.1546584789702843.6947768737488
Winsorized Mean ( 16 / 21 )0.8253968253968250.1187485576265816.95079453505769
Winsorized Mean ( 17 / 21 )0.8253968253968250.1187485576265816.95079453505769
Winsorized Mean ( 18 / 21 )0.8253968253968250.1187485576265816.95079453505769
Winsorized Mean ( 19 / 21 )0.8253968253968250.1187485576265816.95079453505769
Winsorized Mean ( 20 / 21 )0.8253968253968250.1187485576265816.95079453505769
Winsorized Mean ( 21 / 21 )0.8253968253968250.1187485576265816.95079453505769
Trimmed Mean ( 1 / 21 )0.4098360655737710.2607021301121031.57204724563447
Trimmed Mean ( 2 / 21 )0.4237288135593220.2514753542348751.68497153467995
Trimmed Mean ( 3 / 21 )0.438596491228070.2401147697851031.82661188072938
Trimmed Mean ( 4 / 21 )0.4545454545454550.2259557803916032.01165667794683
Trimmed Mean ( 5 / 21 )0.4716981132075470.2198491592415922.14555340959571
Trimmed Mean ( 6 / 21 )0.4901960784313730.2121275033144872.31085583327042
Trimmed Mean ( 7 / 21 )0.5102040816326530.202288036751012.52216636152659
Trimmed Mean ( 8 / 21 )0.5319148936170210.1895782939507282.8057795147965
Trimmed Mean ( 9 / 21 )0.5333333333333330.1814643020797562.93905372693592
Trimmed Mean ( 10 / 21 )0.5581395348837210.1770382818666213.15264884520411
Trimmed Mean ( 11 / 21 )0.5853658536585370.1709928316715233.42333563305755
Trimmed Mean ( 12 / 21 )0.6153846153846150.1627006582786243.78231177363014
Trimmed Mean ( 13 / 21 )0.6216216216216220.161409665469993.85120444808304
Trimmed Mean ( 14 / 21 )0.6285714285714290.1592298390901113.947573094109
Trimmed Mean ( 15 / 21 )0.6363636363636360.1558103318272964.08421976194105
Trimmed Mean ( 16 / 21 )0.6451612903225810.1506144197410164.28352936878119
Trimmed Mean ( 17 / 21 )0.6206896551724140.1522717390746184.07619732292054
Trimmed Mean ( 18 / 21 )0.5925925925925930.1533970441706193.86312914826097
Trimmed Mean ( 19 / 21 )0.560.1536229149573723.64528950746307
Trimmed Mean ( 20 / 21 )0.5217391304347830.1523150108142113.4253953543107
Trimmed Mean ( 21 / 21 )0.4761904761904760.1483086809752143.21080649533968
Median0
Midrange1
Midmean - Weighted Average at Xnp0.714285714285714
Midmean - Weighted Average at X(n+1)p0.714285714285714
Midmean - Empirical Distribution Function0.714285714285714
Midmean - Empirical Distribution Function - Averaging0.714285714285714
Midmean - Empirical Distribution Function - Interpolation0.894736842105263
Midmean - Closest Observation0.714285714285714
Midmean - True Basic - Statistics Graphics Toolkit0.714285714285714
Midmean - MS Excel (old versions)0.714285714285714
Number of observations63

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 0.428571428571429 & 0.276872931933445 & 1.54789933988364 \tabularnewline
Geometric Mean & NaN &  &  \tabularnewline
Harmonic Mean & 0 &  &  \tabularnewline
Quadratic Mean & 2.22182536138823 &  &  \tabularnewline
Winsorized Mean ( 1 / 21 ) & 0.396825396825397 & 0.268255331651371 & 1.47928242239419 \tabularnewline
Winsorized Mean ( 2 / 21 ) & 0.396825396825397 & 0.268255331651371 & 1.47928242239419 \tabularnewline
Winsorized Mean ( 3 / 21 ) & 0.396825396825397 & 0.268255331651371 & 1.47928242239419 \tabularnewline
Winsorized Mean ( 4 / 21 ) & 0.396825396825397 & 0.240050006033457 & 1.6530947171486 \tabularnewline
Winsorized Mean ( 5 / 21 ) & 0.396825396825397 & 0.240050006033457 & 1.6530947171486 \tabularnewline
Winsorized Mean ( 6 / 21 ) & 0.396825396825397 & 0.240050006033457 & 1.6530947171486 \tabularnewline
Winsorized Mean ( 7 / 21 ) & 0.396825396825397 & 0.240050006033457 & 1.6530947171486 \tabularnewline
Winsorized Mean ( 8 / 21 ) & 0.523809523809524 & 0.213302060468419 & 2.45571713024815 \tabularnewline
Winsorized Mean ( 9 / 21 ) & 0.380952380952381 & 0.1898992799422 & 2.00607596336507 \tabularnewline
