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 computationMon, 15 Nov 2010 20:01:37 +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/2010/Nov/15/t12898512426iv9aax9p550qja.htm/, Retrieved Sun, 28 Apr 2024 00:12:19 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=95038, Retrieved Sun, 28 Apr 2024 00:12:19 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact133
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Central Tendency] [Arabica Price in ...] [2008-01-06 21:28:17] [74be16979710d4c4e7c6647856088456]
-  M D    [Central Tendency] [Analyse 2] [2010-11-15 20:01:37] [214713b86cef2e1efaaf6d85aa84ff3c] [Current]
Feedback Forum

Post a new message
Dataseries X:
1,35
1,33
1,33
1,35
1,33
1,32
1,34
1,32
1,34
1,37
1,36
1,32
1,35
1,32
1,35
1,33
1,33
1,34
1,34
1,33
1,32
1,35
1,33
1,29
1,31
1,29
1,30
1,32
1,29
1,29
1,31
1,29
1,28
1,31
1,30
1,26
1,27
1,28
1,27
1,27
1,26
1,27
1,28
1,27
1,28
1,26
1,26
1,27
1,26
1,25
1,27
1,25
1,24
1,27
1,26




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' @ 193.190.124.24

\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' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=95038&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' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=95038&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=95038&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'Sir Ronald Aylmer Fisher' @ 193.190.124.24







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean1.302363636363640.00462727702698034281.453569511815
Geometric Mean1.30191999622994
Harmonic Mean1.30147672515245
Quadratic Mean1.30280745804101
Winsorized Mean ( 1 / 18 )1.302363636363640.00453912016544387286.919841047275
Winsorized Mean ( 2 / 18 )1.3020.00446007352991584291.923438317074
Winsorized Mean ( 3 / 18 )1.302545454545450.0043516952215071299.319090203737
Winsorized Mean ( 4 / 18 )1.302545454545450.0043516952215071299.319090203737
Winsorized Mean ( 5 / 18 )1.302545454545450.0043516952215071299.319090203737
Winsorized Mean ( 6 / 18 )1.302545454545450.0043516952215071299.319090203737
Winsorized Mean ( 7 / 18 )1.301272727272730.00411169429760277316.480903755760
Winsorized Mean ( 8 / 18 )1.301272727272730.00411169429760277316.480903755760
Winsorized Mean ( 9 / 18 )1.302909090909090.00382858931104416340.310486463160
Winsorized Mean ( 10 / 18 )1.302909090909090.00382858931104416340.310486463160
Winsorized Mean ( 11 / 18 )1.300909090909090.00349383995933745372.343640821999
Winsorized Mean ( 12 / 18 )1.300909090909090.00349383995933745372.343640821999
Winsorized Mean ( 13 / 18 )1.300909090909090.00349383995933745372.343640821999
Winsorized Mean ( 14 / 18 )1.300909090909090.00349383995933745372.343640821999
Winsorized Mean ( 15 / 18 )1.300909090909090.00349383995933745372.343640821999
Winsorized Mean ( 16 / 18 )1.300909090909090.00349383995933745372.343640821999
Winsorized Mean ( 17 / 18 )1.3040.00301064329736571433.13002278981
Winsorized Mean ( 18 / 18 )1.300727272727270.00251399510959757517.394511931046
Trimmed Mean ( 1 / 18 )1.302264150943400.00447247272721066291.17318994935
Trimmed Mean ( 2 / 18 )1.302156862745100.00438637574716411296.86395735408
Trimmed Mean ( 3 / 18 )1.302244897959180.00432782197388285300.900754656234
Trimmed Mean ( 4 / 18 )1.302127659574470.00430063749994101302.775497723844
Trimmed Mean ( 5 / 18 )1.3020.00425927389837918305.68590587599
Trimmed Mean ( 6 / 18 )1.301860465116280.00419955982972008309.999266090479
Trimmed Mean ( 7 / 18 )1.301860465116280.00411574073919176316.312554073057
Trimmed Mean ( 8 / 18 )1.301794871794870.00407208652249262319.687429185079
Trimmed Mean ( 9 / 18 )1.301891891891890.0040052112794544325.049492038092
Trimmed Mean ( 10 / 18 )1.301714285714290.00398496574399233326.656330152080
