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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 computationFri, 14 Dec 2007 13:08:07 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2007/Dec/14/t1197662011uf7wh40qfqqqkmc.htm/, Retrieved Thu, 02 May 2024 15:48:56 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=3963, Retrieved Thu, 02 May 2024 15:48:56 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact177
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2007-12-14 20:08:07] [ba3202e2798d2e4685d19d988e9c69df] [Current]
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Dataseries X:
75.6
48.7
111.7
119.5
103.4
96.3
96.6
110.4
104.4
110.7
93.6
114.8
74.9
69.8
104.2
109.3
92.7
91.7
84.4
94.5
103.6
105.9
108
119.9
84.5
76.7
120.5
119.6
102.3
101.7
86.9
93.6
113.6
106.7
96.1
124.6
72.5
89
115.3
119.1
104.4
104.9
76.9
95.3
114.9
98.9
102.9
90
81
66.2
86.7
86.7
103.4
89.5
113.7
120.2
137.8
99.1
110.4
112.3
82.2
72.2
106.7
106.4
110
87.5
79.7
83.3
91.8
89.2
90.6
92.6
61




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

\begin{tabular}{lllllllll}
\hline
Summary of compuational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=3963&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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=3963&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=3963&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 time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean97.47534246575341.9344005683113050.3904641378634
Geometric Mean95.9712986164923
Harmonic Mean94.3073535795681
Quadratic Mean98.8476584904321
Winsorized Mean ( 1 / 24 )97.46301369863011.8365750779454753.0678080460829
Winsorized Mean ( 2 / 24 )97.49315068493151.7778382979263154.8380304320412
Winsorized Mean ( 3 / 24 )97.62876712328771.7410976867161156.0731128805447
Winsorized Mean ( 4 / 24 )97.74383561643841.7098904100077857.1638012847816
Winsorized Mean ( 5 / 24 )97.74383561643841.7019607573960257.430134738233
Winsorized Mean ( 6 / 24 )97.93287671232881.6611587696912758.954555397814
Winsorized Mean ( 7 / 24 )97.96164383561641.6414561672720059.6797196226218
Winsorized Mean ( 8 / 24 )97.66575342465751.5484123296741063.0747712046531
Winsorized Mean ( 9 / 24 )97.6410958904111.5360332538183463.5670456011875
Winsorized Mean ( 10 / 24 )98.01095890410961.4645410105394466.9226455242853
Winsorized Mean ( 11 / 24 )98.0410958904111.4049906097397169.7806057996174
Winsorized Mean ( 12 / 24 )98.22191780821921.3697915696742471.7057397510324
Winsorized Mean ( 13 / 24 )98.1863013698631.3028468347007875.3628889864193
Winsorized Mean ( 14 / 24 )98.2821917808221.2526446034423878.4597574689053
Winsorized Mean ( 15 / 24 )98.09726027397261.2194329167768180.4449830116626
Winsorized Mean ( 16 / 24 )98.5136986301371.1377487769980186.5865124373664
Winsorized Mean ( 17 / 24 )98.5136986301371.1377487769980186.5865124373664
Winsorized Mean ( 18 / 24 )98.46438356164381.1164116962761788.1971981215128
Winsorized Mean ( 19 / 24 )98.43835616438361.0681258393749592.1598865373282
Winsorized Mean ( 20 / 24 )98.49315068493150.960998039931201102.490480305228
Winsorized Mean ( 21 / 24 )98.17671232876710.902833609075954108.742863958344
Winsorized Mean ( 22 / 24 )98.26712328767120.890408587984199110.361832324797
Winsorized Mean ( 23 / 24 )98.33013698630140.856594716812912114.791902233711
Winsorized Mean ( 24 / 24 )98.36301369863010.808722207569237121.627689678856
Trimmed Mean ( 1 / 24 )97.59436619718311.7751548092707454.9779465359848
Trimmed Mean ( 2 / 24 )97.73333333333331.7019842823305957.4231703241722
Trimmed Mean ( 3 / 24 )97.86417910447761.6526594133565559.2161810918533
Trimmed Mean ( 4 / 24 )97.95230769230771.6105677267246160.8184965257638
Trimmed Mean ( 5 / 24 )98.01269841269841.5714449667357862.3710664308475
Trimmed Mean ( 6 / 24 )98.07704918032791.5264935236772464.2498953707094
Trimmed Mean ( 7 / 24 )98.1067796610171.4836235681316666.1264634563359
Trimmed Mean ( 8 / 24 )98.13333333333331.4363028050180168.3235686726262
Trimmed Mean ( 9 / 24 )98.2109090909091.4011267056556770.0942382259074
Trimmed Mean ( 10 / 24 )98.29811320754721.3599989609992372.2780796356818
Trimmed Mean ( 11 / 24 )98.33921568627451.3253488728466474.1987394421344
Trimmed Mean ( 12 / 24 )98.37959183673471.2946973866737575.9865531894561
Trimmed Mean ( 13 / 24 )98.41.2630557779616777.9062981357787
Trimmed Mean ( 14 / 24 )98.42666666666671.2366066309040979.5941605089943
Trimmed Mean ( 15 / 24 )98.44418604651161.2124460797937981.1946920256074
Trimmed Mean ( 16 / 24 )98.48536585365851.1868566856977782.979998377612
