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 computationSun, 19 Oct 2008 02:42:10 -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/Oct/19/t1224405801cu9ydm5cmth0dqv.htm/, Retrieved Mon, 13 May 2024 20:41:24 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=16719, Retrieved Mon, 13 May 2024 20:41:24 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordscentral tendency
Estimated Impact186
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
F     [Central Tendency] [Q1 central tenden...] [2007-10-18 09:40:43] [b731da8b544846036771bbf9bf2f34ce]
F    D    [Central Tendency] [central tendency ...] [2008-10-19 08:42:10] [9b05d7ef5dbcfba4217d280d9092f628] [Current]
Feedback Forum
2008-10-27 09:35:37 [9142cf052ad32d043faa9486189092cf] [reply
Bij de kleding productie kan je zien dat er mediaan de midrange en de mean dicht bij mekaar liggen. De tijdreeksen zijn robuuster. We kunnen dus besluiten dat er geen echte outliers aanwezig zijn omdat de midrange dicht bij de waardes van de mediaan en de mean liggen.

Verklaring midrange
De midrange houdt rekening met de hoogste en de kleinste waarde en vervolgens door 2 gedeeld wordt. Deze extreme waarde beïnvloeden de midrange. De mediaan wordt niet beïnvloed door outliers het gemiddelde wel maar niet in zo’n sterke mate als de midrange.

Post a new message
Dataseries X:
109.20
88.60
94.30
98.30
86.40
80.60
104.10
108.20
93.40
71.90
94.10
94.90
96.40
91.10
84.40
86.40
88.00
75.10
109.70
103.00
82.10
68.00
96.40
94.30
90.00
88.00
76.10
82.50
81.40
66.50
97.20
94.10
80.70
70.50
87.80
89.50
99.60
84.20
75.10
92.00
80.80
73.10
99.80
90.00
83.10
72.40
78.80
87.30
91.00
80.10
73.60
86.40
74.50
71.20
92.40
81.50
85.30
69.90
84.20
90.70
100.30




Summary of computational 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 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 & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=16719&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=16719&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=16719&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'Gwilym Jenkins' @ 72.249.127.135







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean86.89344262295081.3533400673857264.2066578216406
Geometric Mean86.2576130505509
Harmonic Mean85.6188757284786
Quadratic Mean87.5234947379705
Winsorized Mean ( 1 / 20 )86.90983606557381.3450876115005364.6127696980425
Winsorized Mean ( 2 / 20 )86.9393442622951.3221717493994465.7549552860928
Winsorized Mean ( 3 / 20 )86.76721311475411.2657245302203468.5514193990136
Winsorized Mean ( 4 / 20 )86.74098360655741.2398955029325069.958301648328
Winsorized Mean ( 5 / 20 )86.57704918032791.1823090158567273.227090396154
Winsorized Mean ( 6 / 20 )86.57704918032791.1628056174864574.4553069561832
Winsorized Mean ( 7 / 20 )86.63442622950821.1423656914177875.8377346942089
Winsorized Mean ( 8 / 20 )86.52950819672131.0980841345091178.800435665527
Winsorized Mean ( 9 / 20 )86.51.0439521375876282.8582047831092
Winsorized Mean ( 10 / 20 )86.46721311475411.0032099337132686.1905471716237
Winsorized Mean ( 11 / 20 )86.46721311475411.0032099337132686.1905471716237
Winsorized Mean ( 12 / 20 )86.36885245901640.91906801505865893.9743860561876
Winsorized Mean ( 13 / 20 )86.8163934426230.79699291509377108.929943790540
Winsorized Mean ( 14 / 20 )87.11475409836060.74863385983806116.364966603574
Winsorized Mean ( 15 / 20 )87.1885245901640.721818810653629120.790042186920
Winsorized Mean ( 16 / 20 )87.21475409836070.717839944660839121.496100554236
Winsorized Mean ( 17 / 20 )87.04754098360660.682880457249123127.471126255778
Winsorized Mean ( 18 / 20 )86.92950819672130.611087645696527142.253748392569
Winsorized Mean ( 19 / 20 )86.83606557377050.587966918453831147.688692762039
Winsorized Mean ( 20 / 20 )86.73770491803280.515901057646733168.128565802296
Trimmed Mean ( 1 / 20 )86.85254237288141.2982102411059066.9017541402961
Trimmed Mean ( 2 / 20 )86.79122807017541.240531256713569.9629514375226
Trimmed Mean ( 3 / 20 )86.70909090909091.184667117793773.1927894399366
Trimmed Mean ( 4 / 20 )86.68679245283021.1433852092951475.8159120374397
Trimmed Mean ( 5 / 20 )86.67058823529411.1020526093902778.6446921832945
Trimmed Mean ( 6 / 20 )86.69387755102041.0700523231026781.018353662975
Trimmed Mean ( 7 / 20 )86.71914893617021.0352154508036283.7691795160628
Trimmed Mean ( 8 / 20 )86.73555555555550.99634258212986687.0539482214464
Trimmed Mean ( 9 / 20 )86.77209302325580.9584983039560190.5292087269443
Trimmed Mean ( 10 / 20 )86.81707317073170.92386319359302793.9717847542865
Trimmed Mean ( 11 / 20 )86.87179487179490.88872794747025597.7484674799229
Trimmed Mean ( 12 / 20 )86.93243243243240.840527987701135103.425981888116
Trimmed Mean ( 13 / 20 )87.01428571428570.79915020892356108.883517444727
Trimmed Mean ( 14 / 20 )87.04242424242420.778134305993157111.860412234787
Trimmed Mean ( 15 / 20 )87.03225806451610.760961292118509114.371465363526
Trimmed Mean ( 16 / 20 )87.01034482758620.742106986225427117.247710158540
Trimmed Mean ( 17 / 20 )86.98148148148150.713205456966791121.95851929037
Trimmed Mean ( 18 / 20 )86.9720.680282294345517127.84692578788
