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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 13:02:47 -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/t119498387556n144tp6joe6p2.htm/, Retrieved Tue, 30 Apr 2024 06:13:46 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=5378, Retrieved Tue, 30 Apr 2024 06:13:46 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact249
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2007-11-13 20:02:47] [bc15d8d2f79dc0888573b215bcd9118f] [Current]
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Dataseries X:
100,70
97,90
96,50
96,60
96,60
95,50
91,80
89,30
87,00
85,90
88,00
87,90
89,20
90,90
91,60
90,20
89,10
87,50
86,30
86,00
84,40
86,10
91,00
92,70
88,00
84,30
82,20
80,80
79,40
80,20
82,20
82,20
81,20
82,10
88,10
88,50
92,10
98,60
100,90
100,60
101,10
102,10
103,60
102,80
108,30
104,00
106,10
106,30
109,00
111,00
113,70
112,70
110,30
114,50
119,30
121,80
125,40
129,70
129,40
134,50
141,20
141,40
152,20
167,70
173,30
168,70
172,60
169,80
172,00
179,40
174,60
172,50
172,60
176,30
178,90
179,60
179,90
180,30
180,90
177,70




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

\begin{tabular}{lllllllll}
\hline
Summary of compuational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=5378&T=0

[TABLE]
[ROW][C]Summary of compuational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=5378&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=5378&T=0

As an alternative you can also use a QR Code:  

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

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







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean115.591253.8649324890324429.9077022245575
Geometric Mean111.091131995945
Harmonic Mean107.262472293388
Quadratic Mean120.587792188928
Winsorized Mean ( 1 / 26 )115.593753.8621624197036229.9298003134914
Winsorized Mean ( 2 / 26 )115.598753.8583209823712629.9608950442881
Winsorized Mean ( 3 / 26 )115.60253.8542484265475529.9935258982647
Winsorized Mean ( 4 / 26 )115.63753.8471234424756330.0581724836952
Winsorized Mean ( 5 / 26 )115.61253.839896480919430.108233535587
Winsorized Mean ( 6 / 26 )115.52253.8212393505315330.2316838603504
Winsorized Mean ( 7 / 26 )115.43.7961852104314830.3989383033509
Winsorized Mean ( 8 / 26 )115.443.7392024296802430.8728939315200
Winsorized Mean ( 9 / 26 )115.3053.7088966338395531.0887607241384
Winsorized Mean ( 10 / 26 )115.4053.6721862990853131.4267824670948
Winsorized Mean ( 11 / 26 )115.418753.670789628841331.4424855876125
Winsorized Mean ( 12 / 26 )115.418753.6663126432347631.4808804461823
Winsorized Mean ( 13 / 26 )115.373.6470368586156731.6339001969373
Winsorized Mean ( 14 / 26 )115.10753.5594515715916632.3385492637924
Winsorized Mean ( 15 / 26 )114.9953.5100871369327532.7612949519216
Winsorized Mean ( 16 / 26 )114.8753.4635034304383533.1672834478646
Winsorized Mean ( 17 / 26 )111.60252.8437973671114239.2441814915103
Winsorized Mean ( 18 / 26 )109.17252.4180825748116245.1483754679077
Winsorized Mean ( 19 / 26 )109.148752.4074429641823645.3380419074934
Winsorized Mean ( 20 / 26 )107.573752.1200286179627450.7416499421474
Winsorized Mean ( 21 / 26 )106.471251.90313465083555.9452006999535
Winsorized Mean ( 22 / 26 )106.416251.8872259158449256.3876582588984
Winsorized Mean ( 23 / 26 )105.2951.7094718445595361.5950478126363
Winsorized Mean ( 24 / 26 )104.4851.5189604414812268.7871765100817
Winsorized Mean ( 25 / 26 )103.92251.3814205390453075.2287207716059
Winsorized Mean ( 26 / 26 )102.3951.1642959789427687.9458504125213
Trimmed Mean ( 1 / 26 )115.2179487179493.8455958192146329.9610136203755
Trimmed Mean ( 2 / 26 )114.8223684210533.8238988088920930.027564577296
Trimmed Mean ( 3 / 26 )114.4027027027033.7984412774672730.1183286368940
Trimmed Mean ( 4 / 26 )113.9583333333333.7678520040693830.244906968282
Trimmed Mean ( 5 / 26 )113.4785714285713.7316812150718130.4095030867709