Trimmed Mean ( 17 / 24 )98.48205128205131.1701694387781584.1605053238129
Trimmed Mean ( 18 / 24 )98.47837837837841.1457070619048985.954238786523
Trimmed Mean ( 19 / 24 )98.481.1158280642229688.2573249029897
Trimmed Mean ( 20 / 24 )98.48484848484851.0853721014999590.7383268362486
Trimmed Mean ( 21 / 24 )98.4838709677421.0693691917491592.095294803335
Trimmed Mean ( 22 / 24 )98.52068965517241.0584911106330993.0765394867096
Trimmed Mean ( 23 / 24 )98.55185185185191.0414947943044594.625390727631
Trimmed Mean ( 24 / 24 )98.581.0220241353966896.4556477540893
Median98.9
Midrange93.25
Midmean - Weighted Average at Xnp98.1583333333333
Midmean - Weighted Average at X(n+1)p98.4783783783784
Midmean - Empirical Distribution Function98.4783783783784
Midmean - Empirical Distribution Function - Averaging98.4783783783784
Midmean - Empirical Distribution Function - Interpolation98.4783783783784
Midmean - Closest Observation97.874358974359
Midmean - True Basic - Statistics Graphics Toolkit98.4783783783784
Midmean - MS Excel (old versions)98.4783783783784
Number of observations73

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 97.4753424657534 & 1.93440056831130 & 50.3904641378634 \tabularnewline
Geometric Mean & 95.9712986164923 &  &  \tabularnewline
Harmonic Mean & 94.3073535795681 &  &  \tabularnewline
Quadratic Mean & 98.8476584904321 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 97.4630136986301 & 1.83657507794547 & 53.0678080460829 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 97.4931506849315 & 1.77783829792631 & 54.8380304320412 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 97.6287671232877 & 1.74109768671611 & 56.0731128805447 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 97.7438356164384 & 1.70989041000778 & 57.1638012847816 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 97.7438356164384 & 1.70196075739602 & 57.430134738233 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 97.9328767123288 & 1.66115876969127 & 58.954555397814 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 97.9616438356164 & 1.64145616727200 & 59.6797196226218 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 97.6657534246575 & 1.54841232967410 & 63.0747712046531 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 97.641095890411 & 1.53603325381834 & 63.5670456011875 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 98.0109589041096 & 1.46454101053944 & 66.9226455242853 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 98.041095890411 & 1.40499060973971 & 69.7806057996174 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 98.2219178082192 & 1.36979156967424 & 71.7057397510324 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 98.186301369863 & 1.30284683470078 & 75.3628889864193 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 98.282191780822 & 1.25264460344238 & 78.4597574689053 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 98.0972602739726 & 1.21943291677681 & 80.4449830116626 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 98.513698630137 & 1.13774877699801 & 86.5865124373664 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 98.513698630137 & 1.13774877699801 & 86.5865124373664 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 98.4643835616438 & 1.11641169627617 & 88.1971981215128 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 98.4383561643836 & 1.06812583937495 & 92.1598865373282 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 98.4931506849315 & 0.960998039931201 & 102.490480305228 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 98.1767123287671 & 0.902833609075954 & 108.742863958344 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 98.2671232876712 & 0.890408587984199 & 110.361832324797 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 98.3301369863014 & 0.856594716812912 & 114.791902233711 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 98.3630136986301 & 0.808722207569237 & 121.627689678856 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 97.5943661971831 & 1.77515480927074 & 54.9779465359848 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 97.7333333333333 & 1.70198428233059 & 57.4231703241722 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 97.8641791044776 & 1.65265941335655 & 59.2161810918533 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 97.9523076923077 & 1.61056772672461 & 60.8184965257638 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 98.0126984126984 & 1.57144496673578 & 62.3710664308475 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 98.0770491803279 & 