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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationSun, 20 Apr 2008 10:27:46 -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/2008/Apr/20/t1208709082qdjtrs10pcryzfq.htm/, Retrieved Mon, 13 May 2024 17:41:56 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=10368, Retrieved Mon, 13 May 2024 17:41:56 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact172
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [evolutie prijzen ...] [2008-04-20 16:27:46] [e120e668935a0d64689fc62dff0df290] [Current]
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Dataseries X:
3.42
3.42
3.42
3.41
3.33
3.32
3.32
3.32
3.32
3.32
3.32
3.32
3.32
3.32
3.32
3.32
3.27
3.27
3.27
3.27
3.27
3.27
3.27
3.27
3.27
3.27
3.26
3.26
3.15
3.15
3.15
3.15
3.15
3.15
3.15
3.15
3.15
3.15
3.15
3.15
3.03
3.03
3.03
3.04
3.04
3.04
3.04
3.04
3.04
3.04
3.04
3.04
2.96
2.96
2.96
2.96
2.96
2.96
2.96
2.96
2.96
2.96
2.96
2.95
2.9
2.9
2.9
2.9
2.9
2.9
2.9
2.9




Summary of compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\begin{tabular}{lllllllll}
\hline
Summary of compuational 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 & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=10368&T=0

[TABLE]
[ROW][C]Summary of compuational 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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=10368&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=10368&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 compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean3.134722222222220.0191628106166233163.583635247271
Geometric Mean3.13056539523254
Harmonic Mean3.12641510629064
Quadratic Mean3.13887807274439
Winsorized Mean ( 1 / 24 )3.134722222222220.0191628106166233163.583635247271
Winsorized Mean ( 2 / 24 )3.134722222222220.0191628106166233163.583635247271
Winsorized Mean ( 3 / 24 )3.134305555555560.019076719325465164.300029899358
Winsorized Mean ( 4 / 24 )3.129861111111110.0182793625728648171.223755677198
Winsorized Mean ( 5 / 24 )3.129166666666670.0181744610061440172.173835890309
Winsorized Mean ( 6 / 24 )3.129166666666670.0181744610061440172.173835890309
Winsorized Mean ( 7 / 24 )3.129166666666670.0181744610061440172.173835890309
Winsorized Mean ( 8 / 24 )3.134722222222220.017260514500061181.612328080437
Winsorized Mean ( 9 / 24 )3.135972222222220.0170755704590862183.652559645732
Winsorized Mean ( 10 / 24 )3.135972222222220.0170755704590862183.652559645732
Winsorized Mean ( 11 / 24 )3.135972222222220.0170755704590862183.652559645732
Winsorized Mean ( 12 / 24 )3.135972222222220.0170755704590862183.652559645732
Winsorized Mean ( 13 / 24 )3.135972222222220.0170755704590862183.652559645732
Winsorized Mean ( 14 / 24 )3.135972222222220.0170755704590862183.652559645732
Winsorized Mean ( 15 / 24 )3.135972222222220.0170755704590862183.652559645732
Winsorized Mean ( 16 / 24 )3.124861111111110.0154939448210324201.682731364141
Winsorized Mean ( 17 / 24 )3.124861111111110.0154939448210324201.682731364141
Winsorized Mean ( 18 / 24 )3.124861111111110.0154939448210324201.682731364141
Winsorized Mean ( 19 / 24 )3.124861111111110.0154939448210324201.682731364141
Winsorized Mean ( 20 / 24 )3.144305555555560.0127909433263222245.822804099597
Winsorized Mean ( 21 / 24 )3.144305555555560.0127909433263222245.822804099597
Winsorized Mean ( 22 / 24 )3.144305555555560.0127909433263222245.822804099597
Winsorized Mean ( 23 / 24 )3.14750.0123947051899153253.939077353844
Winsorized Mean ( 24 / 24 )3.14750.0123947051899153253.939077353844
Trimmed Mean ( 1 / 24 )3.1340.0189839204052917165.087080702593
Trimmed Mean ( 2 / 24 )3.133235294117650.0187638636793889166.982416183258
Trimmed Mean ( 3 / 24 )3.132424242424240.0184947048505418169.368706758923
Trimmed Mean ( 4 / 24 )3.131718750.0182051180656628172.024083485996
Trimmed Mean ( 5 / 24 )3.132258064516130.0181311097834588172.756003461725
Trimmed Mean ( 6 / 24 )3.1330.0180556265390463173.519317827310
Trimmed Mean ( 7 / 24 )3.133793103448280.0179463264868965174.620310498442
Trimmed Mean ( 8 / 24 )3.134642857142860.0177956734230219176.146346509575
Trimmed Mean ( 9 / 24 )3.134629629629630.0178014379301325176.088563290926
Trimmed Mean ( 10 / 24 )3.134423076923080.0178192988182036175.900472229640
Trimmed Mean ( 11 / 24 )3.13420.0178110032489665175.969874138441
Trimmed Mean ( 12 / 24 )3.133958333333330.0177695541660461176.366739651897
Trimmed Mean ( 13 / 24 )3.133695652173910.0176858214333730177.186887472507
Trimmed Mean ( 14 / 24 )3.133409090909090.0175477096010544178.56513255273
Trimmed Mean ( 15 / 24 )3.133095238095240.0173388987376742180.697475975658