Trimmed Mean ( 6 / 26 )112.9764705882353.6884974835149030.6294015634181
Trimmed Mean ( 7 / 26 )112.4621212121213.6396756721410430.8989402745232
Trimmed Mean ( 8 / 26 )111.93753.5850622213501931.2233074598751
Trimmed Mean ( 9 / 26 )111.3725806451613.5294246765754131.5554490748406
Trimmed Mean ( 10 / 26 )110.793.4660937977338831.963935907457
Trimmed Mean ( 11 / 26 )110.1534482758623.3932330220465432.4626830990304
Trimmed Mean ( 12 / 26 )109.4696428571433.3007397042304833.1651849786393
Trimmed Mean ( 13 / 26 )108.7351851851853.1836487790928234.1542653508938
Trimmed Mean ( 14 / 26 )107.953.0376167277349835.5377289749433
Trimmed Mean ( 15 / 26 )107.1322.8694398799225237.3355095360606
Trimmed Mean ( 16 / 26 )106.2583333333332.6597752820167839.9501168582794
Trimmed Mean ( 17 / 26 )105.3217391304352.3883167986795444.0987306159156
Trimmed Mean ( 18 / 26 )104.652.2158770258427047.2273500647904
Trimmed Mean ( 19 / 26 )104.1714285714292.1080738705833049.415454564979
Trimmed Mean ( 20 / 26 )103.64751.9631443495523952.7966779537288
Trimmed Mean ( 21 / 26 )103.2342105263161.8523610565616455.7311492598208
Trimmed Mean ( 22 / 26 )102.8916666666671.7638088970738458.334928935535
Trimmed Mean ( 23 / 26 )102.5147058823531.6419475217086962.4348248205103
Trimmed Mean ( 24 / 26 )102.21251.5304750343096666.7848202085205
Trimmed Mean ( 25 / 26 )101.961.435883323790771.0085550202142
Trimmed Mean ( 26 / 26 )101.7357142857141.3458363608567375.5929303477517
Median101
Midrange130.15
Midmean - Weighted Average at Xnp103.268292682927
Midmean - Weighted Average at X(n+1)p103.6475
Midmean - Empirical Distribution Function103.268292682927
Midmean - Empirical Distribution Function - Averaging103.6475
Midmean - Empirical Distribution Function - Interpolation103.6475
Midmean - Closest Observation103.268292682927
Midmean - True Basic - Statistics Graphics Toolkit103.6475
Midmean - MS Excel (old versions)104.171428571429
Number of observations80

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 115.59125 & 3.86493248903244 & 29.9077022245575 \tabularnewline
Geometric Mean & 111.091131995945 &  &  \tabularnewline
Harmonic Mean & 107.262472293388 &  &  \tabularnewline
Quadratic Mean & 120.587792188928 &  &  \tabularnewline
Winsorized Mean ( 1 / 26 ) & 115.59375 & 3.86216241970362 & 29.9298003134914 \tabularnewline
Winsorized Mean ( 2 / 26 ) & 115.59875 & 3.85832098237126 & 29.9608950442881 \tabularnewline
Winsorized Mean ( 3 / 26 ) & 115.6025 & 3.85424842654755 & 29.9935258982647 \tabularnewline
Winsorized Mean ( 4 / 26 ) & 115.6375 & 3.84712344247563 & 30.0581724836952 \tabularnewline
Winsorized Mean ( 5 / 26 ) & 115.6125 & 3.8398964809194 & 30.108233535587 \tabularnewline
Winsorized Mean ( 6 / 26 ) & 115.5225 & 3.82123935053153 & 30.2316838603504 \tabularnewline
Winsorized Mean ( 7 / 26 ) & 115.4 & 3.79618521043148 & 30.3989383033509 \tabularnewline
Winsorized Mean ( 8 / 26 ) & 115.44 & 3.73920242968024 & 30.8728939315200 \tabularnewline
Winsorized Mean ( 9 / 26 ) & 115.305 & 3.70889663383955 & 31.0887607241384 \tabularnewline
Winsorized Mean ( 10 / 26 ) & 115.405 & 3.67218629908531 & 31.4267824670948 \tabularnewline
Winsorized Mean ( 11 / 26 ) & 115.41875 & 3.6707896288413 & 31.4424855876125 \tabularnewline
Winsorized Mean ( 12 / 26 ) & 115.41875 & 3.66631264323476 & 31.4808804461823 \tabularnewline
Winsorized Mean ( 13 / 26 ) & 115.37 & 3.64703685861567 & 31.6339001969373 \tabularnewline
Winsorized Mean ( 14 / 26 ) & 115.1075 & 3.55945157159166 & 32.3385492637924 \tabularnewline
Winsorized Mean ( 15 / 26 ) & 114.995 & 3.51008713693275 & 32.7612949519216 \tabularnewline
Winsorized Mean ( 16 / 26 ) & 114.875 & 3.46350343043835 & 33.1672834478646 \tabularnewline
Winsorized Mean ( 17 / 26 ) & 111.6025 & 2.84379736711142 & 39.2441814915103 \tabularnewline
Winsorized Mean ( 18 / 26 ) & 109.1725 & 2.41808257481162 & 45.1483754679077 \tabularnewline
