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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, 15 Nov 2011 14:28:08 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Nov/15/t1321385303zm3p5pz1q7cppr4.htm/, Retrieved Fri, 26 Apr 2024 00:17:27 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=143415, Retrieved Fri, 26 Apr 2024 00:17:27 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact54
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Central Tendency] [Arabica Price in ...] [2008-01-06 21:28:17] [74be16979710d4c4e7c6647856088456]
- RM D    [Central Tendency] [] [2011-11-15 19:28:08] [2e63149daec6ba44c7d6fab36a0b0c34] [Current]
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Dataseries X:
115
112
109
101
107
99
120
133
128
135
160
144
168
112
170
110
150
144
124
156
160
133
177
186
190
133
154
179
166
177
160
150
177
159
147
161
168
120
170
180
123
167
150
123
144
154
178
181
100
132
120
146
160
120
158
148
190
138
189
170
156
177
165
181
147
163
169
173
133
156
179
126
163
156
136
183
189
170
167
189
178




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'George Udny Yule' @ yule.wessa.net

\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 & 2 seconds \tabularnewline
R Server & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=143415&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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=143415&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=143415&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 time2 seconds
R Server'George Udny Yule' @ yule.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean151.7407407407412.7777098757132954.6280020341489
Geometric Mean149.567202822293
Harmonic Mean147.259660138489
Quadratic Mean153.761198528236
Winsorized Mean ( 1 / 27 )151.7530864197532.774805680227754.6896265569487
Winsorized Mean ( 2 / 27 )151.7530864197532.7648884772118754.8857893077777
Winsorized Mean ( 3 / 27 )151.9753086419752.7163755415837155.947826916955
Winsorized Mean ( 4 / 27 )152.0740740740742.6962924806647856.4011787165536
Winsorized Mean ( 5 / 27 )151.9506172839512.6533173526044857.2681655041364
Winsorized Mean ( 6 / 27 )151.8765432098772.5898890960125858.6421030320206
Winsorized Mean ( 7 / 27 )151.7037037037042.5645641005954859.1537968064354
Winsorized Mean ( 8 / 27 )1522.5085655731050660.5923965590651
Winsorized Mean ( 9 / 27 )152.4444444444442.3941801865006163.672920402562
Winsorized Mean ( 10 / 27 )152.3209876543212.376637003119564.0909770631312
Winsorized Mean ( 11 / 27 )152.3209876543212.376637003119564.0909770631312
Winsorized Mean ( 12 / 27 )152.1728395061732.3560920591501464.5869667592965
Winsorized Mean ( 13 / 27 )152.6543209876542.2757552330623967.0785323350586
Winsorized Mean ( 14 / 27 )152.4814814814812.2519614983052267.7105188504491
Winsorized Mean ( 15 / 27 )152.6666666666672.2218749728690268.7107368915245
Winsorized Mean ( 16 / 27 )153.0617283950622.1590568413405970.8928664888801
Winsorized Mean ( 17 / 27 )153.4814814814812.0942389459392273.28747360901
Winsorized Mean ( 18 / 27 )153.4814814814811.8400643365623483.4109321243733
Winsorized Mean ( 19 / 27 )153.0123456790121.7155330513744689.1923041391833
Winsorized Mean ( 20 / 27 )153.0123456790121.7155330513744689.1923041391833
Winsorized Mean ( 21 / 27 )153.0123456790121.7155330513744689.1923041391833
Winsorized Mean ( 22 / 27 )153.0123456790121.7155330513744689.1923041391833
Winsorized Mean ( 23 / 27 )153.2962962962961.5984603360159495.9024711732151
Winsorized Mean ( 24 / 27 )153.2962962962961.52007598539407100.84778509053
Winsorized Mean ( 25 / 27 )153.9135802469141.433311534165107.383200775384