Trimmed Mean ( 16 / 24 )3.132750.0170368661347182183.880648895632
Trimmed Mean ( 17 / 24 )3.133684210526320.0169528718876537184.846805384549
Trimmed Mean ( 18 / 24 )3.134722222222220.0167923173623711186.675975362795
Trimmed Mean ( 19 / 24 )3.135882352941180.0165258812146693189.755832818016
Trimmed Mean ( 20 / 24 )3.13718750.0161097194102134194.738804576016
Trimmed Mean ( 21 / 24 )3.136333333333330.0161990728650075193.611903561980
Trimmed Mean ( 22 / 24 )3.135357142857140.0162282181476563193.204029815803
Trimmed Mean ( 23 / 24 )3.134230769230770.0161642823431366193.898541407350
Trimmed Mean ( 24 / 24 )3.13250.0160642956335750194.997656383573
Median3.15
Midrange3.16
Midmean - Weighted Average at Xnp3.10702127659575
Midmean - Weighted Average at X(n+1)p3.10702127659575
Midmean - Empirical Distribution Function3.10702127659575
Midmean - Empirical Distribution Function - Averaging3.10702127659575
Midmean - Empirical Distribution Function - Interpolation3.10702127659575
Midmean - Closest Observation3.10702127659575
Midmean - True Basic - Statistics Graphics Toolkit3.10702127659575
Midmean - MS Excel (old versions)3.10702127659575
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 3.13472222222222 & 0.0191628106166233 & 163.583635247271 \tabularnewline
Geometric Mean & 3.13056539523254 &  &  \tabularnewline
Harmonic Mean & 3.12641510629064 &  &  \tabularnewline
Quadratic Mean & 3.13887807274439 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 3.13472222222222 & 0.0191628106166233 & 163.583635247271 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 3.13472222222222 & 0.0191628106166233 & 163.583635247271 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 3.13430555555556 & 0.019076719325465 & 164.300029899358 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 3.12986111111111 & 0.0182793625728648 & 171.223755677198 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 3.12916666666667 & 0.0181744610061440 & 172.173835890309 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 3.12916666666667 & 0.0181744610061440 & 172.173835890309 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 3.12916666666667 & 0.0181744610061440 & 172.173835890309 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 3.13472222222222 & 0.017260514500061 & 181.612328080437 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 3.13597222222222 & 0.0170755704590862 & 183.652559645732 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 3.13597222222222 & 0.0170755704590862 & 183.652559645732 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 3.13597222222222 & 0.0170755704590862 & 183.652559645732 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 3.13597222222222 & 0.0170755704590862 & 183.652559645732 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 3.13597222222222 & 0.0170755704590862 & 183.652559645732 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 3.13597222222222 & 0.0170755704590862 & 183.652559645732 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 3.13597222222222 & 0.0170755704590862 & 183.652559645732 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 3.12486111111111 & 0.0154939448210324 & 201.682731364141 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 3.12486111111111 & 0.0154939448210324 & 201.682731364141 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 3.12486111111111 & 0.0154939448210324 & 201.682731364141 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 3.12486111111111 & 0.0154939448210324 & 201.682731364141 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 3.14430555555556 & 0.0127909433263222 & 245.822804099597 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 3.14430555555556 & 0.0127909433263222 & 245.822804099597 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 3.14430555555556 & 0.0127909433263222 & 245.822804099597 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 3.1475 & 0.0123947051899153 & 253.939077353844 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 3.1475 & 0.0123947051899153 & 253.939077353844 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 3.134 & 0.0189839204052917 & 165.087080702593 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 3.13323529411765 & 0.0187638636793889 & 166.982416183258 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 3.13242424242424 & 0.0184947048505418 & 169.368706758923 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 3.13171875 & 0.0182051180656628 & 172.024083485996 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 3.13225806451613 & 0.0181311097834588 & 172.756003461725 