Winsorized Mean ( 19 / 26 ) & 109.14875 & 2.40744296418236 & 45.3380419074934 \tabularnewline
Winsorized Mean ( 20 / 26 ) & 107.57375 & 2.12002861796274 & 50.7416499421474 \tabularnewline
Winsorized Mean ( 21 / 26 ) & 106.47125 & 1.903134650835 & 55.9452006999535 \tabularnewline
Winsorized Mean ( 22 / 26 ) & 106.41625 & 1.88722591584492 & 56.3876582588984 \tabularnewline
Winsorized Mean ( 23 / 26 ) & 105.295 & 1.70947184455953 & 61.5950478126363 \tabularnewline
Winsorized Mean ( 24 / 26 ) & 104.485 & 1.51896044148122 & 68.7871765100817 \tabularnewline
Winsorized Mean ( 25 / 26 ) & 103.9225 & 1.38142053904530 & 75.2287207716059 \tabularnewline
Winsorized Mean ( 26 / 26 ) & 102.395 & 1.16429597894276 & 87.9458504125213 \tabularnewline
Trimmed Mean ( 1 / 26 ) & 115.217948717949 & 3.84559581921463 & 29.9610136203755 \tabularnewline
Trimmed Mean ( 2 / 26 ) & 114.822368421053 & 3.82389880889209 & 30.027564577296 \tabularnewline
Trimmed Mean ( 3 / 26 ) & 114.402702702703 & 3.79844127746727 & 30.1183286368940 \tabularnewline
Trimmed Mean ( 4 / 26 ) & 113.958333333333 & 3.76785200406938 & 30.244906968282 \tabularnewline
Trimmed Mean ( 5 / 26 ) & 113.478571428571 & 3.73168121507181 & 30.4095030867709 \tabularnewline
Trimmed Mean ( 6 / 26 ) & 112.976470588235 & 3.68849748351490 & 30.6294015634181 \tabularnewline
Trimmed Mean ( 7 / 26 ) & 112.462121212121 & 3.63967567214104 & 30.8989402745232 \tabularnewline
Trimmed Mean ( 8 / 26 ) & 111.9375 & 3.58506222135019 & 31.2233074598751 \tabularnewline
Trimmed Mean ( 9 / 26 ) & 111.372580645161 & 3.52942467657541 & 31.5554490748406 \tabularnewline
Trimmed Mean ( 10 / 26 ) & 110.79 & 3.46609379773388 & 31.963935907457 \tabularnewline
Trimmed Mean ( 11 / 26 ) & 110.153448275862 & 3.39323302204654 & 32.4626830990304 \tabularnewline
Trimmed Mean ( 12 / 26 ) & 109.469642857143 & 3.30073970423048 & 33.1651849786393 \tabularnewline
Trimmed Mean ( 13 / 26 ) & 108.735185185185 & 3.18364877909282 & 34.1542653508938 \tabularnewline
Trimmed Mean ( 14 / 26 ) & 107.95 & 3.03761672773498 & 35.5377289749433 \tabularnewline
Trimmed Mean ( 15 / 26 ) & 107.132 & 2.86943987992252 & 37.3355095360606 \tabularnewline
Trimmed Mean ( 16 / 26 ) & 106.258333333333 & 2.65977528201678 & 39.9501168582794 \tabularnewline
Trimmed Mean ( 17 / 26 ) & 105.321739130435 & 2.38831679867954 & 44.0987306159156 \tabularnewline
Trimmed Mean ( 18 / 26 ) & 104.65 & 2.21587702584270 & 47.2273500647904 \tabularnewline
Trimmed Mean ( 19 / 26 ) & 104.171428571429 & 2.10807387058330 & 49.415454564979 \tabularnewline
Trimmed Mean ( 20 / 26 ) & 103.6475 & 1.96314434955239 & 52.7966779537288 \tabularnewline
Trimmed Mean ( 21 / 26 ) & 103.234210526316 & 1.85236105656164 & 55.7311492598208 \tabularnewline
Trimmed Mean ( 22 / 26 ) & 102.891666666667 & 1.76380889707384 & 58.334928935535 \tabularnewline
Trimmed Mean ( 23 / 26 ) & 102.514705882353 & 1.64194752170869 & 62.4348248205103 \tabularnewline
Trimmed Mean ( 24 / 26 ) & 102.2125 & 1.53047503430966 & 66.7848202085205 \tabularnewline
Trimmed Mean ( 25 / 26 ) & 101.96 & 1.4358833237907 & 71.0085550202142 \tabularnewline
Trimmed Mean ( 26 / 26 ) & 101.735714285714 & 1.34583636085673 & 75.5929303477517 \tabularnewline
Median & 101 &  &  \tabularnewline
Midrange & 130.15 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 103.268292682927 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 103.6475 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 103.268292682927 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 103.6475 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 103.6475 &  &  \tabularnewline
Midmean - Closest Observation & 103.268292682927 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 103.6475 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 104.171428571429 &  &  \tabularnewline