1.52649352367724 & 64.2498953707094 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 98.106779661017 & 1.48362356813166 & 66.1264634563359 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 98.1333333333333 & 1.43630280501801 & 68.3235686726262 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 98.210909090909 & 1.40112670565567 & 70.0942382259074 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 98.2981132075472 & 1.35999896099923 & 72.2780796356818 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 98.3392156862745 & 1.32534887284664 & 74.1987394421344 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 98.3795918367347 & 1.29469738667375 & 75.9865531894561 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 98.4 & 1.26305577796167 & 77.9062981357787 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 98.4266666666667 & 1.23660663090409 & 79.5941605089943 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 98.4441860465116 & 1.21244607979379 & 81.1946920256074 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 98.4853658536585 & 1.18685668569777 & 82.979998377612 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 98.4820512820513 & 1.17016943877815 & 84.1605053238129 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 98.4783783783784 & 1.14570706190489 & 85.954238786523 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 98.48 & 1.11582806422296 & 88.2573249029897 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 98.4848484848485 & 1.08537210149995 & 90.7383268362486 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 98.483870967742 & 1.06936919174915 & 92.095294803335 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 98.5206896551724 & 1.05849111063309 & 93.0765394867096 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 98.5518518518519 & 1.04149479430445 & 94.625390727631 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 98.58 & 1.02202413539668 & 96.4556477540893 \tabularnewline
Median & 98.9 &  &  \tabularnewline
Midrange & 93.25 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 98.1583333333333 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 98.4783783783784 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 98.4783783783784 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 98.4783783783784 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 98.4783783783784 &  &  \tabularnewline
Midmean - Closest Observation & 97.874358974359 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 98.4783783783784 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 98.4783783783784 &  &  \tabularnewline
Number of observations & 73 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=3963&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]97.4753424657534[/C][C]1.93440056831130[/C][C]50.3904641378634[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]95.9712986164923[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]94.3073535795681[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]98.8476584904321[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]97.4630136986301[/C][C]1.83657507794547[/C][C]53.0678080460829[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]97.4931506849315[/C][C]1.77783829792631[/C][C]54.8380304320412[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]97.6287671232877[/C][C]1.74109768671611[/C][C]56.0731128805447[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]97.7438356164384[/C][C]1.70989041000778[/C][C]57.1638012847816[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]97.7438356164384[/C][C]1.70196075739602[/C][C]57.430134738233[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]97.9328767123288[/C][C]1.66115876969127[/C][C]58.954555397814[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]97.9616438356164[/C][C]1.64145616727200[/C][C]59.6797196226218[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]97.6657534246575[/C][C]1.54841232967410[/C][C]63.0747712046531[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]97.641095890411[/C][C]1.53603325381834[/C][C]63.5670456011875[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]98.0109589041096[/C][C]1.46454101053944[/C][C]66.9226455242853[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]98.041095890411[/C][C]1.40499060973971[/C][C]69.7806057996174[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]98.2219178082192[/C][C]1.36979156967424[/C][C]71.7057397510324[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]98.186301369863[/C][C]1.30284683470078[/C][C]75.3628889864193[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