Free Statistics

of Irreproducible Research!

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationSat, 13 Nov 2010 11:37:47 +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/13/t1289648230oqmvi0odfi8l6ed.htm/, Retrieved Mon, 29 Apr 2024 04:54:26 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=94355, Retrieved Mon, 29 Apr 2024 04:54:26 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact184
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Central Tendency] [Arabica Price in ...] [2008-01-06 21:28:17] [74be16979710d4c4e7c6647856088456]
-  M D    [Central Tendency] [ws6tut] [2010-11-13 11:37:47] [0cadca125c925bcc9e6efbdd1941e458] [Current]
-    D      [Central Tendency] [ws6tut] [2010-11-13 15:04:19] [4a7069087cf9e0eda253aeed7d8c30d6]
-             [Central Tendency] [Tutorial2] [2010-11-16 20:36:04] [fc9068db680cd880760a7c0fccd81a61]
F    D        [Central Tendency] [mini tutorial sam...] [2010-11-17 08:42:10] [f9eaed74daea918f73b9f505c5b1f19e]
Feedback Forum

Post a new message
Dataseries X:
4
3
5
4
2
4
3
2
4
2
4
2
5
3
4
3
4
2
3
4
2
4
4
3
4
2
4
4
4
2
4
4
4
4
3
4
3
3
3
2
4
4
4
3
4
4
3
1
4
4
2
2
4
3
1
4
2
4
5
3
2
4
2
2
2
4
5
4
5
2
3
4
3
2
3
4
1
2
2
3
3
2
2
4
3
3
4
4
2
2
4
3
2
4
3
3
4
4
3
3
3
2
2
1
2
3
3
3
3
4
2
3
3
4
3
3
3
4
4
3
4
5
2
4
3




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=94355&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=94355&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=94355&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 Mean3.1680.085561522856646237.0259889519243
Geometric Mean3.00066268317862
Harmonic Mean2.80164363093015
Quadratic Mean3.30817170050165
Winsorized Mean ( 1 / 41 )3.1680.085561522856646237.0259889519243
Winsorized Mean ( 2 / 41 )3.1680.085561522856646237.0259889519243
Winsorized Mean ( 3 / 41 )3.1680.085561522856646237.0259889519243
Winsorized Mean ( 4 / 41 )3.20.080321932890249939.839678713564
Winsorized Mean ( 5 / 41 )3.20.080321932890249939.839678713564
Winsorized Mean ( 6 / 41 )3.1520.073665328650331142.7881074821735
Winsorized Mean ( 7 / 41 )3.1520.073665328650331142.7881074821735
Winsorized Mean ( 8 / 41 )3.1520.073665328650331142.7881074821735
Winsorized Mean ( 9 / 41 )3.1520.073665328650331142.7881074821735
Winsorized Mean ( 10 / 41 )3.1520.073665328650331142.7881074821735
Winsorized Mean ( 11 / 41 )3.1520.073665328650331142.7881074821735
Winsorized Mean ( 12 / 41 )3.1520.073665328650331142.7881074821735
Winsorized Mean ( 13 / 41 )3.1520.073665328650331142.7881074821735
Winsorized Mean ( 14 / 41 )3.1520.073665328650331142.7881074821735
Winsorized Mean ( 15 / 41 )3.1520.073665328650331142.7881074821735
Winsorized Mean ( 16 / 41 )3.1520.073665328650331142.7881074821735
Winsorized Mean ( 17 / 41 )3.1520.073665328650331142.7881074821735
Winsorized Mean ( 18 / 41 )3.1520.073665328650331142.7881074821735
Winsorized Mean ( 19 / 41 )3.1520.073665328650331142.7881074821735
Winsorized Mean ( 20 / 41 )3.1520.073665328650331142.7881074821735
Winsorized Mean ( 21 / 41 )3.1520.073665328650331142.7881074821735
Winsorized Mean ( 22 / 41 )3.1520.073665328650331142.7881074821735
Winsorized Mean ( 23 / 41 )3.1520.073665328650331142.7881074821735
Winsorized Mean ( 24 / 41 )3.1520.073665328650331142.7881074821735
Winsorized Mean ( 25 / 41 )3.1520.073665328650331142.7881074821735
