FreeStatistics.org

Free Statistics

of Irreproducible Research!

Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationSat, 18 Oct 2008 05:25:37 -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/18/t1224329462fwpjxwhz7j59x8o.htm/, Retrieved Wed, 15 May 2024 02:34:28 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=16586, Retrieved Wed, 15 May 2024 02:34:28 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact178

Tree of Dependent Computations

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 09:35:57] [b731da8b544846036771bbf9bf2f34ce]
-    D    [Central Tendency] [Central tendancy ...] [2008-10-18 11:25:37] [924502d03698cd41cacbcd1327858815] [Current]
Feedback Forum

Post a new message

Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
72.50
59.40
85.70
88.20
62.80
87.00
79.20
80
79.20
60
40.10
69.00
59.40
73.80
57.40
81.10
46.60
41.40
71.20
67.90
72.00
64
39.70
51.90
73.70
70.90
60.80
61.00
54.50
39.10
66.60
58.50
59.80
80.90
37.30
44.60
48.70
54.00
49.50
61.60
35.00
35.70
51.30
49.00
41.50
72.50
42.10
44.10
45.10
50.30
40.90
47.20
36.90
40.90
38.30
46.30
28.40
78.40
36.80
50.70
42.80

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001

\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 & 3 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=16586&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ 193.190.124.10:1001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=16586&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=16586&T=0

As an alternative you can also use a QR Code:  
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 time3 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001






Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean56.80655737704922.0085457709367428.2824310996686
Geometric Mean54.6790982579778
Harmonic Mean52.5986969234595
Quadratic Mean58.8985596417166
Winsorized Mean ( 1 / 20 )56.89508196721311.9807536047636528.7239573010910
Winsorized Mean ( 2 / 20 )56.87540983606561.9659723546156928.9299133339969
Winsorized Mean ( 3 / 20 )56.70327868852461.9045573287908429.7724189402711
Winsorized Mean ( 4 / 20 )56.69672131147541.9006253891856329.8305608428016
Winsorized Mean ( 5 / 20 )56.6557377049181.8795004634998030.144040294313
Winsorized Mean ( 6 / 20 )56.67540983606561.8467570982637330.6891522926054
Winsorized Mean ( 7 / 20 )56.76721311475411.8317654318526930.9904380373302
Winsorized Mean ( 8 / 20 )56.74098360655741.7979836567046331.5581197832205
Winsorized Mean ( 9 / 20 )56.12131147540981.6598968213936333.8101204557348
Winsorized Mean ( 10 / 20 )56.23606557377051.6361891495978334.3701494338800
Winsorized Mean ( 11 / 20 )56.01967213114751.5983407032522335.0486426436874
Winsorized Mean ( 12 / 20 )56.11803278688521.5829651712262735.4512113133939
Winsorized Mean ( 13 / 20 )56.03278688524591.5613898833482535.8864800411598
Winsorized Mean ( 14 / 20 )55.98688524590161.5090717941288237.1002131666126
Winsorized Mean ( 15 / 20 )56.08524590163931.4705187294596638.1397698499547
Winsorized Mean ( 16 / 20 )55.9278688524591.3371900460987141.8249216075383
Winsorized Mean ( 17 / 20 )55.76065573770491.2672315651955744.00194666008
Winsorized Mean ( 18 / 20 )55.52459016393441.1850633603169146.8536890289867
Winsorized Mean ( 19 / 20 )55.08852459016391.0074316702768554.6821449190942
Winsorized Mean ( 20 / 20 )54.79344262295080.9360242303752158.5384874075179
Trimmed Mean ( 1 / 20 )56.75593220338981.9470448035161229.1497823269889
Trimmed Mean ( 2 / 20 )56.60701754385961.9049678814564029.7154708459348
Trimmed Mean ( 3 / 20 )56.45818181818181.8621458439577130.3188829174564
Trimmed Mean ( 4 / 20 )56.36415094339621.8374236047221930.6756432205072
Trimmed Mean ( 5 / 20 )56.26470588235291.8066583246954831.1429699314267
Trimmed Mean ( 6 / 20 )56.16734693877551.7737393428632431.6660659102863
Trimmed Mean ( 7 / 20 )56.05744680851061.7405001691642532.2076652456909
Trimmed Mean ( 8 / 20 )55.921.7004829973400032.8847745537436
Trimmed Mean ( 9 / 20 )55.77441860465121.6565755182469433.6685034822163
Trimmed Mean ( 10 / 20 )55.71707317073171.6352366220923534.0727894776717
Trimmed Mean ( 11 / 20 )55.63589743589741.6101419756994834.5534109883249
Trimmed Mean ( 12 / 20 )55.57837837837841.5836302952201235.0955513708792
Trimmed Mean ( 13 / 20 )55.51.5483577637955335.8444290445843
Trimmed Mean ( 14 / 20 )55.42424242424241.5026745745341336.8837294271951
Trimmed Mean ( 15 / 20 )55.34516129032261.4509458443439138.1441950477128
Trimmed Mean ( 16 / 20 )55.24137931034481.3852807974265439.8773876119324
Trimmed Mean ( 17 / 20 )55.14444444444441.3314873260850741.4156735585189
Trimmed Mean ( 18 / 20 )55.0561.2717845729525143.2903505600676
Trimmed Mean ( 19 / 20 )54.98695652173911.2076551667965345.5320012148828
Trimmed Mean ( 20 / 20 )54.97142857142861.1764179460011146.7278051633673
Median54.5
Midrange58.3
Midmean - Weighted Average at Xnp54.8266666666667
Midmean - Weighted Average at X(n+1)p55.3451612903226
Midmean - Empirical Distribution Function55.3451612903226
Midmean - Empirical Distribution Function - Averaging55.3451612903226
Midmean - Empirical Distribution Function - Interpolation55.3451612903226
Midmean - Closest Observation54.93125
Midmean - True Basic - Statistics Graphics Toolkit55.3451612903226
Midmean - MS Excel (old versions)55.3451612903226
Number of observations61