]98.282191780822[/C][C]1.25264460344238[/C][C]78.4597574689053[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]98.0972602739726[/C][C]1.21943291677681[/C][C]80.4449830116626[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]98.513698630137[/C][C]1.13774877699801[/C][C]86.5865124373664[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]98.513698630137[/C][C]1.13774877699801[/C][C]86.5865124373664[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]98.4643835616438[/C][C]1.11641169627617[/C][C]88.1971981215128[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]98.4383561643836[/C][C]1.06812583937495[/C][C]92.1598865373282[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]98.4931506849315[/C][C]0.960998039931201[/C][C]102.490480305228[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]98.1767123287671[/C][C]0.902833609075954[/C][C]108.742863958344[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]98.2671232876712[/C][C]0.890408587984199[/C][C]110.361832324797[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]98.3301369863014[/C][C]0.856594716812912[/C][C]114.791902233711[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]98.3630136986301[/C][C]0.808722207569237[/C][C]121.627689678856[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]97.5943661971831[/C][C]1.77515480927074[/C][C]54.9779465359848[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]97.7333333333333[/C][C]1.70198428233059[/C][C]57.4231703241722[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]97.8641791044776[/C][C]1.65265941335655[/C][C]59.2161810918533[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]97.9523076923077[/C][C]1.61056772672461[/C][C]60.8184965257638[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]98.0126984126984[/C][C]1.57144496673578[/C][C]62.3710664308475[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]98.0770491803279[/C][C]1.52649352367724[/C][C]64.2498953707094[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]98.106779661017[/C][C]1.48362356813166[/C][C]66.1264634563359[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]98.1333333333333[/C][C]1.43630280501801[/C][C]68.3235686726262[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]98.210909090909[/C][C]1.40112670565567[/C][C]70.0942382259074[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]98.2981132075472[/C][C]1.35999896099923[/C][C]72.2780796356818[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]98.3392156862745[/C][C]1.32534887284664[/C][C]74.1987394421344[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]98.3795918367347[/C][C]1.29469738667375[/C][C]75.9865531894561[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]98.4[/C][C]1.26305577796167[/C][C]77.9062981357787[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]98.4266666666667[/C][C]1.23660663090409[/C][C]79.5941605089943[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]98.4441860465116[/C][C]1.21244607979379[/C][C]81.1946920256074[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]98.4853658536585[/C][C]1.18685668569777[/C][C]82.979998377612[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]98.4820512820513[/C][C]1.17016943877815[/C][C]84.1605053238129[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]98.4783783783784[/C][C]1.14570706190489[/C][C]85.954238786523[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]98.48[/C][C]1.11582806422296[/C][C]88.2573249029897[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]98.4848484848485[/C][C]1.08537210149995[/C][C]90.7383268362486[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]98.483870967742[/C][C]1.06936919174915[/C][C]92.095294803335[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]98.5206896551724[/C][C]1.05849111063309[/C][C]93.0765394867096[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]98.5518518518519[/C][C]1.04149479430445[/C][C]94.625390727631[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]98.58[/C][C]1.02202413539668[/C][C]96.4556477540893[/C][/ROW]
[ROW][C]Median[/C][C]98.9[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]93.25[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]98.1583333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]98.4783783783784[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]98.4783783783784[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]98.4783783783784[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]98.4783783783784[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]97.874358974359[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]98.4783783783784[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]98.4783783783784[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]73[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=3963&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=3963&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 Mean97.47534246575341.9344005683113050.3904641378634