Winsorized Mean ( 26 / 41 )3.1520.073665328650331142.7881074821735
Winsorized Mean ( 27 / 41 )3.1520.073665328650331142.7881074821735
Winsorized Mean ( 28 / 41 )3.1520.073665328650331142.7881074821735
Winsorized Mean ( 29 / 41 )3.1520.073665328650331142.7881074821735
Winsorized Mean ( 30 / 41 )3.1520.073665328650331142.7881074821735
Winsorized Mean ( 31 / 41 )3.1520.073665328650331142.7881074821735
Winsorized Mean ( 32 / 41 )3.1520.073665328650331142.7881074821735
Winsorized Mean ( 33 / 41 )3.1520.073665328650331142.7881074821735
Winsorized Mean ( 34 / 41 )3.4240.044379594264670577.1525755638952
Winsorized Mean ( 35 / 41 )3.4240.044379594264670577.1525755638952
Winsorized Mean ( 36 / 41 )3.4240.044379594264670577.1525755638952
Winsorized Mean ( 37 / 41 )3.4240.044379594264670577.1525755638952
Winsorized Mean ( 38 / 41 )3.4240.044379594264670577.1525755638952
Winsorized Mean ( 39 / 41 )3.4240.044379594264670577.1525755638952
Winsorized Mean ( 40 / 41 )3.4240.044379594264670577.1525755638952
Winsorized Mean ( 41 / 41 )3.4240.044379594264670577.1525755638952
Trimmed Mean ( 1 / 41 )3.170731707317070.083814272910318637.8304505571475
Trimmed Mean ( 2 / 41 )3.173553719008260.081883547921222338.7569151505434
Trimmed Mean ( 3 / 41 )3.176470588235290.079743802507712439.8334477206311
Trimmed Mean ( 4 / 41 )3.179487179487180.077363900457037541.0978138473363
Trimmed Mean ( 5 / 41 )3.173913043478260.076399597409909541.5435833575032
Trimmed Mean ( 6 / 41 )3.168141592920350.075323422823176942.0605101862886
Trimmed Mean ( 7 / 41 )3.171171171171170.07558006518181141.9577723774488
Trimmed Mean ( 8 / 41 )3.17431192660550.075828235422789341.8618725453224
Trimmed Mean ( 9 / 41 )3.177570093457940.076066547019106241.7735551037936
Trimmed Mean ( 10 / 41 )3.180952380952380.07629342861124241.6936614182216
Trimmed Mean ( 11 / 41 )3.184466019417480.07650709622638541.6231457797669
Trimmed Mean ( 12 / 41 )3.188118811881190.076705520587115141.5630946440213
Trimmed Mean ( 13 / 41 )3.191919191919190.076886388483447241.5147499431109
Trimmed Mean ( 14 / 41 )3.195876288659790.077047056929331441.4795375194031
Trimmed Mean ( 15 / 41 )3.20.07718449849879641.4591020507818
Trimmed Mean ( 16 / 41 )3.204301075268820.077295235813192741.4553502755717
Trimmed Mean ( 17 / 41 )3.208791208791210.077375262595073241.4705049284773
Trimmed Mean ( 18 / 41 )3.213483146067420.077419947967556641.5071726399771
Trimmed Mean ( 19 / 41 )3.21839080459770.077423919691329141.5684302400171
Trimmed Mean ( 20 / 41 )3.223529411764710.07738092069406341.6579356106321
Trimmed Mean ( 21 / 41 )3.22891566265060.077283631410856741.7800717138275
Trimmed Mean ( 22 / 41 )3.234567901234570.077123447896965341.9401360991518
Trimmed Mean ( 23 / 41 )3.240506329113920.076890202055643342.1445937516052
Trimmed Mean ( 24 / 41 )3.246753246753250.076571805113191642.401419712566
Trimmed Mean ( 25 / 41 )3.253333333333330.076153787820432142.720571444254
Trimmed Mean ( 26 / 41 )3.260273972602740.075618699368398243.1146528548366
Trimmed Mean ( 27 / 41 )3.267605633802820.074945309312034743.5998685414473
Trimmed Mean ( 28 / 41 )3.275362318840580.074107528759544844.1974300542133
Trimmed Mean ( 29 / 41 )3.283582089552240.073072921173295244.9356894021672
Trimmed Mean ( 30 / 41 )3.292307692307690.071800595009978745.8534875908777
Trimmed Mean ( 31 / 41 )3.30158730158730.070238131398592347.0056255177294