Number of observations & 80 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=5378&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]115.59125[/C][C]3.86493248903244[/C][C]29.9077022245575[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]111.091131995945[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]107.262472293388[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]120.587792188928[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 26 )[/C][C]115.59375[/C][C]3.86216241970362[/C][C]29.9298003134914[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 26 )[/C][C]115.59875[/C][C]3.85832098237126[/C][C]29.9608950442881[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 26 )[/C][C]115.6025[/C][C]3.85424842654755[/C][C]29.9935258982647[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 26 )[/C][C]115.6375[/C][C]3.84712344247563[/C][C]30.0581724836952[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 26 )[/C][C]115.6125[/C][C]3.8398964809194[/C][C]30.108233535587[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 26 )[/C][C]115.5225[/C][C]3.82123935053153[/C][C]30.2316838603504[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 26 )[/C][C]115.4[/C][C]3.79618521043148[/C][C]30.3989383033509[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 26 )[/C][C]115.44[/C][C]3.73920242968024[/C][C]30.8728939315200[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 26 )[/C][C]115.305[/C][C]3.70889663383955[/C][C]31.0887607241384[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 26 )[/C][C]115.405[/C][C]3.67218629908531[/C][C]31.4267824670948[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 26 )[/C][C]115.41875[/C][C]3.6707896288413[/C][C]31.4424855876125[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 26 )[/C][C]115.41875[/C][C]3.66631264323476[/C][C]31.4808804461823[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 26 )[/C][C]115.37[/C][C]3.64703685861567[/C][C]31.6339001969373[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 26 )[/C][C]115.1075[/C][C]3.55945157159166[/C][C]32.3385492637924[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 26 )[/C][C]114.995[/C][C]3.51008713693275[/C][C]32.7612949519216[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 26 )[/C][C]114.875[/C][C]3.46350343043835[/C][C]33.1672834478646[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 26 )[/C][C]111.6025[/C][C]2.84379736711142[/C][C]39.2441814915103[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 26 )[/C][C]109.1725[/C][C]2.41808257481162[/C][C]45.1483754679077[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 26 )[/C][C]109.14875[/C][C]2.40744296418236[/C][C]45.3380419074934[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 26 )[/C][C]107.57375[/C][C]2.12002861796274[/C][C]50.7416499421474[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 26 )[/C][C]106.47125[/C][C]1.903134650835[/C][C]55.9452006999535[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 26 )[/C][C]106.41625[/C][C]1.88722591584492[/C][C]56.3876582588984[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 26 )[/C][C]105.295[/C][C]1.70947184455953[/C][C]61.5950478126363[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 26 )[/C][C]104.485[/C][C]1.51896044148122[/C][C]68.7871765100817[/C][/ROW]
[ROW][C]Winsorized Mean ( 25 / 26 )[/C][C]103.9225[/C][C]1.38142053904530[/C][C]75.2287207716059[/C][/ROW]