Trimmed Mean ( 11 / 18 )1.301515151515150.00394376214691527330.018673294780
Trimmed Mean ( 12 / 18 )1.301612903225810.00396481227622562328.291180652039
Trimmed Mean ( 13 / 18 )1.301724137931030.00397247194812385327.686174988806
Trimmed Mean ( 14 / 18 )1.301724137931030.00395980650182801328.734279649802
Trimmed Mean ( 15 / 18 )1.301851851851850.00391578004149025332.462967290778
Trimmed Mean ( 16 / 18 )1.302173913043480.00382195249126754340.709078937718
Trimmed Mean ( 17 / 18 )1.302380952380950.00364526842076279357.279849396776
Trimmed Mean ( 18 / 18 )1.302105263157890.00355236083005554366.546453316662
Median1.3
Midrange1.305
Midmean - Weighted Average at Xnp1.29971428571429
Midmean - Weighted Average at X(n+1)p1.29971428571429
Midmean - Empirical Distribution Function1.29971428571429
Midmean - Empirical Distribution Function - Averaging1.29971428571429
Midmean - Empirical Distribution Function - Interpolation1.29971428571429
Midmean - Closest Observation1.29971428571429
Midmean - True Basic - Statistics Graphics Toolkit1.29971428571429
Midmean - MS Excel (old versions)1.29971428571429
Number of observations55

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 1.30236363636364 & 0.00462727702698034 & 281.453569511815 \tabularnewline
Geometric Mean & 1.30191999622994 &  &  \tabularnewline
Harmonic Mean & 1.30147672515245 &  &  \tabularnewline
Quadratic Mean & 1.30280745804101 &  &  \tabularnewline
Winsorized Mean ( 1 / 18 ) & 1.30236363636364 & 0.00453912016544387 & 286.919841047275 \tabularnewline
Winsorized Mean ( 2 / 18 ) & 1.302 & 0.00446007352991584 & 291.923438317074 \tabularnewline
Winsorized Mean ( 3 / 18 ) & 1.30254545454545 & 0.0043516952215071 & 299.319090203737 \tabularnewline
Winsorized Mean ( 4 / 18 ) & 1.30254545454545 & 0.0043516952215071 & 299.319090203737 \tabularnewline
Winsorized Mean ( 5 / 18 ) & 1.30254545454545 & 0.0043516952215071 & 299.319090203737 \tabularnewline
Winsorized Mean ( 6 / 18 ) & 1.30254545454545 & 0.0043516952215071 & 299.319090203737 \tabularnewline
Winsorized Mean ( 7 / 18 ) & 1.30127272727273 & 0.00411169429760277 & 316.480903755760 \tabularnewline
Winsorized Mean ( 8 / 18 ) & 1.30127272727273 & 0.00411169429760277 & 316.480903755760 \tabularnewline
Winsorized Mean ( 9 / 18 ) & 1.30290909090909 & 0.00382858931104416 & 340.310486463160 \tabularnewline
Winsorized Mean ( 10 / 18 ) & 1.30290909090909 & 0.00382858931104416 & 340.310486463160 \tabularnewline
Winsorized Mean ( 11 / 18 ) & 1.30090909090909 & 0.00349383995933745 & 372.343640821999 \tabularnewline
Winsorized Mean ( 12 / 18 ) & 1.30090909090909 & 0.00349383995933745 & 372.343640821999 \tabularnewline
Winsorized Mean ( 13 / 18 ) & 1.30090909090909 & 0.00349383995933745 & 372.343640821999 \tabularnewline
Winsorized Mean ( 14 / 18 ) & 1.30090909090909 & 0.00349383995933745 & 372.343640821999 \tabularnewline
Winsorized Mean ( 15 / 18 ) & 1.30090909090909 & 0.00349383995933745 & 372.343640821999 \tabularnewline
Winsorized Mean ( 16 / 18 ) & 1.30090909090909 & 0.00349383995933745 & 372.343640821999 \tabularnewline
Winsorized Mean ( 17 / 18 ) & 1.304 & 0.00301064329736571 & 433.13002278981 \tabularnewline
Winsorized Mean ( 18 / 18 ) & 1.30072727272727 & 0.00251399510959757 & 517.394511931046 \tabularnewline
Trimmed Mean ( 1 / 18 ) & 1.30226415094340 & 0.00447247272721066 & 291.17318994935 \tabularnewline
Trimmed Mean ( 2 / 18 ) & 1.30215686274510 & 0.00438637574716411 & 296.86395735408 \tabularnewline
Trimmed Mean ( 3 / 18 ) & 1.30224489795918 & 0.00432782197388285 & 300.900754656234 \tabularnewline
Trimmed Mean ( 4 / 18 ) & 1.30212765957447 & 0.00430063749994101 & 302.775497723844 \tabularnewline
Trimmed Mean ( 5 / 18 ) & 1.302 & 0.00425927389837918 & 305.68590587599 \tabularnewline
Trimmed Mean ( 6 / 18 ) & 1.30186046511628 & 0.00419955982972008 & 309.999266090479 \tabularnewline