Trimmed Mean ( 32 / 41 )3.311475409836070.068316939016533348.4722450611357
Trimmed Mean ( 33 / 41 )3.322033898305080.065944905391606650.3758990717714
Trimmed Mean ( 34 / 41 )3.333333333333330.062994078834871252.9150262212918
Trimmed Mean ( 35 / 41 )3.327272727272730.063852446986986352.1087739668122
Trimmed Mean ( 36 / 41 )3.320754716981130.064728891497758451.3025117554521
Trimmed Mean ( 37 / 41 )3.313725490196080.065620394237966750.4984087443781
Trimmed Mean ( 38 / 41 )3.306122448979590.06652247352247649.6993312773096
Trimmed Mean ( 39 / 41 )3.297872340425530.06742861107915648.909094932329
Trimmed Mean ( 40 / 41 )3.288888888888890.068329432425405148.1328290335113
Trimmed Mean ( 41 / 41 )3.279069767441860.06921151712956747.3775161047734
Median3
Midrange3
Midmean - Weighted Average at Xnp3.14782608695652
Midmean - Weighted Average at X(n+1)p3.14782608695652
Midmean - Empirical Distribution Function3.14782608695652
Midmean - Empirical Distribution Function - Averaging3.14782608695652
Midmean - Empirical Distribution Function - Interpolation3.14782608695652
Midmean - Closest Observation3.14782608695652
Midmean - True Basic - Statistics Graphics Toolkit3.14782608695652
Midmean - MS Excel (old versions)3.14782608695652
Number of observations125

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 3.168 & 0.0855615228566462 & 37.0259889519243 \tabularnewline
Geometric Mean & 3.00066268317862 &  &  \tabularnewline
Harmonic Mean & 2.80164363093015 &  &  \tabularnewline
Quadratic Mean & 3.30817170050165 &  &  \tabularnewline
Winsorized Mean ( 1 / 41 ) & 3.168 & 0.0855615228566462 & 37.0259889519243 \tabularnewline
Winsorized Mean ( 2 / 41 ) & 3.168 & 0.0855615228566462 & 37.0259889519243 \tabularnewline
Winsorized Mean ( 3 / 41 ) & 3.168 & 0.0855615228566462 & 37.0259889519243 \tabularnewline
Winsorized Mean ( 4 / 41 ) & 3.2 & 0.0803219328902499 & 39.839678713564 \tabularnewline
Winsorized Mean ( 5 / 41 ) & 3.2 & 0.0803219328902499 & 39.839678713564 \tabularnewline
Winsorized Mean ( 6 / 41 ) & 3.152 & 0.0736653286503311 & 42.7881074821735 \tabularnewline
Winsorized Mean ( 7 / 41 ) & 3.152 & 0.0736653286503311 & 42.7881074821735 \tabularnewline
Winsorized Mean ( 8 / 41 ) & 3.152 & 0.0736653286503311 & 42.7881074821735 \tabularnewline
Winsorized Mean ( 9 / 41 ) & 3.152 & 0.0736653286503311 & 42.7881074821735 \tabularnewline
Winsorized Mean ( 10 / 41 ) & 3.152 & 0.0736653286503311 & 42.7881074821735 \tabularnewline
Winsorized Mean ( 11 / 41 ) & 3.152 & 0.0736653286503311 & 42.7881074821735 \tabularnewline
Winsorized Mean ( 12 / 41 ) & 3.152 & 0.0736653286503311 & 42.7881074821735 \tabularnewline
Winsorized Mean ( 13 / 41 ) & 3.152 & 0.0736653286503311 & 42.7881074821735 \tabularnewline
Winsorized Mean ( 14 / 41 ) & 3.152 & 0.0736653286503311 & 42.7881074821735 \tabularnewline
Winsorized Mean ( 15 / 41 ) & 3.152 & 0.0736653286503311 & 42.7881074821735 \tabularnewline
Winsorized Mean ( 16 / 41 ) & 3.152 & 0.0736653286503311 & 42.7881074821735 \tabularnewline
Winsorized Mean ( 17 / 41 ) & 3.152 & 0.0736653286503311 & 42.7881074821735 \tabularnewline
Winsorized Mean ( 18 / 41 ) & 3.152 & 0.0736653286503311 & 42.7881074821735 \tabularnewline
Winsorized Mean ( 19 / 41 ) & 3.152 & 0.0736653286503311 & 42.7881074821735 \tabularnewline
Winsorized Mean ( 20 / 41 ) & 3.152 & 0.0736653286503311 & 42.7881074821735 \tabularnewline
