Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationMon, 10 Oct 2016 18:35:42 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Oct/10/t1476120968dlq5ahbvhv1vg09.htm/, Retrieved Wed, 08 May 2024 14:40:53 +0200
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Wed, 08 May 2024 14:40:53 +0200
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact0
Dataseries X:
149
143
135
126
119
133
134
123
147
144
150
140
165
173
167
161
151
163
158
152
176
170
168
164
185
186
184
179
171
187
191
176
204
196
193
179
195
201
192
181
171
177
176
155
173
167
164
152
173
162
158
154
151
160
160
143
170
166
153
144




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=&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=&T=0

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







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean1642.5389619303203164.593327706694
Geometric Mean162.809593288767
Harmonic Mean161.586358269242
Quadratic Mean165.155482298752
Winsorized Mean ( 1 / 20 )164.0166666666672.5067695540250265.4294952654549
Winsorized Mean ( 2 / 20 )163.952.4402955503138167.1844850837503
Winsorized Mean ( 3 / 20 )164.252.3433551927358470.0918070419533
Winsorized Mean ( 4 / 20 )164.1833333333332.2994093649229371.4023939529515
Winsorized Mean ( 5 / 20 )164.1833333333332.2635020697109472.5350930888703
Winsorized Mean ( 6 / 20 )164.5833333333332.1391285604462376.93943055905
Winsorized Mean ( 7 / 20 )164.4666666666671.9787667600735983.1157415745908
Winsorized Mean ( 8 / 20 )164.3333333333331.9533639919693484.1283723919041
Winsorized Mean ( 9 / 20 )164.3333333333331.8979124223969186.5863626762048
Winsorized Mean ( 10 / 20 )164.1666666666671.8675290582551887.9058164803316
Winsorized Mean ( 11 / 20 )164.1666666666671.6726727937504598.1463124647196
Winsorized Mean ( 12 / 20 )164.1666666666671.5375096649674106.774396549987
Winsorized Mean ( 13 / 20 )164.3833333333331.50180525392463109.457156914157
Winsorized Mean ( 14 / 20 )164.151.38898511907686118.179811824836
Winsorized Mean ( 15 / 20 )163.91.3503922844988121.372138956519
Winsorized Mean ( 16 / 20 )164.1666666666671.30777048960588125.531710626183
Winsorized Mean ( 17 / 20 )164.1666666666671.30777048960588125.531710626183
Winsorized Mean ( 18 / 20 )163.5666666666671.12705973820556145.126882916683
Winsorized Mean ( 19 / 20 )163.8833333333331.07726680375771152.128825247077
Winsorized Mean ( 20 / 20 )164.2166666666671.02596011713837160.061452607636
Trimmed Mean ( 1 / 20 )164.0862068965522.4095600684330268.097993922708
Trimmed Mean ( 2 / 20 )164.1607142857142.2894133521968271.7042704971529
Trimmed Mean ( 3 / 20 )164.2777777777782.1857195925902875.1595851245919
Trimmed Mean ( 4 / 20 )164.2884615384622.1049637053762778.0481207912773
Trimmed Mean ( 5 / 20 )164.322.0212019055149281.2981620251036
Trimmed Mean ( 6 / 20 )164.3541666666671.9276564942158885.2611277786405
Trimmed Mean ( 7 / 20 )164.3043478260871.8493684952242388.8434880611319
Trimmed Mean ( 8 / 20 )164.2727272727271.7971564444412391.40702679549
Trimmed Mean ( 9 / 20 )164.2619047619051.7354202762451294.6525213577159
Trimmed Mean ( 10 / 20 )164.251.6690047702379298.411941612717
Trimmed Mean ( 11 / 20 )164.2631578947371.58795439527978103.443246470435
Trimmed Mean ( 12 / 20 )164.2777777777781.53458081299257107.050587617749
Trimmed Mean ( 13 / 20 )164.2941176470591.49778768035041109.69119308594
Trimmed Mean ( 14 / 20 )164.281251.45374542339723113.005514828101
Trimmed Mean ( 15 / 20 )164.31.42163092353769115.571487141785
Trimmed Mean ( 16 / 20 )164.3571428571431.38225171494809118.905363675613
Trimmed Mean ( 17 / 20 )164.3846153846151.33367845631999123.256557535015
Trimmed Mean ( 18 / 20 )164.4166666666671.25385877823174131.128536579324
Trimmed Mean ( 19 / 20 )164.5454545454551.19835253564432137.309722849615
Trimmed Mean ( 20 / 20 )164.651.12454669229779146.4145518614
Median164.5
Midrange161.5
Midmean - Weighted Average at Xnp163.870967741935
Midmean - Weighted Average at X(n+1)p163.870967741935
Midmean - Empirical Distribution Function163.870967741935
Midmean - Empirical Distribution Function - Averaging163.870967741935
Midmean - Empirical Distribution Function - Interpolation163.870967741935
Midmean - Closest Observation163.870967741935
Midmean - True Basic - Statistics Graphics Toolkit163.870967741935
Midmean - MS Excel (old versions)164.28125
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 164 & 2.53896193032031 & 64.593327706694 \tabularnewline