Winsorized Mean ( 10 / 21 ) & 0.380952380952381 & 0.1898992799422 & 2.00607596336507 \tabularnewline
Winsorized Mean ( 11 / 21 ) & 0.380952380952381 & 0.1898992799422 & 2.00607596336507 \tabularnewline
Winsorized Mean ( 12 / 21 ) & 0.571428571428571 & 0.154658478970284 & 3.6947768737488 \tabularnewline
Winsorized Mean ( 13 / 21 ) & 0.571428571428571 & 0.154658478970284 & 3.6947768737488 \tabularnewline
Winsorized Mean ( 14 / 21 ) & 0.571428571428571 & 0.154658478970284 & 3.6947768737488 \tabularnewline
Winsorized Mean ( 15 / 21 ) & 0.571428571428571 & 0.154658478970284 & 3.6947768737488 \tabularnewline
Winsorized Mean ( 16 / 21 ) & 0.825396825396825 & 0.118748557626581 & 6.95079453505769 \tabularnewline
Winsorized Mean ( 17 / 21 ) & 0.825396825396825 & 0.118748557626581 & 6.95079453505769 \tabularnewline
Winsorized Mean ( 18 / 21 ) & 0.825396825396825 & 0.118748557626581 & 6.95079453505769 \tabularnewline
Winsorized Mean ( 19 / 21 ) & 0.825396825396825 & 0.118748557626581 & 6.95079453505769 \tabularnewline
Winsorized Mean ( 20 / 21 ) & 0.825396825396825 & 0.118748557626581 & 6.95079453505769 \tabularnewline
Winsorized Mean ( 21 / 21 ) & 0.825396825396825 & 0.118748557626581 & 6.95079453505769 \tabularnewline
Trimmed Mean ( 1 / 21 ) & 0.409836065573771 & 0.260702130112103 & 1.57204724563447 \tabularnewline
Trimmed Mean ( 2 / 21 ) & 0.423728813559322 & 0.251475354234875 & 1.68497153467995 \tabularnewline
Trimmed Mean ( 3 / 21 ) & 0.43859649122807 & 0.240114769785103 & 1.82661188072938 \tabularnewline
Trimmed Mean ( 4 / 21 ) & 0.454545454545455 & 0.225955780391603 & 2.01165667794683 \tabularnewline
Trimmed Mean ( 5 / 21 ) & 0.471698113207547 & 0.219849159241592 & 2.14555340959571 \tabularnewline
Trimmed Mean ( 6 / 21 ) & 0.490196078431373 & 0.212127503314487 & 2.31085583327042 \tabularnewline
Trimmed Mean ( 7 / 21 ) & 0.510204081632653 & 0.20228803675101 & 2.52216636152659 \tabularnewline
Trimmed Mean ( 8 / 21 ) & 0.531914893617021 & 0.189578293950728 & 2.8057795147965 \tabularnewline
Trimmed Mean ( 9 / 21 ) & 0.533333333333333 & 0.181464302079756 & 2.93905372693592 \tabularnewline
Trimmed Mean ( 10 / 21 ) & 0.558139534883721 & 0.177038281866621 & 3.15264884520411 \tabularnewline
Trimmed Mean ( 11 / 21 ) & 0.585365853658537 & 0.170992831671523 & 3.42333563305755 \tabularnewline
Trimmed Mean ( 12 / 21 ) & 0.615384615384615 & 0.162700658278624 & 3.78231177363014 \tabularnewline
Trimmed Mean ( 13 / 21 ) & 0.621621621621622 & 0.16140966546999 & 3.85120444808304 \tabularnewline
Trimmed Mean ( 14 / 21 ) & 0.628571428571429 & 0.159229839090111 & 3.947573094109 \tabularnewline
Trimmed Mean ( 15 / 21 ) & 0.636363636363636 & 0.155810331827296 & 4.08421976194105 \tabularnewline
Trimmed Mean ( 16 / 21 ) & 0.645161290322581 & 0.150614419741016 & 4.28352936878119 \tabularnewline
Trimmed Mean ( 17 / 21 ) & 0.620689655172414 & 0.152271739074618 & 4.07619732292054 \tabularnewline
Trimmed Mean ( 18 / 21 ) & 0.592592592592593 & 0.153397044170619 & 3.86312914826097 \tabularnewline
Trimmed Mean ( 19 / 21 ) & 0.56 & 0.153622914957372 & 3.64528950746307 \tabularnewline
Trimmed Mean ( 20 / 21 ) & 0.521739130434783 & 0.152315010814211 & 3.4253953543107 \tabularnewline
Trimmed Mean ( 21 / 21 ) & 0.476190476190476 & 0.148308680975214 & 3.21080649533968 \tabularnewline
Median & 0 &  &  \tabularnewline
Midrange & 1 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 0.714285714285714 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 0.714285714285714 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 0.714285714285714 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 0.714285714285714 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 0.894736842105263 &  &  \tabularnewline