[ROW][C]Winsorized Mean ( 26 / 26 )[/C][C]102.395[/C][C]1.16429597894276[/C][C]87.9458504125213[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 26 )[/C][C]115.217948717949[/C][C]3.84559581921463[/C][C]29.9610136203755[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 26 )[/C][C]114.822368421053[/C][C]3.82389880889209[/C][C]30.027564577296[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 26 )[/C][C]114.402702702703[/C][C]3.79844127746727[/C][C]30.1183286368940[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 26 )[/C][C]113.958333333333[/C][C]3.76785200406938[/C][C]30.244906968282[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 26 )[/C][C]113.478571428571[/C][C]3.73168121507181[/C][C]30.4095030867709[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 26 )[/C][C]112.976470588235[/C][C]3.68849748351490[/C][C]30.6294015634181[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 26 )[/C][C]112.462121212121[/C][C]3.63967567214104[/C][C]30.8989402745232[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 26 )[/C][C]111.9375[/C][C]3.58506222135019[/C][C]31.2233074598751[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 26 )[/C][C]111.372580645161[/C][C]3.52942467657541[/C][C]31.5554490748406[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 26 )[/C][C]110.79[/C][C]3.46609379773388[/C][C]31.963935907457[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 26 )[/C][C]110.153448275862[/C][C]3.39323302204654[/C][C]32.4626830990304[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 26 )[/C][C]109.469642857143[/C][C]3.30073970423048[/C][C]33.1651849786393[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 26 )[/C][C]108.735185185185[/C][C]3.18364877909282[/C][C]34.1542653508938[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 26 )[/C][C]107.95[/C][C]3.03761672773498[/C][C]35.5377289749433[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 26 )[/C][C]107.132[/C][C]2.86943987992252[/C][C]37.3355095360606[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 26 )[/C][C]106.258333333333[/C][C]2.65977528201678[/C][C]39.9501168582794[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 26 )[/C][C]105.321739130435[/C][C]2.38831679867954[/C][C]44.0987306159156[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 26 )[/C][C]104.65[/C][C]2.21587702584270[/C][C]47.2273500647904[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 26 )[/C][C]104.171428571429[/C][C]2.10807387058330[/C][C]49.415454564979[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 26 )[/C][C]103.6475[/C][C]1.96314434955239[/C][C]52.7966779537288[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 26 )[/C][C]103.234210526316[/C][C]1.85236105656164[/C][C]55.7311492598208[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 26 )[/C][C]102.891666666667[/C][C]1.76380889707384[/C][C]58.334928935535[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 26 )[/C][C]102.514705882353[/C][C]1.64194752170869[/C][C]62.4348248205103[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 26 )[/C][C]102.2125[/C][C]1.53047503430966[/C][C]66.7848202085205[/C][/ROW]
[ROW][C]Trimmed Mean ( 25 / 26 )[/C][C]101.96[/C][C]1.4358833237907[/C][C]71.0085550202142[/C][/ROW]
[ROW][C]Trimmed Mean ( 26 / 26 )[/C][C]101.735714285714[/C][C]1.34583636085673[/C][C]75.5929303477517[/C][/ROW]
[ROW][C]Median[/C][C]101[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]130.15[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]103.268292682927[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]103.6475[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]103.268292682927[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]103.6475[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]103.6475[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]103.268292682927[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]103.6475[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]104.171428571429[/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=5378&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=5378&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 Mean115.591253.8649324890324429.9077022245575
Geometric Mean111.091131995945
Harmonic Mean107.262472293388
Quadratic Mean120.587792188928
Winsorized Mean ( 1 / 26 )115.593753.8621624197036229.9298003134914
Winsorized Mean ( 2 / 26 )115.598753.8583209823712629.9608950442881
Winsorized Mean ( 3 / 26 )115.60253.8542484265475529.9935258982647
