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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationThu, 05 Nov 2009 08:46:14 -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/2009/Nov/05/t12574360202y45m1d0utby681.htm/, Retrieved Thu, 02 May 2024 23:38:14 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=54147, Retrieved Thu, 02 May 2024 23:38:14 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP1W52
Estimated Impact93
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Central Tendency ...] [2009-11-05 15:46:14] [4223c028d657302779e6d755411cae22] [Current]
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Dataseries X:
7054
8620
8771
11379
12066
12657
27630
29722
29789
30630
31879
32228
32745
33008
33091
33425
33520
34077
34418
34568
34571
34801
34931
35502
36222
36279
36432
37013
37848
37898
37967
38064
38401
38529
38683
38708
39018
39253
39341
39383
39401
39486
39525
39556
40439
40600
40809
40870
40891
40898
41117
41519
41547
41629
41697
41756
41888
42438
43412
44720
44953
45315
45409
45633
47060
47221
48138
48428
49267
50380
50530
50669
51321
52073
56231
68184
68897
68906
69116
70249
70938




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=54147&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=54147&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=54147&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 Mean39916.50617283951418.298615051828.1439365090134
Geometric Mean37171.0295699665
Harmonic Mean32743.5572529146
Quadratic Mean41883.8052469324
Winsorized Mean ( 1 / 27 )39927.33333333331410.5108316396728.3070022843562
Winsorized Mean ( 2 / 27 )39903.08641975311402.0742108225128.4600387852113
Winsorized Mean ( 3 / 27 )39991.90123456791374.0539708078729.1050439678543
Winsorized Mean ( 4 / 27 )40025.38271604941365.1785392403629.3187898619628
Winsorized Mean ( 5 / 27 )40017.85185185191344.2863606682729.7688446619054
Winsorized Mean ( 6 / 27 )40241.5555555556874.20632293625546.0321030628028
Winsorized Mean ( 7 / 27 )40063.012345679765.89986905056752.3084204144628
Winsorized Mean ( 8 / 27 )39995.3580246914750.492057785453.2921802566602
Winsorized Mean ( 9 / 27 )40016.3580246914721.42247735706255.4686876007685
Winsorized Mean ( 10 / 27 )40153.3950617284694.18940576313157.8421317415342
Winsorized Mean ( 11 / 27 )40180.4197530864683.4078127577558.7942060406753
Winsorized Mean ( 12 / 27 )40092.1234567901642.23471906880162.4259671213682
Winsorized Mean ( 13 / 27 )39999.6790123457612.59335061544765.2956467323057
Winsorized Mean ( 14 / 27 )39963.9012345679601.98195125032966.3872083732112
Winsorized Mean ( 15 / 27 )39855.9382716049564.89971232355470.5540070248379
Winsorized Mean ( 16 / 27 )39842.9012345679557.06658915663871.5226904828154
Winsorized Mean ( 17 / 27 )39660.3086419753493.50460260339380.3646175390353
Winsorized Mean ( 18 / 27 )39686.3086419753475.38486800591983.4824819065995
Winsorized Mean ( 19 / 27 )39699.4444444444467.21706992799384.9700214304304
Winsorized Mean ( 20 / 27 )39610.8024691358453.82231166135187.2826246116652
Winsorized Mean ( 21 / 27 )39610.024691358436.71650796107190.6996277202529
Winsorized Mean ( 22 / 27 )39290.0740740741381.678417568489102.940256156936
Winsorized Mean ( 23 / 27 )39175.6419753086322.289201998592121.554311259487
Winsorized Mean ( 24 / 27 )39226.012345679272.020477110144144.202424620393
Winsorized Mean ( 25 / 27 )39202.8641975309264.642600683699148.135122978126
Winsorized Mean ( 26 / 27 )39233.037037037255.604309627473153.491297131166
Winsorized Mean ( 27 / 27 )39404.037037037226.794814976307173.743112430298
Trimmed Mean ( 1 / 27 )39939.81012658231335.6434589942129.9030477464835
Trimmed Mean ( 2 / 27 )39952.93506493511246.5309877949432.0512971246788
Trimmed Mean ( 3 / 27 )39979.85333333331144.5300384430734.9312398892726
Trimmed Mean ( 4 / 27 )39975.3972602741033.6320066112638.6746898360205
Trimmed Mean ( 5 / 27 )39961.1408450704897.13121886459844.5432507583951
Trimmed Mean ( 6 / 27 )39947.8260869565723.79168025123455.1924361345108
Trimmed Mean ( 7 / 27 )39888.6417910448679.36460813257458.7146302788572