Midmean - Closest Observation & 0.714285714285714 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 0.714285714285714 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 0.714285714285714 &  &  \tabularnewline
Number of observations & 63 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=270872&T=1

[TABLE]
[ROW][C]Central Tendency - Ungrouped Data[/C][/ROW]
[ROW][C]Measure[/C][C]Value[/C][C]S.E.[/C][C]Value/S.E.[/C][/ROW]
[ROW][C]Arithmetic Mean[/C][C]0.428571428571429[/C][C]0.276872931933445[/C][C]1.54789933988364[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]NaN[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]0[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]2.22182536138823[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 21 )[/C][C]0.396825396825397[/C][C]0.268255331651371[/C][C]1.47928242239419[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 21 )[/C][C]0.396825396825397[/C][C]0.268255331651371[/C][C]1.47928242239419[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 21 )[/C][C]0.396825396825397[/C][C]0.268255331651371[/C][C]1.47928242239419[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 21 )[/C][C]0.396825396825397[/C][C]0.240050006033457[/C][C]1.6530947171486[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 21 )[/C][C]0.396825396825397[/C][C]0.240050006033457[/C][C]1.6530947171486[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 21 )[/C][C]0.396825396825397[/C][C]0.240050006033457[/C][C]1.6530947171486[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 21 )[/C][C]0.396825396825397[/C][C]0.240050006033457[/C][C]1.6530947171486[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 21 )[/C][C]0.523809523809524[/C][C]0.213302060468419[/C][C]2.45571713024815[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 21 )[/C][C]0.380952380952381[/C][C]0.1898992799422[/C][C]2.00607596336507[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 21 )[/C][C]0.380952380952381[/C][C]0.1898992799422[/C][C]2.00607596336507[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 21 )[/C][C]0.380952380952381[/C][C]0.1898992799422[/C][C]2.00607596336507[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 21 )[/C][C]0.571428571428571[/C][C]0.154658478970284[/C][C]3.6947768737488[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 21 )[/C][C]0.571428571428571[/C][C]0.154658478970284[/C][C]3.6947768737488[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 21 )[/C][C]0.571428571428571[/C][C]0.154658478970284[/C][C]3.6947768737488[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 21 )[/C][C]0.571428571428571[/C][C]0.154658478970284[/C][C]3.6947768737488[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 21 )[/C][C]0.825396825396825[/C][C]0.118748557626581[/C][C]6.95079453505769[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 21 )[/C][C]0.825396825396825[/C][C]0.118748557626581[/C][C]6.95079453505769[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 21 )[/C][C]0.825396825396825[/C][C]0.118748557626581[/C][C]6.95079453505769[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 21 )[/C][C]0.825396825396825[/C][C]0.118748557626581[/C][C]6.95079453505769[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 21 )[/C][C]0.825396825396825[/C][C]0.118748557626581[/C][C]6.95079453505769[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 21 )[/C][C]0.825396825396825[/C][C]0.118748557626581[/C][C]6.95079453505769[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 21 )[/C][C]0.409836065573771[/C][C]0.260702130112103[/C][C]1.57204724563447[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 21 )[/C][C]0.423728813559322[/C][C]0.251475354234875[/C][C]1.68497153467995[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 21 )[/C][C]0.43859649122807[/C][C]0.240114769785103[/C][C]1.82661188072938[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 21 )[/C][C]0.454545454545455[/C][C]0.225955780391603[/C][C]2.01165667794683[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 21 )[/C][C]0.471698113207547[/C][C]0.219849159241592[/C][C]2.14555340959571[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 21 )[/C][C]0.490196078431373[/C][C]0.212127503314487[/C][C]2.31085583327042[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 21 )[/C][C]0.510204081632653[/C][C]0.20228803675101[/C][C]2.52216636152659[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 21 )[/C][C]0.531914893617021[/C][C]0.189578293950728[/C][C]2.8057795147965[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 21 )[/C][C]0.533333333333333[/C][C]0.181464302079756[/C][C]2.93905372693592[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 21 )[/C][C]0.558139534883721[/C][C]0.177038281866621[/C][C]3.15264884520411[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 21 )[/C][C]0.585365853658537[/C][C]0.170992831671523[/C][C]3.42333563305755[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 21 )[/C][C]0.615384615384615[/C][C]0.162700658278624[/C][C]3.78231177363014[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 21 )[/C][C]0.621621621621622[/C][C]0.16140966546999[/C][C]3.85120444808304[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 21 )[/C][C]0.628571428571429[/C][C]0.159229839090111[/C][C]3.947573094109[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 21 )[/C][C]0.636363636363636[/C][C]0.155810331827296[/C][C]4.08421976194105[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 21 )[/C][C]0.645161290322581[/C][C]0.150614419741016[/C][C]4.28352936878119[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 21 )[/C][C]0.620689655172414[/C][C]0.152271739074618[/C][C]4.07619732292054[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 21 )[/C][C]0.592592592592593[/C][C]0.153397044170619[/C][C]3.86312914826097[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 21 )[/C][C]0.56[/C][C]0.153622914957372[/C][C]3.64528950746307[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 21 )[/C][C]0.521739130434783[/C][C]0.152315010814211[/C][C]3.4253953543107[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 21 )[/C][C]0.476190476190476[/C][C]0.148308680975214[/C][C]3.21080649533968[/C][/ROW]
[ROW][C]Median[/C][C]0[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]1[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]0.714285714285714[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]0.714285714285714[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]0.714285714285714[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]0.714285714285714[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]0.894736842105263[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]0.714285714285714[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]0.714285714285714[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]0.714285714285714[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]63[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=270872&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=270872&T=1

As an alternative you can also use a QR Code:  
QR Code


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

Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean0.4285714285714290.2768729319334451.54789933988364
Geometric MeanNaN
Harmonic Mean0
Quadratic Mean2.22182536138823
Winsorized Mean ( 1 / 21 )0.3968253968253970.2682553316513711.47928242239419
