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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 computationWed, 24 Nov 2010 15:40:00 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Nov/24/t129061454081elwblhmnoawhe.htm/, Retrieved Fri, 03 May 2024 16:02:22 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=100362, Retrieved Fri, 03 May 2024 16:02:22 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact138
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2010-11-24 15:40:00] [b7dd4adfab743bef2d672ff51f950617] [Current]
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Dataseries X:
22631
23956
23284
24334
24319
25252
24427
25434
25496
26681
25624
26706
25834
26513
26005
27158
26521
27652
26566
27597
27605
28621
27090
27652
28440
29076
27326
28477
29303
29301
27972
29247
29871
30079
28873
30897
30902
31321
29714
32006
31338
32562
31024
32678
33031
34115
32574
33984
34795
35680
34342
36136
36226
36226
34736
36588
45176
38351
36629
38146
39232
39257
37869
38394
40681
40797
39500
41366
42270
43536
42109
45262
46406
46275
44171
47037




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'RServer@AstonUniversity' @ vre.aston.ac.uk

\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 & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=100362&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]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=100362&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=100362&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'RServer@AstonUniversity' @ vre.aston.ac.uk







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean32556.0789473684749.2150371243.4535845309709
Geometric Mean31940.1987154781
Harmonic Mean31359.7013394689
Quadratic Mean33196.3479062952
Winsorized Mean ( 1 / 25 )32556.3684210526745.64578953640643.6619758039458
Winsorized Mean ( 2 / 25 )32570.6052631579741.9592744483943.8981038243272
Winsorized Mean ( 3 / 25 )32544.9473684211730.2049916205944.5696040726755
Winsorized Mean ( 4 / 25 )32541.2105263158729.03795735798144.6358247850969
Winsorized Mean ( 5 / 25 )32481.2105263158713.25010827402545.5397204283869
Winsorized Mean ( 6 / 25 )32496.2105263158692.99878567924546.8921608491197
Winsorized Mean ( 7 / 25 )32396.3684210526666.75119477513648.5883920042744
Winsorized Mean ( 8 / 25 )32385.9473684211662.51309285830748.8834827832565
Winsorized Mean ( 9 / 25 )32313.1184210526643.54647236522250.2110100958093
Winsorized Mean ( 10 / 25 )32265.8815789474625.91122260664851.5502525175599
Winsorized Mean ( 11 / 25 )32273.8421052632619.50126971327752.0964906499715
Winsorized Mean ( 12 / 25 )32167.5789473684576.10456904827755.8363545015954
Winsorized Mean ( 13 / 25 )32127.3815789474568.92529986858856.4702986250888
Winsorized Mean ( 14 / 25 )32131.0657894737567.06917747974456.6616332989134
Winsorized Mean ( 15 / 25 )31988.3684210526537.11412026701859.5559997662138
Winsorized Mean ( 16 / 25 )31984.5789473684534.9832665896559.7861296695503
Winsorized Mean ( 17 / 25 )32024.6184210526516.59966174473461.991171873583
Winsorized Mean ( 18 / 25 )31975.1184210526504.252873059263.4108799957173
Winsorized Mean ( 19 / 25 )31707.1184210526452.12254198492970.1294792377539
Winsorized Mean ( 20 / 25 )31767.6447368421441.45396322890571.9613988840095
Winsorized Mean ( 21 / 25 )31669.8289473684426.77107071925974.2080031197843
Winsorized Mean ( 22 / 25 )31683.4342105263425.04688712903174.5410334011179
Winsorized Mean ( 23 / 25 )31656.1973684211421.17491845639475.1616394547924
Winsorized Mean ( 24 / 25 )31613.25388.17225111422981.4412929034875
Winsorized Mean ( 25 / 25 )31476.0789473684329.09502427812195.6443477576487
Trimmed Mean ( 1 / 25 )32494.5135135135731.56187112636644.4179977060349
Trimmed Mean ( 2 / 25 )32429.2222222222714.86390007248845.3641906087772
Trimmed Mean ( 3 / 25 )32352.4714285714697.299430922646.3968131822017
Trimmed Mean ( 4 / 25 )32280.7647058824681.65020487605847.356788679836
