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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationTue, 02 Dec 2008 11:14:43 -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/2008/Dec/02/t1228241759xy53jkc8cvd1vfs.htm/, Retrieved Fri, 17 May 2024 04:18:17 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=28194, Retrieved Fri, 17 May 2024 04:18:17 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact140
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [central tendency-...] [2008-12-02 18:14:43] [541f63fa3157af9df10fc4d202b2a90b] [Current]
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Dataseries X:
93,5
98,8
106,2
98,3
102,1
117,1
101,5
80,5
105,9
109,5
97,2
114,5
93,5
100,9
121,1
116,5
109,3
118,1
108,3
105,4
116,2
111,2
105,8
122,7
99,5
107,9
124,6
115
110,3
132,7
99,7
96,5
118,7
112,9
130,5
137,9
115
116,8
140,9
120,7
134,2
147,3
112,4
107,1
128,4
137,7
135
151
137,4
132,4
161,3
139,8
146
166,5
143,3
121
152,6
154,4
154,6
158




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

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=28194&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=28194&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=28194&T=0

As an alternative you can also use a QR Code:  

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

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







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean120.9016666666672.5520928507835947.3735376162138
Geometric Mean119.353171574922
Harmonic Mean117.847962819664
Quadratic Mean122.480571928776
Winsorized Mean ( 1 / 20 )121.0316666666672.4774126421019848.8540603247978
Winsorized Mean ( 2 / 20 )120.9216666666672.4481355660030749.3933703451269
Winsorized Mean ( 3 / 20 )120.9016666666672.3785879727013450.8291759877015
Winsorized Mean ( 4 / 20 )120.9352.3673673964618451.084170619543
Winsorized Mean ( 5 / 20 )120.8766666666672.3166230130423552.1779616217845
Winsorized Mean ( 6 / 20 )120.7666666666672.2717780520752453.1595357901921
Winsorized Mean ( 7 / 20 )120.4166666666672.1641926335654455.640456768529
Winsorized Mean ( 8 / 20 )120.272.1237722275649756.6303666838589
Winsorized Mean ( 9 / 20 )120.0452.0132041877800059.6288248994635
Winsorized Mean ( 10 / 20 )119.7451.9205555119746762.3491480737681
Winsorized Mean ( 11 / 20 )119.6533333333331.8656415667924864.1352205391996
Winsorized Mean ( 12 / 20 )119.9333333333331.6959384293979770.717976109491
Winsorized Mean ( 13 / 20 )119.9766666666671.6756554778959371.5998415242958
Winsorized Mean ( 14 / 20 )119.931.6597925471079372.2560179035443
Winsorized Mean ( 15 / 20 )119.4051.5440324800453677.333217754909
Winsorized Mean ( 16 / 20 )119.4316666666671.4732175702917081.0685869318125
Winsorized Mean ( 17 / 20 )119.2333333333331.3696955549942587.050974867064
Winsorized Mean ( 18 / 20 )119.2633333333331.3379594182546989.13822923636
Winsorized Mean ( 19 / 20 )118.9783333333331.1949424770843599.5682517066756
Winsorized Mean ( 20 / 20 )118.3451.07282936812307110.311111455726
Trimmed Mean ( 1 / 20 )120.8120689655172.4189637924776149.9437276991138
Trimmed Mean ( 2 / 20 )120.5767857142862.346340050021351.3893055327556
Trimmed Mean ( 3 / 20 )120.3851851851852.2756211205577552.9021215779889
Trimmed Mean ( 4 / 20 )120.1865384615382.2206286882518554.1227532083057
Trimmed Mean ( 5 / 20 )119.9622.154829203895155.6712336101418
Trimmed Mean ( 6 / 20 )119.7333333333332.0883697986888457.3333963211433
Trimmed Mean ( 7 / 20 )119.5086956521742.0169494976827059.2522003101611
Trimmed Mean ( 8 / 20 )119.3318181818181.9571054821222660.9736262413493
Trimmed Mean ( 9 / 20 )119.1642857142861.8896804584222163.0605482441102
Trimmed Mean ( 10 / 20 )119.01751.831368017112564.9883032180795
Trimmed Mean ( 11 / 20 )118.9026315789471.7782248842212066.8659136614333
Trimmed Mean ( 12 / 20 )118.7888888888891.7197257892243969.0743196579401
Trimmed Mean ( 13 / 20 )118.6205882352941.6837631830330870.4496864111344
Trimmed Mean ( 14 / 20 )118.4251.6348399349487572.4382843043974
Trimmed Mean ( 15 / 20 )118.211.5658008123347175.4949154891171
Trimmed Mean ( 16 / 20 )118.0392857142861.5022235660777078.5763772981445
Trimmed Mean ( 17 / 20 )117.8384615384621.4272952033945782.5606792891925
Trimmed Mean ( 18 / 20 )117.6333333333331.3483170759128187.2445624510805
Trimmed Mean ( 19 / 20 )117.3863636363641.2282796094123295.5697405841724
Trimmed Mean ( 20 / 20 )117.1351.09830671106888106.650536520899
Median116.65
Midrange123.5
Midmean - Weighted Average at Xnp117.812903225806
Midmean - Weighted Average at X(n+1)p118.21
Midmean - Empirical Distribution Function117.812903225806
Midmean - Empirical Distribution Function - Averaging118.21
Midmean - Empirical Distribution Function - Interpolation118.21
Midmean - Closest Observation117.812903225806
Midmean - True Basic - Statistics Graphics Toolkit118.21