Trimmed Mean ( 7 / 18 ) & 1.30186046511628 & 0.00411574073919176 & 316.312554073057 \tabularnewline
Trimmed Mean ( 8 / 18 ) & 1.30179487179487 & 0.00407208652249262 & 319.687429185079 \tabularnewline
Trimmed Mean ( 9 / 18 ) & 1.30189189189189 & 0.0040052112794544 & 325.049492038092 \tabularnewline
Trimmed Mean ( 10 / 18 ) & 1.30171428571429 & 0.00398496574399233 & 326.656330152080 \tabularnewline
Trimmed Mean ( 11 / 18 ) & 1.30151515151515 & 0.00394376214691527 & 330.018673294780 \tabularnewline
Trimmed Mean ( 12 / 18 ) & 1.30161290322581 & 0.00396481227622562 & 328.291180652039 \tabularnewline
Trimmed Mean ( 13 / 18 ) & 1.30172413793103 & 0.00397247194812385 & 327.686174988806 \tabularnewline
Trimmed Mean ( 14 / 18 ) & 1.30172413793103 & 0.00395980650182801 & 328.734279649802 \tabularnewline
Trimmed Mean ( 15 / 18 ) & 1.30185185185185 & 0.00391578004149025 & 332.462967290778 \tabularnewline
Trimmed Mean ( 16 / 18 ) & 1.30217391304348 & 0.00382195249126754 & 340.709078937718 \tabularnewline
Trimmed Mean ( 17 / 18 ) & 1.30238095238095 & 0.00364526842076279 & 357.279849396776 \tabularnewline
Trimmed Mean ( 18 / 18 ) & 1.30210526315789 & 0.00355236083005554 & 366.546453316662 \tabularnewline
Median & 1.3 &  &  \tabularnewline
Midrange & 1.305 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 1.29971428571429 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 1.29971428571429 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 1.29971428571429 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 1.29971428571429 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 1.29971428571429 &  &  \tabularnewline
Midmean - Closest Observation & 1.29971428571429 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 1.29971428571429 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 1.29971428571429 &  &  \tabularnewline
Number of observations & 55 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=95038&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]1.30236363636364[/C][C]0.00462727702698034[/C][C]281.453569511815[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]1.30191999622994[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]1.30147672515245[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]1.30280745804101[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 18 )[/C][C]1.30236363636364[/C][C]0.00453912016544387[/C][C]286.919841047275[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 18 )[/C][C]1.302[/C][C]0.00446007352991584[/C][C]291.923438317074[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 18 )[/C][C]1.30254545454545[/C][C]0.0043516952215071[/C][C]299.319090203737[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 18 )[/C][C]1.30254545454545[/C][C]0.0043516952215071[/C][C]299.319090203737[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 18 )[/C][C]1.30254545454545[/C][C]0.0043516952215071[/C][C]299.319090203737[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 18 )[/C][C]1.30254545454545[/C][C]0.0043516952215071[/C][C]299.319090203737[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 18 )[/C][C]1.30127272727273[/C][C]0.00411169429760277[/C][C]316.480903755760[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 18 )[/C][C]1.30127272727273[/C][C]0.00411169429760277[/C][C]316.480903755760[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 18 )[/C][C]1.30290909090909[/C][C]0.00382858931104416[/C][C]340.310486463160[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 18 )[/C][C]1.30290909090909[/C][C]0.00382858931104416[/C][C]340.310486463160[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 18 )[/C][C]1.30090909090909[/C][C]0.00349383995933745[/C][C]372.343640821999[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 