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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 03:57:05 -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/t1197456173ajip80lszl3khch.htm/, Retrieved Fri, 03 May 2024 00:44:19 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=3204, Retrieved Fri, 03 May 2024 00:44:19 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact234
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2007-12-12 10:57:05] [6bdd947de0ee04552c8f0fc807f31807] [Current]
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Dataseries X:
2171,7
2293,9
2493,7
2382,5
2286
2391,8
2163,6
2095,9
2442,1
2611,2
2498,6
2342,2
2326,8
2417,4
2572,8
2403,6
2294,1
2353,6
2201,2
1925,8
2428,8
2603,2
2330,1
2482,9
2255,6
2518
2960,7
2571,5
2348,4
2817,9
2166,6
2284,7
2864,3
2738,3
2734,9
2893,3
2503,3
2685,1
3034,9
2826,9
2529,1
2867,3
2202,9
2401,3
2869,8
2589
2945,2
2896,6
2809,3
2926,4
3634,7
2772,1
3023,5
3022,9
2565,5
2797,5
3101
3092,9
3140,5
2751,5
2947,4
3128,4
3569
3190,2
3468,7
3500,2
3057,7




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=3204&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=3204&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=3204&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 Mean2664.4552238806045.994774656687957.9295201198071
Geometric Mean2639.04039901268
Harmonic Mean2614.39462641566
Quadratic Mean2690.52892821878
Winsorized Mean ( 1 / 22 )2666.0134328358245.136942938127159.0649977445381
Winsorized Mean ( 2 / 22 )2665.9805970149344.163869443971560.3656479964266
Winsorized Mean ( 3 / 22 )2664.7044776119443.742447997565360.9180464193559
Winsorized Mean ( 4 / 22 )2648.3820895522439.621515447040866.8420190311028
Winsorized Mean ( 5 / 22 )2646.8746268656738.482597777696468.781079753398
Winsorized Mean ( 6 / 22 )2645.9432835820938.247027903904569.1803632488781
Winsorized Mean ( 7 / 22 )2648.5865671641836.77691219291872.0176439302647
Winsorized Mean ( 8 / 22 )2651.0940298507536.048011471849873.54341950099
Winsorized Mean ( 9 / 22 )2646.5402985074635.162874954027575.2651852832738
Winsorized Mean ( 10 / 22 )2644.3164179104534.385871939522376.9012466096908
Winsorized Mean ( 11 / 22 )2642.477611940334.061109303534477.5804918269676
Winsorized Mean ( 12 / 22 )2648.2268656716433.158581564245779.8655051194101
Winsorized Mean ( 13 / 22 )2636.7985074626931.075030404900384.8526444899916
Winsorized Mean ( 14 / 22 )2636.5477611940330.263912093560187.1185375189833
Winsorized Mean ( 15 / 22 )2637.4432835820929.983636742272387.962754693586
Winsorized Mean ( 16 / 22 )2634.1955223880629.111668409722490.4859002003581
Winsorized Mean ( 17 / 22 )2633.9671641791026.922314945197697.8358350513595
Winsorized Mean ( 18 / 22 )2635.5791044776126.439990298925999.6815458205624
Winsorized Mean ( 19 / 22 )2631.6089552238825.0927885232431104.875109945882
Winsorized Mean ( 20 / 22 )2631.5492537313424.8902005253912105.726317915632
Winsorized Mean ( 21 / 22 )2634.9343283582124.1598923943721109.062337089382
Winsorized Mean ( 22 / 22 )2626.3970149253721.9127845447474119.856835609463
Trimmed Mean ( 1 / 22 )2660.8923076923143.48688663461261.1883837546203
Trimmed Mean ( 2 / 22 )2655.4460317460341.481987455812264.0144360145398
Trimmed Mean ( 3 / 22 )2649.6606557377039.68353860854166.7697677335514
Trimmed Mean ( 4 / 22 )2643.9661016949237.67660674157370.1752713515339
Trimmed Mean ( 5 / 22 )2642.6684210526336.856923899522371.7007319508528
Trimmed Mean ( 6 / 22 )2641.6436363636436.206149445468372.9611868929153
Trimmed Mean ( 7 / 22 )2640.7377358490635.451974836182374.487747101578