Trimmed Mean ( 8 / 27 )39857.6655.78629507461760.7783363259595
Trimmed Mean ( 9 / 27 )39835.4603174603631.20234093347363.1104445185492
Trimmed Mean ( 10 / 27 )39808.7704918033608.24591140392165.448480204197
Trimmed Mean ( 11 / 27 )39761.4576271186586.25070751710867.823300027247
Trimmed Mean ( 12 / 27 )39707.3333333333561.51463587254970.7146898702495
Trimmed Mean ( 13 / 27 )39660.1090909091540.1238906843873.4278001305526
Trimmed Mean ( 14 / 27 )39620.1886792453520.00561991534776.1918470913741
Trimmed Mean ( 15 / 27 )39581.1960784314497.04126630244279.633621515737
Trimmed Mean ( 16 / 27 )39550.9183673469476.33953515567683.0309379094914
Trimmed Mean ( 17 / 27 )39519.4680851064451.56860215521887.515978516864
Trimmed Mean ( 18 / 27 )39504.5555555556434.53026252036390.9132434791105
Trimmed Mean ( 19 / 27 )39485.5348837209416.37688618577894.831236299950
Trimmed Mean ( 20 / 27 )39463.2926829268394.258026881960100.095089997348
Trimmed Mean ( 21 / 27 )39447.9743589744368.129859017314107.15776890328
Trimmed Mean ( 22 / 27 )39431.0810810811337.185904066984116.941665133332
Trimmed Mean ( 23 / 27 )39445.9142857143311.319645433200126.705509479897
Trimmed Mean ( 24 / 27 )39474.7575757576293.232080590946134.619505124421
Trimmed Mean ( 25 / 27 )39501.8387096774282.791975281098139.685147255017
Trimmed Mean ( 26 / 27 )39535.2413793103269.265149667661146.826432711795
Trimmed Mean ( 27 / 27 )39570.1111111111251.878652629639157.099899884310
Median39401
Midrange38996
Midmean - Weighted Average at Xnp39326.05
Midmean - Weighted Average at X(n+1)p39463.2926829268
Midmean - Empirical Distribution Function39463.2926829268
Midmean - Empirical Distribution Function - Averaging39463.2926829268
Midmean - Empirical Distribution Function - Interpolation39463.2926829268
Midmean - Closest Observation39346.7380952381
Midmean - True Basic - Statistics Graphics Toolkit39463.2926829268
Midmean - MS Excel (old versions)39463.2926829268
Number of observations81

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 39916.5061728395 & 1418.2986150518 & 28.1439365090134 \tabularnewline
Geometric Mean & 37171.0295699665 &  &  \tabularnewline
Harmonic Mean & 32743.5572529146 &  &  \tabularnewline
Quadratic Mean & 41883.8052469324 &  &  \tabularnewline
Winsorized Mean ( 1 / 27 ) & 39927.3333333333 & 1410.51083163967 & 28.3070022843562 \tabularnewline
Winsorized Mean ( 2 / 27 ) & 39903.0864197531 & 1402.07421082251 & 28.4600387852113 \tabularnewline
Winsorized Mean ( 3 / 27 ) & 39991.9012345679 & 1374.05397080787 & 29.1050439678543 \tabularnewline
Winsorized Mean ( 4 / 27 ) & 40025.3827160494 & 1365.17853924036 & 29.3187898619628 \tabularnewline
Winsorized Mean ( 5 / 27 ) & 40017.8518518519 & 1344.28636066827 & 29.7688446619054 \tabularnewline
Winsorized Mean ( 6 / 27 ) & 40241.5555555556 & 874.206322936255 & 46.0321030628028 \tabularnewline
Winsorized Mean ( 7 / 27 ) & 40063.012345679 & 765.899869050567 & 52.3084204144628 \tabularnewline
Winsorized Mean ( 8 / 27 ) & 39995.3580246914 & 750.4920577854 & 53.2921802566602 \tabularnewline
Winsorized Mean ( 9 / 27 ) & 40016.3580246914 & 721.422477357062 & 55.4686876007685 \tabularnewline
Winsorized Mean ( 10 / 27 ) & 40153.3950617284 & 694.189405763131 & 57.8421317415342 \tabularnewline
Winsorized Mean ( 11 / 27 ) & 40180.4197530864 & 683.40781275775 & 58.7942060406753 \tabularnewline
Winsorized Mean ( 12 / 27 ) & 40092.1234567901 & 642.234719068801 & 62.4259671213682 \tabularnewline
Winsorized Mean ( 13 / 27 ) & 39999.6790123457 & 612.593350615447 & 65.2956467323057 \tabularnewline
Winsorized Mean ( 14 / 27 ) & 39963.9012345679 & 601.981951250329 & 66.3872083732112 \tabularnewline
Winsorized Mean ( 15 / 27 ) & 39855.9382716049 & 564.899712323554 & 70.5540070248379 \tabularnewline
Winsorized Mean ( 16 / 27 ) & 39842.9012345679 & 557.066589156638 & 71.5226904828154 \tabularnewline
Winsorized Mean ( 17 / 27 ) & 39660.3086419753 & 493.504602603393 & 80.3646175390353 \tabularnewline
Winsorized Mean ( 18 / 27 ) & 39686.3086419753 & 475.384868005919 & 83.4824819065995 \tabularnewline
Winsorized Mean ( 19 / 27 ) & 39699.4444444444 & 467.217069927993 & 84.9700214304304 \tabularnewline