Winsorized Mean ( 26 / 27 )155.5185185185191.13639443779181136.852586871786
Winsorized Mean ( 27 / 27 )155.5185185185191.13639443779181136.852586871786
Trimmed Mean ( 1 / 27 )151.9240506329112.7247868788554855.756305864452
Trimmed Mean ( 2 / 27 )152.1038961038962.6662483989318657.0479090263425
Trimmed Mean ( 3 / 27 )152.2933333333332.6037238290144758.4905863042232
Trimmed Mean ( 4 / 27 )152.410958904112.5518098463238659.7266129071775
Trimmed Mean ( 5 / 27 )152.5070422535212.4975539937073561.0625606644606
Trimmed Mean ( 6 / 27 )152.637681159422.4460043635143262.4028654389302
Trimmed Mean ( 7 / 27 )152.7910447761192.4012413224167263.6300247500086
Trimmed Mean ( 8 / 27 )152.9846153846152.353137462444565.0130380507778
Trimmed Mean ( 9 / 27 )153.1428571428572.3079436214482166.3546785630585
Trimmed Mean ( 10 / 27 )153.2459016393442.2775521009444267.2853549983768
Trimmed Mean ( 11 / 27 )153.3728813559322.2429704860858668.3793577790579
Trimmed Mean ( 12 / 27 )153.5087719298252.1996415188422269.7880862017116
Trimmed Mean ( 13 / 27 )153.6727272727272.1493174150121371.4983865107052
Trimmed Mean ( 14 / 27 )153.7924528301892.102828023655973.136010696115
Trimmed Mean ( 15 / 27 )153.9411764705882.0483205487319575.1548269951636
Trimmed Mean ( 16 / 27 )154.0816326530611.985242478784377.613507820675
Trimmed Mean ( 17 / 27 )154.1914893617021.9182261062988780.3823328518907
Trimmed Mean ( 18 / 27 )154.2666666666671.8462082354070683.5586494026517
Trimmed Mean ( 19 / 27 )154.3488372093021.8077242047909885.3829565374154
Trimmed Mean ( 20 / 27 )154.4878048780491.7806966132153186.7569487870807
Trimmed Mean ( 21 / 27 )154.6410256410261.7419516795332988.7745782262213
Trimmed Mean ( 22 / 27 )154.8108108108111.6871880037852691.7567043290305
Trimmed Mean ( 23 / 27 )1551.6098436690112196.2826409692338
Trimmed Mean ( 24 / 27 )155.1818181818181.53460990098766101.121345614898
Trimmed Mean ( 25 / 27 )155.3870967741941.44926931486168107.217544165712
Trimmed Mean ( 26 / 27 )155.5517241379311.35514546407729114.785997711209
Trimmed Mean ( 27 / 27 )155.5555555555561.32188820028589117.676786525451
Median156
Midrange144.5
Midmean - Weighted Average at Xnp154.348837209302
Midmean - Weighted Average at X(n+1)p154.348837209302
Midmean - Empirical Distribution Function154.348837209302
Midmean - Empirical Distribution Function - Averaging154.348837209302
Midmean - Empirical Distribution Function - Interpolation154.348837209302
Midmean - Closest Observation154.348837209302
Midmean - True Basic - Statistics Graphics Toolkit154.348837209302
Midmean - MS Excel (old versions)154.348837209302
Number of observations81

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 151.740740740741 & 2.77770987571329 & 54.6280020341489 \tabularnewline
Geometric Mean & 149.567202822293 &  &  \tabularnewline
Harmonic Mean & 147.259660138489 &  &  \tabularnewline
Quadratic Mean & 153.761198528236 &  &  \tabularnewline
Winsorized Mean ( 1 / 27 ) & 151.753086419753 & 2.7748056802277 & 54.6896265569487 \tabularnewline
Winsorized Mean ( 2 / 27 ) & 151.753086419753 & 2.76488847721187 & 54.8857893077777 \tabularnewline
Winsorized Mean ( 3 / 27 ) & 151.975308641975 & 2.71637554158371 & 55.947826916955 \tabularnewline
Winsorized Mean ( 4 / 27 ) & 152.074074074074 & 2.69629248066478 & 56.4011787165536 \tabularnewline
Winsorized Mean ( 5 / 27 ) & 151.950617283951 & 2.65331735260448 & 57.2681655041364 \tabularnewline
Winsorized Mean ( 6 / 27 ) & 151.876543209877 & 2.58988909601258 & 58.6421030320206 \tabularnewline
Winsorized Mean ( 7 / 27 ) & 151.703703703704 & 2.56456410059548 & 59.1537968064354 \tabularnewline