Trimmed Mean ( 8 / 22 )2639.2647058823534.886791120628375.652263252202
Trimmed Mean ( 9 / 22 )2637.2428571428634.329544652593776.8213759847703
Trimmed Mean ( 10 / 22 )2635.7702127659633.811359737761477.9551675297536
Trimmed Mean ( 11 / 22 )2634.4977777777833.298186847972979.1183552968188
Trimmed Mean ( 12 / 22 )2633.3674418604732.674396172497680.5942190318731
Trimmed Mean ( 13 / 22 )2631.3439024390232.027310192332182.1593785627684
Trimmed Mean ( 14 / 22 )2630.6230769230831.633274274350983.1599996291265
Trimmed Mean ( 15 / 22 )2629.8567567567631.233727184278484.1992613062365
Trimmed Mean ( 16 / 22 )2628.8885714285730.688661791368885.6631869222772
Trimmed Mean ( 17 / 22 )2628.2151515151530.094909881581887.3308862480969
Trimmed Mean ( 18 / 22 )2627.4838709677429.766114492382888.2709724052201
Trimmed Mean ( 19 / 22 )2626.4448275862129.314072423066789.5967230237005
Trimmed Mean ( 20 / 22 )2625.7703703703728.937486317615690.7394077547068
Trimmed Mean ( 21 / 22 )2624.99628.288048406821392.795231478995
Trimmed Mean ( 22 / 22 )2623.6173913043527.394136625011695.7729541623486
Median2589
Midrange2780.25
Midmean - Weighted Average at Xnp2620.13823529412
Midmean - Weighted Average at X(n+1)p2628.88857142857
Midmean - Empirical Distribution Function2628.88857142857
Midmean - Empirical Distribution Function - Averaging2628.88857142857
Midmean - Empirical Distribution Function - Interpolation2628.21515151515
Midmean - Closest Observation2620.13823529412
Midmean - True Basic - Statistics Graphics Toolkit2628.88857142857
Midmean - MS Excel (old versions)2628.88857142857
Number of observations67

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 2664.45522388060 & 45.9947746566879 & 57.9295201198071 \tabularnewline
Geometric Mean & 2639.04039901268 &  &  \tabularnewline
Harmonic Mean & 2614.39462641566 &  &  \tabularnewline
Quadratic Mean & 2690.52892821878 &  &  \tabularnewline
Winsorized Mean ( 1 / 22 ) & 2666.01343283582 & 45.1369429381271 & 59.0649977445381 \tabularnewline
Winsorized Mean ( 2 / 22 ) & 2665.98059701493 & 44.1638694439715 & 60.3656479964266 \tabularnewline
Winsorized Mean ( 3 / 22 ) & 2664.70447761194 & 43.7424479975653 & 60.9180464193559 \tabularnewline
Winsorized Mean ( 4 / 22 ) & 2648.38208955224 & 39.6215154470408 & 66.8420190311028 \tabularnewline
Winsorized Mean ( 5 / 22 ) & 2646.87462686567 & 38.4825977776964 & 68.781079753398 \tabularnewline
Winsorized Mean ( 6 / 22 ) & 2645.94328358209 & 38.2470279039045 & 69.1803632488781 \tabularnewline
Winsorized Mean ( 7 / 22 ) & 2648.58656716418 & 36.776912192918 & 72.0176439302647 \tabularnewline
Winsorized Mean ( 8 / 22 ) & 2651.09402985075 & 36.0480114718498 & 73.54341950099 \tabularnewline
Winsorized Mean ( 9 / 22 ) & 2646.54029850746 & 35.1628749540275 & 75.2651852832738 \tabularnewline
Winsorized Mean ( 10 / 22 ) & 2644.31641791045 & 34.3858719395223 & 76.9012466096908 \tabularnewline
Winsorized Mean ( 11 / 22 ) & 2642.4776119403 & 34.0611093035344 & 77.5804918269676 \tabularnewline
Winsorized Mean ( 12 / 22 ) & 2648.22686567164 & 33.1585815642457 & 79.8655051194101 \tabularnewline
Winsorized Mean ( 13 / 22 ) & 2636.79850746269 & 31.0750304049003 & 84.8526444899916 \tabularnewline
Winsorized Mean ( 14 / 22 ) & 2636.54776119403 & 30.2639120935601 & 87.1185375189833 \tabularnewline
Winsorized Mean ( 15 / 22 ) & 2637.44328358209 & 29.9836367422723 & 87.962754693586 \tabularnewline
Winsorized Mean ( 16 / 22 ) & 2634.19552238806 & 29.1116684097224 & 90.4859002003581 \tabularnewline
