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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationWed, 12 Dec 2007 03:49:41 -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/Dec/12/t1197455746gtimvkmfim4sfm6.htm/, Retrieved Thu, 02 May 2024 19:39:25 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=3202, Retrieved Thu, 02 May 2024 19:39:25 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact236
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Centr. Ten. Frank...] [2007-12-12 10:49:41] [6bdd947de0ee04552c8f0fc807f31807] [Current]
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Dataseries X:
1962,3
2095,2
2161
2115,1
1929
2004,5
2009,9
1524,9
2061,1
2261,6
2103,6
2224,3
2173,8
2119,2
2226,4
2159,6
1918,3
2116,1
1948,3
1514,3
2180,5
2312,6
2019,8
2200,8
2028,9
2178,7
2433,7
2230,5
1884,2
2372,7
1918,6
1679,4
2327,3
2225,2
2211,7
2463,6
2029,5
2173,6
2387
2234
2179,9
2397
1960,2
1824,1
2479,3
2234,9
2345,9
2428,9
2179,4
2216,9
2642,3
2340,5
2474,6
2641,8
2165,1
1996,2
2562,9
2529,9
2549,6
2455,1
2472
2424,7
2820,1
2666
2654,6
2732,2
2546,9




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

\begin{tabular}{lllllllll}
\hline
Summary of compuational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 3 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=3202&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ 193.190.124.10:1001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=3202&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=3202&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 time3 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean2224.5044776119432.772819942277767.876505028555
Geometric Mean2207.94748443037
Harmonic Mean2190.6152658002
Quadratic Mean2240.38121329731
Winsorized Mean ( 1 / 22 )2223.3507462686632.384054835170368.6557244787645
Winsorized Mean ( 2 / 22 )2225.9865671641830.550226596090472.8631769771897
Winsorized Mean ( 3 / 22 )2231.9552238806028.860849212964177.3350502409339
Winsorized Mean ( 4 / 22 )2234.8089552238827.972822771410479.8921500874757
Winsorized Mean ( 5 / 22 )2237.3164179104527.499106732502281.359603410902
Winsorized Mean ( 6 / 22 )2230.277611940326.019853935564585.7144554870812
Winsorized Mean ( 7 / 22 )2229.9746268656725.558057669147487.2513340306608
Winsorized Mean ( 8 / 22 )2231.9567164179125.093853340181388.9443596469901
Winsorized Mean ( 9 / 22 )2231.2716417910524.393373028298991.4704021949951
Winsorized Mean ( 10 / 22 )2224.0328358209023.002723511695296.6856309293176
Winsorized Mean ( 11 / 22 )2228.8268656716421.9449040354632101.564666770465
Winsorized Mean ( 12 / 22 )2229.8477611940321.6291675312951103.094479154950
Winsorized Mean ( 13 / 22 )2229.2656716417921.1894853677557105.206220583068
Winsorized Mean ( 14 / 22 )2229.5582089552220.5710587570619108.383250239360
Winsorized Mean ( 15 / 22 )2226.8044776119419.4728852100220114.354111041844
Winsorized Mean ( 16 / 22 )2225.8014925373119.2669871940027115.524107122994
Winsorized Mean ( 17 / 22 )2232.7537313432817.8923923465314124.787881245859
Winsorized Mean ( 18 / 22 )2234.4731343283615.3951547444941145.141323449672
Winsorized Mean ( 19 / 22 )2234.0194029850714.6191850305674152.814223112571
Winsorized Mean ( 20 / 22 )2233.1835820895513.4861985496557165.590293948813
Winsorized Mean ( 21 / 22 )2225.0970149253712.1518553806029183.107595114828
Winsorized Mean ( 22 / 22 )2224.3417910447811.7472902943361189.349350813033
Trimmed Mean ( 1 / 22 )2226.2676923076930.579958094415672.8015285512849
Trimmed Mean ( 2 / 22 )2229.3698412698428.360501805271478.6082649939383
Trimmed Mean ( 3 / 22 )2231.2278688524626.899646749579782.9463631855063