Winsorized Mean ( 8 / 27 ) & 152 & 2.50856557310506 & 60.5923965590651 \tabularnewline
Winsorized Mean ( 9 / 27 ) & 152.444444444444 & 2.39418018650061 & 63.672920402562 \tabularnewline
Winsorized Mean ( 10 / 27 ) & 152.320987654321 & 2.3766370031195 & 64.0909770631312 \tabularnewline
Winsorized Mean ( 11 / 27 ) & 152.320987654321 & 2.3766370031195 & 64.0909770631312 \tabularnewline
Winsorized Mean ( 12 / 27 ) & 152.172839506173 & 2.35609205915014 & 64.5869667592965 \tabularnewline
Winsorized Mean ( 13 / 27 ) & 152.654320987654 & 2.27575523306239 & 67.0785323350586 \tabularnewline
Winsorized Mean ( 14 / 27 ) & 152.481481481481 & 2.25196149830522 & 67.7105188504491 \tabularnewline
Winsorized Mean ( 15 / 27 ) & 152.666666666667 & 2.22187497286902 & 68.7107368915245 \tabularnewline
Winsorized Mean ( 16 / 27 ) & 153.061728395062 & 2.15905684134059 & 70.8928664888801 \tabularnewline
Winsorized Mean ( 17 / 27 ) & 153.481481481481 & 2.09423894593922 & 73.28747360901 \tabularnewline
Winsorized Mean ( 18 / 27 ) & 153.481481481481 & 1.84006433656234 & 83.4109321243733 \tabularnewline
Winsorized Mean ( 19 / 27 ) & 153.012345679012 & 1.71553305137446 & 89.1923041391833 \tabularnewline
Winsorized Mean ( 20 / 27 ) & 153.012345679012 & 1.71553305137446 & 89.1923041391833 \tabularnewline
Winsorized Mean ( 21 / 27 ) & 153.012345679012 & 1.71553305137446 & 89.1923041391833 \tabularnewline
Winsorized Mean ( 22 / 27 ) & 153.012345679012 & 1.71553305137446 & 89.1923041391833 \tabularnewline
Winsorized Mean ( 23 / 27 ) & 153.296296296296 & 1.59846033601594 & 95.9024711732151 \tabularnewline
Winsorized Mean ( 24 / 27 ) & 153.296296296296 & 1.52007598539407 & 100.84778509053 \tabularnewline
Winsorized Mean ( 25 / 27 ) & 153.913580246914 & 1.433311534165 & 107.383200775384 \tabularnewline
Winsorized Mean ( 26 / 27 ) & 155.518518518519 & 1.13639443779181 & 136.852586871786 \tabularnewline
Winsorized Mean ( 27 / 27 ) & 155.518518518519 & 1.13639443779181 & 136.852586871786 \tabularnewline
Trimmed Mean ( 1 / 27 ) & 151.924050632911 & 2.72478687885548 & 55.756305864452 \tabularnewline
Trimmed Mean ( 2 / 27 ) & 152.103896103896 & 2.66624839893186 & 57.0479090263425 \tabularnewline
Trimmed Mean ( 3 / 27 ) & 152.293333333333 & 2.60372382901447 & 58.4905863042232 \tabularnewline
Trimmed Mean ( 4 / 27 ) & 152.41095890411 & 2.55180984632386 & 59.7266129071775 \tabularnewline
Trimmed Mean ( 5 / 27 ) & 152.507042253521 & 2.49755399370735 & 61.0625606644606 \tabularnewline
Trimmed Mean ( 6 / 27 ) & 152.63768115942 & 2.44600436351432 & 62.4028654389302 \tabularnewline
Trimmed Mean ( 7 / 27 ) & 152.791044776119 & 2.40124132241672 & 63.6300247500086 \tabularnewline
Trimmed Mean ( 8 / 27 ) & 152.984615384615 & 2.3531374624445 & 65.0130380507778 \tabularnewline
Trimmed Mean ( 9 / 27 ) & 153.142857142857 & 2.30794362144821 & 66.3546785630585 \tabularnewline
Trimmed Mean ( 10 / 27 ) & 153.245901639344 & 2.27755210094442 & 67.2853549983768 \tabularnewline
Trimmed Mean ( 11 / 27 ) & 153.372881355932 & 2.24297048608586 & 68.3793577790579 \tabularnewline
Trimmed Mean ( 12 / 27 ) & 153.508771929825 & 2.19964151884222 & 69.7880862017116 \tabularnewline
Trimmed Mean ( 13 / 27 ) & 153.672727272727 & 2.14931741501213 & 71.4983865107052 \tabularnewline
Trimmed Mean ( 14 / 27 ) & 153.792452830189 & 2.1028280236559 & 73.136010696115 \tabularnewline
Trimmed Mean ( 15 / 27 ) & 153.941176470588 & 2.04832054873195 & 75.1548269951636 \tabularnewline
Trimmed Mean ( 16 / 27 ) & 154.081632653061 & 1.9852424787843 & 77.613507820675 \tabularnewline