Trimmed Mean ( 19 / 20 )86.97826086956520.655109335886746132.769075488495
Trimmed Mean ( 20 / 20 )870.620905636569527140.117909833563
Median87.3
Midrange88.1
Midmean - Weighted Average at Xnp87.0322580645161
Midmean - Weighted Average at X(n+1)p87.0322580645161
Midmean - Empirical Distribution Function87.0322580645161
Midmean - Empirical Distribution Function - Averaging87.0322580645161
Midmean - Empirical Distribution Function - Interpolation87.0322580645161
Midmean - Closest Observation86.815625
Midmean - True Basic - Statistics Graphics Toolkit87.0322580645161
Midmean - MS Excel (old versions)87.0322580645161
Number of observations61

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 86.8934426229508 & 1.35334006738572 & 64.2066578216406 \tabularnewline
Geometric Mean & 86.2576130505509 &  &  \tabularnewline
Harmonic Mean & 85.6188757284786 &  &  \tabularnewline
Quadratic Mean & 87.5234947379705 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 86.9098360655738 & 1.34508761150053 & 64.6127696980425 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 86.939344262295 & 1.32217174939944 & 65.7549552860928 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 86.7672131147541 & 1.26572453022034 & 68.5514193990136 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 86.7409836065574 & 1.23989550293250 & 69.958301648328 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 86.5770491803279 & 1.18230901585672 & 73.227090396154 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 86.5770491803279 & 1.16280561748645 & 74.4553069561832 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 86.6344262295082 & 1.14236569141778 & 75.8377346942089 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 86.5295081967213 & 1.09808413450911 & 78.800435665527 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 86.5 & 1.04395213758762 & 82.8582047831092 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 86.4672131147541 & 1.00320993371326 & 86.1905471716237 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 86.4672131147541 & 1.00320993371326 & 86.1905471716237 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 86.3688524590164 & 0.919068015058658 & 93.9743860561876 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 86.816393442623 & 0.79699291509377 & 108.929943790540 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 87.1147540983606 & 0.74863385983806 & 116.364966603574 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 87.188524590164 & 0.721818810653629 & 120.790042186920 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 87.2147540983607 & 0.717839944660839 & 121.496100554236 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 87.0475409836066 & 0.682880457249123 & 127.471126255778 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 86.9295081967213 & 0.611087645696527 & 142.253748392569 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 86.8360655737705 & 0.587966918453831 & 147.688692762039 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 86.7377049180328 & 0.515901057646733 & 168.128565802296 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 86.8525423728814 & 1.29821024110590 & 66.9017541402961 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 86.7912280701754 & 1.2405312567135 & 69.9629514375226 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 86.7090909090909 & 1.1846671177937 & 73.1927894399366 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 86.6867924528302 & 1.14338520929514 & 75.8159120374397 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 86.6705882352941 & 1.10205260939027 & 78.6446921832945 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 86.6938775510204 & 1.07005232310267 & 81.018353662975 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 86.7191489361702 & 1.03521545080362 & 83.7691795160628 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 86.7355555555555 & 0.996342582129866 & 87.0539482214464 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 86.7720930232558 & 0.95849830395601 & 90.5292087269443 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 86.8170731707317 & 0.923863193593027 & 93.9717847542865 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 86.8717948717949 & 0.888727947470255 & 97.7484674799229 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 86.9324324324324 & 0.840527987701135 & 103.425981888116 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 87.0142857142857 & 0.79915020892356 & 108.883517444727 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 87.0424242424242 & 0.778134305993157 & 111.860412234787 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 87.0322580645161 & 0.760961292118509 & 114.371465363526 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 87.0103448275862 & 0.742106986225427 & 117.247710158540 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 86.9814814814815 & 0.713205456966791 & 121.95851929037 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 86.972 & 0.680282294345517 & 127.84692578788 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 86.9782608695652 & 0.655109335886746 & 132.769075488495 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 87 & 0.620905636569527 & 140.117909833563 \tabularnewline