Geometric Mean & 162.809593288767 &  &  \tabularnewline
Harmonic Mean & 161.586358269242 &  &  \tabularnewline
Quadratic Mean & 165.155482298752 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 164.016666666667 & 2.50676955402502 & 65.4294952654549 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 163.95 & 2.44029555031381 & 67.1844850837503 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 164.25 & 2.34335519273584 & 70.0918070419533 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 164.183333333333 & 2.29940936492293 & 71.4023939529515 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 164.183333333333 & 2.26350206971094 & 72.5350930888703 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 164.583333333333 & 2.13912856044623 & 76.93943055905 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 164.466666666667 & 1.97876676007359 & 83.1157415745908 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 164.333333333333 & 1.95336399196934 & 84.1283723919041 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 164.333333333333 & 1.89791242239691 & 86.5863626762048 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 164.166666666667 & 1.86752905825518 & 87.9058164803316 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 164.166666666667 & 1.67267279375045 & 98.1463124647196 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 164.166666666667 & 1.5375096649674 & 106.774396549987 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 164.383333333333 & 1.50180525392463 & 109.457156914157 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 164.15 & 1.38898511907686 & 118.179811824836 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 163.9 & 1.3503922844988 & 121.372138956519 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 164.166666666667 & 1.30777048960588 & 125.531710626183 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 164.166666666667 & 1.30777048960588 & 125.531710626183 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 163.566666666667 & 1.12705973820556 & 145.126882916683 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 163.883333333333 & 1.07726680375771 & 152.128825247077 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 164.216666666667 & 1.02596011713837 & 160.061452607636 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 164.086206896552 & 2.40956006843302 & 68.097993922708 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 164.160714285714 & 2.28941335219682 & 71.7042704971529 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 164.277777777778 & 2.18571959259028 & 75.1595851245919 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 164.288461538462 & 2.10496370537627 & 78.0481207912773 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 164.32 & 2.02120190551492 & 81.2981620251036 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 164.354166666667 & 1.92765649421588 & 85.2611277786405 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 164.304347826087 & 1.84936849522423 & 88.8434880611319 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 164.272727272727 & 1.79715644444123 & 91.40702679549 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 164.261904761905 & 1.73542027624512 & 94.6525213577159 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 164.25 & 1.66900477023792 & 98.411941612717 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 164.263157894737 & 1.58795439527978 & 103.443246470435 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 164.277777777778 & 1.53458081299257 & 107.050587617749 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 164.294117647059 & 1.49778768035041 & 109.69119308594 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 164.28125 & 1.45374542339723 & 113.005514828101 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 164.3 & 1.42163092353769 & 115.571487141785 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 164.357142857143 & 1.38225171494809 & 118.905363675613 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 164.384615384615 & 1.33367845631999 & 123.256557535015 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 164.416666666667 & 1.25385877823174 & 131.128536579324 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 164.545454545455 & 1.19835253564432 & 137.309722849615 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 164.65 & 1.12454669229779 & 146.4145518614 \tabularnewline