Winsorized Mean ( 20 / 27 ) & 39610.8024691358 & 453.822311661351 & 87.2826246116652 \tabularnewline
Winsorized Mean ( 21 / 27 ) & 39610.024691358 & 436.716507961071 & 90.6996277202529 \tabularnewline
Winsorized Mean ( 22 / 27 ) & 39290.0740740741 & 381.678417568489 & 102.940256156936 \tabularnewline
Winsorized Mean ( 23 / 27 ) & 39175.6419753086 & 322.289201998592 & 121.554311259487 \tabularnewline
Winsorized Mean ( 24 / 27 ) & 39226.012345679 & 272.020477110144 & 144.202424620393 \tabularnewline
Winsorized Mean ( 25 / 27 ) & 39202.8641975309 & 264.642600683699 & 148.135122978126 \tabularnewline
Winsorized Mean ( 26 / 27 ) & 39233.037037037 & 255.604309627473 & 153.491297131166 \tabularnewline
Winsorized Mean ( 27 / 27 ) & 39404.037037037 & 226.794814976307 & 173.743112430298 \tabularnewline
Trimmed Mean ( 1 / 27 ) & 39939.8101265823 & 1335.64345899421 & 29.9030477464835 \tabularnewline
Trimmed Mean ( 2 / 27 ) & 39952.9350649351 & 1246.53098779494 & 32.0512971246788 \tabularnewline
Trimmed Mean ( 3 / 27 ) & 39979.8533333333 & 1144.53003844307 & 34.9312398892726 \tabularnewline
Trimmed Mean ( 4 / 27 ) & 39975.397260274 & 1033.63200661126 & 38.6746898360205 \tabularnewline
Trimmed Mean ( 5 / 27 ) & 39961.1408450704 & 897.131218864598 & 44.5432507583951 \tabularnewline
Trimmed Mean ( 6 / 27 ) & 39947.8260869565 & 723.791680251234 & 55.1924361345108 \tabularnewline
Trimmed Mean ( 7 / 27 ) & 39888.6417910448 & 679.364608132574 & 58.7146302788572 \tabularnewline
Trimmed Mean ( 8 / 27 ) & 39857.6 & 655.786295074617 & 60.7783363259595 \tabularnewline
Trimmed Mean ( 9 / 27 ) & 39835.4603174603 & 631.202340933473 & 63.1104445185492 \tabularnewline
Trimmed Mean ( 10 / 27 ) & 39808.7704918033 & 608.245911403921 & 65.448480204197 \tabularnewline
Trimmed Mean ( 11 / 27 ) & 39761.4576271186 & 586.250707517108 & 67.823300027247 \tabularnewline
Trimmed Mean ( 12 / 27 ) & 39707.3333333333 & 561.514635872549 & 70.7146898702495 \tabularnewline
Trimmed Mean ( 13 / 27 ) & 39660.1090909091 & 540.12389068438 & 73.4278001305526 \tabularnewline
Trimmed Mean ( 14 / 27 ) & 39620.1886792453 & 520.005619915347 & 76.1918470913741 \tabularnewline
Trimmed Mean ( 15 / 27 ) & 39581.1960784314 & 497.041266302442 & 79.633621515737 \tabularnewline
Trimmed Mean ( 16 / 27 ) & 39550.9183673469 & 476.339535155676 & 83.0309379094914 \tabularnewline
Trimmed Mean ( 17 / 27 ) & 39519.4680851064 & 451.568602155218 & 87.515978516864 \tabularnewline
Trimmed Mean ( 18 / 27 ) & 39504.5555555556 & 434.530262520363 & 90.9132434791105 \tabularnewline
Trimmed Mean ( 19 / 27 ) & 39485.5348837209 & 416.376886185778 & 94.831236299950 \tabularnewline
Trimmed Mean ( 20 / 27 ) & 39463.2926829268 & 394.258026881960 & 100.095089997348 \tabularnewline
Trimmed Mean ( 21 / 27 ) & 39447.9743589744 & 368.129859017314 & 107.15776890328 \tabularnewline
Trimmed Mean ( 22 / 27 ) & 39431.0810810811 & 337.185904066984 & 116.941665133332 \tabularnewline
Trimmed Mean ( 23 / 27 ) & 39445.9142857143 & 311.319645433200 & 126.705509479897 \tabularnewline
Trimmed Mean ( 24 / 27 ) & 39474.7575757576 & 293.232080590946 & 134.619505124421 \tabularnewline
Trimmed Mean ( 25 / 27 ) & 39501.8387096774 & 282.791975281098 & 139.685147255017 \tabularnewline
Trimmed Mean ( 26 / 27 ) & 39535.2413793103 & 269.265149667661 & 146.826432711795 \tabularnewline
Trimmed Mean ( 27 / 27 ) & 39570.1111111111 & 251.878652629639 & 157.099899884310 \tabularnewline
Median & 39401 &  &  \tabularnewline
Midrange & 38996 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 39326.05 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 39463.2926829268 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 39463.2926829268 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 39463.2926829268 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 39463.2926829268 &  &  \tabularnewline
Midmean - Closest Observation & 39346.7380952381 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 39463.2926829268 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 39463.2926829268 &  &  \tabularnewline