Midmean - MS Excel (old versions)118.425
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 120.901666666667 & 2.55209285078359 & 47.3735376162138 \tabularnewline
Geometric Mean & 119.353171574922 &  &  \tabularnewline
Harmonic Mean & 117.847962819664 &  &  \tabularnewline
Quadratic Mean & 122.480571928776 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 121.031666666667 & 2.47741264210198 & 48.8540603247978 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 120.921666666667 & 2.44813556600307 & 49.3933703451269 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 120.901666666667 & 2.37858797270134 & 50.8291759877015 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 120.935 & 2.36736739646184 & 51.084170619543 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 120.876666666667 & 2.31662301304235 & 52.1779616217845 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 120.766666666667 & 2.27177805207524 & 53.1595357901921 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 120.416666666667 & 2.16419263356544 & 55.640456768529 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 120.27 & 2.12377222756497 & 56.6303666838589 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 120.045 & 2.01320418778000 & 59.6288248994635 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 119.745 & 1.92055551197467 & 62.3491480737681 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 119.653333333333 & 1.86564156679248 & 64.1352205391996 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 119.933333333333 & 1.69593842939797 & 70.717976109491 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 119.976666666667 & 1.67565547789593 & 71.5998415242958 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 119.93 & 1.65979254710793 & 72.2560179035443 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 119.405 & 1.54403248004536 & 77.333217754909 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 119.431666666667 & 1.47321757029170 & 81.0685869318125 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 119.233333333333 & 1.36969555499425 & 87.050974867064 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 119.263333333333 & 1.33795941825469 & 89.13822923636 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 118.978333333333 & 1.19494247708435 & 99.5682517066756 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 118.345 & 1.07282936812307 & 110.311111455726 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 120.812068965517 & 2.41896379247761 & 49.9437276991138 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 120.576785714286 & 2.3463400500213 & 51.3893055327556 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 120.385185185185 & 2.27562112055775 & 52.9021215779889 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 120.186538461538 & 2.22062868825185 & 54.1227532083057 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 119.962 & 2.1548292038951 & 55.6712336101418 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 119.733333333333 & 2.08836979868884 & 57.3333963211433 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 119.508695652174 & 2.01694949768270 & 59.2522003101611 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 119.331818181818 & 1.95710548212226 & 60.9736262413493 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 119.164285714286 & 1.88968045842221 & 63.0605482441102 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 119.0175 & 1.8313680171125 & 64.9883032180795 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 118.902631578947 & 1.77822488422120 & 66.8659136614333 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 118.788888888889 & 1.71972578922439 & 69.0743196579401 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 118.620588235294 & 1.68376318303308 & 70.4496864111344 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 118.425 & 1.63483993494875 & 72.4382843043974 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 118.21 & 1.56580081233471 & 75.4949154891171 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 118.039285714286 & 1.50222356607770 & 78.5763772981445 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 117.838461538462 & 1.42729520339457 & 82.5606792891925 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 117.633333333333 & 1.34831707591281 & 87.2445624510805 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 117.386363636364 & 1.22827960941232 & 95.5697405841724 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 117.135 & 1.09830671106888 & 106.650536520899 \tabularnewline
Median & 116.65 &  &  \tabularnewline
Midrange & 123.5 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 117.812903225806 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 118.21 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 117.812903225806 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 118.21 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 118.21 &  &  \tabularnewline