Winsorized Mean ( 21 / 41 ) & 3.152 & 0.0736653286503311 & 42.7881074821735 \tabularnewline
Winsorized Mean ( 22 / 41 ) & 3.152 & 0.0736653286503311 & 42.7881074821735 \tabularnewline
Winsorized Mean ( 23 / 41 ) & 3.152 & 0.0736653286503311 & 42.7881074821735 \tabularnewline
Winsorized Mean ( 24 / 41 ) & 3.152 & 0.0736653286503311 & 42.7881074821735 \tabularnewline
Winsorized Mean ( 25 / 41 ) & 3.152 & 0.0736653286503311 & 42.7881074821735 \tabularnewline
Winsorized Mean ( 26 / 41 ) & 3.152 & 0.0736653286503311 & 42.7881074821735 \tabularnewline
Winsorized Mean ( 27 / 41 ) & 3.152 & 0.0736653286503311 & 42.7881074821735 \tabularnewline
Winsorized Mean ( 28 / 41 ) & 3.152 & 0.0736653286503311 & 42.7881074821735 \tabularnewline
Winsorized Mean ( 29 / 41 ) & 3.152 & 0.0736653286503311 & 42.7881074821735 \tabularnewline
Winsorized Mean ( 30 / 41 ) & 3.152 & 0.0736653286503311 & 42.7881074821735 \tabularnewline
Winsorized Mean ( 31 / 41 ) & 3.152 & 0.0736653286503311 & 42.7881074821735 \tabularnewline
Winsorized Mean ( 32 / 41 ) & 3.152 & 0.0736653286503311 & 42.7881074821735 \tabularnewline
Winsorized Mean ( 33 / 41 ) & 3.152 & 0.0736653286503311 & 42.7881074821735 \tabularnewline
Winsorized Mean ( 34 / 41 ) & 3.424 & 0.0443795942646705 & 77.1525755638952 \tabularnewline
Winsorized Mean ( 35 / 41 ) & 3.424 & 0.0443795942646705 & 77.1525755638952 \tabularnewline
Winsorized Mean ( 36 / 41 ) & 3.424 & 0.0443795942646705 & 77.1525755638952 \tabularnewline
Winsorized Mean ( 37 / 41 ) & 3.424 & 0.0443795942646705 & 77.1525755638952 \tabularnewline
Winsorized Mean ( 38 / 41 ) & 3.424 & 0.0443795942646705 & 77.1525755638952 \tabularnewline
Winsorized Mean ( 39 / 41 ) & 3.424 & 0.0443795942646705 & 77.1525755638952 \tabularnewline
Winsorized Mean ( 40 / 41 ) & 3.424 & 0.0443795942646705 & 77.1525755638952 \tabularnewline
Winsorized Mean ( 41 / 41 ) & 3.424 & 0.0443795942646705 & 77.1525755638952 \tabularnewline
Trimmed Mean ( 1 / 41 ) & 3.17073170731707 & 0.0838142729103186 & 37.8304505571475 \tabularnewline
Trimmed Mean ( 2 / 41 ) & 3.17355371900826 & 0.0818835479212223 & 38.7569151505434 \tabularnewline
Trimmed Mean ( 3 / 41 ) & 3.17647058823529 & 0.0797438025077124 & 39.8334477206311 \tabularnewline
Trimmed Mean ( 4 / 41 ) & 3.17948717948718 & 0.0773639004570375 & 41.0978138473363 \tabularnewline
Trimmed Mean ( 5 / 41 ) & 3.17391304347826 & 0.0763995974099095 & 41.5435833575032 \tabularnewline
Trimmed Mean ( 6 / 41 ) & 3.16814159292035 & 0.0753234228231769 & 42.0605101862886 \tabularnewline
Trimmed Mean ( 7 / 41 ) & 3.17117117117117 & 0.075580065181811 & 41.9577723774488 \tabularnewline
Trimmed Mean ( 8 / 41 ) & 3.1743119266055 & 0.0758282354227893 & 41.8618725453224 \tabularnewline
Trimmed Mean ( 9 / 41 ) & 3.17757009345794 & 0.0760665470191062 & 41.7735551037936 \tabularnewline
Trimmed Mean ( 10 / 41 ) & 3.18095238095238 & 0.076293428611242 & 41.6936614182216 \tabularnewline
Trimmed Mean ( 11 / 41 ) & 3.18446601941748 & 0.076507096226385 & 41.6231457797669 \tabularnewline
Trimmed Mean ( 12 / 41 ) & 3.18811881188119 & 0.0767055205871151 & 41.5630946440213 \tabularnewline
Trimmed Mean ( 13 / 41 ) & 3.19191919191919 & 0.0768863884834472 & 41.5147499431109 \tabularnewline
Trimmed Mean ( 14 / 41 ) & 3.19587628865979 & 0.0770470569293314 & 41.4795375194031 \tabularnewline
