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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 computationTue, 13 Nov 2007 13:12:33 -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/Nov/13/t11949844466pggeuo3m0fggzg.htm/, Retrieved Tue, 30 Apr 2024 06:21:06 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=5383, Retrieved Tue, 30 Apr 2024 06:21:06 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact233
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2007-11-13 20:12:33] [bc15d8d2f79dc0888573b215bcd9118f] [Current]
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Dataseries X:
101,30
97,60
96,40
97,00
96,40
94,70
89,30
85,90
83,30
81,50
85,00
84,80
87,50
89,00
90,00
89,60
87,40
84,80
81,90
81,10
79,10
80,50
88,50
90,90
84,90
80,00
76,50
75,40
73,50
74,30
77,70
77,90
76,70
77,20
86,00
86,90
92,00
101,70
104,50
101,70
100,60
100,30
102,50
101,00
108,60
103,40
106,40
106,60
108,90
110,50
114,00
112,80
109,60
116,00
124,60
129,00
131,50
138,60
138,10
146,30
157,60
158,40
176,30
199,90
210,40
202,60
207,10
202,00
203,40
216,30
207,30
203,50
204,40
203,70
205,70
208,00
209,30
208,70
206,50
204,50




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=5383&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=5383&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=5383&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 Mean122.191255.3808501262799922.7085399392969
Geometric Mean114.245469217907
Harmonic Mean107.894969991047
Quadratic Mean131.217498356736
Winsorized Mean ( 1 / 26 )122.12755.3638670323880422.7685547129657
Winsorized Mean ( 2 / 26 )122.12755.3550987105157222.8058354480339
Winsorized Mean ( 3 / 26 )122.146255.3459676462880222.8482957776246
Winsorized Mean ( 4 / 26 )122.121255.3377381350102822.8788387348951
Winsorized Mean ( 5 / 26 )122.108755.3255026486928122.9290562891697
Winsorized Mean ( 6 / 26 )122.131255.3184829954251622.9635499643516
Winsorized Mean ( 7 / 26 )122.096255.3060409934833123.0108003594308
Winsorized Mean ( 8 / 26 )122.136255.2774494114437623.1430451488851
Winsorized Mean ( 9 / 26 )122.10255.2401097241265923.3015158896032
Winsorized Mean ( 10 / 26 )122.15255.2312939727897923.3503413563389
Winsorized Mean ( 11 / 26 )122.138755.2038932278686323.4706487338951
Winsorized Mean ( 12 / 26 )122.168755.1919736600401423.5303100515066
Winsorized Mean ( 13 / 26 )122.21755.1823284119194323.5835111721013
Winsorized Mean ( 14 / 26 )122.32255.1307252599450323.841171335943
Winsorized Mean ( 15 / 26 )122.491255.0817012232119324.1043785574191
Winsorized Mean ( 16 / 26 )122.071254.9987207837498224.4204978195297
Winsorized Mean ( 17 / 26 )117.07754.0334075548058129.0269451844761
Winsorized Mean ( 18 / 26 )113.07253.3047166020129934.2154906508851
Winsorized Mean ( 19 / 26 )113.096253.2489323678486234.8102814078861
Winsorized Mean ( 20 / 26 )110.296252.7677353557030839.8507211943975
Winsorized Mean ( 21 / 26 )108.511252.4149671707743244.9328054282443
Winsorized Mean ( 22 / 26 )108.511252.3777801807182445.6355263114452
Winsorized Mean ( 23 / 26 )106.64252.0812125048890051.2405627726554
Winsorized Mean ( 24 / 26 )106.19251.9336623078723154.9178103992977
Winsorized Mean ( 25 / 26 )104.973751.7128634177354861.2855344524682
Winsorized Mean ( 26 / 26 )102.276251.3108230622302578.0244511612316
Trimmed Mean ( 1 / 26 )121.6089743589745.3472909433243822.7421652660947
Trimmed Mean ( 2 / 26 )121.0631578947375.3243574168272922.7376091454951
Trimmed Mean ( 3 / 26 )120.4878378378385.2991358025965222.7372617585683
Trimmed Mean ( 4 / 26 )119.8736111111115.2695203065156422.7484864159058
Trimmed Mean ( 5 / 26 )119.2314285714295.2334750450372422.7824586045352
Trimmed Mean ( 6 / 26 )118.5544117647065.1903251465134622.8414229201697
Trimmed Mean ( 7 / 26 )117.8318181818185.1366497744008922.9394300481701
Trimmed Mean ( 8 / 26 )117.07031255.0713821648483523.0844982086852
Trimmed Mean ( 9 / 26 )116.2532258064524.9949819968994123.2740029650987