Median & 164.5 &  &  \tabularnewline
Midrange & 161.5 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 163.870967741935 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 163.870967741935 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 163.870967741935 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 163.870967741935 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 163.870967741935 &  &  \tabularnewline
Midmean - Closest Observation & 163.870967741935 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 163.870967741935 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 164.28125 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]164[/C][C]2.53896193032031[/C][C]64.593327706694[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]162.809593288767[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]161.586358269242[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]165.155482298752[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]164.016666666667[/C][C]2.50676955402502[/C][C]65.4294952654549[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]163.95[/C][C]2.44029555031381[/C][C]67.1844850837503[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]164.25[/C][C]2.34335519273584[/C][C]70.0918070419533[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]164.183333333333[/C][C]2.29940936492293[/C][C]71.4023939529515[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]164.183333333333[/C][C]2.26350206971094[/C][C]72.5350930888703[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]164.583333333333[/C][C]2.13912856044623[/C][C]76.93943055905[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]164.466666666667[/C][C]1.97876676007359[/C][C]83.1157415745908[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]164.333333333333[/C][C]1.95336399196934[/C][C]84.1283723919041[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]164.333333333333[/C][C]1.89791242239691[/C][C]86.5863626762048[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]164.166666666667[/C][C]1.86752905825518[/C][C]87.9058164803316[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]164.166666666667[/C][C]1.67267279375045[/C][C]98.1463124647196[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]164.166666666667[/C][C]1.5375096649674[/C][C]106.774396549987[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]164.383333333333[/C][C]1.50180525392463[/C][C]109.457156914157[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]164.15[/C][C]1.38898511907686[/C][C]118.179811824836[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]163.9[/C][C]1.3503922844988[/C][C]121.372138956519[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]164.166666666667[/C][C]1.30777048960588[/C][C]125.531710626183[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]164.166666666667[/C][C]1.30777048960588[/C][C]125.531710626183[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]163.566666666667[/C][C]1.12705973820556[/C][C]145.126882916683[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]163.883333333333[/C][C]1.07726680375771[/C][C]152.128825247077[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]164.216666666667[/C][C]1.02596011713837[/C][C]160.061452607636[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]164.086206896552[/C][C]2.40956006843302[/C][C]68.097993922708[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]164.160714285714[/C][C]2.28941335219682[/C][C]71.7042704971529[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]164.277777777778[/C][C]2.18571959259028[/C][C]75.1595851245919[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]164.288461538462[/C][C]2.10496370537627[/C][C]78.0481207912773[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]164.32[/C][C]2.02120190551492[/C][C]81.2981620251036[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]164.354166666667[/C][C]1.92765649421588[/C][C]85.2611277786405[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]164.304347826087[/C][C]1.84936849522423[/C][C]88.8434880611319[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]164.272727272727[/C][C]1.79715644444123[/C][C]91.40702679549[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]164.261904761905[/C][C]1.73542027624512[/C][C]94.6525213577159[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]164.25[/C][C]1.66900477023