Free Statistics

of Irreproducible Research!

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationTue, 20 Oct 2009 15:44:40 -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/Oct/20/t1256075231f71zwqjyb9r54xd.htm/, Retrieved Thu, 02 May 2024 19:01:26 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=49207, Retrieved Thu, 02 May 2024 19:01:26 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsgemiddelden
Estimated Impact139
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Data Series] [tijdreeks 2: werk...] [2009-10-12 19:58:30] [616e2df490b611f6cb7080068870ecbd]
-   PD  [Univariate Data Series] [Y[t]-X[t]] [2009-10-20 21:41:47] [616e2df490b611f6cb7080068870ecbd]
- RM        [Central Tendency] [Y[t]-X[t] (gemidd...] [2009-10-20 21:44:40] [88e98f4c87ea17c4967db8279bda8533] [Current]
Feedback Forum

Post a new message
Dataseries X:
1.7
1.8
1.8
1.5
1.5
1.9
2.8
3.1
2.8
2.3
1.7
1.6
1.7
1.8
1.7
1.6
1.4
1.9
2.6
2.8
2.6
1.9
1.5
1.4
1.3
1.2
1
0.8
1.1
1.7
2.9
3.4
3.1
2.4
2
1.9
1.9
2
2.2
2.2
2
1.9
1.7
1.5
1.3
1.6
1.7
1.5
1.1
0.8
0.7
0.7
0.7
0.8
1
1.4
1.4
1.8
1.7
1.6
1.2
0.7
0.3
0
-0.2
-0.2
0.1
0.4




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=49207&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' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=49207&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=49207&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' @ 72.249.127.135







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean1.583823529411760.094111302189556816.8292595316731
Geometric MeanNaN
Harmonic Mean0
Quadratic Mean1.76122450718410
Winsorized Mean ( 1 / 22 )1.579411764705880.092936647626403516.9944989952184
Winsorized Mean ( 2 / 22 )1.585294117647060.091333519053696917.357199570018
Winsorized Mean ( 3 / 22 )1.580882352941180.088128959924882317.9382844673154
Winsorized Mean ( 4 / 22 )1.586764705882350.08401430779743818.8868390097090
Winsorized Mean ( 5 / 22 )1.594117647058820.082378022017976919.3512493746323
Winsorized Mean ( 6 / 22 )1.620588235294120.077140477752313621.0082732504922
Winsorized Mean ( 7 / 22 )1.60.072670132793160622.0172984209902
Winsorized Mean ( 8 / 22 )1.60.072670132793160622.0172984209902
Winsorized Mean ( 9 / 22 )1.573529411764710.067522884848835923.3036460940225
Winsorized Mean ( 10 / 22 )1.573529411764710.062104504489369925.3368000389414
Winsorized Mean ( 11 / 22 )1.557352941176470.0593835827943226.2253112374592
Winsorized Mean ( 12 / 22 )1.557352941176470.0593835827943226.2253112374592
Winsorized Mean ( 13 / 22 )1.557352941176470.04644122553974933.5338467724874
Winsorized Mean ( 14 / 22 )1.557352941176470.04644122553974933.5338467724874
Winsorized Mean ( 15 / 22 )1.579411764705880.042608062459124837.0683779911621
Winsorized Mean ( 16 / 22 )1.555882352941180.039330567754384739.5591124607582
Winsorized Mean ( 17 / 22 )1.580882352941180.035137841757270544.9908780357595
Winsorized Mean ( 18 / 22 )1.580882352941180.035137841757270544.9908780357595
Winsorized Mean ( 19 / 22 )1.608823529411760.030773985207858952.2786866421484
Winsorized Mean ( 20 / 22 )1.608823529411760.030773985207858952.2786866421484
Winsorized Mean ( 21 / 22 )1.639705882352940.026347754216424962.2332312987332
Winsorized Mean ( 22 / 22 )1.607352941176470.021805688345200873.7125522354919
Trimmed Mean ( 1 / 22 )1.583333333333330.088856588925601917.8189749626674
Trimmed Mean ( 2 / 22 )1.58750.083911683542404518.9187003881022
Trimmed Mean ( 3 / 22 )1.588709677419350.078964237556305420.1193568960446
Trimmed Mean ( 4 / 22 )1.591666666666670.074496110188015921.365768798526