Trimmed Mean ( 5 / 25 )32205.7878787879663.24106321342348.5581934911416
Trimmed Mean ( 6 / 25 )32140.375646.10648390313149.7447027707258
Trimmed Mean ( 7 / 25 )32067.6774193548630.93511378557150.8256343936079
Trimmed Mean ( 8 / 25 )32008.2619.19163348922251.6935279303272
Trimmed Mean ( 9 / 25 )31946.3275862069605.6232166730952.7495094420253
Trimmed Mean ( 10 / 25 )31891.0178571429593.16988953532153.7637166345812
Trimmed Mean ( 11 / 25 )31838.2592592593581.43455700937354.7581131452185
Trimmed Mean ( 12 / 25 )31780.3846153846567.85104500795555.966058167489
Trimmed Mean ( 13 / 25 )31731.34559.77112058120256.686275574656
Trimmed Mean ( 14 / 25 )31683.1041666667550.54663377145257.5484477120956
Trimmed Mean ( 15 / 25 )31630.2391304348538.60531127900558.7261923862646
Trimmed Mean ( 16 / 25 )31589529.3598801041259.6739594126151
Trimmed Mean ( 17 / 25 )31544.2619047619517.14361455156460.9971021920385
Trimmed Mean ( 18 / 25 )31490.575504.46005647000262.4243180329434
Trimmed Mean ( 19 / 25 )31436.7368421053489.88565403734264.1715808230404
Trimmed Mean ( 20 / 25 )31406.6944444444482.6619455495365.0697547922214
Trimmed Mean ( 21 / 25 )31366.3529411765474.02943883391866.1696307687887
Trimmed Mean ( 22 / 25 )31332.03125464.80587450737267.4088538214099
Trimmed Mean ( 23 / 25 )31291.5666666667450.76367303411169.4190072062411
Trimmed Mean ( 24 / 25 )31248.5357142857430.341683129272.6133138836659
Trimmed Mean ( 25 / 25 )31204.1153846154410.59389004754975.997515162736
Median30963
Midrange34834
Midmean - Weighted Average at Xnp31327.0256410256
Midmean - Weighted Average at X(n+1)p31436.7368421053
Midmean - Empirical Distribution Function31327.0256410256
Midmean - Empirical Distribution Function - Averaging31436.7368421053
Midmean - Empirical Distribution Function - Interpolation31436.7368421053
Midmean - Closest Observation31327.0256410256
Midmean - True Basic - Statistics Graphics Toolkit31436.7368421053
Midmean - MS Excel (old versions)31490.575
Number of observations76

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 32556.0789473684 & 749.21503712 & 43.4535845309709 \tabularnewline
Geometric Mean & 31940.1987154781 &  &  \tabularnewline
Harmonic Mean & 31359.7013394689 &  &  \tabularnewline
Quadratic Mean & 33196.3479062952 &  &  \tabularnewline
Winsorized Mean ( 1 / 25 ) & 32556.3684210526 & 745.645789536406 & 43.6619758039458 \tabularnewline
Winsorized Mean ( 2 / 25 ) & 32570.6052631579 & 741.95927444839 & 43.8981038243272 \tabularnewline
Winsorized Mean ( 3 / 25 ) & 32544.9473684211 & 730.20499162059 & 44.5696040726755 \tabularnewline
Winsorized Mean ( 4 / 25 ) & 32541.2105263158 & 729.037957357981 & 44.6358247850969 \tabularnewline
Winsorized Mean ( 5 / 25 ) & 32481.2105263158 & 713.250108274025 & 45.5397204283869 \tabularnewline
Winsorized Mean ( 6 / 25 ) & 32496.2105263158 & 692.998785679245 & 46.8921608491197 \tabularnewline
Winsorized Mean ( 7 / 25 ) & 32396.3684210526 & 666.751194775136 & 48.5883920042744 \tabularnewline
Winsorized Mean ( 8 / 25 ) & 32385.9473684211 & 662.513092858307 & 48.8834827832565 \tabularnewline
Winsorized Mean ( 9 / 25 ) & 32313.1184210526 & 643.546472365222 & 50.2110100958093 \tabularnewline
Winsorized Mean ( 10 / 25 ) & 32265.8815789474 & 625.911222606648 & 51.5502525175599 \tabularnewline
Winsorized Mean ( 11 / 25 ) & 32273.8421052632 & 619.501269713277 & 52.0964906499715 \tabularnewline
Winsorized Mean ( 12 / 25 ) & 32167.5789473684 & 576.104569048277 & 55.8363545015954 \tabularnewline
Winsorized Mean ( 13 / 25 ) & 32127.3815789474 & 568.925299868588 & 56.4702986250888 \tabularnewline
Winsorized Mean ( 14 / 25 ) & 32131.0657894737 & 567.069177479744 & 56.6616332989134 \tabularnewline
Winsorized Mean ( 15 / 25 ) & 31988.3684210526 & 537.114120267018 & 59.5559997662138 \tabularnewline
Winsorized Mean ( 16 / 25 ) & 31984.5789473684 & 534.98326658965 & 59.7861296695503 \tabularnewline
Winsorized Mean ( 17 / 25 ) & 32024.6184210526 & 516.599661744734 & 61.991171873583 \tabularnewline