Trimmed Mean ( 10 / 26 )115.3866666666674.9062818413327323.5181488545149
Trimmed Mean ( 11 / 26 )114.4534482758624.795342830136723.8676258048894
Trimmed Mean ( 12 / 26 )113.4553571428574.6601835979403324.3456839754127
Trimmed Mean ( 13 / 26 )112.3796296296304.4899782648933525.0289919014338
Trimmed Mean ( 14 / 26 )111.2153846153854.2726394474350626.0296676056177
Trimmed Mean ( 15 / 26 )109.9464.0001257225140327.4856361091822
Trimmed Mean ( 16 / 26 )108.5520833333333.6468034550231229.7663651666813
Trimmed Mean ( 17 / 26 )107.0826086956523.1847315456492433.6237472957308
Trimmed Mean ( 18 / 26 )106.0136363636362.8771179181422636.8471642038533
Trimmed Mean ( 19 / 26 )105.2666666666672.6891049304813339.1456151351538
Trimmed Mean ( 20 / 26 )104.44252.4431035524407742.7499276056707
Trimmed Mean ( 21 / 26 )103.8263157894742.2636740620151645.8662832833124
Trimmed Mean ( 22 / 26 )103.3305555555562.1269428819147248.5817256467815
Trimmed Mean ( 23 / 26 )102.7764705882351.9409649860490252.9512234001937
Trimmed Mean ( 24 / 26 )102.356251.7856108192951457.3228213527539
Trimmed Mean ( 25 / 26 )101.931.6101556289456363.304439749558
Trimmed Mean ( 26 / 26 )101.5821428571431.4415696689217870.4663430752681
Median101.5
Midrange144.9
Midmean - Weighted Average at Xnp103.990243902439
Midmean - Weighted Average at X(n+1)p104.4425
Midmean - Empirical Distribution Function103.990243902439
Midmean - Empirical Distribution Function - Averaging104.4425
Midmean - Empirical Distribution Function - Interpolation104.4425
Midmean - Closest Observation103.990243902439
Midmean - True Basic - Statistics Graphics Toolkit104.4425
Midmean - MS Excel (old versions)105.266666666667
Number of observations80

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 122.19125 & 5.38085012627999 & 22.7085399392969 \tabularnewline
Geometric Mean & 114.245469217907 &  &  \tabularnewline
Harmonic Mean & 107.894969991047 &  &  \tabularnewline
Quadratic Mean & 131.217498356736 &  &  \tabularnewline
Winsorized Mean ( 1 / 26 ) & 122.1275 & 5.36386703238804 & 22.7685547129657 \tabularnewline
Winsorized Mean ( 2 / 26 ) & 122.1275 & 5.35509871051572 & 22.8058354480339 \tabularnewline
Winsorized Mean ( 3 / 26 ) & 122.14625 & 5.34596764628802 & 22.8482957776246 \tabularnewline
Winsorized Mean ( 4 / 26 ) & 122.12125 & 5.33773813501028 & 22.8788387348951 \tabularnewline
Winsorized Mean ( 5 / 26 ) & 122.10875 & 5.32550264869281 & 22.9290562891697 \tabularnewline
Winsorized Mean ( 6 / 26 ) & 122.13125 & 5.31848299542516 & 22.9635499643516 \tabularnewline
Winsorized Mean ( 7 / 26 ) & 122.09625 & 5.30604099348331 & 23.0108003594308 \tabularnewline
Winsorized Mean ( 8 / 26 ) & 122.13625 & 5.27744941144376 & 23.1430451488851 \tabularnewline
Winsorized Mean ( 9 / 26 ) & 122.1025 & 5.24010972412659 & 23.3015158896032 \tabularnewline
Winsorized Mean ( 10 / 26 ) & 122.1525 & 5.23129397278979 & 23.3503413563389 \tabularnewline
Winsorized Mean ( 11 / 26 ) & 122.13875 & 5.20389322786863 & 23.4706487338951 \tabularnewline
Winsorized Mean ( 12 / 26 ) & 122.16875 & 5.19197366004014 & 23.5303100515066 \tabularnewline
Winsorized Mean ( 13 / 26 ) & 122.2175 & 5.18232841191943 & 23.5835111721013 \tabularnewline
Winsorized Mean ( 14 / 26 ) & 122.3225 & 5.13072525994503 & 23.841171335943 \tabularnewline
Winsorized Mean ( 15 / 26 ) & 122.49125 & 5.08170122321193 & 24.1043785574191 \tabularnewline
Winsorized Mean ( 16 / 26 ) & 122.07125 & 4.99872078374982 & 24.4204978195297 \tabularnewline
Winsorized Mean ( 17 / 26 ) & 117.0775 & 4.03340755480581 & 29.0269451844761 \tabularnewline
Winsorized Mean ( 18 / 26 ) & 113.0725 & 3.30471660201299 & 34.2154906508851 \tabularnewline
Winsorized Mean ( 19 / 26 ) & 113.09625 & 3.24893236784862 & 34.8102814078861 \tabularnewline
Winsorized Mean ( 20 / 26 ) & 110.29625 & 2.76773535570308 & 39.8507211943975 \tabularnewline