Median & 87.3 &  &  \tabularnewline
Midrange & 88.1 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 87.0322580645161 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 87.0322580645161 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 87.0322580645161 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 87.0322580645161 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 87.0322580645161 &  &  \tabularnewline
Midmean - Closest Observation & 86.815625 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 87.0322580645161 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 87.0322580645161 &  &  \tabularnewline
Number of observations & 61 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=16719&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]86.8934426229508[/C][C]1.35334006738572[/C][C]64.2066578216406[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]86.2576130505509[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]85.6188757284786[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]87.5234947379705[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]86.9098360655738[/C][C]1.34508761150053[/C][C]64.6127696980425[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]86.939344262295[/C][C]1.32217174939944[/C][C]65.7549552860928[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]86.7672131147541[/C][C]1.26572453022034[/C][C]68.5514193990136[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]86.7409836065574[/C][C]1.23989550293250[/C][C]69.958301648328[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]86.5770491803279[/C][C]1.18230901585672[/C][C]73.227090396154[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]86.5770491803279[/C][C]1.16280561748645[/C][C]74.4553069561832[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]86.6344262295082[/C][C]1.14236569141778[/C][C]75.8377346942089[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]86.5295081967213[/C][C]1.09808413450911[/C][C]78.800435665527[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]86.5[/C][C]1.04395213758762[/C][C]82.8582047831092[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]86.4672131147541[/C][C]1.00320993371326[/C][C]86.1905471716237[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]86.4672131147541[/C][C]1.00320993371326[/C][C]86.1905471716237[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]86.3688524590164[/C][C]0.919068015058658[/C][C]93.9743860561876[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]86.816393442623[/C][C]0.79699291509377[/C][C]108.929943790540[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]87.1147540983606[/C][C]0.74863385983806[/C][C]116.364966603574[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]87.188524590164[/C][C]0.721818810653629[/C][C]120.790042186920[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]87.2147540983607[/C][C]0.717839944660839[/C][C]121.496100554236[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]87.0475409836066[/C][C]0.682880457249123[/C][C]127.471126255778[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]86.9295081967213[/C][C]0.611087645696527[/C][C]142.253748392569[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]86.8360655737705[/C][C]0.587966918453831[/C][C]147.688692762039[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]86.7377049180328[/C][C]0.515901057646733[/C][C]168.128565802296[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]86.8525423728814[/C][C]1.29821024110590[/C][C]66.9017541402961[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]86.7912280701754[/C][C]1.2405312567135[/C][C]69.9629514375226[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]86.7090909090909[/C][C]1.1846671177937[/C][C]73.1927894399366[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]86.6867924528302[/C][C]1.14338520929514[/C][C]75.8159120374397[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]86.6705882352941[/C][C]1.10205260939027[/C][C]78.6446921832945[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]86.6938775510204[/C][C]1.07005232310267[/C][C]81.018353662975[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]86.7191489361702[/C][C]1.03521545080362[/C][C]83.7691795160628[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]86.7355555555555[/C][C]0.996342582129866[/C][C]87.0539482214464[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]86.7720930232558[/C][C]0.95849830395601[/C][C]90.5292087269443[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]86.8170731707317[/C][C]0.923863193593027[/C][C]93.9717847542865[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]86.8717948717949[/C][C]0.888727947470255[/C][C]97.7484674799229[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]86.9324324324324[/C][C]0.840527987701135[/C][C]103.425981888116[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]87.0142857142857[/C][C]0.79915020892356[/C][C]108.883517444727[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]87.0424242424242[/C][C]0.778134305993157[/C][C]111.860412234787[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]87.0322580645161[/C][C]0.760961292118509[/C][C]114.371465363526[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]87.0103448275862[/C][C]0.742106986225427[/C][C]117.247710158540[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]86.9814814814815[/C][C]0.713205456966791[/C][C]121.95851929037[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]86.972[/C][C]0.680282294345517[/C][C]127.84692578788[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]86.9782608695652[/C][C]0.655109335886746[/C][C]132.769075488495[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]87[/C][C]0.620905636569527[/C][C]140.117909833563[/C][/ROW]