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 56.8065573770492 & 2.00854577093674 & 28.2824310996686 \tabularnewline
Geometric Mean & 54.6790982579778 &  &  \tabularnewline
Harmonic Mean & 52.5986969234595 &  &  \tabularnewline
Quadratic Mean & 58.8985596417166 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 56.8950819672131 & 1.98075360476365 & 28.7239573010910 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 56.8754098360656 & 1.96597235461569 & 28.9299133339969 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 56.7032786885246 & 1.90455732879084 & 29.7724189402711 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 56.6967213114754 & 1.90062538918563 & 29.8305608428016 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 56.655737704918 & 1.87950046349980 & 30.144040294313 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 56.6754098360656 & 1.84675709826373 & 30.6891522926054 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 56.7672131147541 & 1.83176543185269 & 30.9904380373302 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 56.7409836065574 & 1.79798365670463 & 31.5581197832205 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 56.1213114754098 & 1.65989682139363 & 33.8101204557348 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 56.2360655737705 & 1.63618914959783 & 34.3701494338800 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 56.0196721311475 & 1.59834070325223 & 35.0486426436874 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 56.1180327868852 & 1.58296517122627 & 35.4512113133939 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 56.0327868852459 & 1.56138988334825 & 35.8864800411598 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 55.9868852459016 & 1.50907179412882 & 37.1002131666126 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 56.0852459016393 & 1.47051872945966 & 38.1397698499547 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 55.927868852459 & 1.33719004609871 & 41.8249216075383 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 55.7606557377049 & 1.26723156519557 & 44.00194666008 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 55.5245901639344 & 1.18506336031691 & 46.8536890289867 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 55.0885245901639 & 1.00743167027685 & 54.6821449190942 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 54.7934426229508 & 0.93602423037521 & 58.5384874075179 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 56.7559322033898 & 1.94704480351612 & 29.1497823269889 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 56.6070175438596 & 1.90496788145640 & 29.7154708459348 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 56.4581818181818 & 1.86214584395771 & 30.3188829174564 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 56.3641509433962 & 1.83742360472219 & 30.6756432205072 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 56.2647058823529 & 1.80665832469548 & 31.1429699314267 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 56.1673469387755 & 1.77373934286324 & 31.6660659102863 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 56.0574468085106 & 1.74050016916425 & 32.2076652456909 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 55.92 & 1.70048299734000 & 32.8847745537436 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 55.7744186046512 & 1.65657551824694 & 33.6685034822163 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 55.7170731707317 & 1.63523662209235 & 34.0727894776717 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 55.6358974358974 & 1.61014197569948 & 34.5534109883249 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 55.5783783783784 & 1.58363029522012 & 35.0955513708792 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 55.5 & 1.54835776379553 & 35.8444290445843 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 55.4242424242424 & 1.50267457453413 & 36.8837294271951 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 55.3451612903226 & 1.45094584434391 & 38.1441950477128 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 55.2413793103448 & 1.38528079742654 & 39.8773876119324 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 55.1444444444444 & 1.33148732608507 & 41.4156735585189 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 55.056 & 1.27178457295251 & 43.2903505600676 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 54.9869565217391 & 1.20765516679653 & 45.5320012148828 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 54.9714285714286 & 1.17641794600111 & 46.7278051633673 \tabularnewline
Median & 54.5 &  &  \tabularnewline
Midrange & 58.3 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 54.8266666666667 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 55.3451612903226 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 55.3451612903226 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 55.3451612903226 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 55.3451612903226 &  &  \tabularnewline
Midmean - Closest Observation & 54.93125 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 55.3451612903226 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 55.3451612903226 &  &  \tabularnewline