Winsorized Mean ( 18 / 25 ) & 31975.1184210526 & 504.2528730592 & 63.4108799957173 \tabularnewline
Winsorized Mean ( 19 / 25 ) & 31707.1184210526 & 452.122541984929 & 70.1294792377539 \tabularnewline
Winsorized Mean ( 20 / 25 ) & 31767.6447368421 & 441.453963228905 & 71.9613988840095 \tabularnewline
Winsorized Mean ( 21 / 25 ) & 31669.8289473684 & 426.771070719259 & 74.2080031197843 \tabularnewline
Winsorized Mean ( 22 / 25 ) & 31683.4342105263 & 425.046887129031 & 74.5410334011179 \tabularnewline
Winsorized Mean ( 23 / 25 ) & 31656.1973684211 & 421.174918456394 & 75.1616394547924 \tabularnewline
Winsorized Mean ( 24 / 25 ) & 31613.25 & 388.172251114229 & 81.4412929034875 \tabularnewline
Winsorized Mean ( 25 / 25 ) & 31476.0789473684 & 329.095024278121 & 95.6443477576487 \tabularnewline
Trimmed Mean ( 1 / 25 ) & 32494.5135135135 & 731.561871126366 & 44.4179977060349 \tabularnewline
Trimmed Mean ( 2 / 25 ) & 32429.2222222222 & 714.863900072488 & 45.3641906087772 \tabularnewline
Trimmed Mean ( 3 / 25 ) & 32352.4714285714 & 697.2994309226 & 46.3968131822017 \tabularnewline
Trimmed Mean ( 4 / 25 ) & 32280.7647058824 & 681.650204876058 & 47.356788679836 \tabularnewline
Trimmed Mean ( 5 / 25 ) & 32205.7878787879 & 663.241063213423 & 48.5581934911416 \tabularnewline
Trimmed Mean ( 6 / 25 ) & 32140.375 & 646.106483903131 & 49.7447027707258 \tabularnewline
Trimmed Mean ( 7 / 25 ) & 32067.6774193548 & 630.935113785571 & 50.8256343936079 \tabularnewline
Trimmed Mean ( 8 / 25 ) & 32008.2 & 619.191633489222 & 51.6935279303272 \tabularnewline
Trimmed Mean ( 9 / 25 ) & 31946.3275862069 & 605.62321667309 & 52.7495094420253 \tabularnewline
Trimmed Mean ( 10 / 25 ) & 31891.0178571429 & 593.169889535321 & 53.7637166345812 \tabularnewline
Trimmed Mean ( 11 / 25 ) & 31838.2592592593 & 581.434557009373 & 54.7581131452185 \tabularnewline
Trimmed Mean ( 12 / 25 ) & 31780.3846153846 & 567.851045007955 & 55.966058167489 \tabularnewline
Trimmed Mean ( 13 / 25 ) & 31731.34 & 559.771120581202 & 56.686275574656 \tabularnewline
Trimmed Mean ( 14 / 25 ) & 31683.1041666667 & 550.546633771452 & 57.5484477120956 \tabularnewline
Trimmed Mean ( 15 / 25 ) & 31630.2391304348 & 538.605311279005 & 58.7261923862646 \tabularnewline
Trimmed Mean ( 16 / 25 ) & 31589 & 529.35988010412 & 59.6739594126151 \tabularnewline
Trimmed Mean ( 17 / 25 ) & 31544.2619047619 & 517.143614551564 & 60.9971021920385 \tabularnewline
Trimmed Mean ( 18 / 25 ) & 31490.575 & 504.460056470002 & 62.4243180329434 \tabularnewline
Trimmed Mean ( 19 / 25 ) & 31436.7368421053 & 489.885654037342 & 64.1715808230404 \tabularnewline
Trimmed Mean ( 20 / 25 ) & 31406.6944444444 & 482.66194554953 & 65.0697547922214 \tabularnewline
Trimmed Mean ( 21 / 25 ) & 31366.3529411765 & 474.029438833918 & 66.1696307687887 \tabularnewline
Trimmed Mean ( 22 / 25 ) & 31332.03125 & 464.805874507372 & 67.4088538214099 \tabularnewline
Trimmed Mean ( 23 / 25 ) & 31291.5666666667 & 450.763673034111 & 69.4190072062411 \tabularnewline
Trimmed Mean ( 24 / 25 ) & 31248.5357142857 & 430.3416831292 & 72.6133138836659 \tabularnewline
Trimmed Mean ( 25 / 25 ) & 31204.1153846154 & 410.593890047549 & 75.997515162736 \tabularnewline
Median & 30963 &  &  \tabularnewline
Midrange & 34834 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 31327.0256410256 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 31436.7368421053 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 31327.0256410256 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 31436.7368421053 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 31436.7368421053 &  &  \tabularnewline
Midmean - Closest Observation & 31327.0256410256 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 31436.7368421053 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 31490.575 &  &  \tabularnewline