[ROW][C]Median[/C][C]87.3[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]88.1[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]87.0322580645161[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]87.0322580645161[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]87.0322580645161[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]87.0322580645161[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]87.0322580645161[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]86.815625[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]87.0322580645161[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]87.0322580645161[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]61[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=16719&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=16719&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 Mean86.89344262295081.3533400673857264.2066578216406
Geometric Mean86.2576130505509
Harmonic Mean85.6188757284786
Quadratic Mean87.5234947379705
Winsorized Mean ( 1 / 20 )86.90983606557381.3450876115005364.6127696980425
Winsorized Mean ( 2 / 20 )86.9393442622951.3221717493994465.7549552860928
Winsorized Mean ( 3 / 20 )86.76721311475411.2657245302203468.5514193990136
Winsorized Mean ( 4 / 20 )86.74098360655741.2398955029325069.958301648328
Winsorized Mean ( 5 / 20 )86.57704918032791.1823090158567273.227090396154
Winsorized Mean ( 6 / 20 )86.57704918032791.1628056174864574.4553069561832
Winsorized Mean ( 7 / 20 )86.63442622950821.1423656914177875.8377346942089
Winsorized Mean ( 8 / 20 )86.52950819672131.0980841345091178.800435665527
Winsorized Mean ( 9 / 20 )86.51.0439521375876282.8582047831092
Winsorized Mean ( 10 / 20 )86.46721311475411.0032099337132686.1905471716237
Winsorized Mean ( 11 / 20 )86.46721311475411.0032099337132686.1905471716237
Winsorized Mean ( 12 / 20 )86.36885245901640.91906801505865893.9743860561876
Winsorized Mean ( 13 / 20 )86.8163934426230.79699291509377108.929943790540
Winsorized Mean ( 14 / 20 )87.11475409836060.74863385983806116.364966603574
Winsorized Mean ( 15 / 20 )87.1885245901640.721818810653629120.790042186920
Winsorized Mean ( 16 / 20 )87.21475409836070.717839944660839121.496100554236
Winsorized Mean ( 17 / 20 )87.04754098360660.682880457249123127.471126255778
Winsorized Mean ( 18 / 20 )86.92950819672130.611087645696527142.253748392569
Winsorized Mean ( 19 / 20 )86.83606557377050.587966918453831147.688692762039
Winsorized Mean ( 20 / 20 )86.73770491803280.515901057646733168.128565802296
Trimmed Mean ( 1 / 20 )86.85254237288141.2982102411059066.9017541402961
Trimmed Mean ( 2 / 20 )86.79122807017541.240531256713569.9629514375226
Trimmed Mean ( 3 / 20 )86.70909090909091.184667117793773.1927894399366
Trimmed Mean ( 4 / 20 )86.68679245283021.1433852092951475.8159120374397
Trimmed Mean ( 5 / 20 )86.67058823529411.1020526093902778.6446921832945
Trimmed Mean ( 6 / 20 )86.69387755102041.0700523231026781.018353662975
Trimmed Mean ( 7 / 20 )86.71914893617021.0352154508036283.7691795160628
Trimmed Mean ( 8 / 20 )86.73555555555550.99634258212986687.0539482214464
Trimmed Mean ( 9 / 20 )86.77209302325580.9584983039560190.5292087269443
Trimmed Mean ( 10 / 20 )86.81707317073170.92386319359302793.9717847542865
Trimmed Mean ( 11 / 20 )86.87179487179490.88872794747025597.7484674799229
Trimmed Mean ( 12 / 20 )86.93243243243240.840527987701135103.425981888116
Trimmed Mean ( 13 / 20 )87.01428571428570.79915020892356108.883517444727
Trimmed Mean ( 14 / 20 )87.04242424242420.778134305993157111.860412234787
Trimmed Mean ( 15 / 20 )87.03225806451610.760961292118509114.371465363526
Trimmed Mean ( 16 / 20 )87.01034482758620.742106986225427117.247710158540
Trimmed Mean ( 17 / 20 )86.98148148148150.713205456966791121.95851929037
Trimmed Mean ( 18 / 20 )86.9720.680282294345517127.84692578788
Trimmed Mean ( 19 / 20 )86.97826086956520.655109335886746132.769075488495
Trimmed Mean ( 20 / 20 )870.620905636569527140.117909833563
Median87.3
Midrange88.1
Midmean - Weighted Average at Xnp87.0322580645161
Midmean - Weighted Average at X(n+1)p87.0322580645161
Midmean - Empirical Distribution Function87.0322580645161
Midmean - Empirical Distribution Function - Averaging87.0322580645161
Midmean - Empirical Distribution Function - Interpolation87.0322580645161
Midmean - Closest Observation86.815625
Midmean - True Basic - Statistics Graphics Toolkit87.0322580645161
Midmean - MS Excel (old versions)87.0322580645161
Number of observations61



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')