Trimmed Mean ( 5 / 22 )1.593103448275860.070683383960386722.5385848698004
Trimmed Mean ( 6 / 22 )1.592857142857140.066540542414280323.9381448522021
Trimmed Mean ( 7 / 22 )1.587037037037040.063060002500934525.1670944195335
Trimmed Mean ( 8 / 22 )1.584615384615380.060064358104573526.3819581965153
Trimmed Mean ( 9 / 22 )1.5820.056256700281216428.1210947690122
Trimmed Mean ( 10 / 22 )1.583333333333330.052872566366989229.9462167647281
Trimmed Mean ( 11 / 22 )1.584782608695650.050020999580934331.682345854194
Trimmed Mean ( 12 / 22 )1.588636363636360.047027488373233433.7810165626572
Trimmed Mean ( 13 / 22 )1.592857142857140.043026186168430437.0206445121987
Trimmed Mean ( 14 / 22 )1.59750.041368807151381638.6160518033367
Trimmed Mean ( 15 / 22 )1.602631578947370.039102091656455740.9858273830417
Trimmed Mean ( 16 / 22 )1.605555555555560.037149300757042743.2189980117237
Trimmed Mean ( 17 / 22 )1.611764705882350.035264396279558345.7051552252616
Trimmed Mean ( 18 / 22 )1.6156250.033932266200714247.6132360403914
Trimmed Mean ( 19 / 22 )1.620.031948233991449650.7070281391318
Trimmed Mean ( 20 / 22 )1.621428571428570.030583887092059853.0157780973997
Trimmed Mean ( 21 / 22 )1.623076923076920.028451141552164557.0478664309848
Trimmed Mean ( 22 / 22 )1.620833333333330.026905071087836760.2426705375286
Median1.65
Midrange1.6
Midmean - Weighted Average at Xnp1.59189189189189
Midmean - Weighted Average at X(n+1)p1.62
Midmean - Empirical Distribution Function1.59189189189189
Midmean - Empirical Distribution Function - Averaging1.62
Midmean - Empirical Distribution Function - Interpolation1.62
Midmean - Closest Observation1.59189189189189
Midmean - True Basic - Statistics Graphics Toolkit1.62
Midmean - MS Excel (old versions)1.59189189189189
Number of observations68

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 1.58382352941176 & 0.0941113021895568 & 16.8292595316731 \tabularnewline
Geometric Mean & NaN &  &  \tabularnewline
Harmonic Mean & 0 &  &  \tabularnewline
Quadratic Mean & 1.76122450718410 &  &  \tabularnewline
Winsorized Mean ( 1 / 22 ) & 1.57941176470588 & 0.0929366476264035 & 16.9944989952184 \tabularnewline
Winsorized Mean ( 2 / 22 ) & 1.58529411764706 & 0.0913335190536969 & 17.357199570018 \tabularnewline
Winsorized Mean ( 3 / 22 ) & 1.58088235294118 & 0.0881289599248823 & 17.9382844673154 \tabularnewline
Winsorized Mean ( 4 / 22 ) & 1.58676470588235 & 0.084014307797438 & 18.8868390097090 \tabularnewline
Winsorized Mean ( 5 / 22 ) & 1.59411764705882 & 0.0823780220179769 & 19.3512493746323 \tabularnewline
Winsorized Mean ( 6 / 22 ) & 1.62058823529412 & 0.0771404777523136 & 21.0082732504922 \tabularnewline
Winsorized Mean ( 7 / 22 ) & 1.6 & 0.0726701327931606 & 22.0172984209902 \tabularnewline
Winsorized Mean ( 8 / 22 ) & 1.6 & 0.0726701327931606 & 22.0172984209902 \tabularnewline
Winsorized Mean ( 9 / 22 ) & 1.57352941176471 & 0.0675228848488359 & 23.3036460940225 \tabularnewline
Winsorized Mean ( 10 / 22 ) & 1.57352941176471 & 0.0621045044893699 & 25.3368000389414 \tabularnewline
Winsorized Mean ( 11 / 22 ) & 1.55735294117647 & 0.05938358279432 & 26.2253112374592 \tabularnewline
Winsorized Mean ( 12 / 22 ) & 1.55735294117647 & 0.05938358279432 & 26.2253112374592 \tabularnewline
Winsorized Mean ( 13 / 22 ) & 1.55735294117647 & 0.046441225539749 & 33.5338467724874 \tabularnewline
Winsorized Mean ( 14 / 22 ) & 1.55735294117647 & 0.046441225539749 & 33.5338467724874 \tabularnewline
Winsorized Mean ( 15 / 22 ) & 1.57941176470588 & 0.0426080624591248 & 37.0683779911621 \tabularnewline