792[/C][C]98.411941612717[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]164.263157894737[/C][C]1.58795439527978[/C][C]103.443246470435[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]164.277777777778[/C][C]1.53458081299257[/C][C]107.050587617749[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]164.294117647059[/C][C]1.49778768035041[/C][C]109.69119308594[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]164.28125[/C][C]1.45374542339723[/C][C]113.005514828101[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]164.3[/C][C]1.42163092353769[/C][C]115.571487141785[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]164.357142857143[/C][C]1.38225171494809[/C][C]118.905363675613[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]164.384615384615[/C][C]1.33367845631999[/C][C]123.256557535015[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]164.416666666667[/C][C]1.25385877823174[/C][C]131.128536579324[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]164.545454545455[/C][C]1.19835253564432[/C][C]137.309722849615[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]164.65[/C][C]1.12454669229779[/C][C]146.4145518614[/C][/ROW]
[ROW][C]Median[/C][C]164.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]161.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]163.870967741935[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]163.870967741935[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]163.870967741935[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]163.870967741935[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]163.870967741935[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]163.870967741935[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]163.870967741935[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]164.28125[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]60[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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 Mean1642.5389619303203164.593327706694
Geometric Mean162.809593288767
Harmonic Mean161.586358269242
Quadratic Mean165.155482298752
Winsorized Mean ( 1 / 20 )164.0166666666672.5067695540250265.4294952654549
Winsorized Mean ( 2 / 20 )163.952.4402955503138167.1844850837503
Winsorized Mean ( 3 / 20 )164.252.3433551927358470.0918070419533
Winsorized Mean ( 4 / 20 )164.1833333333332.2994093649229371.4023939529515
Winsorized Mean ( 5 / 20 )164.1833333333332.2635020697109472.5350930888703
Winsorized Mean ( 6 / 20 )164.5833333333332.1391285604462376.93943055905
Winsorized Mean ( 7 / 20 )164.4666666666671.9787667600735983.1157415745908
Winsorized Mean ( 8 / 20 )164.3333333333331.9533639919693484.1283723919041
Winsorized Mean ( 9 / 20 )164.3333333333331.8979124223969186.5863626762048
Winsorized Mean ( 10 / 20 )164.1666666666671.8675290582551887.9058164803316
Winsorized Mean ( 11 / 20 )164.1666666666671.6726727937504598.1463124647196
Winsorized Mean ( 12 / 20 )164.1666666666671.5375096649674106.774396549987
Winsorized Mean ( 13 / 20 )164.3833333333331.50180525392463109.457156914157
Winsorized Mean ( 14 / 20 )164.151.38898511907686118.179811824836
Winsorized Mean ( 15 / 20 )163.91.3503922844988121.372138956519
Winsorized Mean ( 16 / 20 )164.1666666666671.30777048960588125.531710626183
Winsorized Mean ( 17 / 20 )164.1666666666671.30777048960588125.531710626183
Winsorized Mean ( 18 / 20 )163.5666666666671.12705973820556145.126882916683
Winsorized Mean ( 19 / 20 )163.8833333333331.07726680375771152.128825247077
Winsorized Mean ( 20 / 20 )164.2166666666671.02596011713837160.061452607636
Trimmed Mean ( 1 / 20 )164.0862068965522.4095600684330268.097993922708
Trimmed Mean ( 2 / 20 )164.1607142857142.2894133521968271.7042704971529
Trimmed Mean ( 3 / 20 )164.2777777777782.1857195925902875.1595851245919
Trimmed Mean ( 4 / 20 )164.2884615384622.1049637053762778.0481207912773
Trimmed Mean ( 5 / 20 )164.322.0212019055149281.2981620251036
Trimmed Mean ( 6 / 20 )164.3541666666671.9276564942158885.2611277786405
Trimmed Mean ( 7 / 20 )164.3043478260871.8493684952242388.8434880611319
Trimmed Mean ( 8 / 20 )164.2727272727271.7971564444412391.40702679549
Trimmed Mean ( 9 / 20 )164.2619047619051.7354202762451294.6525213577159
Trimmed Mean ( 10 / 20 )164.251.6690047702379298.411941612717
Trimmed Mean ( 11 / 20 )164.2631578947371.58795439527978103.443246470435
Trimmed Mean ( 12 / 20 )164.2777777777781.53458081299257107.050587617749