Trimmed Mean ( 15 / 41 ) & 3.2 & 0.077184498498796 & 41.4591020507818 \tabularnewline
Trimmed Mean ( 16 / 41 ) & 3.20430107526882 & 0.0772952358131927 & 41.4553502755717 \tabularnewline
Trimmed Mean ( 17 / 41 ) & 3.20879120879121 & 0.0773752625950732 & 41.4705049284773 \tabularnewline
Trimmed Mean ( 18 / 41 ) & 3.21348314606742 & 0.0774199479675566 & 41.5071726399771 \tabularnewline
Trimmed Mean ( 19 / 41 ) & 3.2183908045977 & 0.0774239196913291 & 41.5684302400171 \tabularnewline
Trimmed Mean ( 20 / 41 ) & 3.22352941176471 & 0.077380920694063 & 41.6579356106321 \tabularnewline
Trimmed Mean ( 21 / 41 ) & 3.2289156626506 & 0.0772836314108567 & 41.7800717138275 \tabularnewline
Trimmed Mean ( 22 / 41 ) & 3.23456790123457 & 0.0771234478969653 & 41.9401360991518 \tabularnewline
Trimmed Mean ( 23 / 41 ) & 3.24050632911392 & 0.0768902020556433 & 42.1445937516052 \tabularnewline
Trimmed Mean ( 24 / 41 ) & 3.24675324675325 & 0.0765718051131916 & 42.401419712566 \tabularnewline
Trimmed Mean ( 25 / 41 ) & 3.25333333333333 & 0.0761537878204321 & 42.720571444254 \tabularnewline
Trimmed Mean ( 26 / 41 ) & 3.26027397260274 & 0.0756186993683982 & 43.1146528548366 \tabularnewline
Trimmed Mean ( 27 / 41 ) & 3.26760563380282 & 0.0749453093120347 & 43.5998685414473 \tabularnewline
Trimmed Mean ( 28 / 41 ) & 3.27536231884058 & 0.0741075287595448 & 44.1974300542133 \tabularnewline
Trimmed Mean ( 29 / 41 ) & 3.28358208955224 & 0.0730729211732952 & 44.9356894021672 \tabularnewline
Trimmed Mean ( 30 / 41 ) & 3.29230769230769 & 0.0718005950099787 & 45.8534875908777 \tabularnewline
Trimmed Mean ( 31 / 41 ) & 3.3015873015873 & 0.0702381313985923 & 47.0056255177294 \tabularnewline
Trimmed Mean ( 32 / 41 ) & 3.31147540983607 & 0.0683169390165333 & 48.4722450611357 \tabularnewline
Trimmed Mean ( 33 / 41 ) & 3.32203389830508 & 0.0659449053916066 & 50.3758990717714 \tabularnewline
Trimmed Mean ( 34 / 41 ) & 3.33333333333333 & 0.0629940788348712 & 52.9150262212918 \tabularnewline
Trimmed Mean ( 35 / 41 ) & 3.32727272727273 & 0.0638524469869863 & 52.1087739668122 \tabularnewline
Trimmed Mean ( 36 / 41 ) & 3.32075471698113 & 0.0647288914977584 & 51.3025117554521 \tabularnewline
Trimmed Mean ( 37 / 41 ) & 3.31372549019608 & 0.0656203942379667 & 50.4984087443781 \tabularnewline
Trimmed Mean ( 38 / 41 ) & 3.30612244897959 & 0.066522473522476 & 49.6993312773096 \tabularnewline
Trimmed Mean ( 39 / 41 ) & 3.29787234042553 & 0.067428611079156 & 48.909094932329 \tabularnewline
Trimmed Mean ( 40 / 41 ) & 3.28888888888889 & 0.0683294324254051 & 48.1328290335113 \tabularnewline
Trimmed Mean ( 41 / 41 ) & 3.27906976744186 & 0.069211517129567 & 47.3775161047734 \tabularnewline
Median & 3 &  &  \tabularnewline
Midrange & 3 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 3.14782608695652 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 3.14782608695652 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 3.14782608695652 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 3.14782608695652 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 3.14782608695652 &  &  \tabularnewline
Midmean - Closest Observation & 3.14782608695652 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 3.14782608695652 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 3.14782608695652 &  &  \tabularnewline