Winsorized Mean ( 16 / 22 ) & 1.55588235294118 & 0.0393305677543847 & 39.5591124607582 \tabularnewline
Winsorized Mean ( 17 / 22 ) & 1.58088235294118 & 0.0351378417572705 & 44.9908780357595 \tabularnewline
Winsorized Mean ( 18 / 22 ) & 1.58088235294118 & 0.0351378417572705 & 44.9908780357595 \tabularnewline
Winsorized Mean ( 19 / 22 ) & 1.60882352941176 & 0.0307739852078589 & 52.2786866421484 \tabularnewline
Winsorized Mean ( 20 / 22 ) & 1.60882352941176 & 0.0307739852078589 & 52.2786866421484 \tabularnewline
Winsorized Mean ( 21 / 22 ) & 1.63970588235294 & 0.0263477542164249 & 62.2332312987332 \tabularnewline
Winsorized Mean ( 22 / 22 ) & 1.60735294117647 & 0.0218056883452008 & 73.7125522354919 \tabularnewline
Trimmed Mean ( 1 / 22 ) & 1.58333333333333 & 0.0888565889256019 & 17.8189749626674 \tabularnewline
Trimmed Mean ( 2 / 22 ) & 1.5875 & 0.0839116835424045 & 18.9187003881022 \tabularnewline
Trimmed Mean ( 3 / 22 ) & 1.58870967741935 & 0.0789642375563054 & 20.1193568960446 \tabularnewline
Trimmed Mean ( 4 / 22 ) & 1.59166666666667 & 0.0744961101880159 & 21.365768798526 \tabularnewline
Trimmed Mean ( 5 / 22 ) & 1.59310344827586 & 0.0706833839603867 & 22.5385848698004 \tabularnewline
Trimmed Mean ( 6 / 22 ) & 1.59285714285714 & 0.0665405424142803 & 23.9381448522021 \tabularnewline
Trimmed Mean ( 7 / 22 ) & 1.58703703703704 & 0.0630600025009345 & 25.1670944195335 \tabularnewline
Trimmed Mean ( 8 / 22 ) & 1.58461538461538 & 0.0600643581045735 & 26.3819581965153 \tabularnewline
Trimmed Mean ( 9 / 22 ) & 1.582 & 0.0562567002812164 & 28.1210947690122 \tabularnewline
Trimmed Mean ( 10 / 22 ) & 1.58333333333333 & 0.0528725663669892 & 29.9462167647281 \tabularnewline
Trimmed Mean ( 11 / 22 ) & 1.58478260869565 & 0.0500209995809343 & 31.682345854194 \tabularnewline
Trimmed Mean ( 12 / 22 ) & 1.58863636363636 & 0.0470274883732334 & 33.7810165626572 \tabularnewline
Trimmed Mean ( 13 / 22 ) & 1.59285714285714 & 0.0430261861684304 & 37.0206445121987 \tabularnewline
Trimmed Mean ( 14 / 22 ) & 1.5975 & 0.0413688071513816 & 38.6160518033367 \tabularnewline
Trimmed Mean ( 15 / 22 ) & 1.60263157894737 & 0.0391020916564557 & 40.9858273830417 \tabularnewline
Trimmed Mean ( 16 / 22 ) & 1.60555555555556 & 0.0371493007570427 & 43.2189980117237 \tabularnewline
Trimmed Mean ( 17 / 22 ) & 1.61176470588235 & 0.0352643962795583 & 45.7051552252616 \tabularnewline
Trimmed Mean ( 18 / 22 ) & 1.615625 & 0.0339322662007142 & 47.6132360403914 \tabularnewline
Trimmed Mean ( 19 / 22 ) & 1.62 & 0.0319482339914496 & 50.7070281391318 \tabularnewline
Trimmed Mean ( 20 / 22 ) & 1.62142857142857 & 0.0305838870920598 & 53.0157780973997 \tabularnewline
Trimmed Mean ( 21 / 22 ) & 1.62307692307692 & 0.0284511415521645 & 57.0478664309848 \tabularnewline
Trimmed Mean ( 22 / 22 ) & 1.62083333333333 & 0.0269050710878367 & 60.2426705375286 \tabularnewline
Median & 1.65 &  &  \tabularnewline
Midrange & 1.6 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 1.59189189189189 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 1.62 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 1.59189189189189 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 1.62 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 1.62 &  &  \tabularnewline
Midmean - Closest Observation & 1.59189189189189 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 1.62 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 1.59189189189189 &  &  \tabularnewline