18 )[/C][C]1.30090909090909[/C][C]0.00349383995933745[/C][C]372.343640821999[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 18 )[/C][C]1.30090909090909[/C][C]0.00349383995933745[/C][C]372.343640821999[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 18 )[/C][C]1.30090909090909[/C][C]0.00349383995933745[/C][C]372.343640821999[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 18 )[/C][C]1.30090909090909[/C][C]0.00349383995933745[/C][C]372.343640821999[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 18 )[/C][C]1.30090909090909[/C][C]0.00349383995933745[/C][C]372.343640821999[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 18 )[/C][C]1.304[/C][C]0.00301064329736571[/C][C]433.13002278981[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 18 )[/C][C]1.30072727272727[/C][C]0.00251399510959757[/C][C]517.394511931046[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 18 )[/C][C]1.30226415094340[/C][C]0.00447247272721066[/C][C]291.17318994935[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 18 )[/C][C]1.30215686274510[/C][C]0.00438637574716411[/C][C]296.86395735408[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 18 )[/C][C]1.30224489795918[/C][C]0.00432782197388285[/C][C]300.900754656234[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 18 )[/C][C]1.30212765957447[/C][C]0.00430063749994101[/C][C]302.775497723844[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 18 )[/C][C]1.302[/C][C]0.00425927389837918[/C][C]305.68590587599[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 18 )[/C][C]1.30186046511628[/C][C]0.00419955982972008[/C][C]309.999266090479[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 18 )[/C][C]1.30186046511628[/C][C]0.00411574073919176[/C][C]316.312554073057[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 18 )[/C][C]1.30179487179487[/C][C]0.00407208652249262[/C][C]319.687429185079[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 18 )[/C][C]1.30189189189189[/C][C]0.0040052112794544[/C][C]325.049492038092[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 18 )[/C][C]1.30171428571429[/C][C]0.00398496574399233[/C][C]326.656330152080[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 18 )[/C][C]1.30151515151515[/C][C]0.00394376214691527[/C][C]330.018673294780[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 18 )[/C][C]1.30161290322581[/C][C]0.00396481227622562[/C][C]328.291180652039[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 18 )[/C][C]1.30172413793103[/C][C]0.00397247194812385[/C][C]327.686174988806[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 18 )[/C][C]1.30172413793103[/C][C]0.00395980650182801[/C][C]328.734279649802[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 18 )[/C][C]1.30185185185185[/C][C]0.00391578004149025[/C][C]332.462967290778[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 18 )[/C][C]1.30217391304348[/C][C]0.00382195249126754[/C][C]340.709078937718[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 18 )[/C][C]1.30238095238095[/C][C]0.00364526842076279[/C][C]357.279849396776[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 18 )[/C][C]1.30210526315789[/C][C]0.00355236083005554[/C][C]366.546453316662[/C][/ROW]
[ROW][C]Median[/C][C]1.3[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]1.305[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]1.29971428571429[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]1.29971428571429[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]1.29971428571429[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]1.29971428571429[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]1.29971428571429[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]1.29971428571429[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]1.29971428571429[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]1.29971428571429[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]55[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=95038&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=95038&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 Mean1.302363636363640.00462727702698034281.453569511815
