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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationTue, 16 Dec 2008 08:47:28 -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/2008/Dec/16/t1229442507kjism7no67cdovj.htm/, Retrieved Wed, 15 May 2024 05:59:25 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=33988, Retrieved Wed, 15 May 2024 05:59:25 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact176
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Paper: Central Te...] [2008-12-16 15:47:28] [8da7502cfecb272886bc60b3f290b8b8] [Current]
-    D    [Central Tendency] [Paper: Central Te...] [2008-12-16 15:59:22] [9e54d1454d464f1bf9ee4a54d5d56945]
-    D      [Central Tendency] [Paper: Central Te...] [2008-12-16 16:45:52] [9e54d1454d464f1bf9ee4a54d5d56945]
-    D        [Central Tendency] [Paper: Central Te...] [2008-12-16 16:49:56] [9e54d1454d464f1bf9ee4a54d5d56945]
- RMPD        [Histogram] [Paper: histogram ...] [2008-12-16 17:12:52] [9e54d1454d464f1bf9ee4a54d5d56945]
-    D          [Histogram] [Paper: Histogram ...] [2008-12-16 17:16:37] [9e54d1454d464f1bf9ee4a54d5d56945]
-    D            [Histogram] [] [2008-12-22 22:01:25] [187876c4ad94aebda16017e4a72ae602]
-                 [Histogram] [] [2008-12-22 22:08:37] [187876c4ad94aebda16017e4a72ae602]
- RMPD          [Back to Back Histogram] [Paper: Bihistogra...] [2008-12-16 17:21:03] [9e54d1454d464f1bf9ee4a54d5d56945]
-                 [Back to Back Histogram] [] [2008-12-22 22:11:19] [187876c4ad94aebda16017e4a72ae602]
-               [Histogram] [] [2008-12-22 21:53:40] [84af9210cb1d82626c16de257e3e8f09]
-    D          [Histogram] [] [2008-12-22 22:06:44] [187876c4ad94aebda16017e4a72ae602]
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Dataseries X:
11178,4
9516,4
12102,8
12989,0
11610,2
10205,5
11356,2
11307,1
12648,6
11947,2
11714,1
12192,5
11268,8
9097,4
12639,8
13040,1
11687,3
11191,7
11391,9
11793,1
13933,2
12778,1
11810,3
13698,4
11956,6
10723,8
13938,9
13979,8
13807,4
12973,9
12509,8
12934,1
14908,3
13772,1
13012,6
14049,9
11816,5
11593,2
14466,2
13615,9
14733,9
13880,7
13527,5
13584,0
16170,2
13260,6
14741,9
15486,5
13154,5
12621,2
15031,6
15452,4
15428
13105,9
14716,8
14180,0
16202,2
14392,4
15140,6
15960,1
14351,3
13230,2
15202,1
17157,3
16159,1
13405,7
17224,7
17338,4
17370,6
18817,8
16593,2
17979,5
17015,2




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time7 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001

\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 & 7 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=33988&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]7 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=33988&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=33988&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 time7 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean13640.7287671233240.11787597460356.8084683897755
Geometric Mean13489.5812286118
Harmonic Mean13339.0313653266
Quadratic Mean13792.0540925683
Winsorized Mean ( 1 / 24 )13634.9849315068235.47281216504957.9047101282748
Winsorized Mean ( 2 / 24 )13637.1821917808227.14757585974660.0366618052802
Winsorized Mean ( 3 / 24 )13657.1589041096222.65838388126461.3368275923194
Winsorized Mean ( 4 / 24 )13675.8383561644216.96143305819563.033499380031
Winsorized Mean ( 5 / 24 )13672.1328767123215.77367808056563.3633026898092
Winsorized Mean ( 6 / 24 )13666.7904109589212.18012649938564.4112652605025
Winsorized Mean ( 7 / 24 )13629.9972602740203.05743387887267.1238525963276
Winsorized Mean ( 8 / 24 )13592.5287671233193.84275301791070.1214182913889
Winsorized Mean ( 9 / 24 )13592.9849315068192.40462635363170.6479110669802
Winsorized Mean ( 10 / 24 )13619.0397260274187.86323852179972.4944370872594
Winsorized Mean ( 11 / 24 )13591.6150684932181.9498047603474.6998057315626
Winsorized Mean ( 12 / 24 )13526.4369863014166.59184740151681.1950716513769
Winsorized Mean ( 13 / 24 )13525.1369863014164.87275075125382.03379227115
Winsorized Mean ( 14 / 24 )13535.6082191781161.82402944529383.6439944399852
Winsorized Mean ( 15 / 24 )13492.7246575342153.93787056419587.6504566945244
Winsorized Mean ( 16 / 24 )13480.6041095890151.66710649540388.8828462617085
Winsorized Mean ( 17 / 24 )13485.6575342466143.24392303867894.14470958468
Winsorized Mean ( 18 / 24 )13457.5726027397138.40376505484197.2341510898008
Winsorized Mean ( 19 / 24 )13452.3150684932126.494106318437106.347366371586
Winsorized Mean ( 20 / 24 )13474.698630137122.576109964349109.929240159898
Winsorized Mean ( 21 / 24 )13561.0575342466109.094763502121124.305302096218
Winsorized Mean ( 22 / 24 )13519.106849315193.739330784651144.220219369528
Winsorized Mean ( 23 / 24 )13501.715068493189.723597055691150.481205742484
Winsorized Mean ( 24 / 24 )13491.095890411087.4828246991678154.214223612504
Trimmed Mean ( 1 / 24 )13631.8028169014226.77580042375460.1113645787116