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 3.133 & 0.0180556265390463 & 173.519317827310 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 3.13379310344828 & 0.0179463264868965 & 174.620310498442 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 3.13464285714286 & 0.0177956734230219 & 176.146346509575 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 3.13462962962963 & 0.0178014379301325 & 176.088563290926 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 3.13442307692308 & 0.0178192988182036 & 175.900472229640 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 3.1342 & 0.0178110032489665 & 175.969874138441 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 3.13395833333333 & 0.0177695541660461 & 176.366739651897 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 3.13369565217391 & 0.0176858214333730 & 177.186887472507 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 3.13340909090909 & 0.0175477096010544 & 178.56513255273 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 3.13309523809524 & 0.0173388987376742 & 180.697475975658 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 3.13275 & 0.0170368661347182 & 183.880648895632 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 3.13368421052632 & 0.0169528718876537 & 184.846805384549 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 3.13472222222222 & 0.0167923173623711 & 186.675975362795 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 3.13588235294118 & 0.0165258812146693 & 189.755832818016 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 3.1371875 & 0.0161097194102134 & 194.738804576016 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 3.13633333333333 & 0.0161990728650075 & 193.611903561980 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 3.13535714285714 & 0.0162282181476563 & 193.204029815803 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 3.13423076923077 & 0.0161642823431366 & 193.898541407350 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 3.1325 & 0.0160642956335750 & 194.997656383573 \tabularnewline
Median & 3.15 &  &  \tabularnewline
Midrange & 3.16 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 3.10702127659575 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 3.10702127659575 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 3.10702127659575 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 3.10702127659575 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 3.10702127659575 &  &  \tabularnewline
Midmean - Closest Observation & 3.10702127659575 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 3.10702127659575 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 3.10702127659575 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=10368&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]3.13472222222222[/C][C]0.0191628106166233[/C][C]163.583635247271[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]3.13056539523254[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]3.12641510629064[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]3.13887807274439[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]3.13472222222222[/C][C]0.0191628106166233[/C][C]163.583635247271[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]3.13472222222222[/C][C]0.0191628106166233[/C][C]163.583635247271[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]3.13430555555556[/C][C]0.019076719325465[/C][C]164.300029899358[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]3.12986111111111[/C][C]0.0182793625728648[/C][C]171.223755677198[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]3.12916666666667[/C][C]0.0181744610061440[/C][C]172.173835890309[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]3.12916666666667[/C][C]0.0181744610061440[/C][C]172.173835890309[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]3.12916666666667[/C][C]0.0181744610061440[/C][C]172.173835890309[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]3.13472222222222[/C][C]0.017260514500061[/C][C]181.612328080437[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]3.13597222222222[/C][C]0.0170755704590862[/C][C]183.652559645732[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]3.13597222222222[/C][C]0.0170755704590862[/C][C]183.652559645732[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]3.13597222222222[/C][C]0.0170755704590862[/C][C]183.652559645732[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]3.13597222222222[/C][C]0.0170755704590862[/C][C]183.652559645732[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]3.13597222222222[/C][C]0.0170755704590862[/C][C]183.652559645732[