Number of observations & 76 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=100362&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]32556.0789473684[/C][C]749.21503712[/C][C]43.4535845309709[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]31940.1987154781[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]31359.7013394689[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]33196.3479062952[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 25 )[/C][C]32556.3684210526[/C][C]745.645789536406[/C][C]43.6619758039458[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 25 )[/C][C]32570.6052631579[/C][C]741.95927444839[/C][C]43.8981038243272[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 25 )[/C][C]32544.9473684211[/C][C]730.20499162059[/C][C]44.5696040726755[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 25 )[/C][C]32541.2105263158[/C][C]729.037957357981[/C][C]44.6358247850969[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 25 )[/C][C]32481.2105263158[/C][C]713.250108274025[/C][C]45.5397204283869[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 25 )[/C][C]32496.2105263158[/C][C]692.998785679245[/C][C]46.8921608491197[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 25 )[/C][C]32396.3684210526[/C][C]666.751194775136[/C][C]48.5883920042744[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 25 )[/C][C]32385.9473684211[/C][C]662.513092858307[/C][C]48.8834827832565[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 25 )[/C][C]32313.1184210526[/C][C]643.546472365222[/C][C]50.2110100958093[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 25 )[/C][C]32265.8815789474[/C][C]625.911222606648[/C][C]51.5502525175599[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 25 )[/C][C]32273.8421052632[/C][C]619.501269713277[/C][C]52.0964906499715[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 25 )[/C][C]32167.5789473684[/C][C]576.104569048277[/C][C]55.8363545015954[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 25 )[/C][C]32127.3815789474[/C][C]568.925299868588[/C][C]56.4702986250888[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 25 )[/C][C]32131.0657894737[/C][C]567.069177479744[/C][C]56.6616332989134[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 25 )[/C][C]31988.3684210526[/C][C]537.114120267018[/C][C]59.5559997662138[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 25 )[/C][C]31984.5789473684[/C][C]534.98326658965[/C][C]59.7861296695503[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 25 )[/C][C]32024.6184210526[/C][C]516.599661744734[/C][C]61.991171873583[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 25 )[/C][C]31975.1184210526[/C][C]504.2528730592[/C][C]63.4108799957173[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 25 )[/C][C]31707.1184210526[/C][C]452.122541984929[/C][C]70.1294792377539[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 25 )[/C][C]31767.6447368421[/C][C]441.453963228905[/C][C]71.9613988840095[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 25 )[/C][C]31669.8289473684[/C][C]426.771070719259[/C][C]74.2080031197843[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 25 )[/C][C]31683.4342105263[/C][C]425.046887129031[/C][C]74.5410334011179[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 25 )[/C][C]31656.1973684211[/C][C]421.174918456394[/C][C]75.1616394547924[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 25 )[/C][C]31613.25[/C][C]388.172251114229[/C][C]81.4412929034875[/C][/ROW]