Trimmed Mean ( 4 / 22 )2230.9525423728825.944133135661285.9906372938841
Trimmed Mean ( 5 / 22 )2229.8192982456125.117669498658588.7749278795435
Trimmed Mean ( 6 / 22 )2227.9927272727324.252240530261991.8675008394642
Trimmed Mean ( 7 / 22 )2227.5113207547223.630634292607494.2637126525025
Trimmed Mean ( 8 / 22 )2227.0490196078422.975761545773196.9303679084167
Trimmed Mean ( 9 / 22 )2226.2102040816322.266056891543099.9822382079324
Trimmed Mean ( 10 / 22 )2225.4085106383021.5393821765940103.318121773083
Trimmed Mean ( 11 / 22 )2225.6133333333320.9540164178709106.214163860022
Trimmed Mean ( 12 / 22 )2225.1581395348820.4425896357074108.849132090788
Trimmed Mean ( 13 / 22 )2224.5195121951219.8329733510957112.162683467339
Trimmed Mean ( 14 / 22 )2223.8923076923119.1212560868864116.304718559650
Trimmed Mean ( 15 / 22 )2223.1594594594618.3132959540491121.395922669393
Trimmed Mean ( 16 / 22 )2222.6942857142917.5051079905925126.974040200654
Trimmed Mean ( 17 / 22 )2222.316.4224624440817135.320753971392
Trimmed Mean ( 18 / 22 )2220.9709677419415.3031855518156145.131283955348
Trimmed Mean ( 19 / 22 )2219.2379310344814.5076295655309152.970402298335
Trimmed Mean ( 20 / 22 )2217.3074074074113.5708459993285163.387559443024
Trimmed Mean ( 21 / 22 )2215.1812.5551768871118176.435586684082
Trimmed Mean ( 22 / 22 )2213.8043478260911.5610930563910191.487460314342
Median2211.7
Midrange2167.2
Midmean - Weighted Average at Xnp2216.62941176471
Midmean - Weighted Average at X(n+1)p2222.69428571429
Midmean - Empirical Distribution Function2222.69428571429
Midmean - Empirical Distribution Function - Averaging2222.69428571429
Midmean - Empirical Distribution Function - Interpolation2222.3
Midmean - Closest Observation2216.62941176471
Midmean - True Basic - Statistics Graphics Toolkit2222.69428571429
Midmean - MS Excel (old versions)2222.69428571429
Number of observations67

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 2224.50447761194 & 32.7728199422777 & 67.876505028555 \tabularnewline
Geometric Mean & 2207.94748443037 &  &  \tabularnewline
Harmonic Mean & 2190.6152658002 &  &  \tabularnewline
Quadratic Mean & 2240.38121329731 &  &  \tabularnewline
Winsorized Mean ( 1 / 22 ) & 2223.35074626866 & 32.3840548351703 & 68.6557244787645 \tabularnewline
Winsorized Mean ( 2 / 22 ) & 2225.98656716418 & 30.5502265960904 & 72.8631769771897 \tabularnewline
Winsorized Mean ( 3 / 22 ) & 2231.95522388060 & 28.8608492129641 & 77.3350502409339 \tabularnewline
Winsorized Mean ( 4 / 22 ) & 2234.80895522388 & 27.9728227714104 & 79.8921500874757 \tabularnewline
Winsorized Mean ( 5 / 22 ) & 2237.31641791045 & 27.4991067325022 & 81.359603410902 \tabularnewline
Winsorized Mean ( 6 / 22 ) & 2230.2776119403 & 26.0198539355645 & 85.7144554870812 \tabularnewline
Winsorized Mean ( 7 / 22 ) & 2229.97462686567 & 25.5580576691474 & 87.2513340306608 \tabularnewline
Winsorized Mean ( 8 / 22 ) & 2231.95671641791 & 25.0938533401813 & 88.9443596469901 \tabularnewline
Winsorized Mean ( 9 / 22 ) & 2231.27164179105 & 24.3933730282989 & 91.4704021949951 \tabularnewline
Winsorized Mean ( 10 / 22 ) & 2224.03283582090 & 23.0027235116952 & 96.6856309293176 \tabularnewline
Winsorized Mean ( 11 / 22 ) & 2228.82686567164 & 21.9449040354632 & 101.564666770465 \tabularnewline
Winsorized Mean ( 12 / 22 ) & 2229.84776119403 & 21.6291675312951 & 103.094479154950 \tabularnewline
Winsorized Mean ( 13 / 22 ) & 2229.26567164179 & 21.1894853677557 & 105.206220583068 \tabularnewline
Winsorized Mean ( 14 / 22 ) & 2229.55820895522 & 20.5710587570619 & 108.383250239360 \tabularnewline