Winsorized Mean ( 2 / 21 )0.3968253968253970.2682553316513711.47928242239419
Winsorized Mean ( 3 / 21 )0.3968253968253970.2682553316513711.47928242239419
Winsorized Mean ( 4 / 21 )0.3968253968253970.2400500060334571.6530947171486
Winsorized Mean ( 5 / 21 )0.3968253968253970.2400500060334571.6530947171486
Winsorized Mean ( 6 / 21 )0.3968253968253970.2400500060334571.6530947171486
Winsorized Mean ( 7 / 21 )0.3968253968253970.2400500060334571.6530947171486
Winsorized Mean ( 8 / 21 )0.5238095238095240.2133020604684192.45571713024815
Winsorized Mean ( 9 / 21 )0.3809523809523810.18989927994222.00607596336507
Winsorized Mean ( 10 / 21 )0.3809523809523810.18989927994222.00607596336507
Winsorized Mean ( 11 / 21 )0.3809523809523810.18989927994222.00607596336507
Winsorized Mean ( 12 / 21 )0.5714285714285710.1546584789702843.6947768737488
Winsorized Mean ( 13 / 21 )0.5714285714285710.1546584789702843.6947768737488
Winsorized Mean ( 14 / 21 )0.5714285714285710.1546584789702843.6947768737488
Winsorized Mean ( 15 / 21 )0.5714285714285710.1546584789702843.6947768737488
Winsorized Mean ( 16 / 21 )0.8253968253968250.1187485576265816.95079453505769
Winsorized Mean ( 17 / 21 )0.8253968253968250.1187485576265816.95079453505769
Winsorized Mean ( 18 / 21 )0.8253968253968250.1187485576265816.95079453505769
Winsorized Mean ( 19 / 21 )0.8253968253968250.1187485576265816.95079453505769
Winsorized Mean ( 20 / 21 )0.8253968253968250.1187485576265816.95079453505769
Winsorized Mean ( 21 / 21 )0.8253968253968250.1187485576265816.95079453505769
Trimmed Mean ( 1 / 21 )0.4098360655737710.2607021301121031.57204724563447
Trimmed Mean ( 2 / 21 )0.4237288135593220.2514753542348751.68497153467995
Trimmed Mean ( 3 / 21 )0.438596491228070.2401147697851031.82661188072938
Trimmed Mean ( 4 / 21 )0.4545454545454550.2259557803916032.01165667794683
Trimmed Mean ( 5 / 21 )0.4716981132075470.2198491592415922.14555340959571
Trimmed Mean ( 6 / 21 )0.4901960784313730.2121275033144872.31085583327042
Trimmed Mean ( 7 / 21 )0.5102040816326530.202288036751012.52216636152659
Trimmed Mean ( 8 / 21 )0.5319148936170210.1895782939507282.8057795147965
Trimmed Mean ( 9 / 21 )0.5333333333333330.1814643020797562.93905372693592
Trimmed Mean ( 10 / 21 )0.5581395348837210.1770382818666213.15264884520411
Trimmed Mean ( 11 / 21 )0.5853658536585370.1709928316715233.42333563305755
Trimmed Mean ( 12 / 21 )0.6153846153846150.1627006582786243.78231177363014
Trimmed Mean ( 13 / 21 )0.6216216216216220.161409665469993.85120444808304
Trimmed Mean ( 14 / 21 )0.6285714285714290.1592298390901113.947573094109
Trimmed Mean ( 15 / 21 )0.6363636363636360.1558103318272964.08421976194105
Trimmed Mean ( 16 / 21 )0.6451612903225810.1506144197410164.28352936878119
Trimmed Mean ( 17 / 21 )0.6206896551724140.1522717390746184.07619732292054
Trimmed Mean ( 18 / 21 )0.5925925925925930.1533970441706193.86312914826097
Trimmed Mean ( 19 / 21 )0.560.1536229149573723.64528950746307
Trimmed Mean ( 20 / 21 )0.5217391304347830.1523150108142113.4253953543107
Trimmed Mean ( 21 / 21 )0.4761904761904760.1483086809752143.21080649533968
Median0
Midrange1
Midmean - Weighted Average at Xnp0.714285714285714
Midmean - Weighted Average at X(n+1)p0.714285714285714
Midmean - Empirical Distribution Function0.714285714285714
Midmean - Empirical Distribution Function - Averaging0.714285714285714
Midmean - Empirical Distribution Function - Interpolation0.894736842105263
Midmean - Closest Observation0.714285714285714
Midmean - True Basic - Statistics Graphics Toolkit0.714285714285714
Midmean - MS Excel (old versions)0.714285714285714
Number of observations63


Figures (Output of Computation)

Input Parameters & R Code

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')