Trimmed Mean ( 2 / 24 )13628.4362318841216.41586927458662.9733682542127
Trimmed Mean ( 3 / 24 )13623.6716417910209.47259054800265.0379680040721
Trimmed Mean ( 4 / 24 )13611.1353846154203.22710541921166.9749999958851
Trimmed Mean ( 5 / 24 )13592.3920634921197.79574044336868.7193365894742
Trimmed Mean ( 6 / 24 )13573.3065573770191.57167940228070.8523650245532
Trimmed Mean ( 7 / 24 )13554.0288135593185.01869790437673.2576164846028
Trimmed Mean ( 8 / 24 )13540.1298245614179.49853864508275.4330922511518
Trimmed Mean ( 9 / 24 )13531.4363636364175.02769343867377.3102592954957
Trimmed Mean ( 10 / 24 )13522.0169811321169.77707552977179.6457174146632
Trimmed Mean ( 11 / 24 )13508.1294117647164.20368738650982.264470589925
Trimmed Mean ( 12 / 24 )13496.8224489796158.56326339084385.1194795083853
Trimmed Mean ( 13 / 24 )13492.9893617021154.93848677141687.0861052206393
Trimmed Mean ( 14 / 24 )13488.9777777778150.58198410922789.5789616372255
Trimmed Mean ( 15 / 24 )13483.3232558140145.5489203506992.6377414777576
Trimmed Mean ( 16 / 24 )13482.2073170732140.78597826307495.7638500893901
Trimmed Mean ( 17 / 24 )13482.3948717949134.92909573735799.9220723900698
Trimmed Mean ( 18 / 24 )13482.0162162162129.169850847908104.374326731171
Trimmed Mean ( 19 / 24 )13484.8485714286122.518253990433110.063995626982
Trimmed Mean ( 20 / 24 )13488.6363636364116.661457552932115.622045588760
Trimmed Mean ( 21 / 24 )13490.2774193548109.452770558830123.252041501352
Trimmed Mean ( 22 / 24 )13481.7931034483103.352273257359130.445056296701
Trimmed Mean ( 23 / 24 )13477.207407407499.5952565441485135.3197719957
Trimmed Mean ( 24 / 24 )13474.09695.0808283304263141.712017412960
Median13527.5
Midrange13957.6
Midmean - Weighted Average at Xnp13442.3972222222
Midmean - Weighted Average at X(n+1)p13482.0162162162
Midmean - Empirical Distribution Function13482.0162162162
Midmean - Empirical Distribution Function - Averaging13482.0162162162
Midmean - Empirical Distribution Function - Interpolation13482.0162162162
Midmean - Closest Observation13441.6263157895
Midmean - True Basic - Statistics Graphics Toolkit13482.0162162162
Midmean - MS Excel (old versions)13482.0162162162
Number of observations73

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 13640.7287671233 & 240.117875974603 & 56.8084683897755 \tabularnewline
Geometric Mean & 13489.5812286118 &  &  \tabularnewline
Harmonic Mean & 13339.0313653266 &  &  \tabularnewline
Quadratic Mean & 13792.0540925683 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 13634.9849315068 & 235.472812165049 & 57.9047101282748 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 13637.1821917808 & 227.147575859746 & 60.0366618052802 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 13657.1589041096 & 222.658383881264 & 61.3368275923194 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 13675.8383561644 & 216.961433058195 & 63.033499380031 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 13672.1328767123 & 215.773678080565 & 63.3633026898092 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 13666.7904109589 & 212.180126499385 & 64.4112652605025 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 13629.9972602740 & 203.057433878872 & 67.1238525963276 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 13592.5287671233 & 193.842753017910 & 70.1214182913889 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 13592.9849315068 & 192.404626353631 & 70.6479110669802 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 13619.0397260274 & 187.863238521799 & 72.4944370872594 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 13591.6150684932 & 181.94980476034 & 74.6998057315626 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 13526.4369863014 & 166.591847401516 & 81.1950716513769 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 13525.1369863014 & 164.872750751253 & 82.03379227115 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 13535.6082191781 & 161.824029445293 & 83.6439944399852 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 13492.7246575342 & 153.937870564195 & 87.6504566945244 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 13480.6041095890 & 151.667106495403 & 88.8828462617085 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 13485.6575342466 & 143.243923038678 & 94.14470958468 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 13457.5726027397 & 138.403765054841 & 97.2341510898008 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 13452.3150684932 & 126.494106318437 & 106.347366371586 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 13474.698630137 & 122.576109964349 & 109.929240159898 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 13561.0575342466 & 109.094763502121 & 124.305302096218 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 13519.1068493151 & 93.739330784651 & 144.220219369528 