Winsorized Mean ( 15 / 22 ) & 2226.80447761194 & 19.4728852100220 & 114.354111041844 \tabularnewline
Winsorized Mean ( 16 / 22 ) & 2225.80149253731 & 19.2669871940027 & 115.524107122994 \tabularnewline
Winsorized Mean ( 17 / 22 ) & 2232.75373134328 & 17.8923923465314 & 124.787881245859 \tabularnewline
Winsorized Mean ( 18 / 22 ) & 2234.47313432836 & 15.3951547444941 & 145.141323449672 \tabularnewline
Winsorized Mean ( 19 / 22 ) & 2234.01940298507 & 14.6191850305674 & 152.814223112571 \tabularnewline
Winsorized Mean ( 20 / 22 ) & 2233.18358208955 & 13.4861985496557 & 165.590293948813 \tabularnewline
Winsorized Mean ( 21 / 22 ) & 2225.09701492537 & 12.1518553806029 & 183.107595114828 \tabularnewline
Winsorized Mean ( 22 / 22 ) & 2224.34179104478 & 11.7472902943361 & 189.349350813033 \tabularnewline
Trimmed Mean ( 1 / 22 ) & 2226.26769230769 & 30.5799580944156 & 72.8015285512849 \tabularnewline
Trimmed Mean ( 2 / 22 ) & 2229.36984126984 & 28.3605018052714 & 78.6082649939383 \tabularnewline
Trimmed Mean ( 3 / 22 ) & 2231.22786885246 & 26.8996467495797 & 82.9463631855063 \tabularnewline
Trimmed Mean ( 4 / 22 ) & 2230.95254237288 & 25.9441331356612 & 85.9906372938841 \tabularnewline
Trimmed Mean ( 5 / 22 ) & 2229.81929824561 & 25.1176694986585 & 88.7749278795435 \tabularnewline
Trimmed Mean ( 6 / 22 ) & 2227.99272727273 & 24.2522405302619 & 91.8675008394642 \tabularnewline
Trimmed Mean ( 7 / 22 ) & 2227.51132075472 & 23.6306342926074 & 94.2637126525025 \tabularnewline
Trimmed Mean ( 8 / 22 ) & 2227.04901960784 & 22.9757615457731 & 96.9303679084167 \tabularnewline
Trimmed Mean ( 9 / 22 ) & 2226.21020408163 & 22.2660568915430 & 99.9822382079324 \tabularnewline
Trimmed Mean ( 10 / 22 ) & 2225.40851063830 & 21.5393821765940 & 103.318121773083 \tabularnewline
Trimmed Mean ( 11 / 22 ) & 2225.61333333333 & 20.9540164178709 & 106.214163860022 \tabularnewline
Trimmed Mean ( 12 / 22 ) & 2225.15813953488 & 20.4425896357074 & 108.849132090788 \tabularnewline
Trimmed Mean ( 13 / 22 ) & 2224.51951219512 & 19.8329733510957 & 112.162683467339 \tabularnewline
Trimmed Mean ( 14 / 22 ) & 2223.89230769231 & 19.1212560868864 & 116.304718559650 \tabularnewline
Trimmed Mean ( 15 / 22 ) & 2223.15945945946 & 18.3132959540491 & 121.395922669393 \tabularnewline
Trimmed Mean ( 16 / 22 ) & 2222.69428571429 & 17.5051079905925 & 126.974040200654 \tabularnewline
Trimmed Mean ( 17 / 22 ) & 2222.3 & 16.4224624440817 & 135.320753971392 \tabularnewline
Trimmed Mean ( 18 / 22 ) & 2220.97096774194 & 15.3031855518156 & 145.131283955348 \tabularnewline
Trimmed Mean ( 19 / 22 ) & 2219.23793103448 & 14.5076295655309 & 152.970402298335 \tabularnewline
Trimmed Mean ( 20 / 22 ) & 2217.30740740741 & 13.5708459993285 & 163.387559443024 \tabularnewline
Trimmed Mean ( 21 / 22 ) & 2215.18 & 12.5551768871118 & 176.435586684082 \tabularnewline
Trimmed Mean ( 22 / 22 ) & 2213.80434782609 & 11.5610930563910 & 191.487460314342 \tabularnewline
Median & 2211.7 &  &  \tabularnewline
Midrange & 2167.2 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 2216.62941176471 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 2222.69428571429 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 2222.69428571429 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 2222.69428571429 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 2222.3 &  &  \tabularnewline
Midmean - Closest Observation & 2216.62941176471 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 2222.69428571429 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 2222.69428571429 &  &  \tabularnewline