Winsorized Mean ( 21 / 26 ) & 108.51125 & 2.41496717077432 & 44.9328054282443 \tabularnewline
Winsorized Mean ( 22 / 26 ) & 108.51125 & 2.37778018071824 & 45.6355263114452 \tabularnewline
Winsorized Mean ( 23 / 26 ) & 106.6425 & 2.08121250488900 & 51.2405627726554 \tabularnewline
Winsorized Mean ( 24 / 26 ) & 106.1925 & 1.93366230787231 & 54.9178103992977 \tabularnewline
Winsorized Mean ( 25 / 26 ) & 104.97375 & 1.71286341773548 & 61.2855344524682 \tabularnewline
Winsorized Mean ( 26 / 26 ) & 102.27625 & 1.31082306223025 & 78.0244511612316 \tabularnewline
Trimmed Mean ( 1 / 26 ) & 121.608974358974 & 5.34729094332438 & 22.7421652660947 \tabularnewline
Trimmed Mean ( 2 / 26 ) & 121.063157894737 & 5.32435741682729 & 22.7376091454951 \tabularnewline
Trimmed Mean ( 3 / 26 ) & 120.487837837838 & 5.29913580259652 & 22.7372617585683 \tabularnewline
Trimmed Mean ( 4 / 26 ) & 119.873611111111 & 5.26952030651564 & 22.7484864159058 \tabularnewline
Trimmed Mean ( 5 / 26 ) & 119.231428571429 & 5.23347504503724 & 22.7824586045352 \tabularnewline
Trimmed Mean ( 6 / 26 ) & 118.554411764706 & 5.19032514651346 & 22.8414229201697 \tabularnewline
Trimmed Mean ( 7 / 26 ) & 117.831818181818 & 5.13664977440089 & 22.9394300481701 \tabularnewline
Trimmed Mean ( 8 / 26 ) & 117.0703125 & 5.07138216484835 & 23.0844982086852 \tabularnewline
Trimmed Mean ( 9 / 26 ) & 116.253225806452 & 4.99498199689941 & 23.2740029650987 \tabularnewline
Trimmed Mean ( 10 / 26 ) & 115.386666666667 & 4.90628184133273 & 23.5181488545149 \tabularnewline
Trimmed Mean ( 11 / 26 ) & 114.453448275862 & 4.7953428301367 & 23.8676258048894 \tabularnewline
Trimmed Mean ( 12 / 26 ) & 113.455357142857 & 4.66018359794033 & 24.3456839754127 \tabularnewline
Trimmed Mean ( 13 / 26 ) & 112.379629629630 & 4.48997826489335 & 25.0289919014338 \tabularnewline
Trimmed Mean ( 14 / 26 ) & 111.215384615385 & 4.27263944743506 & 26.0296676056177 \tabularnewline
Trimmed Mean ( 15 / 26 ) & 109.946 & 4.00012572251403 & 27.4856361091822 \tabularnewline
Trimmed Mean ( 16 / 26 ) & 108.552083333333 & 3.64680345502312 & 29.7663651666813 \tabularnewline
Trimmed Mean ( 17 / 26 ) & 107.082608695652 & 3.18473154564924 & 33.6237472957308 \tabularnewline
Trimmed Mean ( 18 / 26 ) & 106.013636363636 & 2.87711791814226 & 36.8471642038533 \tabularnewline
Trimmed Mean ( 19 / 26 ) & 105.266666666667 & 2.68910493048133 & 39.1456151351538 \tabularnewline
Trimmed Mean ( 20 / 26 ) & 104.4425 & 2.44310355244077 & 42.7499276056707 \tabularnewline
Trimmed Mean ( 21 / 26 ) & 103.826315789474 & 2.26367406201516 & 45.8662832833124 \tabularnewline
Trimmed Mean ( 22 / 26 ) & 103.330555555556 & 2.12694288191472 & 48.5817256467815 \tabularnewline
Trimmed Mean ( 23 / 26 ) & 102.776470588235 & 1.94096498604902 & 52.9512234001937 \tabularnewline
Trimmed Mean ( 24 / 26 ) & 102.35625 & 1.78561081929514 & 57.3228213527539 \tabularnewline
Trimmed Mean ( 25 / 26 ) & 101.93 & 1.61015562894563 & 63.304439749558 \tabularnewline
Trimmed Mean ( 26 / 26 ) & 101.582142857143 & 1.44156966892178 & 70.4663430752681 \tabularnewline
Median & 101.5 &  &  \tabularnewline
Midrange & 144.9 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 103.990243902439 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 104.4425 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 103.990243902439 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 104.4425 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 104.4425 &  &  \tabularnewline
Midmean - Closest Observation & 103.990243902439 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 104.4425 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 105.266666666667 &  &  \tabularnewline