Number of observations & 61 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=16586&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]56.8065573770492[/C][C]2.00854577093674[/C][C]28.2824310996686[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]54.6790982579778[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]52.5986969234595[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]58.8985596417166[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]56.8950819672131[/C][C]1.98075360476365[/C][C]28.7239573010910[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]56.8754098360656[/C][C]1.96597235461569[/C][C]28.9299133339969[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]56.7032786885246[/C][C]1.90455732879084[/C][C]29.7724189402711[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]56.6967213114754[/C][C]1.90062538918563[/C][C]29.8305608428016[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]56.655737704918[/C][C]1.87950046349980[/C][C]30.144040294313[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]56.6754098360656[/C][C]1.84675709826373[/C][C]30.6891522926054[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]56.7672131147541[/C][C]1.83176543185269[/C][C]30.9904380373302[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]56.7409836065574[/C][C]1.79798365670463[/C][C]31.5581197832205[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]56.1213114754098[/C][C]1.65989682139363[/C][C]33.8101204557348[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]56.2360655737705[/C][C]1.63618914959783[/C][C]34.3701494338800[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]56.0196721311475[/C][C]1.59834070325223[/C][C]35.0486426436874[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]56.1180327868852[/C][C]1.58296517122627[/C][C]35.4512113133939[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]56.0327868852459[/C][C]1.56138988334825[/C][C]35.8864800411598[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]55.9868852459016[/C][C]1.50907179412882[/C][C]37.1002131666126[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]56.0852459016393[/C][C]1.47051872945966[/C][C]38.1397698499547[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]55.927868852459[/C][C]1.33719004609871[/C][C]41.8249216075383[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]55.7606557377049[/C][C]1.26723156519557[/C][C]44.00194666008[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]55.5245901639344[/C][C]1.18506336031691[/C][C]46.8536890289867[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]55.0885245901639[/C][C]1.00743167027685[/C][C]54.6821449190942[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]54.7934426229508[/C][C]0.93602423037521[/C][C]58.5384874075179[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]56.7559322033898[/C][C]1.94704480351612[/C][C]29.1497823269889[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]56.6070175438596[/C][C]1.90496788145640[/C][C]29.7154708459348[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]56.4581818181818[/C][C]1.86214584395771[/C][C]30.3188829174564[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]56.3641509433962[/C][C]1.83742360472219[/C][C]30.6756432205072[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]56.2647058823529[/C][C]1.80665832469548[/C][C]31.1429699314267[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]56.1673469387755[/C][C]1.77373934286324[/C][C]31.6660659102863[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]56.0574468085106[/C][C]1.74050016916425[/C][C]32.2076652456909[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]55.92[/C][C]1.70048299734000[/C][C]32.8847745537436[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]55.7744186046512[/C][C]1.65657551824694[/C][C]33.6685034822163[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]55.7170731707317[/C][C]1.63523662209235[/C][C]34.0727894776717[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]55.6358974358974[/C][C]1.61014197569948[/C][C]34.5534109883249[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]55.5783783783784[/C][C]1.58363029522012[/C][C]35.0955513708792[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]55.5[/C][C]1.54835776379553[/C][C]35.8444290445843[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]55.4242424242424[/C][C]1.50267457453413[/C][C]36.8837294271951[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]55.3451612903226[/C][C]1.45094584434391[/C][C]38.1441950477128[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]55.2413793103448[/C][C]1.38528079742654[/C][C]39.8773876119324[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]55.1444444444444[/C][C]1.33148732608507[/C][C]41.4156735585189[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]55.056[/C][C]1.27178457295251[/C][C]43.2903505600676[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]54.9869565217391[/C][C]1.20765516679653[/C][C]45.5320012148828[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]54.9714285714286[/C][C]1.17641794600111[/C][C]46.7278051633673[/C][/ROW]
[ROW][C]Median[/C][C]54.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]58.3[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]54.8266666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]55.3451612903226[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]55.3451612903226[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]55.3451612903226[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]55.3451612903226[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]54.93125[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]55.3451612903226[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]55.3451612903226[/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=16586&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=16586&T=1