Number of observations & 81 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=54147&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]39916.5061728395[/C][C]1418.2986150518[/C][C]28.1439365090134[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]37171.0295699665[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]32743.5572529146[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]41883.8052469324[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 27 )[/C][C]39927.3333333333[/C][C]1410.51083163967[/C][C]28.3070022843562[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 27 )[/C][C]39903.0864197531[/C][C]1402.07421082251[/C][C]28.4600387852113[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 27 )[/C][C]39991.9012345679[/C][C]1374.05397080787[/C][C]29.1050439678543[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 27 )[/C][C]40025.3827160494[/C][C]1365.17853924036[/C][C]29.3187898619628[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 27 )[/C][C]40017.8518518519[/C][C]1344.28636066827[/C][C]29.7688446619054[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 27 )[/C][C]40241.5555555556[/C][C]874.206322936255[/C][C]46.0321030628028[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 27 )[/C][C]40063.012345679[/C][C]765.899869050567[/C][C]52.3084204144628[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 27 )[/C][C]39995.3580246914[/C][C]750.4920577854[/C][C]53.2921802566602[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 27 )[/C][C]40016.3580246914[/C][C]721.422477357062[/C][C]55.4686876007685[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 27 )[/C][C]40153.3950617284[/C][C]694.189405763131[/C][C]57.8421317415342[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 27 )[/C][C]40180.4197530864[/C][C]683.40781275775[/C][C]58.7942060406753[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 27 )[/C][C]40092.1234567901[/C][C]642.234719068801[/C][C]62.4259671213682[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 27 )[/C][C]39999.6790123457[/C][C]612.593350615447[/C][C]65.2956467323057[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 27 )[/C][C]39963.9012345679[/C][C]601.981951250329[/C][C]66.3872083732112[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 27 )[/C][C]39855.9382716049[/C][C]564.899712323554[/C][C]70.5540070248379[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 27 )[/C][C]39842.9012345679[/C][C]557.066589156638[/C][C]71.5226904828154[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 27 )[/C][C]39660.3086419753[/C][C]493.504602603393[/C][C]80.3646175390353[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 27 )[/C][C]39686.3086419753[/C][C]475.384868005919[/C][C]83.4824819065995[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 27 )[/C][C]39699.4444444444[/C][C]467.217069927993[/C][C]84.9700214304304[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 27 )[/C][C]39610.8024691358[/C][C]453.822311661351[/C][C]87.2826246116652[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 27 )[/C][C]39610.024691358[/C][C]436.716507961071[/C][C]90.6996277202529[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 27 )[/C][C]39290.0740740741[/C][C]381.678417568489[/C][C]102.940256156936[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 27 )[/C][C]39175.6419753086[/C][C]322.289201998592[/C][C]121.554311259487[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 27 )[/C][C]39226.012345679[/C][C]272.020477110144[/C][C]144.202424620393[/C][/ROW]
[ROW][C]Winsorized Mean ( 25 / 27 )[/C][C]39202.8641975309[/C][C]264.642600683699[/C][C]148.135122978126[/C][/ROW]
[ROW][C]Winsorized Mean ( 26 / 27 )[/C][C]39233.037037037[/C][C]255.604309627473[/C][C]153.491297131166[/C][/ROW]