Number of observations & 67 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=3202&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]2224.50447761194[/C][C]32.7728199422777[/C][C]67.876505028555[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]2207.94748443037[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]2190.6152658002[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]2240.38121329731[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 22 )[/C][C]2223.35074626866[/C][C]32.3840548351703[/C][C]68.6557244787645[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 22 )[/C][C]2225.98656716418[/C][C]30.5502265960904[/C][C]72.8631769771897[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 22 )[/C][C]2231.95522388060[/C][C]28.8608492129641[/C][C]77.3350502409339[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 22 )[/C][C]2234.80895522388[/C][C]27.9728227714104[/C][C]79.8921500874757[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 22 )[/C][C]2237.31641791045[/C][C]27.4991067325022[/C][C]81.359603410902[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 22 )[/C][C]2230.2776119403[/C][C]26.0198539355645[/C][C]85.7144554870812[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 22 )[/C][C]2229.97462686567[/C][C]25.5580576691474[/C][C]87.2513340306608[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 22 )[/C][C]2231.95671641791[/C][C]25.0938533401813[/C][C]88.9443596469901[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 22 )[/C][C]2231.27164179105[/C][C]24.3933730282989[/C][C]91.4704021949951[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 22 )[/C][C]2224.03283582090[/C][C]23.0027235116952[/C][C]96.6856309293176[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 22 )[/C][C]2228.82686567164[/C][C]21.9449040354632[/C][C]101.564666770465[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 22 )[/C][C]2229.84776119403[/C][C]21.6291675312951[/C][C]103.094479154950[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 22 )[/C][C]2229.26567164179[/C][C]21.1894853677557[/C][C]105.206220583068[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 22 )[/C][C]2229.55820895522[/C][C]20.5710587570619[/C][C]108.383250239360[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 22 )[/C][C]2226.80447761194[/C][C]19.4728852100220[/C][C]114.354111041844[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 22 )[/C][C]2225.80149253731[/C][C]19.2669871940027[/C][C]115.524107122994[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 22 )[/C][C]2232.75373134328[/C][C]17.8923923465314[/C][C]124.787881245859[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 22 )[/C][C]2234.47313432836[/C][C]15.3951547444941[/C][C]145.141323449672[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 22 )[/C][C]2234.01940298507[/C][C]14.6191850305674[/C][C]152.814223112571[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 22 )[/C][C]2233.18358208955[/C][C]13.4861985496557[/C][C]165.590293948813[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 22 )[/C][C]2225.09701492537[/C][C]12.1518553806029[/C][C]183.107595114828[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 22 )[/C][C]2224.34179104478[/C][C]11.7472902943361[/C][C]189.349350813033[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 22 )[/C][C]2226.26769230769[/C][C]30.5799580944156[/C][C]72.8015285512849[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 22 )[/C][C]2229.36984126984[/C][C]28.3605018052714[/C][C]78.6082649939383[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 22 )[/C][C]2231.22786885246[/C][C]26.8996467495797[/C][C]82.9463631855063[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 