Geometric Mean1.30191999622994
Harmonic Mean1.30147672515245
Quadratic Mean1.30280745804101
Winsorized Mean ( 1 / 18 )1.302363636363640.00453912016544387286.919841047275
Winsorized Mean ( 2 / 18 )1.3020.00446007352991584291.923438317074
Winsorized Mean ( 3 / 18 )1.302545454545450.0043516952215071299.319090203737
Winsorized Mean ( 4 / 18 )1.302545454545450.0043516952215071299.319090203737
Winsorized Mean ( 5 / 18 )1.302545454545450.0043516952215071299.319090203737
Winsorized Mean ( 6 / 18 )1.302545454545450.0043516952215071299.319090203737
Winsorized Mean ( 7 / 18 )1.301272727272730.00411169429760277316.480903755760
Winsorized Mean ( 8 / 18 )1.301272727272730.00411169429760277316.480903755760
Winsorized Mean ( 9 / 18 )1.302909090909090.00382858931104416340.310486463160
Winsorized Mean ( 10 / 18 )1.302909090909090.00382858931104416340.310486463160
Winsorized Mean ( 11 / 18 )1.300909090909090.00349383995933745372.343640821999
Winsorized Mean ( 12 / 18 )1.300909090909090.00349383995933745372.343640821999
Winsorized Mean ( 13 / 18 )1.300909090909090.00349383995933745372.343640821999
Winsorized Mean ( 14 / 18 )1.300909090909090.00349383995933745372.343640821999
Winsorized Mean ( 15 / 18 )1.300909090909090.00349383995933745372.343640821999
Winsorized Mean ( 16 / 18 )1.300909090909090.00349383995933745372.343640821999
Winsorized Mean ( 17 / 18 )1.3040.00301064329736571433.13002278981
Winsorized Mean ( 18 / 18 )1.300727272727270.00251399510959757517.394511931046
Trimmed Mean ( 1 / 18 )1.302264150943400.00447247272721066291.17318994935
Trimmed Mean ( 2 / 18 )1.302156862745100.00438637574716411296.86395735408
Trimmed Mean ( 3 / 18 )1.302244897959180.00432782197388285300.900754656234
Trimmed Mean ( 4 / 18 )1.302127659574470.00430063749994101302.775497723844
Trimmed Mean ( 5 / 18 )1.3020.00425927389837918305.68590587599
Trimmed Mean ( 6 / 18 )1.301860465116280.00419955982972008309.999266090479
Trimmed Mean ( 7 / 18 )1.301860465116280.00411574073919176316.312554073057
Trimmed Mean ( 8 / 18 )1.301794871794870.00407208652249262319.687429185079
Trimmed Mean ( 9 / 18 )1.301891891891890.0040052112794544325.049492038092
Trimmed Mean ( 10 / 18 )1.301714285714290.00398496574399233326.656330152080
Trimmed Mean ( 11 / 18 )1.301515151515150.00394376214691527330.018673294780
Trimmed Mean ( 12 / 18 )1.301612903225810.00396481227622562328.291180652039
Trimmed Mean ( 13 / 18 )1.301724137931030.00397247194812385327.686174988806
Trimmed Mean ( 14 / 18 )1.301724137931030.00395980650182801328.734279649802
Trimmed Mean ( 15 / 18 )1.301851851851850.00391578004149025332.462967290778
Trimmed Mean ( 16 / 18 )1.302173913043480.00382195249126754340.709078937718
Trimmed Mean ( 17 / 18 )1.302380952380950.00364526842076279357.279849396776
Trimmed Mean ( 18 / 18 )1.302105263157890.00355236083005554366.546453316662
Median1.3
Midrange1.305
Midmean - Weighted Average at Xnp1.29971428571429
Midmean - Weighted Average at X(n+1)p1.29971428571429
Midmean - Empirical Distribution Function1.29971428571429
Midmean - Empirical Distribution Function - Averaging1.29971428571429
Midmean - Empirical Distribution Function - Interpolation1.29971428571429
Midmean - Closest Observation1.29971428571429
Midmean - True Basic - Statistics Graphics Toolkit1.29971428571429
Midmean - MS Excel (old versions)1.29971428571429
Number of observations55



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')