Winsorized Mean ( 17 / 22 ) & 2633.96716417910 & 26.9223149451976 & 97.8358350513595 \tabularnewline
Winsorized Mean ( 18 / 22 ) & 2635.57910447761 & 26.4399902989259 & 99.6815458205624 \tabularnewline
Winsorized Mean ( 19 / 22 ) & 2631.60895522388 & 25.0927885232431 & 104.875109945882 \tabularnewline
Winsorized Mean ( 20 / 22 ) & 2631.54925373134 & 24.8902005253912 & 105.726317915632 \tabularnewline
Winsorized Mean ( 21 / 22 ) & 2634.93432835821 & 24.1598923943721 & 109.062337089382 \tabularnewline
Winsorized Mean ( 22 / 22 ) & 2626.39701492537 & 21.9127845447474 & 119.856835609463 \tabularnewline
Trimmed Mean ( 1 / 22 ) & 2660.89230769231 & 43.486886634612 & 61.1883837546203 \tabularnewline
Trimmed Mean ( 2 / 22 ) & 2655.44603174603 & 41.4819874558122 & 64.0144360145398 \tabularnewline
Trimmed Mean ( 3 / 22 ) & 2649.66065573770 & 39.683538608541 & 66.7697677335514 \tabularnewline
Trimmed Mean ( 4 / 22 ) & 2643.96610169492 & 37.676606741573 & 70.1752713515339 \tabularnewline
Trimmed Mean ( 5 / 22 ) & 2642.66842105263 & 36.8569238995223 & 71.7007319508528 \tabularnewline
Trimmed Mean ( 6 / 22 ) & 2641.64363636364 & 36.2061494454683 & 72.9611868929153 \tabularnewline
Trimmed Mean ( 7 / 22 ) & 2640.73773584906 & 35.4519748361823 & 74.487747101578 \tabularnewline
Trimmed Mean ( 8 / 22 ) & 2639.26470588235 & 34.8867911206283 & 75.652263252202 \tabularnewline
Trimmed Mean ( 9 / 22 ) & 2637.24285714286 & 34.3295446525937 & 76.8213759847703 \tabularnewline
Trimmed Mean ( 10 / 22 ) & 2635.77021276596 & 33.8113597377614 & 77.9551675297536 \tabularnewline
Trimmed Mean ( 11 / 22 ) & 2634.49777777778 & 33.2981868479729 & 79.1183552968188 \tabularnewline
Trimmed Mean ( 12 / 22 ) & 2633.36744186047 & 32.6743961724976 & 80.5942190318731 \tabularnewline
Trimmed Mean ( 13 / 22 ) & 2631.34390243902 & 32.0273101923321 & 82.1593785627684 \tabularnewline
Trimmed Mean ( 14 / 22 ) & 2630.62307692308 & 31.6332742743509 & 83.1599996291265 \tabularnewline
Trimmed Mean ( 15 / 22 ) & 2629.85675675676 & 31.2337271842784 & 84.1992613062365 \tabularnewline
Trimmed Mean ( 16 / 22 ) & 2628.88857142857 & 30.6886617913688 & 85.6631869222772 \tabularnewline
Trimmed Mean ( 17 / 22 ) & 2628.21515151515 & 30.0949098815818 & 87.3308862480969 \tabularnewline
Trimmed Mean ( 18 / 22 ) & 2627.48387096774 & 29.7661144923828 & 88.2709724052201 \tabularnewline
Trimmed Mean ( 19 / 22 ) & 2626.44482758621 & 29.3140724230667 & 89.5967230237005 \tabularnewline
Trimmed Mean ( 20 / 22 ) & 2625.77037037037 & 28.9374863176156 & 90.7394077547068 \tabularnewline
Trimmed Mean ( 21 / 22 ) & 2624.996 & 28.2880484068213 & 92.795231478995 \tabularnewline
Trimmed Mean ( 22 / 22 ) & 2623.61739130435 & 27.3941366250116 & 95.7729541623486 \tabularnewline
Median & 2589 &  &  \tabularnewline
Midrange & 2780.25 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 2620.13823529412 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 2628.88857142857 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 2628.88857142857 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 2628.88857142857 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 2628.21515151515 &  &  \tabularnewline
Midmean - Closest Observation & 2620.13823529412 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 2628.88857142857 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 2628.88857142857 &  &  \tabularnewline