[ROW][C]Winsorized Mean ( 27 / 27 )[/C][C]39404.037037037[/C][C]226.794814976307[/C][C]173.743112430298[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 27 )[/C][C]39939.8101265823[/C][C]1335.64345899421[/C][C]29.9030477464835[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 27 )[/C][C]39952.9350649351[/C][C]1246.53098779494[/C][C]32.0512971246788[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 27 )[/C][C]39979.8533333333[/C][C]1144.53003844307[/C][C]34.9312398892726[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 27 )[/C][C]39975.397260274[/C][C]1033.63200661126[/C][C]38.6746898360205[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 27 )[/C][C]39961.1408450704[/C][C]897.131218864598[/C][C]44.5432507583951[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 27 )[/C][C]39947.8260869565[/C][C]723.791680251234[/C][C]55.1924361345108[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 27 )[/C][C]39888.6417910448[/C][C]679.364608132574[/C][C]58.7146302788572[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 27 )[/C][C]39857.6[/C][C]655.786295074617[/C][C]60.7783363259595[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 27 )[/C][C]39835.4603174603[/C][C]631.202340933473[/C][C]63.1104445185492[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 27 )[/C][C]39808.7704918033[/C][C]608.245911403921[/C][C]65.448480204197[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 27 )[/C][C]39761.4576271186[/C][C]586.250707517108[/C][C]67.823300027247[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 27 )[/C][C]39707.3333333333[/C][C]561.514635872549[/C][C]70.7146898702495[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 27 )[/C][C]39660.1090909091[/C][C]540.12389068438[/C][C]73.4278001305526[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 27 )[/C][C]39620.1886792453[/C][C]520.005619915347[/C][C]76.1918470913741[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 27 )[/C][C]39581.1960784314[/C][C]497.041266302442[/C][C]79.633621515737[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 27 )[/C][C]39550.9183673469[/C][C]476.339535155676[/C][C]83.0309379094914[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 27 )[/C][C]39519.4680851064[/C][C]451.568602155218[/C][C]87.515978516864[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 27 )[/C][C]39504.5555555556[/C][C]434.530262520363[/C][C]90.9132434791105[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 27 )[/C][C]39485.5348837209[/C][C]416.376886185778[/C][C]94.831236299950[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 27 )[/C][C]39463.2926829268[/C][C]394.258026881960[/C][C]100.095089997348[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 27 )[/C][C]39447.9743589744[/C][C]368.129859017314[/C][C]107.15776890328[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 27 )[/C][C]39431.0810810811[/C][C]337.185904066984[/C][C]116.941665133332[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 27 )[/C][C]39445.9142857143[/C][C]311.319645433200[/C][C]126.705509479897[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 27 )[/C][C]39474.7575757576[/C][C]293.232080590946[/C][C]134.619505124421[/C][/ROW]
[ROW][C]Trimmed Mean ( 25 / 27 )[/C][C]39501.8387096774[/C][C]282.791975281098[/C][C]139.685147255017[/C][/ROW]
[ROW][C]Trimmed Mean ( 26 / 27 )[/C][C]39535.2413793103[/C][C]269.265149667661[/C][C]146.826432711795[/C][/ROW]
[ROW][C]Trimmed Mean ( 27 / 27 )[/C][C]39570.1111111111[/C][C]251.878652629639[/C][C]157.099899884310[/C][/ROW]
[ROW][C]Median[/C][C]39401[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]38996[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]39326.05[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]39463.2926829268[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]39463.2926829268[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]39463.2926829268[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]39463.2926829268[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]39346.7380952381[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]39463.2926829268[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]39463.2926829268[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]81[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=54147&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=54147&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 Mean39916.50617283951418.298615051828.1439365090134
Geometric Mean37171.0295699665