Geometric Mean95.9712986164923
Harmonic Mean94.3073535795681
Quadratic Mean98.8476584904321
Winsorized Mean ( 1 / 24 )97.46301369863011.8365750779454753.0678080460829
Winsorized Mean ( 2 / 24 )97.49315068493151.7778382979263154.8380304320412
Winsorized Mean ( 3 / 24 )97.62876712328771.7410976867161156.0731128805447
Winsorized Mean ( 4 / 24 )97.74383561643841.7098904100077857.1638012847816
Winsorized Mean ( 5 / 24 )97.74383561643841.7019607573960257.430134738233
Winsorized Mean ( 6 / 24 )97.93287671232881.6611587696912758.954555397814
Winsorized Mean ( 7 / 24 )97.96164383561641.6414561672720059.6797196226218
Winsorized Mean ( 8 / 24 )97.66575342465751.5484123296741063.0747712046531
Winsorized Mean ( 9 / 24 )97.6410958904111.5360332538183463.5670456011875
Winsorized Mean ( 10 / 24 )98.01095890410961.4645410105394466.9226455242853
Winsorized Mean ( 11 / 24 )98.0410958904111.4049906097397169.7806057996174
Winsorized Mean ( 12 / 24 )98.22191780821921.3697915696742471.7057397510324
Winsorized Mean ( 13 / 24 )98.1863013698631.3028468347007875.3628889864193
Winsorized Mean ( 14 / 24 )98.2821917808221.2526446034423878.4597574689053
Winsorized Mean ( 15 / 24 )98.09726027397261.2194329167768180.4449830116626
Winsorized Mean ( 16 / 24 )98.5136986301371.1377487769980186.5865124373664
Winsorized Mean ( 17 / 24 )98.5136986301371.1377487769980186.5865124373664
Winsorized Mean ( 18 / 24 )98.46438356164381.1164116962761788.1971981215128
Winsorized Mean ( 19 / 24 )98.43835616438361.0681258393749592.1598865373282
Winsorized Mean ( 20 / 24 )98.49315068493150.960998039931201102.490480305228
Winsorized Mean ( 21 / 24 )98.17671232876710.902833609075954108.742863958344
Winsorized Mean ( 22 / 24 )98.26712328767120.890408587984199110.361832324797
Winsorized Mean ( 23 / 24 )98.33013698630140.856594716812912114.791902233711
Winsorized Mean ( 24 / 24 )98.36301369863010.808722207569237121.627689678856
Trimmed Mean ( 1 / 24 )97.59436619718311.7751548092707454.9779465359848
Trimmed Mean ( 2 / 24 )97.73333333333331.7019842823305957.4231703241722
Trimmed Mean ( 3 / 24 )97.86417910447761.6526594133565559.2161810918533
Trimmed Mean ( 4 / 24 )97.95230769230771.6105677267246160.8184965257638
Trimmed Mean ( 5 / 24 )98.01269841269841.5714449667357862.3710664308475
Trimmed Mean ( 6 / 24 )98.07704918032791.5264935236772464.2498953707094
Trimmed Mean ( 7 / 24 )98.1067796610171.4836235681316666.1264634563359
Trimmed Mean ( 8 / 24 )98.13333333333331.4363028050180168.3235686726262
Trimmed Mean ( 9 / 24 )98.2109090909091.4011267056556770.0942382259074
Trimmed Mean ( 10 / 24 )98.29811320754721.3599989609992372.2780796356818
Trimmed Mean ( 11 / 24 )98.33921568627451.3253488728466474.1987394421344
Trimmed Mean ( 12 / 24 )98.37959183673471.2946973866737575.9865531894561
Trimmed Mean ( 13 / 24 )98.41.2630557779616777.9062981357787
Trimmed Mean ( 14 / 24 )98.42666666666671.2366066309040979.5941605089943
Trimmed Mean ( 15 / 24 )98.44418604651161.2124460797937981.1946920256074
Trimmed Mean ( 16 / 24 )98.48536585365851.1868566856977782.979998377612
Trimmed Mean ( 17 / 24 )98.48205128205131.1701694387781584.1605053238129
Trimmed Mean ( 18 / 24 )98.47837837837841.1457070619048985.954238786523
Trimmed Mean ( 19 / 24 )98.481.1158280642229688.2573249029897
Trimmed Mean ( 20 / 24 )98.48484848484851.0853721014999590.7383268362486
Trimmed Mean ( 21 / 24 )98.4838709677421.0693691917491592.095294803335
Trimmed Mean ( 22 / 24 )98.52068965517241.0584911106330993.0765394867096
Trimmed Mean ( 23 / 24 )98.55185185185191.0414947943044594.625390727631
Trimmed Mean ( 24 / 24 )98.581.0220241353966896.4556477540893
Median98.9
Midrange93.25
Midmean - Weighted Average at Xnp98.1583333333333
Midmean - Weighted Average at X(n+1)p98.4783783783784
Midmean - Empirical Distribution Function98.4783783783784
Midmean - Empirical Distribution Function - Averaging98.4783783783784
Midmean - Empirical Distribution Function - Interpolation98.4783783783784
Midmean - Closest Observation97.874358974359
Midmean - True Basic - Statistics Graphics Toolkit98.4783783783784
Midmean - MS Excel (old versions)98.4783783783784
Number of observations73



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')