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 13501.7150684931 & 89.723597055691 & 150.481205742484 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 13491.0958904110 & 87.4828246991678 & 154.214223612504 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 13631.8028169014 & 226.775800423754 & 60.1113645787116 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 13628.4362318841 & 216.415869274586 & 62.9733682542127 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 13623.6716417910 & 209.472590548002 & 65.0379680040721 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 13611.1353846154 & 203.227105419211 & 66.9749999958851 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 13592.3920634921 & 197.795740443368 & 68.7193365894742 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 13573.3065573770 & 191.571679402280 & 70.8523650245532 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 13554.0288135593 & 185.018697904376 & 73.2576164846028 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 13540.1298245614 & 179.498538645082 & 75.4330922511518 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 13531.4363636364 & 175.027693438673 & 77.3102592954957 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 13522.0169811321 & 169.777075529771 & 79.6457174146632 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 13508.1294117647 & 164.203687386509 & 82.264470589925 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 13496.8224489796 & 158.563263390843 & 85.1194795083853 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 13492.9893617021 & 154.938486771416 & 87.0861052206393 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 13488.9777777778 & 150.581984109227 & 89.5789616372255 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 13483.3232558140 & 145.54892035069 & 92.6377414777576 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 13482.2073170732 & 140.785978263074 & 95.7638500893901 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 13482.3948717949 & 134.929095737357 & 99.9220723900698 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 13482.0162162162 & 129.169850847908 & 104.374326731171 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 13484.8485714286 & 122.518253990433 & 110.063995626982 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 13488.6363636364 & 116.661457552932 & 115.622045588760 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 13490.2774193548 & 109.452770558830 & 123.252041501352 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 13481.7931034483 & 103.352273257359 & 130.445056296701 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 13477.2074074074 & 99.5952565441485 & 135.3197719957 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 13474.096 & 95.0808283304263 & 141.712017412960 \tabularnewline
Median & 13527.5 &  &  \tabularnewline
Midrange & 13957.6 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 13442.3972222222 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 13482.0162162162 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 13482.0162162162 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 13482.0162162162 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 13482.0162162162 &  &  \tabularnewline
Midmean - Closest Observation & 13441.6263157895 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 13482.0162162162 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 13482.0162162162 &  &  \tabularnewline
Number of observations & 73 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=33988&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]13640.7287671233[/C][C]240.117875974603[/C][C]56.8084683897755[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]13489.5812286118[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]13339.0313653266[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]13792.0540925683[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]13634.9849315068[/C][C]235.472812165049[/C][C]57.9047101282748[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]13637.1821917808[/C][C]227.147575859746[/C][C]60.0366618052802[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]13657.1589041096[/C][C]222.658383881264[/C][C]61.3368275923194[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]13675.8383561644[/C][C]216.961433058195[/C][C]63.033499380031[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]13672.1328767123[/C][C]215.773678080565[/C][C]63.3633026898092[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]13666.7904109589[/C][C]212.180126499385[/C][C]64.4112652605025[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]13629.9972602740[/C][C]203.057433878872[/C][C]67.1238525963276[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]13592.5287671233[/C][C]193.842753017910[/C][C]70.1214182913889[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]13592.9849