Harmonic Mean32743.5572529146
Quadratic Mean41883.8052469324
Winsorized Mean ( 1 / 27 )39927.33333333331410.5108316396728.3070022843562
Winsorized Mean ( 2 / 27 )39903.08641975311402.0742108225128.4600387852113
Winsorized Mean ( 3 / 27 )39991.90123456791374.0539708078729.1050439678543
Winsorized Mean ( 4 / 27 )40025.38271604941365.1785392403629.3187898619628
Winsorized Mean ( 5 / 27 )40017.85185185191344.2863606682729.7688446619054
Winsorized Mean ( 6 / 27 )40241.5555555556874.20632293625546.0321030628028
Winsorized Mean ( 7 / 27 )40063.012345679765.89986905056752.3084204144628
Winsorized Mean ( 8 / 27 )39995.3580246914750.492057785453.2921802566602
Winsorized Mean ( 9 / 27 )40016.3580246914721.42247735706255.4686876007685
Winsorized Mean ( 10 / 27 )40153.3950617284694.18940576313157.8421317415342
Winsorized Mean ( 11 / 27 )40180.4197530864683.4078127577558.7942060406753
Winsorized Mean ( 12 / 27 )40092.1234567901642.23471906880162.4259671213682
Winsorized Mean ( 13 / 27 )39999.6790123457612.59335061544765.2956467323057
Winsorized Mean ( 14 / 27 )39963.9012345679601.98195125032966.3872083732112
Winsorized Mean ( 15 / 27 )39855.9382716049564.89971232355470.5540070248379
Winsorized Mean ( 16 / 27 )39842.9012345679557.06658915663871.5226904828154
Winsorized Mean ( 17 / 27 )39660.3086419753493.50460260339380.3646175390353
Winsorized Mean ( 18 / 27 )39686.3086419753475.38486800591983.4824819065995
Winsorized Mean ( 19 / 27 )39699.4444444444467.21706992799384.9700214304304
Winsorized Mean ( 20 / 27 )39610.8024691358453.82231166135187.2826246116652
Winsorized Mean ( 21 / 27 )39610.024691358436.71650796107190.6996277202529
Winsorized Mean ( 22 / 27 )39290.0740740741381.678417568489102.940256156936
Winsorized Mean ( 23 / 27 )39175.6419753086322.289201998592121.554311259487
Winsorized Mean ( 24 / 27 )39226.012345679272.020477110144144.202424620393
Winsorized Mean ( 25 / 27 )39202.8641975309264.642600683699148.135122978126
Winsorized Mean ( 26 / 27 )39233.037037037255.604309627473153.491297131166
Winsorized Mean ( 27 / 27 )39404.037037037226.794814976307173.743112430298
Trimmed Mean ( 1 / 27 )39939.81012658231335.6434589942129.9030477464835
Trimmed Mean ( 2 / 27 )39952.93506493511246.5309877949432.0512971246788
Trimmed Mean ( 3 / 27 )39979.85333333331144.5300384430734.9312398892726
Trimmed Mean ( 4 / 27 )39975.3972602741033.6320066112638.6746898360205
Trimmed Mean ( 5 / 27 )39961.1408450704897.13121886459844.5432507583951
Trimmed Mean ( 6 / 27 )39947.8260869565723.79168025123455.1924361345108
Trimmed Mean ( 7 / 27 )39888.6417910448679.36460813257458.7146302788572
Trimmed Mean ( 8 / 27 )39857.6655.78629507461760.7783363259595
Trimmed Mean ( 9 / 27 )39835.4603174603631.20234093347363.1104445185492
Trimmed Mean ( 10 / 27 )39808.7704918033608.24591140392165.448480204197
Trimmed Mean ( 11 / 27 )39761.4576271186586.25070751710867.823300027247
Trimmed Mean ( 12 / 27 )39707.3333333333561.51463587254970.7146898702495
Trimmed Mean ( 13 / 27 )39660.1090909091540.1238906843873.4278001305526
Trimmed Mean ( 14 / 27 )39620.1886792453520.00561991534776.1918470913741
Trimmed Mean ( 15 / 27 )39581.1960784314497.04126630244279.633621515737
Trimmed Mean ( 16 / 27 )39550.9183673469476.33953515567683.0309379094914
Trimmed Mean ( 17 / 27 )39519.4680851064451.56860215521887.515978516864
Trimmed Mean ( 18 / 27 )39504.5555555556434.53026252036390.9132434791105
Trimmed Mean ( 19 / 27 )39485.5348837209416.37688618577894.831236299950
Trimmed Mean ( 20 / 27 )39463.2926829268394.258026881960100.095089997348
Trimmed Mean ( 21 / 27 )39447.9743589744368.129859017314107.15776890328
Trimmed Mean ( 22 / 27 )39431.0810810811337.185904066984116.941665133332
Trimmed Mean ( 23 / 27 )39445.9142857143311.319645433200126.705509479897
Trimmed Mean ( 24 / 27 )39474.7575757576293.232080590946134.619505124421
Trimmed Mean ( 25 / 27 )39501.8387096774282.791975281098139.685147255017
Trimmed Mean ( 26 / 27 )39535.2413793103269.265149667661146.826432711795
Trimmed Mean ( 27 / 27 )39570.1111111111251.878652629639157.099899884310
Median39401
Midrange38996