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]3.13597222222222[/C][C]0.0170755704590862[/C][C]183.652559645732[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]3.13597222222222[/C][C]0.0170755704590862[/C][C]183.652559645732[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]3.12486111111111[/C][C]0.0154939448210324[/C][C]201.682731364141[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]3.12486111111111[/C][C]0.0154939448210324[/C][C]201.682731364141[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]3.12486111111111[/C][C]0.0154939448210324[/C][C]201.682731364141[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]3.12486111111111[/C][C]0.0154939448210324[/C][C]201.682731364141[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]3.14430555555556[/C][C]0.0127909433263222[/C][C]245.822804099597[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]3.14430555555556[/C][C]0.0127909433263222[/C][C]245.822804099597[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]3.14430555555556[/C][C]0.0127909433263222[/C][C]245.822804099597[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]3.1475[/C][C]0.0123947051899153[/C][C]253.939077353844[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]3.1475[/C][C]0.0123947051899153[/C][C]253.939077353844[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]3.134[/C][C]0.0189839204052917[/C][C]165.087080702593[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]3.13323529411765[/C][C]0.0187638636793889[/C][C]166.982416183258[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]3.13242424242424[/C][C]0.0184947048505418[/C][C]169.368706758923[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]3.13171875[/C][C]0.0182051180656628[/C][C]172.024083485996[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]3.13225806451613[/C][C]0.0181311097834588[/C][C]172.756003461725[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]3.133[/C][C]0.0180556265390463[/C][C]173.519317827310[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]3.13379310344828[/C][C]0.0179463264868965[/C][C]174.620310498442[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]3.13464285714286[/C][C]0.0177956734230219[/C][C]176.146346509575[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]3.13462962962963[/C][C]0.0178014379301325[/C][C]176.088563290926[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]3.13442307692308[/C][C]0.0178192988182036[/C][C]175.900472229640[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]3.1342[/C][C]0.0178110032489665[/C][C]175.969874138441[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]3.13395833333333[/C][C]0.0177695541660461[/C][C]176.366739651897[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]3.13369565217391[/C][C]0.0176858214333730[/C][C]177.186887472507[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]3.13340909090909[/C][C]0.0175477096010544[/C][C]178.56513255273[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]3.13309523809524[/C][C]0.0173388987376742[/C][C]180.697475975658[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]3.13275[/C][C]0.0170368661347182[/C][C]183.880648895632[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]3.13368421052632[/C][C]0.0169528718876537[/C][C]184.846805384549[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]3.13472222222222[/C][C]0.0167923173623711[/C][C]186.675975362795[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]3.13588235294118[/C][C]0.0165258812146693[/C][C]189.755832818016[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]3.1371875[/C][C]0.0161097194102134[/C][C]194.738804576016[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]3.13633333333333[/C][C]0.0161990728650075[/C][C]193.611903561980[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]3.13535714285714[/C][C]0.0162282181476563[/C][C]193.204029815803[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]3.13423076923077[/C][C]0.0161642823431366[/C][C]193.898541407350[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]3.1325[/C][C]0.0160642956335750[/C][C]194.997656383573[/C][/ROW]
[ROW][C]Median[/C][C]3.15[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]3.16[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]3.10702127659575[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]3.10702127659575[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]3.10702127659575[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]3.10702127659575[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]3.10702127659575[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]3.10702127659575[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]3.10702127659575[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]3.10702127659575[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]72[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=10368&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=10368&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 Mean3.134722222222220.0191628106166233163.583635247271