Trimmed Mean ( 17 / 27 ) & 154.191489361702 & 1.91822610629887 & 80.3823328518907 \tabularnewline
Trimmed Mean ( 18 / 27 ) & 154.266666666667 & 1.84620823540706 & 83.5586494026517 \tabularnewline
Trimmed Mean ( 19 / 27 ) & 154.348837209302 & 1.80772420479098 & 85.3829565374154 \tabularnewline
Trimmed Mean ( 20 / 27 ) & 154.487804878049 & 1.78069661321531 & 86.7569487870807 \tabularnewline
Trimmed Mean ( 21 / 27 ) & 154.641025641026 & 1.74195167953329 & 88.7745782262213 \tabularnewline
Trimmed Mean ( 22 / 27 ) & 154.810810810811 & 1.68718800378526 & 91.7567043290305 \tabularnewline
Trimmed Mean ( 23 / 27 ) & 155 & 1.60984366901121 & 96.2826409692338 \tabularnewline
Trimmed Mean ( 24 / 27 ) & 155.181818181818 & 1.53460990098766 & 101.121345614898 \tabularnewline
Trimmed Mean ( 25 / 27 ) & 155.387096774194 & 1.44926931486168 & 107.217544165712 \tabularnewline
Trimmed Mean ( 26 / 27 ) & 155.551724137931 & 1.35514546407729 & 114.785997711209 \tabularnewline
Trimmed Mean ( 27 / 27 ) & 155.555555555556 & 1.32188820028589 & 117.676786525451 \tabularnewline
Median & 156 &  &  \tabularnewline
Midrange & 144.5 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 154.348837209302 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 154.348837209302 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 154.348837209302 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 154.348837209302 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 154.348837209302 &  &  \tabularnewline
Midmean - Closest Observation & 154.348837209302 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 154.348837209302 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 154.348837209302 &  &  \tabularnewline
Number of observations & 81 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=143415&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]151.740740740741[/C][C]2.77770987571329[/C][C]54.6280020341489[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]149.567202822293[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]147.259660138489[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]153.761198528236[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 27 )[/C][C]151.753086419753[/C][C]2.7748056802277[/C][C]54.6896265569487[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 27 )[/C][C]151.753086419753[/C][C]2.76488847721187[/C][C]54.8857893077777[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 27 )[/C][C]151.975308641975[/C][C]2.71637554158371[/C][C]55.947826916955[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 27 )[/C][C]152.074074074074[/C][C]2.69629248066478[/C][C]56.4011787165536[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 27 )[/C][C]151.950617283951[/C][C]2.65331735260448[/C][C]57.2681655041364[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 27 )[/C][C]151.876543209877[/C][C]2.58988909601258[/C][C]58.6421030320206[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 27 )[/C][C]151.703703703704[/C][C]2.56456410059548[/C][C]59.1537968064354[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 27 )[/C][C]152[/C][C]2.50856557310506[/C][C]60.5923965590651[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 27 )[/C][C]152.444444444444[/C][C]2.39418018650061[/C][C]63.672920402562[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 27 )[/C][C]152.320987654321[/C][C]2.3766370031195[/C][C]64.0909770631312[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 27 )[/C][C]152.320987654321[/C][C]2.3766370031195[/C][C]64.0909770631312[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 27 )[/C][C]152.172839506173[/C][C]2.35609205915014[/C][C]64.5869667592965[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 