Midmean - Weighted Average at Xnp39326.05
Midmean - Weighted Average at X(n+1)p39463.2926829268
Midmean - Empirical Distribution Function39463.2926829268
Midmean - Empirical Distribution Function - Averaging39463.2926829268
Midmean - Empirical Distribution Function - Interpolation39463.2926829268
Midmean - Closest Observation39346.7380952381
Midmean - True Basic - Statistics Graphics Toolkit39463.2926829268
Midmean - MS Excel (old versions)39463.2926829268
Number of observations81



Parameters (Session):
Parameters (R input):
R code (references can be found in the software module):
geomean <- function(x) {
return(exp(mean(log(x))))
}
harmean <- function(x) {
return(1/mean(1/x))
}
quamean <- function(x) {
return(sqrt(mean(x*x)))
}
winmean <- function(x) {
x <-sort(x[!is.na(x)])
n<-length(x)
denom <- 3
nodenom <- n/denom
if (nodenom>40) denom <- n/40
sqrtn = sqrt(n)
roundnodenom = floor(nodenom)
win <- array(NA,dim=c(roundnodenom,2))
for (j in 1:roundnodenom) {
win[j,1] <- (j*x[j+1]+sum(x[(j+1):(n-j)])+j*x[n-j])/n
win[j,2] <- sd(c(rep(x[j+1],j),x[(j+1):(n-j)],rep(x[n-j],j)))/sqrtn
}
return(win)
}
trimean <- function(x) {
x <-sort(x[!is.na(x)])
n<-length(x)
denom <- 3
nodenom <- n/denom
if (nodenom>40) denom <- n/40
sqrtn = sqrt(n)
roundnodenom = floor(nodenom)
tri <- array(NA,dim=c(roundnodenom,2))
for (j in 1:roundnodenom) {
tri[j,1] <- mean(x,trim=j/n)
tri[j,2] <- sd(x[(j+1):(n-j)]) / sqrt(n-j*2)
}
return(tri)
}
midrange <- function(x) {
return((max(x)+min(x))/2)
}
q1 <- function(data,n,p,i,f) {
np <- n*p;
i <<- floor(np)
f <<- np - i
qvalue <- (1-f)*data[i] + f*data[i+1]
}
q2 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
qvalue <- (1-f)*data[i] + f*data[i+1]
}
q3 <- function(data,n,p,i,f) {
np <- n*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
qvalue <- data[i+1]
}
}
q4 <- function(data,n,p,i,f) {
np <- n*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- (data[i]+data[i+1])/2
} else {
qvalue <- data[i+1]
}
}
q5 <- function(data,n,p,i,f) {
np <- (n-1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i+1]
} else {
qvalue <- data[i+1] + f*(data[i+2]-data[i+1])
}
}
q6 <- function(data,n,p,i,f) {
np <- n*p+0.5
i <<- floor(np)
f <<- np - i
qvalue <- data[i]
}
q7 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
qvalue <- f*data[i] + (1-f)*data[i+1]
}
}
q8 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
if (f == 0.5) {
qvalue <- (data[i]+data[i+1])/2
} else {
if (f < 0.5) {
qvalue <- data[i]
} else {
qvalue <- data[i+1]
}
}
}
}
midmean <- function(x,def) {
x <-sort(x[!is.na(x)])
n<-length(x)
if (def==1) {
qvalue1 <- q1(x,n,0.25,i,f)
qvalue3 <- q1(x,n,0.75,i,f)
}
if (def==2) {
qvalue1 <- q2(x,n,0.25,i,f)
qvalue3 <- q2(x,n,0.75,i,f)
}
if (def==3) {
qvalue1 <- q3(x,n,0.25,i,f)
qvalue3 <- q3(x,n,0.75,i,f)
}
if (def==4) {
qvalue1 <- q4(x,n,0.25,i,f)
qvalue3 <- q4(x,n,0.75,i,f)
}
if (def==5) {
qvalue1 <- q5(x,n,0.25,i,f)
qvalue3 <- q5(x,n,0.75,i,f)
}
if (def==6) {
qvalue1 <- q6(x,n,0.25,i,f)
qvalue3 <- q6(x,n,0.75,i,f)
}
if (def==7) {
qvalue1 <- q7(x,n,0.25,i,f)
qvalue3 <- q7(x,n,0.75,i,f)
}
if (def==8) {
qvalue1 <- q8(x,n,0.25,i,f)
qvalue3 <- q8(x,n,0.75,i,f)
}
midm <- 0
myn <- 0
roundno4 <- round(n/4)
round3no4 <- round(3*n/4)
for (i in 1:n) {
if ((x[i]>=qvalue1) & (x[i]<=qvalue3)){
midm = midm + x[i]
myn = myn + 1
}
}
midm = midm / myn
return(midm)
}
(arm <- mean(x))
sqrtn <- sqrt(length(x))
(armse <- sd(x) / sqrtn)
(armose <- arm / armse)
(geo <- geomean(x))
(har <- harmean(x))
(qua <- quamean(x))
(win <- winmean(x))
(tri <- trimean(x))
(midr <- midrange(x))
midm <- array(NA,dim=8)
for (j in 1:8) midm[j] <- midmean(x,j)
midm
bitmap(file='test1.png')
lb <- win[,1] - 2*win[,2]
ub <- win[,1] + 2*win[,2]
if ((ylimmin == '') | (ylimmax == '')) plot(win[,1],type='b',main=main, xlab='j', pch=19, ylab='Winsorized Mean(j/n)', ylim=c(min(lb),max(ub))) else plot(win[,1],type='l',main=main, xlab='j', pch=19, ylab='Winsorized Mean(j/n)', ylim=c(ylimmin,ylimmax))
lines(ub,lty=3)
lines(lb,lty=3)
grid()
dev.off()
bitmap(file='test2.png')
lb <- tri[,1] - 2*tri[,2]
ub <- tri[,1] + 2*tri[,2]