Winsorized Mean ( 4 / 26 )115.63753.8471234424756330.0581724836952
Winsorized Mean ( 5 / 26 )115.61253.839896480919430.108233535587
Winsorized Mean ( 6 / 26 )115.52253.8212393505315330.2316838603504
Winsorized Mean ( 7 / 26 )115.43.7961852104314830.3989383033509
Winsorized Mean ( 8 / 26 )115.443.7392024296802430.8728939315200
Winsorized Mean ( 9 / 26 )115.3053.7088966338395531.0887607241384
Winsorized Mean ( 10 / 26 )115.4053.6721862990853131.4267824670948
Winsorized Mean ( 11 / 26 )115.418753.670789628841331.4424855876125
Winsorized Mean ( 12 / 26 )115.418753.6663126432347631.4808804461823
Winsorized Mean ( 13 / 26 )115.373.6470368586156731.6339001969373
Winsorized Mean ( 14 / 26 )115.10753.5594515715916632.3385492637924
Winsorized Mean ( 15 / 26 )114.9953.5100871369327532.7612949519216
Winsorized Mean ( 16 / 26 )114.8753.4635034304383533.1672834478646
Winsorized Mean ( 17 / 26 )111.60252.8437973671114239.2441814915103
Winsorized Mean ( 18 / 26 )109.17252.4180825748116245.1483754679077
Winsorized Mean ( 19 / 26 )109.148752.4074429641823645.3380419074934
Winsorized Mean ( 20 / 26 )107.573752.1200286179627450.7416499421474
Winsorized Mean ( 21 / 26 )106.471251.90313465083555.9452006999535
Winsorized Mean ( 22 / 26 )106.416251.8872259158449256.3876582588984
Winsorized Mean ( 23 / 26 )105.2951.7094718445595361.5950478126363
Winsorized Mean ( 24 / 26 )104.4851.5189604414812268.7871765100817
Winsorized Mean ( 25 / 26 )103.92251.3814205390453075.2287207716059
Winsorized Mean ( 26 / 26 )102.3951.1642959789427687.9458504125213
Trimmed Mean ( 1 / 26 )115.2179487179493.8455958192146329.9610136203755
Trimmed Mean ( 2 / 26 )114.8223684210533.8238988088920930.027564577296
Trimmed Mean ( 3 / 26 )114.4027027027033.7984412774672730.1183286368940
Trimmed Mean ( 4 / 26 )113.9583333333333.7678520040693830.244906968282
Trimmed Mean ( 5 / 26 )113.4785714285713.7316812150718130.4095030867709
Trimmed Mean ( 6 / 26 )112.9764705882353.6884974835149030.6294015634181
Trimmed Mean ( 7 / 26 )112.4621212121213.6396756721410430.8989402745232
Trimmed Mean ( 8 / 26 )111.93753.5850622213501931.2233074598751
Trimmed Mean ( 9 / 26 )111.3725806451613.5294246765754131.5554490748406
Trimmed Mean ( 10 / 26 )110.793.4660937977338831.963935907457
Trimmed Mean ( 11 / 26 )110.1534482758623.3932330220465432.4626830990304
Trimmed Mean ( 12 / 26 )109.4696428571433.3007397042304833.1651849786393
Trimmed Mean ( 13 / 26 )108.7351851851853.1836487790928234.1542653508938
Trimmed Mean ( 14 / 26 )107.953.0376167277349835.5377289749433
Trimmed Mean ( 15 / 26 )107.1322.8694398799225237.3355095360606
Trimmed Mean ( 16 / 26 )106.2583333333332.6597752820167839.9501168582794
Trimmed Mean ( 17 / 26 )105.3217391304352.3883167986795444.0987306159156
Trimmed Mean ( 18 / 26 )104.652.2158770258427047.2273500647904
Trimmed Mean ( 19 / 26 )104.1714285714292.1080738705833049.415454564979
Trimmed Mean ( 20 / 26 )103.64751.9631443495523952.7966779537288
Trimmed Mean ( 21 / 26 )103.2342105263161.8523610565616455.7311492598208
Trimmed Mean ( 22 / 26 )102.8916666666671.7638088970738458.334928935535
Trimmed Mean ( 23 / 26 )102.5147058823531.6419475217086962.4348248205103
Trimmed Mean ( 24 / 26 )102.21251.5304750343096666.7848202085205
Trimmed Mean ( 25 / 26 )101.961.435883323790771.0085550202142
Trimmed Mean ( 26 / 26 )101.7357142857141.3458363608567375.5929303477517
Median101
Midrange130.15
Midmean - Weighted Average at Xnp103.268292682927
Midmean - Weighted Average at X(n+1)p103.6475
Midmean - Empirical Distribution Function103.268292682927
Midmean - Empirical Distribution Function - Averaging103.6475
Midmean - Empirical Distribution Function - Interpolation103.6475
Midmean - Closest Observation103.268292682927
Midmean - True Basic - Statistics Graphics Toolkit103.6475
Midmean - MS Excel (old versions)104.171428571429
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')