[ROW][C]Winsorized Mean ( 25 / 25 )[/C][C]31476.0789473684[/C][C]329.095024278121[/C][C]95.6443477576487[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 25 )[/C][C]32494.5135135135[/C][C]731.561871126366[/C][C]44.4179977060349[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 25 )[/C][C]32429.2222222222[/C][C]714.863900072488[/C][C]45.3641906087772[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 25 )[/C][C]32352.4714285714[/C][C]697.2994309226[/C][C]46.3968131822017[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 25 )[/C][C]32280.7647058824[/C][C]681.650204876058[/C][C]47.356788679836[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 25 )[/C][C]32205.7878787879[/C][C]663.241063213423[/C][C]48.5581934911416[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 25 )[/C][C]32140.375[/C][C]646.106483903131[/C][C]49.7447027707258[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 25 )[/C][C]32067.6774193548[/C][C]630.935113785571[/C][C]50.8256343936079[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 25 )[/C][C]32008.2[/C][C]619.191633489222[/C][C]51.6935279303272[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 25 )[/C][C]31946.3275862069[/C][C]605.62321667309[/C][C]52.7495094420253[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 25 )[/C][C]31891.0178571429[/C][C]593.169889535321[/C][C]53.7637166345812[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 25 )[/C][C]31838.2592592593[/C][C]581.434557009373[/C][C]54.7581131452185[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 25 )[/C][C]31780.3846153846[/C][C]567.851045007955[/C][C]55.966058167489[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 25 )[/C][C]31731.34[/C][C]559.771120581202[/C][C]56.686275574656[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 25 )[/C][C]31683.1041666667[/C][C]550.546633771452[/C][C]57.5484477120956[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 25 )[/C][C]31630.2391304348[/C][C]538.605311279005[/C][C]58.7261923862646[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 25 )[/C][C]31589[/C][C]529.35988010412[/C][C]59.6739594126151[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 25 )[/C][C]31544.2619047619[/C][C]517.143614551564[/C][C]60.9971021920385[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 25 )[/C][C]31490.575[/C][C]504.460056470002[/C][C]62.4243180329434[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 25 )[/C][C]31436.7368421053[/C][C]489.885654037342[/C][C]64.1715808230404[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 25 )[/C][C]31406.6944444444[/C][C]482.66194554953[/C][C]65.0697547922214[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 25 )[/C][C]31366.3529411765[/C][C]474.029438833918[/C][C]66.1696307687887[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 25 )[/C][C]31332.03125[/C][C]464.805874507372[/C][C]67.4088538214099[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 25 )[/C][C]31291.5666666667[/C][C]450.763673034111[/C][C]69.4190072062411[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 25 )[/C][C]31248.5357142857[/C][C]430.3416831292[/C][C]72.6133138836659[/C][/ROW]
[ROW][C]Trimmed Mean ( 25 / 25 )[/C][C]31204.1153846154[/C][C]410.593890047549[/C][C]75.997515162736[/C][/ROW]
[ROW][C]Median[/C][C]30963[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]34834[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]31327.0256410256[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]31436.7368421053[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]31327.0256410256[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]31436.7368421053[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]31436.7368421053[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]31327.0256410256[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]31436.7368421053[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]31490.575[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]76[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=100362&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=100362&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 Mean32556.0789473684749.2150371243.4535845309709
Geometric Mean31940.1987154781
Harmonic Mean31359.7013394689
Quadratic Mean33196.3479062952
Winsorized Mean ( 1 / 25 )32556.3684210526745.64578953640643.6619758039458
Winsorized Mean ( 2 / 25 )32570.6052631579741.9592744483943.8981038243272
Winsorized Mean ( 3 / 25 )32544.9473684211730.2049916205944.5696040726755