Number of observations & 67 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=3204&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]2664.45522388060[/C][C]45.9947746566879[/C][C]57.9295201198071[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]2639.04039901268[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]2614.39462641566[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]2690.52892821878[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 22 )[/C][C]2666.01343283582[/C][C]45.1369429381271[/C][C]59.0649977445381[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 22 )[/C][C]2665.98059701493[/C][C]44.1638694439715[/C][C]60.3656479964266[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 22 )[/C][C]2664.70447761194[/C][C]43.7424479975653[/C][C]60.9180464193559[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 22 )[/C][C]2648.38208955224[/C][C]39.6215154470408[/C][C]66.8420190311028[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 22 )[/C][C]2646.87462686567[/C][C]38.4825977776964[/C][C]68.781079753398[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 22 )[/C][C]2645.94328358209[/C][C]38.2470279039045[/C][C]69.1803632488781[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 22 )[/C][C]2648.58656716418[/C][C]36.776912192918[/C][C]72.0176439302647[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 22 )[/C][C]2651.09402985075[/C][C]36.0480114718498[/C][C]73.54341950099[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 22 )[/C][C]2646.54029850746[/C][C]35.1628749540275[/C][C]75.2651852832738[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 22 )[/C][C]2644.31641791045[/C][C]34.3858719395223[/C][C]76.9012466096908[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 22 )[/C][C]2642.4776119403[/C][C]34.0611093035344[/C][C]77.5804918269676[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 22 )[/C][C]2648.22686567164[/C][C]33.1585815642457[/C][C]79.8655051194101[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 22 )[/C][C]2636.79850746269[/C][C]31.0750304049003[/C][C]84.8526444899916[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 22 )[/C][C]2636.54776119403[/C][C]30.2639120935601[/C][C]87.1185375189833[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 22 )[/C][C]2637.44328358209[/C][C]29.9836367422723[/C][C]87.962754693586[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 22 )[/C][C]2634.19552238806[/C][C]29.1116684097224[/C][C]90.4859002003581[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 22 )[/C][C]2633.96716417910[/C][C]26.9223149451976[/C][C]97.8358350513595[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 22 )[/C][C]2635.57910447761[/C][C]26.4399902989259[/C][C]99.6815458205624[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 22 )[/C][C]2631.60895522388[/C][C]25.0927885232431[/C][C]104.875109945882[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 22 )[/C][C]2631.54925373134[/C][C]24.8902005253912[/C][C]105.726317915632[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 22 )[/C][C]2634.93432835821[/C][C]24.1598923943721[/C][C]109.062337089382[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 22 )[/C][C]2626.39701492537[/C][C]21.9127845447474[/C][C]119.856835609463[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 22 )[/C][C]2660.89230769231[/C][C]43.486886634612[/C][C]61.1883837546203[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 22 )[/C][C]2655.44603174603[/C][C]41.4819874558122[/C][C]64.0144360145398[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 22 )[/C][C]2649.66065573770[/C][C]39.683538608541[/C][C]66.7697677335514[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 22 )[/C][C]2643.96610169492[/C][C]37.676606741573[/C][C]70.1752713515339[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 22 )[/C][C]2642.66842105263[/C][C]36.8569238995223[/C][C]71.7007319508528[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 22 )[/C][C]2641.64363636364[/C][C]36.2061494454683[/C][C]72.9611868929153[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 22 )[/C][C]2640.73773584906[/C][C]35.4519748361823[/C][C]74.487747101578[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 22 )[/C][C]2639.26470588235[/C][C]34.8867911206283[/C][C]75.652263252202[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 22 )[/C][C]2637.24285714286[/C][C]34.3295446525937[/C][C]76.8213759847703[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 22 )[/C][C]2635.77021276596[/C][C]33.8113597377614[/C][C]77.9551675297536[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 22 )[/C][C]2634.49777777778[/C][C]33.2981868479729[/C][C]79.1183552968188[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 22 )[/C][C]2633.36744186047[/C][C]32.6743961724976[/C][C]80.5942190318731[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 22 )[/C][C]2631.34390243902[/C][C]32.0273101923321[/C][C]82.1593785627684[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 22 )[/C][C]2630.62307692308[/C][C]31.6332742743509[/C][C]83.1599996291265[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 22 )[/C][C]2629.85675675676[/C][C]31.2337271842784[/C][C]84.1992613062365[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 22 )[/C][C]2628.88857142857[/C][C]30.6886617913688[/C][C]85.6631869222772[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 22 )[/C][C]2628.21515151515[/C][C]30.0949098815818[/C][C]87.3308862480969[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 22 )[/C][C]2627.48387096774[/C][C]29.7661144923828[/C][C]88.2709724052201[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 22 )[/C][C]2626.44482758621[/C][C]29.3140724230667[/C][C]89.5967230237005[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 22 )[/C][C]2625.77037037037[/C][C]28.9374863176156[/C][C]90.7394077547068[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 22 )[/C][C]2624.996[/C][C]28.2880484068213[/C][C]92.795231478995[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 22 )[/C][C]2623.61739130435[/C][C]27.3941366250116[/C][C]95.7729541623486[/C][/ROW]
[ROW][C]Median[/C][C]2589[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]2780.25[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]2620.13823529412[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]2628.88857142857[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]2628.88857142857[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]2628.88857142857[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]2628.21515151515[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]2620.13823529412[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]2628.88857142857[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]2628.88857142857[/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=3204&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=3204&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 Mean2664.4552238806045.994774656687957.9295201198071
Geometric Mean2639.04039901268
Harmonic Mean2614.39462641566
Quadratic Mean2690.52892821878
Winsorized Mean ( 1 / 22 )2666.0134328358245.136942938127159.0649977445381
Winsorized Mean ( 2 / 22 )2665.9805970149344.163869443971560.3656479964266
Winsorized Mean ( 3 / 22 )2664.7044776119443.742447997565360.9180464193559