Number of observations & 68 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=49207&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]1.58382352941176[/C][C]0.0941113021895568[/C][C]16.8292595316731[/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]1.76122450718410[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 22 )[/C][C]1.57941176470588[/C][C]0.0929366476264035[/C][C]16.9944989952184[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 22 )[/C][C]1.58529411764706[/C][C]0.0913335190536969[/C][C]17.357199570018[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 22 )[/C][C]1.58088235294118[/C][C]0.0881289599248823[/C][C]17.9382844673154[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 22 )[/C][C]1.58676470588235[/C][C]0.084014307797438[/C][C]18.8868390097090[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 22 )[/C][C]1.59411764705882[/C][C]0.0823780220179769[/C][C]19.3512493746323[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 22 )[/C][C]1.62058823529412[/C][C]0.0771404777523136[/C][C]21.0082732504922[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 22 )[/C][C]1.6[/C][C]0.0726701327931606[/C][C]22.0172984209902[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 22 )[/C][C]1.6[/C][C]0.0726701327931606[/C][C]22.0172984209902[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 22 )[/C][C]1.57352941176471[/C][C]0.0675228848488359[/C][C]23.3036460940225[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 22 )[/C][C]1.57352941176471[/C][C]0.0621045044893699[/C][C]25.3368000389414[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 22 )[/C][C]1.55735294117647[/C][C]0.05938358279432[/C][C]26.2253112374592[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 22 )[/C][C]1.55735294117647[/C][C]0.05938358279432[/C][C]26.2253112374592[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 22 )[/C][C]1.55735294117647[/C][C]0.046441225539749[/C][C]33.5338467724874[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 22 )[/C][C]1.55735294117647[/C][C]0.046441225539749[/C][C]33.5338467724874[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 22 )[/C][C]1.57941176470588[/C][C]0.0426080624591248[/C][C]37.0683779911621[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 22 )[/C][C]1.55588235294118[/C][C]0.0393305677543847[/C][C]39.5591124607582[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 22 )[/C][C]1.58088235294118[/C][C]0.0351378417572705[/C][C]44.9908780357595[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 22 )[/C][C]1.58088235294118[/C][C]0.0351378417572705[/C][C]44.9908780357595[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 22 )[/C][C]1.60882352941176[/C][C]0.0307739852078589[/C][C]52.2786866421484[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 22 )[/C][C]1.60882352941176[/C][C]0.0307739852078589[/C][C]52.2786866421484[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 22 )[/C][C]1.63970588235294[/C][C]0.0263477542164249[/C][C]62.2332312987332[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 22 )[/C][C]1.60735294117647[/C][C]0.0218056883452008[/C][C]73.7125522354919[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 22 )[/C][C]1.58333333333333[/C][C]0.0888565889256019[/C][C]17.8189749626674[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 22 )[/C][C]1.5875[/C][C]0.0839116835424045[/C][C]18.9187003881022[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 22 )[/C][C]1.58870967741935[/C][C]0.0789642375563054[/C][C]20.1193568960446[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 22 )[/C][C]1.59166666666667[/C][C]0.0744961101880159[/C][C]21.365768798526[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 