Winsorized Mean ( 4 / 25 )32541.2105263158729.03795735798144.6358247850969
Winsorized Mean ( 5 / 25 )32481.2105263158713.25010827402545.5397204283869
Winsorized Mean ( 6 / 25 )32496.2105263158692.99878567924546.8921608491197
Winsorized Mean ( 7 / 25 )32396.3684210526666.75119477513648.5883920042744
Winsorized Mean ( 8 / 25 )32385.9473684211662.51309285830748.8834827832565
Winsorized Mean ( 9 / 25 )32313.1184210526643.54647236522250.2110100958093
Winsorized Mean ( 10 / 25 )32265.8815789474625.91122260664851.5502525175599
Winsorized Mean ( 11 / 25 )32273.8421052632619.50126971327752.0964906499715
Winsorized Mean ( 12 / 25 )32167.5789473684576.10456904827755.8363545015954
Winsorized Mean ( 13 / 25 )32127.3815789474568.92529986858856.4702986250888
Winsorized Mean ( 14 / 25 )32131.0657894737567.06917747974456.6616332989134
Winsorized Mean ( 15 / 25 )31988.3684210526537.11412026701859.5559997662138
Winsorized Mean ( 16 / 25 )31984.5789473684534.9832665896559.7861296695503
Winsorized Mean ( 17 / 25 )32024.6184210526516.59966174473461.991171873583
Winsorized Mean ( 18 / 25 )31975.1184210526504.252873059263.4108799957173
Winsorized Mean ( 19 / 25 )31707.1184210526452.12254198492970.1294792377539
Winsorized Mean ( 20 / 25 )31767.6447368421441.45396322890571.9613988840095
Winsorized Mean ( 21 / 25 )31669.8289473684426.77107071925974.2080031197843
Winsorized Mean ( 22 / 25 )31683.4342105263425.04688712903174.5410334011179
Winsorized Mean ( 23 / 25 )31656.1973684211421.17491845639475.1616394547924
Winsorized Mean ( 24 / 25 )31613.25388.17225111422981.4412929034875
Winsorized Mean ( 25 / 25 )31476.0789473684329.09502427812195.6443477576487
Trimmed Mean ( 1 / 25 )32494.5135135135731.56187112636644.4179977060349
Trimmed Mean ( 2 / 25 )32429.2222222222714.86390007248845.3641906087772
Trimmed Mean ( 3 / 25 )32352.4714285714697.299430922646.3968131822017
Trimmed Mean ( 4 / 25 )32280.7647058824681.65020487605847.356788679836
Trimmed Mean ( 5 / 25 )32205.7878787879663.24106321342348.5581934911416
Trimmed Mean ( 6 / 25 )32140.375646.10648390313149.7447027707258
Trimmed Mean ( 7 / 25 )32067.6774193548630.93511378557150.8256343936079
Trimmed Mean ( 8 / 25 )32008.2619.19163348922251.6935279303272
Trimmed Mean ( 9 / 25 )31946.3275862069605.6232166730952.7495094420253
Trimmed Mean ( 10 / 25 )31891.0178571429593.16988953532153.7637166345812
Trimmed Mean ( 11 / 25 )31838.2592592593581.43455700937354.7581131452185
Trimmed Mean ( 12 / 25 )31780.3846153846567.85104500795555.966058167489
Trimmed Mean ( 13 / 25 )31731.34559.77112058120256.686275574656
Trimmed Mean ( 14 / 25 )31683.1041666667550.54663377145257.5484477120956
Trimmed Mean ( 15 / 25 )31630.2391304348538.60531127900558.7261923862646
Trimmed Mean ( 16 / 25 )31589529.3598801041259.6739594126151
Trimmed Mean ( 17 / 25 )31544.2619047619517.14361455156460.9971021920385
Trimmed Mean ( 18 / 25 )31490.575504.46005647000262.4243180329434
Trimmed Mean ( 19 / 25 )31436.7368421053489.88565403734264.1715808230404
Trimmed Mean ( 20 / 25 )31406.6944444444482.6619455495365.0697547922214
Trimmed Mean ( 21 / 25 )31366.3529411765474.02943883391866.1696307687887
Trimmed Mean ( 22 / 25 )31332.03125464.80587450737267.4088538214099
Trimmed Mean ( 23 / 25 )31291.5666666667450.76367303411169.4190072062411
Trimmed Mean ( 24 / 25 )31248.5357142857430.341683129272.6133138836659
Trimmed Mean ( 25 / 25 )31204.1153846154410.59389004754975.997515162736
Median30963
Midrange34834
Midmean - Weighted Average at Xnp31327.0256410256
Midmean - Weighted Average at X(n+1)p31436.7368421053
Midmean - Empirical Distribution Function31327.0256410256
Midmean - Empirical Distribution Function - Averaging31436.7368421053
Midmean - Empirical Distribution Function - Interpolation31436.7368421053
Midmean - Closest Observation31327.0256410256
Midmean - True Basic - Statistics Graphics Toolkit31436.7368421053
Midmean - MS Excel (old versions)31490.575
Number of observations76



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')