Number of observations & 80 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=5383&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]122.19125[/C][C]5.38085012627999[/C][C]22.7085399392969[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]114.245469217907[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]107.894969991047[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]131.217498356736[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 26 )[/C][C]122.1275[/C][C]5.36386703238804[/C][C]22.7685547129657[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 26 )[/C][C]122.1275[/C][C]5.35509871051572[/C][C]22.8058354480339[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 26 )[/C][C]122.14625[/C][C]5.34596764628802[/C][C]22.8482957776246[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 26 )[/C][C]122.12125[/C][C]5.33773813501028[/C][C]22.8788387348951[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 26 )[/C][C]122.10875[/C][C]5.32550264869281[/C][C]22.9290562891697[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 26 )[/C][C]122.13125[/C][C]5.31848299542516[/C][C]22.9635499643516[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 26 )[/C][C]122.09625[/C][C]5.30604099348331[/C][C]23.0108003594308[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 26 )[/C][C]122.13625[/C][C]5.27744941144376[/C][C]23.1430451488851[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 26 )[/C][C]122.1025[/C][C]5.24010972412659[/C][C]23.3015158896032[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 26 )[/C][C]122.1525[/C][C]5.23129397278979[/C][C]23.3503413563389[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 26 )[/C][C]122.13875[/C][C]5.20389322786863[/C][C]23.4706487338951[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 26 )[/C][C]122.16875[/C][C]5.19197366004014[/C][C]23.5303100515066[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 26 )[/C][C]122.2175[/C][C]5.18232841191943[/C][C]23.5835111721013[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 26 )[/C][C]122.3225[/C][C]5.13072525994503[/C][C]23.841171335943[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 26 )[/C][C]122.49125[/C][C]5.08170122321193[/C][C]24.1043785574191[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 26 )[/C][C]122.07125[/C][C]4.99872078374982[/C][C]24.4204978195297[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 26 )[/C][C]117.0775[/C][C]4.03340755480581[/C][C]29.0269451844761[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 26 )[/C][C]113.0725[/C][C]3.30471660201299[/C][C]34.2154906508851[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 26 )[/C][C]113.09625[/C][C]3.24893236784862[/C][C]34.8102814078861[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 26 )[/C][C]110.29625[/C][C]2.76773535570308[/C][C]39.8507211943975[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 26 )[/C][C]108.51125[/C][C]2.41496717077432[/C][C]44.9328054282443[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 26 )[/C][C]108.51125[/C][C]2.37778018071824[/C][C]45.6355263114452[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 26 )[/C][C]106.6425[/C][C]2.08121250488900[/C][C]51.2405627726554[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 26 )[/C][C]106.1925[/C][C]1.93366230787231[/C][C]54.9178103992977[/C][/ROW]
[ROW][C]Winsorized Mean ( 25 / 26 )[/C][C]104.97375[/C][C]1.71286341773548[/C][C]61.2855344524682[/C][/ROW]
[ROW][C]Winsorized Mean ( 26 / 26 )[/C][C]102.27625[/C][C]1.31082306223025[/C][C]78.0244511612316[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 26 )[/C][C]121.608974358974[/C][C]5.34729094332438[/C][C]22.7421652660947[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 26 )[/C][C]121.063157894737[/C][C]5.32435741682729[/C][C]22.7376091454951[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 26 )[/C][C]120.487837837838[/C][C]5.29913580259652[/C][C]22.7372617585683[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 26 )[/C][C]119.873611111111[/C][C]5.26952030651564[/C][C]22.7484864159058[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 26 )[/C][C]119.231428571429[/C][C]5.23347504503724[/C][C]22.7824586045352[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 26 )[/C][C]118.554411764706[/C][C]5.19032514651346[/C][C]22.8414229201697[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 26 )[/C][C]117.831818181818[/C][C]5.13664977440089[/C][C]22.9394300481701[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 26 )[/C][C]117.0703125[/C][C]5.07138216484835[/C][C]23.0844982086852[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 26 )[/C][C]116.253225806452[/C][C]4.99498199689941[/C][C]23.2740029650987[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 26 )[/C][C]115.386666666667[/C][C]4.90628184133273[/C][C]23.5181488545149[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 26 )[/C][C]114.453448275862[/C][C]4.7953428301367[/C][C]23.8676258048894[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 26 )[/C][C]113.455357142857[/C][C]4.66018359794033[/C][C]24.3456839754127[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 26 )[/C][C]112.379629629630[/C][C]4.48997826489335[/C][C]25.0289919014338[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 26 )[/C][C]111.215384615385[/C][C]4.27263944743506[/C][C]26.0296676056177[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 26 )[/C][C]109.946[/C][C]4.00012572251403[/C][C]27.4856361091822[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 26 )[/C][C]108.552083333333[/C][C]3.64680345502312[/C][C]29.7663651666813[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 26 )[/C][C]107.082608695652[/C][C]3.18473154564924[/C][C]33.6237472957308[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 26 )[/C][C]106.013636363636[/C][C]2.87711791814226[/C][C]36.8471642038533[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 26 )[/C][C]105.266666666667[/C][C]2.68910493048133[/C][C]39.1456151351538[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 26 )[/C][C]104.4425[/C][C]2.44310355244077[/C][C]42.7499276056707[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 26 )[/C][C]103.826315789474[/C][C]2.26367406201516[/C][C]45.8662832833124[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 26 )[/C][C]103.330555555556[/C][C]2.12694288191472[/C][C]48.5817256467815[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 26 )[/C][C]102.776470588235[/C][C]1.94096498604902[/C][C]52.9512234001937[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 26 )[/C][C]102.35625[/C][C]1.78561081929514[/C][C]57.3228213527539[/C][/ROW]
[ROW][C]Trimmed Mean ( 25 / 26 )[/C][C]101.93[/C][C]1.61015562894563[/C][C]63.304439749558[/C][/ROW]
[ROW][C]Trimmed Mean ( 26 / 26 )[/C][C]101.582142857143[/C][C]1.44156966892178[/C][C]70.4663430752681[/C][/ROW]
[ROW][C]Median[/C][C]101.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]144.9[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]103.990243902439[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]104.4425[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]103.990243902439[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]104.4425[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]104.4425[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]103.990243902439[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]104.4425[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]105.266666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]80[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=5383&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=5383&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 Mean122.191255.3808501262799922.7085399392969
Geometric Mean114.245469217907
Harmonic Mean107.894969991047
Quadratic Mean131.217498356736
Winsorized Mean ( 1 / 26 )122.12755.3638670323880422.7685547129657
Winsorized Mean ( 2 / 26 )122.12755.3550987105157222.8058354480339
Winsorized Mean ( 3 / 26 )122.146255.3459676462880222.8482957776246
Winsorized Mean ( 4 / 26 )122.121255.3377381350102822.8788387348951