Trimmed Mean ( 13 / 20 )164.2941176470591.49778768035041109.69119308594
Trimmed Mean ( 14 / 20 )164.281251.45374542339723113.005514828101
Trimmed Mean ( 15 / 20 )164.31.42163092353769115.571487141785
Trimmed Mean ( 16 / 20 )164.3571428571431.38225171494809118.905363675613
Trimmed Mean ( 17 / 20 )164.3846153846151.33367845631999123.256557535015
Trimmed Mean ( 18 / 20 )164.4166666666671.25385877823174131.128536579324
Trimmed Mean ( 19 / 20 )164.5454545454551.19835253564432137.309722849615
Trimmed Mean ( 20 / 20 )164.651.12454669229779146.4145518614
Median164.5
Midrange161.5
Midmean - Weighted Average at Xnp163.870967741935
Midmean - Weighted Average at X(n+1)p163.870967741935
Midmean - Empirical Distribution Function163.870967741935
Midmean - Empirical Distribution Function - Averaging163.870967741935
Midmean - Empirical Distribution Function - Interpolation163.870967741935
Midmean - Closest Observation163.870967741935
Midmean - True Basic - Statistics Graphics Toolkit163.870967741935
Midmean - MS Excel (old versions)164.28125
Number of observations60



Parameters (Session):
Parameters (R input):
R code (references can be found in the software module):
geomean <- function(x) {
return(exp(mean(log(x))))
}
harmean <- function(x) {
return(1/mean(1/x))
}
quamean <- function(x) {
return(sqrt(mean(x*x)))
}
winmean <- function(x) {
x <-sort(x[!is.na(x)])
n<-length(x)
denom <- 3
nodenom <- n/denom
if (nodenom>40) denom <- n/40
sqrtn = sqrt(n)
roundnodenom = floor(nodenom)
win <- array(NA,dim=c(roundnodenom,2))
for (j in 1:roundnodenom) {
win[j,1] <- (j*x[j+1]+sum(x[(j+1):(n-j)])+j*x[n-j])/n
win[j,2] <- sd(c(rep(x[j+1],j),x[(j+1):(n-j)],rep(x[n-j],j)))/sqrtn
}
return(win)
}
trimean <- function(x) {
x <-sort(x[!is.na(x)])
n<-length(x)
denom <- 3
nodenom <- n/denom
if (nodenom>40) denom <- n/40
sqrtn = sqrt(n)
roundnodenom = floor(nodenom)
tri <- array(NA,dim=c(roundnodenom,2))
for (j in 1:roundnodenom) {
tri[j,1] <- mean(x,trim=j/n)
tri[j,2] <- sd(x[(j+1):(n-j)]) / sqrt(n-j*2)
}
return(tri)
}
midrange <- function(x) {
return((max(x)+min(x))/2)
}
q1 <- function(data,n,p,i,f) {
np <- n*p;
i <<- floor(np)
f <<- np - i
qvalue <- (1-f)*data[i] + f*data[i+1]
}
q2 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
qvalue <- (1-f)*data[i] + f*data[i+1]
}
q3 <- function(data,n,p,i,f) {
np <- n*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
qvalue <- data[i+1]
}
}
q4 <- function(data,n,p,i,f) {
np <- n*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- (data[i]+data[i+1])/2
} else {
qvalue <- data[i+1]
}
}
q5 <- function(data,n,p,i,f) {
np <- (n-1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i+1]
} else {
qvalue <- data[i+1] + f*(data[i+2]-data[i+1])
}
}
q6 <- function(data,n,p,i,f) {
np <- n*p+0.5
i <<- floor(np)
f <<- np - i
qvalue <- data[i]
}
q7 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
qvalue <- f*data[i] + (1-f)*data[i+1]
}
}
q8 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
if (f == 0.5) {
qvalue <- (data[i]+data[i+1])/2
} else {
if (f < 0.5) {
qvalue <- data[i]
} else {
qvalue <- data[i+1]
}
}
}
}
midmean <- function(x,def) {
x <-sort(x[!is.na(x)])
n<-length(x)
if (def==1) {
qvalue1 <- q1(x,n,0.25,i,f)
qvalue3 <- q1(x,n,0.75,i,f)
}
if (def==2) {
qvalue1 <- q2(x,n,0.25,i,f)
qvalue3 <- q2(x,n,0.75,i,f)
}
if (def==3) {
qvalue1 <- q3(x,n,0.25,i,f)
qvalue3 <- q3(x,n,0.75,i,f)
}
if (def==4) {
qvalue1 <- q4(x,n,0.25,i,f)
qvalue3 <- q4(x,n,0.75,i,f)
}
if (def==5) {
qvalue1 <- q5(x,n,0.25,i,f)
qvalue3 <- q5(x,n,0.75,i,f)
}
if (def==6) {
qvalue1 <- q6(x,n,0.25,i,f)
qvalue3 <- q6(x,n,0.75,i,f)
}
if (def==7) {
qvalue1 <- q7(x,n,0.25,i,f)
qvalue3 <- q7(x,n,0.75,i,f)
}
if (def==8) {
qvalue1 <- q8(x,n,0.25,i,f)
qvalue3 <- q8(x,n,0.75,i,f)
}
midm <- 0
myn <- 0
roundno4 <- round(n/4)
round3no4 <- round(3*n/4)
for (i in 1:n) {
if ((x[i]>=qvalue1) & (x[i]<=qvalue3)){
midm = midm + x[i]
myn = myn + 1
}
}
midm = midm / myn
return(midm)
}
(arm <- mean(x))
sqrtn <- sqrt(length(x))
(armse <- sd(x) / sqrtn)
(armose <- arm / armse)
(geo <- geomean(x))
(har <- harmean(x))
(qua <- quamean(x))
(win <- winmean(x))
(tri <- trimean(x))
(midr <- midrange(x))
midm <- array(NA,dim=8)
for (j in 1:8) midm[j] <- midmean(x,j)
midm
bitmap(file='test1.png')
lb <- win[,1] - 2*win[,2]
ub <- win[,1] + 2*win[,2]