if ((ylimmin == '') | (ylimmax == '')) plot(tri[,1],type='b',main=main, xlab='j', pch=19, ylab='Trimmed Mean(j/n)', ylim=c(min(lb),max(ub))) else plot(tri[,1],type='l',main=main, xlab='j', pch=19, ylab='Trimmed Mean(j/n)', ylim=c(ylimmin,ylimmax))
lines(ub,lty=3)
lines(lb,lty=3)
grid()
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Central Tendency - Ungrouped Data',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Measure',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.element(a,'S.E.',header=TRUE)
a<-table.element(a,'Value/S.E.',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('arithmetic_mean.htm', 'Arithmetic Mean', 'click to view the definition of the Arithmetic Mean'),header=TRUE)
a<-table.element(a,arm)
a<-table.element(a,hyperlink('arithmetic_mean_standard_error.htm', armse, 'click to view the definition of the Standard Error of the Arithmetic Mean'))
a<-table.element(a,armose)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('geometric_mean.htm', 'Geometric Mean', 'click to view the definition of the Geometric Mean'),header=TRUE)
a<-table.element(a,geo)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('harmonic_mean.htm', 'Harmonic Mean', 'click to view the definition of the Harmonic Mean'),header=TRUE)
a<-table.element(a,har)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('quadratic_mean.htm', 'Quadratic Mean', 'click to view the definition of the Quadratic Mean'),header=TRUE)
a<-table.element(a,qua)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
for (j in 1:length(win[,1])) {
a<-table.row.start(a)
mylabel <- paste('Winsorized Mean (',j)
mylabel <- paste(mylabel,'/')
mylabel <- paste(mylabel,length(win[,1]))
mylabel <- paste(mylabel,')')
a<-table.element(a,hyperlink('winsorized_mean.htm', mylabel, 'click to view the definition of the Winsorized Mean'),header=TRUE)
a<-table.element(a,win[j,1])
a<-table.element(a,win[j,2])
a<-table.element(a,win[j,1]/win[j,2])
a<-table.row.end(a)
}
for (j in 1:length(tri[,1])) {
a<-table.row.start(a)
mylabel <- paste('Trimmed Mean (',j)
mylabel <- paste(mylabel,'/')
mylabel <- paste(mylabel,length(tri[,1]))
mylabel <- paste(mylabel,')')
a<-table.element(a,hyperlink('arithmetic_mean.htm', mylabel, 'click to view the definition of the Trimmed Mean'),header=TRUE)
a<-table.element(a,tri[j,1])
a<-table.element(a,tri[j,2])
a<-table.element(a,tri[j,1]/tri[j,2])
a<-table.row.end(a)
}
a<-table.row.start(a)
a<-table.element(a,hyperlink('median_1.htm', 'Median', 'click to view the definition of the Median'),header=TRUE)
a<-table.element(a,median(x))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('midrange.htm', 'Midrange', 'click to view the definition of the Midrange'),header=TRUE)
a<-table.element(a,midr)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_1.htm','Weighted Average at Xnp',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[1])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_2.htm','Weighted Average at X(n+1)p',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[2])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_3.htm','Empirical Distribution Function',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[3])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_4.htm','Empirical Distribution Function - Averaging',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[4])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_5.htm','Empirical Distribution Function - Interpolation',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[5])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_6.htm','Closest Observation',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[6])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_7.htm','True Basic - Statistics Graphics Toolkit',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[7])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_8.htm','MS Excel (old versions)',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[8])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Number of observations',header=TRUE)
a<-table.element(a,length(x))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')