Number of observations & 125 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=94355&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]3.168[/C][C]0.0855615228566462[/C][C]37.0259889519243[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]3.00066268317862[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]2.80164363093015[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]3.30817170050165[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 41 )[/C][C]3.168[/C][C]0.0855615228566462[/C][C]37.0259889519243[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 41 )[/C][C]3.168[/C][C]0.0855615228566462[/C][C]37.0259889519243[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 41 )[/C][C]3.168[/C][C]0.0855615228566462[/C][C]37.0259889519243[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 41 )[/C][C]3.2[/C][C]0.0803219328902499[/C][C]39.839678713564[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 41 )[/C][C]3.2[/C][C]0.0803219328902499[/C][C]39.839678713564[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 41 )[/C][C]3.152[/C][C]0.0736653286503311[/C][C]42.7881074821735[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 41 )[/C][C]3.152[/C][C]0.0736653286503311[/C][C]42.7881074821735[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 41 )[/C][C]3.152[/C][C]0.0736653286503311[/C][C]42.7881074821735[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 41 )[/C][C]3.152[/C][C]0.0736653286503311[/C][C]42.7881074821735[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 41 )[/C][C]3.152[/C][C]0.0736653286503311[/C][C]42.7881074821735[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 41 )[/C][C]3.152[/C][C]0.0736653286503311[/C][C]42.7881074821735[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 41 )[/C][C]3.152[/C][C]0.0736653286503311[/C][C]42.7881074821735[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 41 )[/C][C]3.152[/C][C]0.0736653286503311[/C][C]42.7881074821735[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 41 )[/C][C]3.152[/C][C]0.0736653286503311[/C][C]42.7881074821735[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 41 )[/C][C]3.152[/C][C]0.0736653286503311[/C][C]42.7881074821735[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 41 )[/C][C]3.152[/C][C]0.0736653286503311[/C][C]42.7881074821735[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 41 )[/C][C]3.152[/C][C]0.0736653286503311[/C][C]42.7881074821735[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 41 )[/C][C]3.152[/C][C]0.0736653286503311[/C][C]42.7881074821735[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 41 )[/C][C]3.152[/C][C]0.0736653286503311[/C][C]42.7881074821735[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 41 )[/C][C]3.152[/C][C]0.0736653286503311[/C][C]42.7881074821735[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 41 )[/C][C]3.152[/C][C]0.0736653286503311[/C][C]42.7881074821735[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 41 )[/C][C]3.152[/C][C]0.0736653286503311[/C][C]42.7881074821735[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 41 )[/C][C]3.152[/C][C]0.0736653286503311[/C][C]42.7881074821735[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 41 )[/C][C]3.152[/C][C]0.0736653286503311[/C][C]42.7881074821735[/C][/ROW]
[ROW][C]Winsorized Mean ( 25 / 41 )[/C][C]3.152[/C][C]0.0736653286503311[/C][C]42.7881074821735[/C][/ROW]