Midmean - Closest Observation & 117.812903225806 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 118.21 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 118.425 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=28194&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]120.901666666667[/C][C]2.55209285078359[/C][C]47.3735376162138[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]119.353171574922[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]117.847962819664[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]122.480571928776[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]121.031666666667[/C][C]2.47741264210198[/C][C]48.8540603247978[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]120.921666666667[/C][C]2.44813556600307[/C][C]49.3933703451269[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]120.901666666667[/C][C]2.37858797270134[/C][C]50.8291759877015[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]120.935[/C][C]2.36736739646184[/C][C]51.084170619543[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]120.876666666667[/C][C]2.31662301304235[/C][C]52.1779616217845[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]120.766666666667[/C][C]2.27177805207524[/C][C]53.1595357901921[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]120.416666666667[/C][C]2.16419263356544[/C][C]55.640456768529[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]120.27[/C][C]2.12377222756497[/C][C]56.6303666838589[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]120.045[/C][C]2.01320418778000[/C][C]59.6288248994635[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]119.745[/C][C]1.92055551197467[/C][C]62.3491480737681[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]119.653333333333[/C][C]1.86564156679248[/C][C]64.1352205391996[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]119.933333333333[/C][C]1.69593842939797[/C][C]70.717976109491[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]119.976666666667[/C][C]1.67565547789593[/C][C]71.5998415242958[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]119.93[/C][C]1.65979254710793[/C][C]72.2560179035443[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]119.405[/C][C]1.54403248004536[/C][C]77.333217754909[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]119.431666666667[/C][C]1.47321757029170[/C][C]81.0685869318125[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]119.233333333333[/C][C]1.36969555499425[/C][C]87.050974867064[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]119.263333333333[/C][C]1.33795941825469[/C][C]89.13822923636[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]118.978333333333[/C][C]1.19494247708435[/C][C]99.5682517066756[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]118.345[/C][C]1.07282936812307[/C][C]110.311111455726[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]120.812068965517[/C][C]2.41896379247761[/C][C]49.9437276991138[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]120.576785714286[/C][C]2.3463400500213[/C][C]51.3893055327556[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]120.385185185185[/C][C]2.27562112055775[/C][C]52.9021215779889[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]120.186538461538[/C][C]2.22062868825185[/C][C]54.1227532083057[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]119.962[/C][C]2.1548292038951[/C][C]55.6712336101418[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]119.733333333333[/C][C]2.08836979868884[/C][C]57.3333963211433[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]119.508695652174[/C][C]2.01694949768270[/C][C]59.2522003101611[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]119.331818181818[/C][C]1.95710548212226[/C][C]60.9736262413493[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]119.164285714286[/C][C]1.88968045842221[/C][C]63.0605482441102[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]119.0175[/C][C]1.8313680171125[/C][C]64.9883032180795[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]118.902631578947[/C][C]1.77822488422120[/C][C]66.8659136614333[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]118.788888888889[/C][C]1.71972578922439[/C][C]69.0743196579401[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]118.620588235294[/C][C]1.68376318303308[/C][C]70.4496864111344[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]118.425[/C][C]1.63483993494875[/C][C]72.4382843043974[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]118.21[/C][C]1.56580081233471[/C][C]75.4949154891171[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]118.039285714286[/C][C]1.50222356607770[/C][C]78.5763772981445[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]117.838461538462[/C][C]1.42729520339457[/C][C]82.5606792891925[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]117.633333333333[/C][C]1.34831707591281[/C][C]87.2445624510805[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]117.386363636364[/C][C]1.22827960941232[/C][C]95.5697405841724[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]117.135[/C][C]1.09830671106888[/C][C]106.650536520899[/C][/ROW]