22 )[/C][C]1.59310344827586[/C][C]0.0706833839603867[/C][C]22.5385848698004[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 22 )[/C][C]1.59285714285714[/C][C]0.0665405424142803[/C][C]23.9381448522021[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 22 )[/C][C]1.58703703703704[/C][C]0.0630600025009345[/C][C]25.1670944195335[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 22 )[/C][C]1.58461538461538[/C][C]0.0600643581045735[/C][C]26.3819581965153[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 22 )[/C][C]1.582[/C][C]0.0562567002812164[/C][C]28.1210947690122[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 22 )[/C][C]1.58333333333333[/C][C]0.0528725663669892[/C][C]29.9462167647281[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 22 )[/C][C]1.58478260869565[/C][C]0.0500209995809343[/C][C]31.682345854194[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 22 )[/C][C]1.58863636363636[/C][C]0.0470274883732334[/C][C]33.7810165626572[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 22 )[/C][C]1.59285714285714[/C][C]0.0430261861684304[/C][C]37.0206445121987[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 22 )[/C][C]1.5975[/C][C]0.0413688071513816[/C][C]38.6160518033367[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 22 )[/C][C]1.60263157894737[/C][C]0.0391020916564557[/C][C]40.9858273830417[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 22 )[/C][C]1.60555555555556[/C][C]0.0371493007570427[/C][C]43.2189980117237[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 22 )[/C][C]1.61176470588235[/C][C]0.0352643962795583[/C][C]45.7051552252616[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 22 )[/C][C]1.615625[/C][C]0.0339322662007142[/C][C]47.6132360403914[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 22 )[/C][C]1.62[/C][C]0.0319482339914496[/C][C]50.7070281391318[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 22 )[/C][C]1.62142857142857[/C][C]0.0305838870920598[/C][C]53.0157780973997[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 22 )[/C][C]1.62307692307692[/C][C]0.0284511415521645[/C][C]57.0478664309848[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 22 )[/C][C]1.62083333333333[/C][C]0.0269050710878367[/C][C]60.2426705375286[/C][/ROW]
[ROW][C]Median[/C][C]1.65[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]1.6[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]1.59189189189189[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]1.62[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]1.59189189189189[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]1.62[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]1.62[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]1.59189189189189[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]1.62[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]1.59189189189189[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]68[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=49207&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=49207&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 Mean1.583823529411760.094111302189556816.8292595316731
Geometric MeanNaN
Harmonic Mean0
Quadratic Mean1.76122450718410
Winsorized Mean ( 1 / 22 )1.579411764705880.092936647626403516.9944989952184
Winsorized Mean ( 2 / 22 )1.585294117647060.091333519053696917.357199570018
Winsorized Mean ( 3 / 22 )1.580882352941180.088128959924882317.9382844673154
Winsorized Mean ( 4 / 22 )1.586764705882350.08401430779743818.8868390097090