22 )[/C][C]2230.95254237288[/C][C]25.9441331356612[/C][C]85.9906372938841[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 22 )[/C][C]2229.81929824561[/C][C]25.1176694986585[/C][C]88.7749278795435[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 22 )[/C][C]2227.99272727273[/C][C]24.2522405302619[/C][C]91.8675008394642[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 22 )[/C][C]2227.51132075472[/C][C]23.6306342926074[/C][C]94.2637126525025[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 22 )[/C][C]2227.04901960784[/C][C]22.9757615457731[/C][C]96.9303679084167[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 22 )[/C][C]2226.21020408163[/C][C]22.2660568915430[/C][C]99.9822382079324[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 22 )[/C][C]2225.40851063830[/C][C]21.5393821765940[/C][C]103.318121773083[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 22 )[/C][C]2225.61333333333[/C][C]20.9540164178709[/C][C]106.214163860022[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 22 )[/C][C]2225.15813953488[/C][C]20.4425896357074[/C][C]108.849132090788[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 22 )[/C][C]2224.51951219512[/C][C]19.8329733510957[/C][C]112.162683467339[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 22 )[/C][C]2223.89230769231[/C][C]19.1212560868864[/C][C]116.304718559650[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 22 )[/C][C]2223.15945945946[/C][C]18.3132959540491[/C][C]121.395922669393[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 22 )[/C][C]2222.69428571429[/C][C]17.5051079905925[/C][C]126.974040200654[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 22 )[/C][C]2222.3[/C][C]16.4224624440817[/C][C]135.320753971392[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 22 )[/C][C]2220.97096774194[/C][C]15.3031855518156[/C][C]145.131283955348[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 22 )[/C][C]2219.23793103448[/C][C]14.5076295655309[/C][C]152.970402298335[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 22 )[/C][C]2217.30740740741[/C][C]13.5708459993285[/C][C]163.387559443024[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 22 )[/C][C]2215.18[/C][C]12.5551768871118[/C][C]176.435586684082[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 22 )[/C][C]2213.80434782609[/C][C]11.5610930563910[/C][C]191.487460314342[/C][/ROW]
[ROW][C]Median[/C][C]2211.7[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]2167.2[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]2216.62941176471[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]2222.69428571429[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]2222.69428571429[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]2222.69428571429[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]2222.3[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]2216.62941176471[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]2222.69428571429[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]2222.69428571429[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]67[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=3202&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=3202&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 Mean2224.5044776119432.772819942277767.876505028555
Geometric Mean2207.94748443037
Harmonic Mean2190.6152658002
Quadratic Mean2240.38121329731
Winsorized Mean ( 1 / 22 )2223.3507462686632.384054835170368.6557244787645
Winsorized Mean ( 2 / 22 )2225.9865671641830.550226596090472.8631769771897
Winsorized Mean ( 3 / 22 )2231.9552238806028.860849212964177.3350502409339