Geometric Mean3.13056539523254
Harmonic Mean3.12641510629064
Quadratic Mean3.13887807274439
Winsorized Mean ( 1 / 24 )3.134722222222220.0191628106166233163.583635247271
Winsorized Mean ( 2 / 24 )3.134722222222220.0191628106166233163.583635247271
Winsorized Mean ( 3 / 24 )3.134305555555560.019076719325465164.300029899358
Winsorized Mean ( 4 / 24 )3.129861111111110.0182793625728648171.223755677198
Winsorized Mean ( 5 / 24 )3.129166666666670.0181744610061440172.173835890309
Winsorized Mean ( 6 / 24 )3.129166666666670.0181744610061440172.173835890309
Winsorized Mean ( 7 / 24 )3.129166666666670.0181744610061440172.173835890309
Winsorized Mean ( 8 / 24 )3.134722222222220.017260514500061181.612328080437
Winsorized Mean ( 9 / 24 )3.135972222222220.0170755704590862183.652559645732
Winsorized Mean ( 10 / 24 )3.135972222222220.0170755704590862183.652559645732
Winsorized Mean ( 11 / 24 )3.135972222222220.0170755704590862183.652559645732
Winsorized Mean ( 12 / 24 )3.135972222222220.0170755704590862183.652559645732
Winsorized Mean ( 13 / 24 )3.135972222222220.0170755704590862183.652559645732
Winsorized Mean ( 14 / 24 )3.135972222222220.0170755704590862183.652559645732
Winsorized Mean ( 15 / 24 )3.135972222222220.0170755704590862183.652559645732
Winsorized Mean ( 16 / 24 )3.124861111111110.0154939448210324201.682731364141
Winsorized Mean ( 17 / 24 )3.124861111111110.0154939448210324201.682731364141
Winsorized Mean ( 18 / 24 )3.124861111111110.0154939448210324201.682731364141
Winsorized Mean ( 19 / 24 )3.124861111111110.0154939448210324201.682731364141
Winsorized Mean ( 20 / 24 )3.144305555555560.0127909433263222245.822804099597
Winsorized Mean ( 21 / 24 )3.144305555555560.0127909433263222245.822804099597
Winsorized Mean ( 22 / 24 )3.144305555555560.0127909433263222245.822804099597
Winsorized Mean ( 23 / 24 )3.14750.0123947051899153253.939077353844
Winsorized Mean ( 24 / 24 )3.14750.0123947051899153253.939077353844
Trimmed Mean ( 1 / 24 )3.1340.0189839204052917165.087080702593
Trimmed Mean ( 2 / 24 )3.133235294117650.0187638636793889166.982416183258
Trimmed Mean ( 3 / 24 )3.132424242424240.0184947048505418169.368706758923
Trimmed Mean ( 4 / 24 )3.131718750.0182051180656628172.024083485996
Trimmed Mean ( 5 / 24 )3.132258064516130.0181311097834588172.756003461725
Trimmed Mean ( 6 / 24 )3.1330.0180556265390463173.519317827310
Trimmed Mean ( 7 / 24 )3.133793103448280.0179463264868965174.620310498442
Trimmed Mean ( 8 / 24 )3.134642857142860.0177956734230219176.146346509575
Trimmed Mean ( 9 / 24 )3.134629629629630.0178014379301325176.088563290926
Trimmed Mean ( 10 / 24 )3.134423076923080.0178192988182036175.900472229640
Trimmed Mean ( 11 / 24 )3.13420.0178110032489665175.969874138441
Trimmed Mean ( 12 / 24 )3.133958333333330.0177695541660461176.366739651897
Trimmed Mean ( 13 / 24 )3.133695652173910.0176858214333730177.186887472507
Trimmed Mean ( 14 / 24 )3.133409090909090.0175477096010544178.56513255273
Trimmed Mean ( 15 / 24 )3.133095238095240.0173388987376742180.697475975658
Trimmed Mean ( 16 / 24 )3.132750.0170368661347182183.880648895632
Trimmed Mean ( 17 / 24 )3.133684210526320.0169528718876537184.846805384549
Trimmed Mean ( 18 / 24 )3.134722222222220.0167923173623711186.675975362795
Trimmed Mean ( 19 / 24 )3.135882352941180.0165258812146693189.755832818016
Trimmed Mean ( 20 / 24 )3.13718750.0161097194102134194.738804576016
Trimmed Mean ( 21 / 24 )3.136333333333330.0161990728650075193.611903561980
Trimmed Mean ( 22 / 24 )3.135357142857140.0162282181476563193.204029815803
Trimmed Mean ( 23 / 24 )3.134230769230770.0161642823431366193.898541407350
Trimmed Mean ( 24 / 24 )3.13250.0160642956335750194.997656383573
Median3.15
Midrange3.16
Midmean - Weighted Average at Xnp3.10702127659575
Midmean - Weighted Average at X(n+1)p3.10702127659575
Midmean - Empirical Distribution Function3.10702127659575
Midmean - Empirical Distribution Function - Averaging3.10702127659575
Midmean - Empirical Distribution Function - Interpolation3.10702127659575
Midmean - Closest Observation3.10702127659575
Midmean - True Basic - Statistics Graphics Toolkit3.10702127659575
Midmean - MS Excel (old versions)3.10702127659575
Number of observations72



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')