Winsorized Mean ( 5 / 22 )1.594117647058820.082378022017976919.3512493746323
Winsorized Mean ( 6 / 22 )1.620588235294120.077140477752313621.0082732504922
Winsorized Mean ( 7 / 22 )1.60.072670132793160622.0172984209902
Winsorized Mean ( 8 / 22 )1.60.072670132793160622.0172984209902
Winsorized Mean ( 9 / 22 )1.573529411764710.067522884848835923.3036460940225
Winsorized Mean ( 10 / 22 )1.573529411764710.062104504489369925.3368000389414
Winsorized Mean ( 11 / 22 )1.557352941176470.0593835827943226.2253112374592
Winsorized Mean ( 12 / 22 )1.557352941176470.0593835827943226.2253112374592
Winsorized Mean ( 13 / 22 )1.557352941176470.04644122553974933.5338467724874
Winsorized Mean ( 14 / 22 )1.557352941176470.04644122553974933.5338467724874
Winsorized Mean ( 15 / 22 )1.579411764705880.042608062459124837.0683779911621
Winsorized Mean ( 16 / 22 )1.555882352941180.039330567754384739.5591124607582
Winsorized Mean ( 17 / 22 )1.580882352941180.035137841757270544.9908780357595
Winsorized Mean ( 18 / 22 )1.580882352941180.035137841757270544.9908780357595
Winsorized Mean ( 19 / 22 )1.608823529411760.030773985207858952.2786866421484
Winsorized Mean ( 20 / 22 )1.608823529411760.030773985207858952.2786866421484
Winsorized Mean ( 21 / 22 )1.639705882352940.026347754216424962.2332312987332
Winsorized Mean ( 22 / 22 )1.607352941176470.021805688345200873.7125522354919
Trimmed Mean ( 1 / 22 )1.583333333333330.088856588925601917.8189749626674
Trimmed Mean ( 2 / 22 )1.58750.083911683542404518.9187003881022
Trimmed Mean ( 3 / 22 )1.588709677419350.078964237556305420.1193568960446
Trimmed Mean ( 4 / 22 )1.591666666666670.074496110188015921.365768798526
Trimmed Mean ( 5 / 22 )1.593103448275860.070683383960386722.5385848698004
Trimmed Mean ( 6 / 22 )1.592857142857140.066540542414280323.9381448522021
Trimmed Mean ( 7 / 22 )1.587037037037040.063060002500934525.1670944195335
Trimmed Mean ( 8 / 22 )1.584615384615380.060064358104573526.3819581965153
Trimmed Mean ( 9 / 22 )1.5820.056256700281216428.1210947690122
Trimmed Mean ( 10 / 22 )1.583333333333330.052872566366989229.9462167647281
Trimmed Mean ( 11 / 22 )1.584782608695650.050020999580934331.682345854194
Trimmed Mean ( 12 / 22 )1.588636363636360.047027488373233433.7810165626572
Trimmed Mean ( 13 / 22 )1.592857142857140.043026186168430437.0206445121987
Trimmed Mean ( 14 / 22 )1.59750.041368807151381638.6160518033367
Trimmed Mean ( 15 / 22 )1.602631578947370.039102091656455740.9858273830417
Trimmed Mean ( 16 / 22 )1.605555555555560.037149300757042743.2189980117237
Trimmed Mean ( 17 / 22 )1.611764705882350.035264396279558345.7051552252616
Trimmed Mean ( 18 / 22 )1.6156250.033932266200714247.6132360403914
Trimmed Mean ( 19 / 22 )1.620.031948233991449650.7070281391318
Trimmed Mean ( 20 / 22 )1.621428571428570.030583887092059853.0157780973997
Trimmed Mean ( 21 / 22 )1.623076923076920.028451141552164557.0478664309848
Trimmed Mean ( 22 / 22 )1.620833333333330.026905071087836760.2426705375286
Median1.65
Midrange1.6
Midmean - Weighted Average at Xnp1.59189189189189
Midmean - Weighted Average at X(n+1)p1.62
Midmean - Empirical Distribution Function1.59189189189189
Midmean - Empirical Distribution Function - Averaging1.62
Midmean - Empirical Distribution Function - Interpolation1.62
Midmean - Closest Observation1.59189189189189
Midmean - True Basic - Statistics Graphics Toolkit1.62
Midmean - MS Excel (old versions)1.59189189189189
Number of observations68



Parameters (Session):
par1 = 0 ; par2 = 36 ;
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')