if ((ylimmin == '') | (ylimmax == '')) plot(win[,1],type='b',main=main, xlab='j', pch=19, ylab='Winsorized Mean(j/n)', ylim=c(min(lb),max(ub))) else plot(win[,1],type='l',main=main, xlab='j', pch=19, ylab='Winsorized Mean(j/n)', ylim=c(ylimmin,ylimmax))
lines(ub,lty=3)
lines(lb,lty=3)
grid()
dev.off()
bitmap(file='test2.png')
lb <- tri[,1] - 2*tri[,2]
ub <- tri[,1] + 2*tri[,2]
if ((ylimmin == '') | (ylimmax == '')) plot(tri[,1],type='b',main=main, xlab='j', pch=19, ylab='Trimmed Mean(j/n)', ylim=c(min(lb),max(ub))) else plot(tri[,1],type='l',main=main, xlab='j', pch=19, ylab='Trimmed Mean(j/n)', ylim=c(ylimmin,ylimmax))
lines(ub,lty=3)
lines(lb,lty=3)
grid()
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Central Tendency - Ungrouped Data',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Measure',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.element(a,'S.E.',header=TRUE)
a<-table.element(a,'Value/S.E.',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('arithmetic_mean.htm', 'Arithmetic Mean', 'click to view the definition of the Arithmetic Mean'),header=TRUE)
a<-table.element(a,arm)
a<-table.element(a,hyperlink('arithmetic_mean_standard_error.htm', armse, 'click to view the definition of the Standard Error of the Arithmetic Mean'))
a<-table.element(a,armose)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('geometric_mean.htm', 'Geometric Mean', 'click to view the definition of the Geometric Mean'),header=TRUE)
a<-table.element(a,geo)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('harmonic_mean.htm', 'Harmonic Mean', 'click to view the definition of the Harmonic Mean'),header=TRUE)
a<-table.element(a,har)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('quadratic_mean.htm', 'Quadratic Mean', 'click to view the definition of the Quadratic Mean'),header=TRUE)
a<-table.element(a,qua)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
for (j in 1:length(win[,1])) {
a<-table.row.start(a)
mylabel <- paste('Winsorized Mean (',j)
mylabel <- paste(mylabel,'/')
mylabel <- paste(mylabel,length(win[,1]))
mylabel <- paste(mylabel,')')
a<-table.element(a,hyperlink('winsorized_mean.htm', mylabel, 'click to view the definition of the Winsorized Mean'),header=TRUE)
a<-table.element(a,win[j,1])
a<-table.element(a,win[j,2])
a<-table.element(a,win[j,1]/win[j,2])
a<-table.row.end(a)
}
for (j in 1:length(tri[,1])) {
a<-table.row.start(a)
mylabel <- paste('Trimmed Mean (',j)
mylabel <- paste(mylabel,'/')
mylabel <- paste(mylabel,length(tri[,1]))
mylabel <- paste(mylabel,')')
a<-table.element(a,hyperlink('arithmetic_mean.htm', mylabel, 'click to view the definition of the Trimmed Mean'),header=TRUE)
a<-table.element(a,tri[j,1])
a<-table.element(a,tri[j,2])
a<-table.element(a,tri[j,1]/tri[j,2])
a<-table.row.end(a)
}
a<-table.row.start(a)
a<-table.element(a,hyperlink('median_1.htm', 'Median', 'click to view the definition of the Median'),header=TRUE)
a<-table.element(a,median(x))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('midrange.htm', 'Midrange', 'click to view the definition of the Midrange'),header=TRUE)
a<-table.element(a,midr)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_1.htm','Weighted Average at Xnp',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[1])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_2.htm','Weighted Average at X(n+1)p',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[2])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_3.htm','Empirical Distribution Function',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[3])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_4.htm','Empirical Distribution Function - Averaging',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[4])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_5.htm','Empirical Distribution Function - Interpolation',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[5])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_6.htm','Closest Observation',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[6])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_7.htm','True Basic - Statistics Graphics Toolkit',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[7])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_8.htm','MS Excel (old versions)',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[8])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Number of observations',header=TRUE)
a<-table.element(a,length(x))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')