Winsorized Mean ( 4 / 22 )2648.3820895522439.621515447040866.8420190311028
Winsorized Mean ( 5 / 22 )2646.8746268656738.482597777696468.781079753398
Winsorized Mean ( 6 / 22 )2645.9432835820938.247027903904569.1803632488781
Winsorized Mean ( 7 / 22 )2648.5865671641836.77691219291872.0176439302647
Winsorized Mean ( 8 / 22 )2651.0940298507536.048011471849873.54341950099
Winsorized Mean ( 9 / 22 )2646.5402985074635.162874954027575.2651852832738
Winsorized Mean ( 10 / 22 )2644.3164179104534.385871939522376.9012466096908
Winsorized Mean ( 11 / 22 )2642.477611940334.061109303534477.5804918269676
Winsorized Mean ( 12 / 22 )2648.2268656716433.158581564245779.8655051194101
Winsorized Mean ( 13 / 22 )2636.7985074626931.075030404900384.8526444899916
Winsorized Mean ( 14 / 22 )2636.5477611940330.263912093560187.1185375189833
Winsorized Mean ( 15 / 22 )2637.4432835820929.983636742272387.962754693586
Winsorized Mean ( 16 / 22 )2634.1955223880629.111668409722490.4859002003581
Winsorized Mean ( 17 / 22 )2633.9671641791026.922314945197697.8358350513595
Winsorized Mean ( 18 / 22 )2635.5791044776126.439990298925999.6815458205624
Winsorized Mean ( 19 / 22 )2631.6089552238825.0927885232431104.875109945882
Winsorized Mean ( 20 / 22 )2631.5492537313424.8902005253912105.726317915632
Winsorized Mean ( 21 / 22 )2634.9343283582124.1598923943721109.062337089382
Winsorized Mean ( 22 / 22 )2626.3970149253721.9127845447474119.856835609463
Trimmed Mean ( 1 / 22 )2660.8923076923143.48688663461261.1883837546203
Trimmed Mean ( 2 / 22 )2655.4460317460341.481987455812264.0144360145398
Trimmed Mean ( 3 / 22 )2649.6606557377039.68353860854166.7697677335514
Trimmed Mean ( 4 / 22 )2643.9661016949237.67660674157370.1752713515339
Trimmed Mean ( 5 / 22 )2642.6684210526336.856923899522371.7007319508528
Trimmed Mean ( 6 / 22 )2641.6436363636436.206149445468372.9611868929153
Trimmed Mean ( 7 / 22 )2640.7377358490635.451974836182374.487747101578
Trimmed Mean ( 8 / 22 )2639.2647058823534.886791120628375.652263252202
Trimmed Mean ( 9 / 22 )2637.2428571428634.329544652593776.8213759847703
Trimmed Mean ( 10 / 22 )2635.7702127659633.811359737761477.9551675297536
Trimmed Mean ( 11 / 22 )2634.4977777777833.298186847972979.1183552968188
Trimmed Mean ( 12 / 22 )2633.3674418604732.674396172497680.5942190318731
Trimmed Mean ( 13 / 22 )2631.3439024390232.027310192332182.1593785627684
Trimmed Mean ( 14 / 22 )2630.6230769230831.633274274350983.1599996291265
Trimmed Mean ( 15 / 22 )2629.8567567567631.233727184278484.1992613062365
Trimmed Mean ( 16 / 22 )2628.8885714285730.688661791368885.6631869222772
Trimmed Mean ( 17 / 22 )2628.2151515151530.094909881581887.3308862480969
Trimmed Mean ( 18 / 22 )2627.4838709677429.766114492382888.2709724052201
Trimmed Mean ( 19 / 22 )2626.4448275862129.314072423066789.5967230237005
Trimmed Mean ( 20 / 22 )2625.7703703703728.937486317615690.7394077547068
Trimmed Mean ( 21 / 22 )2624.99628.288048406821392.795231478995
Trimmed Mean ( 22 / 22 )2623.6173913043527.394136625011695.7729541623486
Median2589
Midrange2780.25
Midmean - Weighted Average at Xnp2620.13823529412
Midmean - Weighted Average at X(n+1)p2628.88857142857
Midmean - Empirical Distribution Function2628.88857142857
Midmean - Empirical Distribution Function - Averaging2628.88857142857
Midmean - Empirical Distribution Function - Interpolation2628.21515151515
Midmean - Closest Observation2620.13823529412
Midmean - True Basic - Statistics Graphics Toolkit2628.88857142857
Midmean - MS Excel (old versions)2628.88857142857
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')