27 )[/C][C]152.654320987654[/C][C]2.27575523306239[/C][C]67.0785323350586[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 27 )[/C][C]152.481481481481[/C][C]2.25196149830522[/C][C]67.7105188504491[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 27 )[/C][C]152.666666666667[/C][C]2.22187497286902[/C][C]68.7107368915245[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 27 )[/C][C]153.061728395062[/C][C]2.15905684134059[/C][C]70.8928664888801[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 27 )[/C][C]153.481481481481[/C][C]2.09423894593922[/C][C]73.28747360901[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 27 )[/C][C]153.481481481481[/C][C]1.84006433656234[/C][C]83.4109321243733[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 27 )[/C][C]153.012345679012[/C][C]1.71553305137446[/C][C]89.1923041391833[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 27 )[/C][C]153.012345679012[/C][C]1.71553305137446[/C][C]89.1923041391833[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 27 )[/C][C]153.012345679012[/C][C]1.71553305137446[/C][C]89.1923041391833[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 27 )[/C][C]153.012345679012[/C][C]1.71553305137446[/C][C]89.1923041391833[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 27 )[/C][C]153.296296296296[/C][C]1.59846033601594[/C][C]95.9024711732151[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 27 )[/C][C]153.296296296296[/C][C]1.52007598539407[/C][C]100.84778509053[/C][/ROW]
[ROW][C]Winsorized Mean ( 25 / 27 )[/C][C]153.913580246914[/C][C]1.433311534165[/C][C]107.383200775384[/C][/ROW]
[ROW][C]Winsorized Mean ( 26 / 27 )[/C][C]155.518518518519[/C][C]1.13639443779181[/C][C]136.852586871786[/C][/ROW]
[ROW][C]Winsorized Mean ( 27 / 27 )[/C][C]155.518518518519[/C][C]1.13639443779181[/C][C]136.852586871786[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 27 )[/C][C]151.924050632911[/C][C]2.72478687885548[/C][C]55.756305864452[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 27 )[/C][C]152.103896103896[/C][C]2.66624839893186[/C][C]57.0479090263425[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 27 )[/C][C]152.293333333333[/C][C]2.60372382901447[/C][C]58.4905863042232[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 27 )[/C][C]152.41095890411[/C][C]2.55180984632386[/C][C]59.7266129071775[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 27 )[/C][C]152.507042253521[/C][C]2.49755399370735[/C][C]61.0625606644606[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 27 )[/C][C]152.63768115942[/C][C]2.44600436351432[/C][C]62.4028654389302[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 27 )[/C][C]152.791044776119[/C][C]2.40124132241672[/C][C]63.6300247500086[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 27 )[/C][C]152.984615384615[/C][C]2.3531374624445[/C][C]65.0130380507778[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 27 )[/C][C]153.142857142857[/C][C]2.30794362144821[/C][C]66.3546785630585[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 27 )[/C][C]153.245901639344[/C][C]2.27755210094442[/C][C]67.2853549983768[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 27 )[/C][C]153.372881355932[/C][C]2.24297048608586[/C][C]68.3793577790579[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 27 )[/C][C]153.508771929825[/C][C]2.19964151884222[/C][C]69.7880862017116[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 27 )[/C][C]153.672727272727[/C][C]2.14931741501213[/C][C]71.4983865107052[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 27 )[/C][C]153.792452830189[/C][C]2.1028280236559[/C][C]73.136010696115[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 27 )[/C][C]153.941176470588[/C][C]2.04832054873195[/C][C]75.1548269951636[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 27 )[/C][C]154.081632653061[/C][C]1.9852424787843[/C][C]77.613507820675[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 27 )[/C][C]154.191489361702[/C][C]1.91822610629887[/C][C]80.3823328518907[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 27 )[/C][C]154.266666666667[/C][C]1.84620823540706[/C][C]83.5586494026517[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 27 )[/C][C]154.348837209302[/C][C]1.80772420479098[/C][C]85.3829565374154[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 27 )[/C][C]154.487804878049[/C][C]1.78069661321531[/C][C]86.7569487870807[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 27 )[/C][C]154.641025641026[/C][C]1.74195167953329[/C][C]88.7745782262213[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 27 )[/C][C]154.810810810811[/C][C]1.68718800378526[/C][C]91.7567043290305[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 27 )[/C][C]155[/C][C]1.60984366901121[/C][C]96.2826409692338[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 27 )[/C][C]155.181818181818[/C][C]1.53460990098766[/C][C]101.121345614898[/C][/ROW]
[ROW][C]Trimmed Mean ( 25 / 27 )[/C][C]155.387096774194[/C][C]1.44926931486168[/C][C]107.217544165712[/C][/ROW]
[ROW][C]Trimmed Mean ( 26 / 27 )[/C][C]155.551724137931[/C][C]1.35514546407729[/C][C]114.785997711209[/C][/ROW]
[ROW][C]Trimmed Mean ( 27 / 27 )[/C][C]155.555555555556[/C][C]1.32188820028589[/C][C]117.676786525451[/C][/ROW]
[ROW][C]Median[/C][C]156[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]144.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]154.348837209302[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]154.348837209302[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]154.348837209302[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]154.348837209302[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]154.348837209302[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]154.348837209302[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]154.348837209302[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]154.348837209302[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]81[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=143415&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=143415&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 Mean151.7407407407412.7777098757132954.6280020341489
Geometric Mean149.567202822293
Harmonic Mean147.259660138489
Quadratic Mean153.761198528236
Winsorized Mean ( 1 / 27 )151.7530864197532.774805680227754.6896265569487
Winsorized Mean ( 2 / 27 )151.7530864197532.7648884772118754.8857893077777
Winsorized Mean ( 3 / 27 )151.9753086419752.7163755415837155.947826916955
Winsorized Mean ( 4 / 27 )152.0740740740742.6962924806647856.4011787165536
Winsorized Mean ( 5 / 27 )151.9506172839512.6533173526044857.2681655041364
Winsorized Mean ( 6 / 27 )151.8765432098772.5898890960125858.6421030320206
Winsorized Mean ( 7 / 27 )151.7037037037042.5645641005954859.1537968064354
Winsorized Mean ( 8 / 27 )1522.5085655731050660.5923965590651
Winsorized Mean ( 9 / 27 )152.4444444444442.3941801865006163.672920402562
Winsorized Mean ( 10 / 27 )152.3209876543212.376637003119564.0909770631312
Winsorized Mean ( 11 / 27 )152.3209876543212.376637003119564.0909770631312
Winsorized Mean ( 12 / 27 )152.1728395061732.3560920591501464.5869667592965
Winsorized Mean ( 13 / 27 )152.6543209876542.2757552330623967.0785323350586