Winsorized Mean ( 4 / 22 )2234.8089552238827.972822771410479.8921500874757
Winsorized Mean ( 5 / 22 )2237.3164179104527.499106732502281.359603410902
Winsorized Mean ( 6 / 22 )2230.277611940326.019853935564585.7144554870812
Winsorized Mean ( 7 / 22 )2229.9746268656725.558057669147487.2513340306608
Winsorized Mean ( 8 / 22 )2231.9567164179125.093853340181388.9443596469901
Winsorized Mean ( 9 / 22 )2231.2716417910524.393373028298991.4704021949951
Winsorized Mean ( 10 / 22 )2224.0328358209023.002723511695296.6856309293176
Winsorized Mean ( 11 / 22 )2228.8268656716421.9449040354632101.564666770465
Winsorized Mean ( 12 / 22 )2229.8477611940321.6291675312951103.094479154950
Winsorized Mean ( 13 / 22 )2229.2656716417921.1894853677557105.206220583068
Winsorized Mean ( 14 / 22 )2229.5582089552220.5710587570619108.383250239360
Winsorized Mean ( 15 / 22 )2226.8044776119419.4728852100220114.354111041844
Winsorized Mean ( 16 / 22 )2225.8014925373119.2669871940027115.524107122994
Winsorized Mean ( 17 / 22 )2232.7537313432817.8923923465314124.787881245859
Winsorized Mean ( 18 / 22 )2234.4731343283615.3951547444941145.141323449672
Winsorized Mean ( 19 / 22 )2234.0194029850714.6191850305674152.814223112571
Winsorized Mean ( 20 / 22 )2233.1835820895513.4861985496557165.590293948813
Winsorized Mean ( 21 / 22 )2225.0970149253712.1518553806029183.107595114828
Winsorized Mean ( 22 / 22 )2224.3417910447811.7472902943361189.349350813033
Trimmed Mean ( 1 / 22 )2226.2676923076930.579958094415672.8015285512849
Trimmed Mean ( 2 / 22 )2229.3698412698428.360501805271478.6082649939383
Trimmed Mean ( 3 / 22 )2231.2278688524626.899646749579782.9463631855063
Trimmed Mean ( 4 / 22 )2230.9525423728825.944133135661285.9906372938841
Trimmed Mean ( 5 / 22 )2229.8192982456125.117669498658588.7749278795435
Trimmed Mean ( 6 / 22 )2227.9927272727324.252240530261991.8675008394642
Trimmed Mean ( 7 / 22 )2227.5113207547223.630634292607494.2637126525025
Trimmed Mean ( 8 / 22 )2227.0490196078422.975761545773196.9303679084167
Trimmed Mean ( 9 / 22 )2226.2102040816322.266056891543099.9822382079324
Trimmed Mean ( 10 / 22 )2225.4085106383021.5393821765940103.318121773083
Trimmed Mean ( 11 / 22 )2225.6133333333320.9540164178709106.214163860022
Trimmed Mean ( 12 / 22 )2225.1581395348820.4425896357074108.849132090788
Trimmed Mean ( 13 / 22 )2224.5195121951219.8329733510957112.162683467339
Trimmed Mean ( 14 / 22 )2223.8923076923119.1212560868864116.304718559650
Trimmed Mean ( 15 / 22 )2223.1594594594618.3132959540491121.395922669393
Trimmed Mean ( 16 / 22 )2222.6942857142917.5051079905925126.974040200654
Trimmed Mean ( 17 / 22 )2222.316.4224624440817135.320753971392
Trimmed Mean ( 18 / 22 )2220.9709677419415.3031855518156145.131283955348
Trimmed Mean ( 19 / 22 )2219.2379310344814.5076295655309152.970402298335
Trimmed Mean ( 20 / 22 )2217.3074074074113.5708459993285163.387559443024
Trimmed Mean ( 21 / 22 )2215.1812.5551768871118176.435586684082
Trimmed Mean ( 22 / 22 )2213.8043478260911.5610930563910191.487460314342
Median2211.7
Midrange2167.2
Midmean - Weighted Average at Xnp2216.62941176471
Midmean - Weighted Average at X(n+1)p2222.69428571429
Midmean - Empirical Distribution Function2222.69428571429
Midmean - Empirical Distribution Function - Averaging2222.69428571429
Midmean - Empirical Distribution Function - Interpolation2222.3
Midmean - Closest Observation2216.62941176471
Midmean - True Basic - Statistics Graphics Toolkit2222.69428571429
Midmean - MS Excel (old versions)2222.69428571429
Number of observations67



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')