[ROW][C]Median[/C][C]116.65[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]123.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]117.812903225806[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]118.21[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]117.812903225806[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]118.21[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]118.21[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]117.812903225806[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]118.21[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]118.425[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]60[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=28194&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=28194&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 Mean120.9016666666672.5520928507835947.3735376162138
Geometric Mean119.353171574922
Harmonic Mean117.847962819664
Quadratic Mean122.480571928776
Winsorized Mean ( 1 / 20 )121.0316666666672.4774126421019848.8540603247978
Winsorized Mean ( 2 / 20 )120.9216666666672.4481355660030749.3933703451269
Winsorized Mean ( 3 / 20 )120.9016666666672.3785879727013450.8291759877015
Winsorized Mean ( 4 / 20 )120.9352.3673673964618451.084170619543
Winsorized Mean ( 5 / 20 )120.8766666666672.3166230130423552.1779616217845
Winsorized Mean ( 6 / 20 )120.7666666666672.2717780520752453.1595357901921
Winsorized Mean ( 7 / 20 )120.4166666666672.1641926335654455.640456768529
Winsorized Mean ( 8 / 20 )120.272.1237722275649756.6303666838589
Winsorized Mean ( 9 / 20 )120.0452.0132041877800059.6288248994635
Winsorized Mean ( 10 / 20 )119.7451.9205555119746762.3491480737681
Winsorized Mean ( 11 / 20 )119.6533333333331.8656415667924864.1352205391996
Winsorized Mean ( 12 / 20 )119.9333333333331.6959384293979770.717976109491
Winsorized Mean ( 13 / 20 )119.9766666666671.6756554778959371.5998415242958
Winsorized Mean ( 14 / 20 )119.931.6597925471079372.2560179035443
Winsorized Mean ( 15 / 20 )119.4051.5440324800453677.333217754909
Winsorized Mean ( 16 / 20 )119.4316666666671.4732175702917081.0685869318125
Winsorized Mean ( 17 / 20 )119.2333333333331.3696955549942587.050974867064
Winsorized Mean ( 18 / 20 )119.2633333333331.3379594182546989.13822923636
Winsorized Mean ( 19 / 20 )118.9783333333331.1949424770843599.5682517066756
Winsorized Mean ( 20 / 20 )118.3451.07282936812307110.311111455726
Trimmed Mean ( 1 / 20 )120.8120689655172.4189637924776149.9437276991138
Trimmed Mean ( 2 / 20 )120.5767857142862.346340050021351.3893055327556
Trimmed Mean ( 3 / 20 )120.3851851851852.2756211205577552.9021215779889
Trimmed Mean ( 4 / 20 )120.1865384615382.2206286882518554.1227532083057
Trimmed Mean ( 5 / 20 )119.9622.154829203895155.6712336101418
Trimmed Mean ( 6 / 20 )119.7333333333332.0883697986888457.3333963211433
Trimmed Mean ( 7 / 20 )119.5086956521742.0169494976827059.2522003101611
Trimmed Mean ( 8 / 20 )119.3318181818181.9571054821222660.9736262413493
Trimmed Mean ( 9 / 20 )119.1642857142861.8896804584222163.0605482441102
Trimmed Mean ( 10 / 20 )119.01751.831368017112564.9883032180795
Trimmed Mean ( 11 / 20 )118.9026315789471.7782248842212066.8659136614333
Trimmed Mean ( 12 / 20 )118.7888888888891.7197257892243969.0743196579401
Trimmed Mean ( 13 / 20 )118.6205882352941.6837631830330870.4496864111344
Trimmed Mean ( 14 / 20 )118.4251.6348399349487572.4382843043974
Trimmed Mean ( 15 / 20 )118.211.5658008123347175.4949154891171
Trimmed Mean ( 16 / 20 )118.0392857142861.5022235660777078.5763772981445
Trimmed Mean ( 17 / 20 )117.8384615384621.4272952033945782.5606792891925
Trimmed Mean ( 18 / 20 )117.6333333333331.3483170759128187.2445624510805
Trimmed Mean ( 19 / 20 )117.3863636363641.2282796094123295.5697405841724
Trimmed Mean ( 20 / 20 )117.1351.09830671106888106.650536520899
Median116.65
Midrange123.5
Midmean - Weighted Average at Xnp117.812903225806
Midmean - Weighted Average at X(n+1)p118.21
Midmean - Empirical Distribution Function117.812903225806
Midmean - Empirical Distribution Function - Averaging118.21
Midmean - Empirical Distribution Function - Interpolation118.21
Midmean - Closest Observation117.812903225806
Midmean - True Basic - Statistics Graphics Toolkit118.21
Midmean - MS Excel (old versions)118.425
Number of observations60



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')