Winsorized Mean ( 14 / 27 )152.4814814814812.2519614983052267.7105188504491
Winsorized Mean ( 15 / 27 )152.6666666666672.2218749728690268.7107368915245
Winsorized Mean ( 16 / 27 )153.0617283950622.1590568413405970.8928664888801
Winsorized Mean ( 17 / 27 )153.4814814814812.0942389459392273.28747360901
Winsorized Mean ( 18 / 27 )153.4814814814811.8400643365623483.4109321243733
Winsorized Mean ( 19 / 27 )153.0123456790121.7155330513744689.1923041391833
Winsorized Mean ( 20 / 27 )153.0123456790121.7155330513744689.1923041391833
Winsorized Mean ( 21 / 27 )153.0123456790121.7155330513744689.1923041391833
Winsorized Mean ( 22 / 27 )153.0123456790121.7155330513744689.1923041391833
Winsorized Mean ( 23 / 27 )153.2962962962961.5984603360159495.9024711732151
Winsorized Mean ( 24 / 27 )153.2962962962961.52007598539407100.84778509053
Winsorized Mean ( 25 / 27 )153.9135802469141.433311534165107.383200775384
Winsorized Mean ( 26 / 27 )155.5185185185191.13639443779181136.852586871786
Winsorized Mean ( 27 / 27 )155.5185185185191.13639443779181136.852586871786
Trimmed Mean ( 1 / 27 )151.9240506329112.7247868788554855.756305864452
Trimmed Mean ( 2 / 27 )152.1038961038962.6662483989318657.0479090263425
Trimmed Mean ( 3 / 27 )152.2933333333332.6037238290144758.4905863042232
Trimmed Mean ( 4 / 27 )152.410958904112.5518098463238659.7266129071775
Trimmed Mean ( 5 / 27 )152.5070422535212.4975539937073561.0625606644606
Trimmed Mean ( 6 / 27 )152.637681159422.4460043635143262.4028654389302
Trimmed Mean ( 7 / 27 )152.7910447761192.4012413224167263.6300247500086
Trimmed Mean ( 8 / 27 )152.9846153846152.353137462444565.0130380507778
Trimmed Mean ( 9 / 27 )153.1428571428572.3079436214482166.3546785630585
Trimmed Mean ( 10 / 27 )153.2459016393442.2775521009444267.2853549983768
Trimmed Mean ( 11 / 27 )153.3728813559322.2429704860858668.3793577790579
Trimmed Mean ( 12 / 27 )153.5087719298252.1996415188422269.7880862017116
Trimmed Mean ( 13 / 27 )153.6727272727272.1493174150121371.4983865107052
Trimmed Mean ( 14 / 27 )153.7924528301892.102828023655973.136010696115
Trimmed Mean ( 15 / 27 )153.9411764705882.0483205487319575.1548269951636
Trimmed Mean ( 16 / 27 )154.0816326530611.985242478784377.613507820675
Trimmed Mean ( 17 / 27 )154.1914893617021.9182261062988780.3823328518907
Trimmed Mean ( 18 / 27 )154.2666666666671.8462082354070683.5586494026517
Trimmed Mean ( 19 / 27 )154.3488372093021.8077242047909885.3829565374154
Trimmed Mean ( 20 / 27 )154.4878048780491.7806966132153186.7569487870807
Trimmed Mean ( 21 / 27 )154.6410256410261.7419516795332988.7745782262213
Trimmed Mean ( 22 / 27 )154.8108108108111.6871880037852691.7567043290305
Trimmed Mean ( 23 / 27 )1551.6098436690112196.2826409692338
Trimmed Mean ( 24 / 27 )155.1818181818181.53460990098766101.121345614898
Trimmed Mean ( 25 / 27 )155.3870967741941.44926931486168107.217544165712
Trimmed Mean ( 26 / 27 )155.5517241379311.35514546407729114.785997711209
Trimmed Mean ( 27 / 27 )155.5555555555561.32188820028589117.676786525451
Median156
Midrange144.5
Midmean - Weighted Average at Xnp154.348837209302
Midmean - Weighted Average at X(n+1)p154.348837209302
Midmean - Empirical Distribution Function154.348837209302
Midmean - Empirical Distribution Function - Averaging154.348837209302
Midmean - Empirical Distribution Function - Interpolation154.348837209302
Midmean - Closest Observation154.348837209302
Midmean - True Basic - Statistics Graphics Toolkit154.348837209302
Midmean - MS Excel (old versions)154.348837209302
Number of observations81



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')