Winsorized Mean ( 5 / 26 )122.108755.3255026486928122.9290562891697
Winsorized Mean ( 6 / 26 )122.131255.3184829954251622.9635499643516
Winsorized Mean ( 7 / 26 )122.096255.3060409934833123.0108003594308
Winsorized Mean ( 8 / 26 )122.136255.2774494114437623.1430451488851
Winsorized Mean ( 9 / 26 )122.10255.2401097241265923.3015158896032
Winsorized Mean ( 10 / 26 )122.15255.2312939727897923.3503413563389
Winsorized Mean ( 11 / 26 )122.138755.2038932278686323.4706487338951
Winsorized Mean ( 12 / 26 )122.168755.1919736600401423.5303100515066
Winsorized Mean ( 13 / 26 )122.21755.1823284119194323.5835111721013
Winsorized Mean ( 14 / 26 )122.32255.1307252599450323.841171335943
Winsorized Mean ( 15 / 26 )122.491255.0817012232119324.1043785574191
Winsorized Mean ( 16 / 26 )122.071254.9987207837498224.4204978195297
Winsorized Mean ( 17 / 26 )117.07754.0334075548058129.0269451844761
Winsorized Mean ( 18 / 26 )113.07253.3047166020129934.2154906508851
Winsorized Mean ( 19 / 26 )113.096253.2489323678486234.8102814078861
Winsorized Mean ( 20 / 26 )110.296252.7677353557030839.8507211943975
Winsorized Mean ( 21 / 26 )108.511252.4149671707743244.9328054282443
Winsorized Mean ( 22 / 26 )108.511252.3777801807182445.6355263114452
Winsorized Mean ( 23 / 26 )106.64252.0812125048890051.2405627726554
Winsorized Mean ( 24 / 26 )106.19251.9336623078723154.9178103992977
Winsorized Mean ( 25 / 26 )104.973751.7128634177354861.2855344524682
Winsorized Mean ( 26 / 26 )102.276251.3108230622302578.0244511612316
Trimmed Mean ( 1 / 26 )121.6089743589745.3472909433243822.7421652660947
Trimmed Mean ( 2 / 26 )121.0631578947375.3243574168272922.7376091454951
Trimmed Mean ( 3 / 26 )120.4878378378385.2991358025965222.7372617585683
Trimmed Mean ( 4 / 26 )119.8736111111115.2695203065156422.7484864159058
Trimmed Mean ( 5 / 26 )119.2314285714295.2334750450372422.7824586045352
Trimmed Mean ( 6 / 26 )118.5544117647065.1903251465134622.8414229201697
Trimmed Mean ( 7 / 26 )117.8318181818185.1366497744008922.9394300481701
Trimmed Mean ( 8 / 26 )117.07031255.0713821648483523.0844982086852
Trimmed Mean ( 9 / 26 )116.2532258064524.9949819968994123.2740029650987
Trimmed Mean ( 10 / 26 )115.3866666666674.9062818413327323.5181488545149
Trimmed Mean ( 11 / 26 )114.4534482758624.795342830136723.8676258048894
Trimmed Mean ( 12 / 26 )113.4553571428574.6601835979403324.3456839754127
Trimmed Mean ( 13 / 26 )112.3796296296304.4899782648933525.0289919014338
Trimmed Mean ( 14 / 26 )111.2153846153854.2726394474350626.0296676056177
Trimmed Mean ( 15 / 26 )109.9464.0001257225140327.4856361091822
Trimmed Mean ( 16 / 26 )108.5520833333333.6468034550231229.7663651666813
Trimmed Mean ( 17 / 26 )107.0826086956523.1847315456492433.6237472957308
Trimmed Mean ( 18 / 26 )106.0136363636362.8771179181422636.8471642038533
Trimmed Mean ( 19 / 26 )105.2666666666672.6891049304813339.1456151351538
Trimmed Mean ( 20 / 26 )104.44252.4431035524407742.7499276056707
Trimmed Mean ( 21 / 26 )103.8263157894742.2636740620151645.8662832833124
Trimmed Mean ( 22 / 26 )103.3305555555562.1269428819147248.5817256467815
Trimmed Mean ( 23 / 26 )102.7764705882351.9409649860490252.9512234001937
Trimmed Mean ( 24 / 26 )102.356251.7856108192951457.3228213527539
Trimmed Mean ( 25 / 26 )101.931.6101556289456363.304439749558
Trimmed Mean ( 26 / 26 )101.5821428571431.4415696689217870.4663430752681
Median101.5
Midrange144.9
Midmean - Weighted Average at Xnp103.990243902439
Midmean - Weighted Average at X(n+1)p104.4425
Midmean - Empirical Distribution Function103.990243902439
Midmean - Empirical Distribution Function - Averaging104.4425
Midmean - Empirical Distribution Function - Interpolation104.4425
Midmean - Closest Observation103.990243902439
Midmean - True Basic - Statistics Graphics Toolkit104.4425
Midmean - MS Excel (old versions)105.266666666667
Number of observations80



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')