315068[/C][C]192.404626353631[/C][C]70.6479110669802[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]13619.0397260274[/C][C]187.863238521799[/C][C]72.4944370872594[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]13591.6150684932[/C][C]181.94980476034[/C][C]74.6998057315626[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]13526.4369863014[/C][C]166.591847401516[/C][C]81.1950716513769[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]13525.1369863014[/C][C]164.872750751253[/C][C]82.03379227115[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]13535.6082191781[/C][C]161.824029445293[/C][C]83.6439944399852[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]13492.7246575342[/C][C]153.937870564195[/C][C]87.6504566945244[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]13480.6041095890[/C][C]151.667106495403[/C][C]88.8828462617085[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]13485.6575342466[/C][C]143.243923038678[/C][C]94.14470958468[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]13457.5726027397[/C][C]138.403765054841[/C][C]97.2341510898008[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]13452.3150684932[/C][C]126.494106318437[/C][C]106.347366371586[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]13474.698630137[/C][C]122.576109964349[/C][C]109.929240159898[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]13561.0575342466[/C][C]109.094763502121[/C][C]124.305302096218[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]13519.1068493151[/C][C]93.739330784651[/C][C]144.220219369528[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]13501.7150684931[/C][C]89.723597055691[/C][C]150.481205742484[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]13491.0958904110[/C][C]87.4828246991678[/C][C]154.214223612504[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]13631.8028169014[/C][C]226.775800423754[/C][C]60.1113645787116[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]13628.4362318841[/C][C]216.415869274586[/C][C]62.9733682542127[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]13623.6716417910[/C][C]209.472590548002[/C][C]65.0379680040721[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]13611.1353846154[/C][C]203.227105419211[/C][C]66.9749999958851[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]13592.3920634921[/C][C]197.795740443368[/C][C]68.7193365894742[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]13573.3065573770[/C][C]191.571679402280[/C][C]70.8523650245532[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]13554.0288135593[/C][C]185.018697904376[/C][C]73.2576164846028[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]13540.1298245614[/C][C]179.498538645082[/C][C]75.4330922511518[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]13531.4363636364[/C][C]175.027693438673[/C][C]77.3102592954957[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]13522.0169811321[/C][C]169.777075529771[/C][C]79.6457174146632[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]13508.1294117647[/C][C]164.203687386509[/C][C]82.264470589925[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]13496.8224489796[/C][C]158.563263390843[/C][C]85.1194795083853[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]13492.9893617021[/C][C]154.938486771416[/C][C]87.0861052206393[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]13488.9777777778[/C][C]150.581984109227[/C][C]89.5789616372255[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]13483.3232558140[/C][C]145.54892035069[/C][C]92.6377414777576[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]13482.2073170732[/C][C]140.785978263074[/C][C]95.7638500893901[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]13482.3948717949[/C][C]134.929095737357[/C][C]99.9220723900698[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]13482.0162162162[/C][C]129.169850847908[/C][C]104.374326731171[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]13484.8485714286[/C][C]122.518253990433[/C][C]110.063995626982[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]13488.6363636364[/C][C]116.661457552932[/C][C]115.622045588760[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]13490.2774193548[/C][C]109.452770558830[/C][C]123.252041501352[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]13481.7931034483[/C][C]103.352273257359[/C][C]130.445056296701[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]13477.2074074074[/C][C]99.5952565441485[/C][C]135.3197719957[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]13474.096[/C][C]95.0808283304263[/C][C]141.712017412960[/C][/ROW]