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean56.80655737704922.0085457709367428.2824310996686
Geometric Mean54.6790982579778
Harmonic Mean52.5986969234595
Quadratic Mean58.8985596417166
Winsorized Mean ( 1 / 20 )56.89508196721311.9807536047636528.7239573010910
Winsorized Mean ( 2 / 20 )56.87540983606561.9659723546156928.9299133339969
Winsorized Mean ( 3 / 20 )56.70327868852461.9045573287908429.7724189402711
Winsorized Mean ( 4 / 20 )56.69672131147541.9006253891856329.8305608428016
Winsorized Mean ( 5 / 20 )56.6557377049181.8795004634998030.144040294313
Winsorized Mean ( 6 / 20 )56.67540983606561.8467570982637330.6891522926054
Winsorized Mean ( 7 / 20 )56.76721311475411.8317654318526930.9904380373302
Winsorized Mean ( 8 / 20 )56.74098360655741.7979836567046331.5581197832205
Winsorized Mean ( 9 / 20 )56.12131147540981.6598968213936333.8101204557348
Winsorized Mean ( 10 / 20 )56.23606557377051.6361891495978334.3701494338800
Winsorized Mean ( 11 / 20 )56.01967213114751.5983407032522335.0486426436874
Winsorized Mean ( 12 / 20 )56.11803278688521.5829651712262735.4512113133939
Winsorized Mean ( 13 / 20 )56.03278688524591.5613898833482535.8864800411598
Winsorized Mean ( 14 / 20 )55.98688524590161.5090717941288237.1002131666126
Winsorized Mean ( 15 / 20 )56.08524590163931.4705187294596638.1397698499547
Winsorized Mean ( 16 / 20 )55.9278688524591.3371900460987141.8249216075383
Winsorized Mean ( 17 / 20 )55.76065573770491.2672315651955744.00194666008
Winsorized Mean ( 18 / 20 )55.52459016393441.1850633603169146.8536890289867
Winsorized Mean ( 19 / 20 )55.08852459016391.0074316702768554.6821449190942
Winsorized Mean ( 20 / 20 )54.79344262295080.9360242303752158.5384874075179
Trimmed Mean ( 1 / 20 )56.75593220338981.9470448035161229.1497823269889
Trimmed Mean ( 2 / 20 )56.60701754385961.9049678814564029.7154708459348
Trimmed Mean ( 3 / 20 )56.45818181818181.8621458439577130.3188829174564
Trimmed Mean ( 4 / 20 )56.36415094339621.8374236047221930.6756432205072
Trimmed Mean ( 5 / 20 )56.26470588235291.8066583246954831.1429699314267
Trimmed Mean ( 6 / 20 )56.16734693877551.7737393428632431.6660659102863
Trimmed Mean ( 7 / 20 )56.05744680851061.7405001691642532.2076652456909
Trimmed Mean ( 8 / 20 )55.921.7004829973400032.8847745537436
Trimmed Mean ( 9 / 20 )55.77441860465121.6565755182469433.6685034822163
Trimmed Mean ( 10 / 20 )55.71707317073171.6352366220923534.0727894776717
Trimmed Mean ( 11 / 20 )55.63589743589741.6101419756994834.5534109883249
Trimmed Mean ( 12 / 20 )55.57837837837841.5836302952201235.0955513708792
Trimmed Mean ( 13 / 20 )55.51.5483577637955335.8444290445843
Trimmed Mean ( 14 / 20 )55.42424242424241.5026745745341336.8837294271951
Trimmed Mean ( 15 / 20 )55.34516129032261.4509458443439138.1441950477128
Trimmed Mean ( 16 / 20 )55.24137931034481.3852807974265439.8773876119324
Trimmed Mean ( 17 / 20 )55.14444444444441.3314873260850741.4156735585189
Trimmed Mean ( 18 / 20 )55.0561.2717845729525143.2903505600676
Trimmed Mean ( 19 / 20 )54.98695652173911.2076551667965345.5320012148828
Trimmed Mean ( 20 / 20 )54.97142857142861.1764179460011146.7278051633673
Median54.5
Midrange58.3
Midmean - Weighted Average at Xnp54.8266666666667
Midmean - Weighted Average at X(n+1)p55.3451612903226
Midmean - Empirical Distribution Function55.3451612903226
Midmean - Empirical Distribution Function - Averaging55.3451612903226
Midmean - Empirical Distribution Function - Interpolation55.3451612903226
Midmean - Closest Observation54.93125
Midmean - True Basic - Statistics Graphics Toolkit55.3451612903226
Midmean - MS Excel (old versions)55.3451612903226
Number of observations61


Figures (Output of Computation)

Input Parameters & R Code

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')