[ROW][C]Median[/C][C]13527.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]13957.6[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]13442.3972222222[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]13482.0162162162[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]13482.0162162162[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]13482.0162162162[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]13482.0162162162[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]13441.6263157895[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]13482.0162162162[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]13482.0162162162[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]73[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=33988&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=33988&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 Mean13640.7287671233240.11787597460356.8084683897755
Geometric Mean13489.5812286118
Harmonic Mean13339.0313653266
Quadratic Mean13792.0540925683
Winsorized Mean ( 1 / 24 )13634.9849315068235.47281216504957.9047101282748
Winsorized Mean ( 2 / 24 )13637.1821917808227.14757585974660.0366618052802
Winsorized Mean ( 3 / 24 )13657.1589041096222.65838388126461.3368275923194
Winsorized Mean ( 4 / 24 )13675.8383561644216.96143305819563.033499380031
Winsorized Mean ( 5 / 24 )13672.1328767123215.77367808056563.3633026898092
Winsorized Mean ( 6 / 24 )13666.7904109589212.18012649938564.4112652605025
Winsorized Mean ( 7 / 24 )13629.9972602740203.05743387887267.1238525963276
Winsorized Mean ( 8 / 24 )13592.5287671233193.84275301791070.1214182913889
Winsorized Mean ( 9 / 24 )13592.9849315068192.40462635363170.6479110669802
Winsorized Mean ( 10 / 24 )13619.0397260274187.86323852179972.4944370872594
Winsorized Mean ( 11 / 24 )13591.6150684932181.9498047603474.6998057315626
Winsorized Mean ( 12 / 24 )13526.4369863014166.59184740151681.1950716513769
Winsorized Mean ( 13 / 24 )13525.1369863014164.87275075125382.03379227115
Winsorized Mean ( 14 / 24 )13535.6082191781161.82402944529383.6439944399852
Winsorized Mean ( 15 / 24 )13492.7246575342153.93787056419587.6504566945244
Winsorized Mean ( 16 / 24 )13480.6041095890151.66710649540388.8828462617085
Winsorized Mean ( 17 / 24 )13485.6575342466143.24392303867894.14470958468
Winsorized Mean ( 18 / 24 )13457.5726027397138.40376505484197.2341510898008
Winsorized Mean ( 19 / 24 )13452.3150684932126.494106318437106.347366371586
Winsorized Mean ( 20 / 24 )13474.698630137122.576109964349109.929240159898
Winsorized Mean ( 21 / 24 )13561.0575342466109.094763502121124.305302096218
Winsorized Mean ( 22 / 24 )13519.106849315193.739330784651144.220219369528
Winsorized Mean ( 23 / 24 )13501.715068493189.723597055691150.481205742484
Winsorized Mean ( 24 / 24 )13491.095890411087.4828246991678154.214223612504
Trimmed Mean ( 1 / 24 )13631.8028169014226.77580042375460.1113645787116
Trimmed Mean ( 2 / 24 )13628.4362318841216.41586927458662.9733682542127
Trimmed Mean ( 3 / 24 )13623.6716417910209.47259054800265.0379680040721
Trimmed Mean ( 4 / 24 )13611.1353846154203.22710541921166.9749999958851
Trimmed Mean ( 5 / 24 )13592.3920634921197.79574044336868.7193365894742
Trimmed Mean ( 6 / 24 )13573.3065573770191.57167940228070.8523650245532
Trimmed Mean ( 7 / 24 )13554.0288135593185.01869790437673.2576164846028
Trimmed Mean ( 8 / 24 )13540.1298245614179.49853864508275.4330922511518
Trimmed Mean ( 9 / 24 )13531.4363636364175.02769343867377.3102592954957
Trimmed Mean ( 10 / 24 )13522.0169811321169.77707552977179.6457174146632
Trimmed Mean ( 11 / 24 )13508.1294117647164.20368738650982.264470589925
Trimmed Mean ( 12 / 24 )13496.8224489796158.56326339084385.1194795083853
Trimmed Mean ( 13 / 24 )13492.9893617021154.93848677141687.0861052206393
Trimmed Mean ( 14 / 24 )13488.9777777778150.58198410922789.5789616372255
Trimmed Mean ( 15 / 24 )13483.3232558140145.5489203506992.6377414777576
Trimmed Mean ( 16 / 24 )13482.2073170732140.78597826307495.7638500893901
Trimmed Mean ( 17 / 24 )13482.3948717949134.92909573735799.9220723900698
Trimmed Mean ( 18 / 24 )13482.0162162162129.169850847908104.374326731171
Trimmed Mean ( 19 / 24 )13484.8485714286122.518253990433110.063995626982
Trimmed Mean ( 20 / 24 )13488.6363636364116.661457552932115.622045588760
Trimmed Mean ( 21 / 24 )13490.2774193548109.452770558830123.252041501352
Trimmed Mean ( 22 / 24 )13481.7931034483103.352273257359130.445056296701
Trimmed Mean ( 23 / 24 )13477.207407407499.5952565441485135.3197719957
Trimmed Mean ( 24 / 24 )13474.09695.0808283304263141.712017412960
Median13527.5
Midrange13957.6
Midmean - Weighted Average at Xnp13442.3972222222
Midmean - Weighted Average at X(n+1)p13482.0162162162
Midmean - Empirical Distribution Function13482.0162162162
Midmean - Empirical Distribution Function - Averaging13482.0162162162
Midmean - Empirical Distribution Function - Interpolation13482.0162162162
Midmean - Closest Observation13441.6263157895
Midmean - True Basic - Statistics Graphics Toolkit13482.0162162162
Midmean - MS Excel (old versions)13482.0162162162
Number of observations73



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')