[ROW][C]Winsorized Mean ( 26 / 41 )[/C][C]3.152[/C][C]0.0736653286503311[/C][C]42.7881074821735[/C][/ROW]
[ROW][C]Winsorized Mean ( 27 / 41 )[/C][C]3.152[/C][C]0.0736653286503311[/C][C]42.7881074821735[/C][/ROW]
[ROW][C]Winsorized Mean ( 28 / 41 )[/C][C]3.152[/C][C]0.0736653286503311[/C][C]42.7881074821735[/C][/ROW]
[ROW][C]Winsorized Mean ( 29 / 41 )[/C][C]3.152[/C][C]0.0736653286503311[/C][C]42.7881074821735[/C][/ROW]
[ROW][C]Winsorized Mean ( 30 / 41 )[/C][C]3.152[/C][C]0.0736653286503311[/C][C]42.7881074821735[/C][/ROW]
[ROW][C]Winsorized Mean ( 31 / 41 )[/C][C]3.152[/C][C]0.0736653286503311[/C][C]42.7881074821735[/C][/ROW]
[ROW][C]Winsorized Mean ( 32 / 41 )[/C][C]3.152[/C][C]0.0736653286503311[/C][C]42.7881074821735[/C][/ROW]
[ROW][C]Winsorized Mean ( 33 / 41 )[/C][C]3.152[/C][C]0.0736653286503311[/C][C]42.7881074821735[/C][/ROW]
[ROW][C]Winsorized Mean ( 34 / 41 )[/C][C]3.424[/C][C]0.0443795942646705[/C][C]77.1525755638952[/C][/ROW]
[ROW][C]Winsorized Mean ( 35 / 41 )[/C][C]3.424[/C][C]0.0443795942646705[/C][C]77.1525755638952[/C][/ROW]
[ROW][C]Winsorized Mean ( 36 / 41 )[/C][C]3.424[/C][C]0.0443795942646705[/C][C]77.1525755638952[/C][/ROW]
[ROW][C]Winsorized Mean ( 37 / 41 )[/C][C]3.424[/C][C]0.0443795942646705[/C][C]77.1525755638952[/C][/ROW]
[ROW][C]Winsorized Mean ( 38 / 41 )[/C][C]3.424[/C][C]0.0443795942646705[/C][C]77.1525755638952[/C][/ROW]
[ROW][C]Winsorized Mean ( 39 / 41 )[/C][C]3.424[/C][C]0.0443795942646705[/C][C]77.1525755638952[/C][/ROW]
[ROW][C]Winsorized Mean ( 40 / 41 )[/C][C]3.424[/C][C]0.0443795942646705[/C][C]77.1525755638952[/C][/ROW]
[ROW][C]Winsorized Mean ( 41 / 41 )[/C][C]3.424[/C][C]0.0443795942646705[/C][C]77.1525755638952[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 41 )[/C][C]3.17073170731707[/C][C]0.0838142729103186[/C][C]37.8304505571475[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 41 )[/C][C]3.17355371900826[/C][C]0.0818835479212223[/C][C]38.7569151505434[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 41 )[/C][C]3.17647058823529[/C][C]0.0797438025077124[/C][C]39.8334477206311[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 41 )[/C][C]3.17948717948718[/C][C]0.0773639004570375[/C][C]41.0978138473363[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 41 )[/C][C]3.17391304347826[/C][C]0.0763995974099095[/C][C]41.5435833575032[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 41 )[/C][C]3.16814159292035[/C][C]0.0753234228231769[/C][C]42.0605101862886[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 41 )[/C][C]3.17117117117117[/C][C]0.075580065181811[/C][C]41.9577723774488[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 41 )[/C][C]3.1743119266055[/C][C]0.0758282354227893[/C][C]41.8618725453224[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 41 )[/C][C]3.17757009345794[/C][C]0.0760665470191062[/C][C]41.7735551037936[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 41 )[/C][C]3.18095238095238[/C][C]0.076293428611242[/C][C]41.6936614182216[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 41 )[/C][C]3.18446601941748[/C][C]0.076507096226385[/C][C]41.6231457797669[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 41 )[/C][C]3.18811881188119[/C][C]0.0767055205871151[/C][C]41.5630946440213[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 41 )[/C][C]3.19191919191919[/C][C]0.0768863884834472[/C][C]41.5147499431109[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 41 )[/C][C]3.19587628865979[/C][C]0.0770470569293314[/C][C]41.4795375194031[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 41 )[/C][C]3.2[/C][C]0.077184498498796[/C][C]41.4591020507818[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 41 )[/C][C]3.20430107526882[/C][C]0.0772952358131927[/C][C]41.4553502755717[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 41 )[/C][C]3.20879120879121[/C][C]0.0773752625950732[/C][C]41.4705049284773[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 41 )[/C][C]3.21348314606742[/C][C]0.0774199479675566[/C][C]41.5071726399771[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 41 )[/C][C]3.2183908045977[/C][C]0.0774239196913291[/C][C]41.5684302400171[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 41 )[/C][C]3.22352941176471[/C][C]0.077380920694063[/C][C]41.6579356106321[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 41 )[/C][C]3.2289156626506[/C][C]0.0772836314108567[/C][C]41.7800717138275[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 41 )[/C][C]3.23456790123457[/C][C]0.0771234478969653[/C][C]41.9401360991518[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 41 )[/C][C]3.24050632911392[/C][C]0.0768902020556433[/C][C]42.1445937516052[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 41 )[/C][C]3.24675324675325[/C][C]0.0765718051131916[/C][C]42.401419712566[/C][/ROW]
[ROW][C]Trimmed Mean ( 25 / 41 )[/C][C]3.25333333333333[/C][C]0.0761537878204321[/C][C]42.720571444254[/C][/ROW]
[ROW][C]Trimmed Mean ( 26 / 41 )[/C][C]3.26027397260274[/C][C]0.0756186993683982[/C][C]43.1146528548366[/C][/ROW]
[ROW][C]Trimmed Mean ( 27 / 41 )[/C][C]3.26760563380282[/C][C]0.0749453093120347[/C][C]43.5998685414473[/C][/ROW]
[ROW][C]Trimmed Mean ( 28 / 41 )[/C][C]3.27536231884058[/C][C]0.0741075287595448[/C][C]44.1974300542133[/C][/ROW]
[ROW][C]Trimmed Mean ( 29 / 41 )[/C][C]3.28358208955224[/C][C]0.0730729211732952[/C][C]44.9356894021672[/C][/ROW]
[ROW][C]Trimmed Mean ( 30 / 41 )[/C][C]3.29230769230769[/C][C]0.0718005950099787[/C][C]45.8534875908777[/C][/ROW]
[ROW][C]Trimmed Mean ( 31 / 41 )[/C][C]3.3015873015873[/C][C]0.0702381313985923[/C][C]47.0056255177294[/C][/ROW]
[ROW][C]Trimmed Mean ( 32 / 41 )[/C][C]3.31147540983607[/C][C]0.0683169390165333[/C][C]48.4722450611357[/C][/ROW]
[ROW][C]Trimmed Mean ( 33 / 41 )[/C][C]3.32203389830508[/C][C]0.0659449053916066[/C][C]50.3758990717714[/C][/ROW]
[ROW][C]Trimmed Mean ( 34 / 41 )[/C][C]3.33333333333333[/C][C]0.0629940788348712[/C][C]52.9150262212918[/C][/ROW]
[ROW][C]Trimmed Mean ( 35 / 41 )[/C][C]3.32727272727273[/C][C]0.0638524469869863[/C][C]52.1087739668122[/C][/ROW]
[ROW][C]Trimmed Mean ( 36 / 41 )[/C][C]3.32075471698113[/C][C]0.0647288914977584[/C][C]51.3025117554521[/C][/ROW]
[ROW][C]Trimmed Mean ( 37 / 41 )[/C][C]3.31372549019608[/C][C]0.0656203942379667[/C][C]50.4984087443781[/C][/ROW]
[ROW][C]Trimmed Mean ( 38 / 41 )[/C][C]3.30612244897959[/C][C]0.066522473522476[/C][C]49.6993312773096[/C][/ROW]
[ROW][C]Trimmed Mean ( 39 / 41 )[/C][C]3.29787234042553[/C][C]0.067428611079156[/C][C]48.909094932329[/C][/ROW]
[ROW][C]Trimmed Mean ( 40 / 41 )[/C][C]3.28888888888889[/C][C]0.0683294324254051[/C][C]48.1328290335113[/C][/ROW]
[ROW][C]Trimmed Mean ( 41 / 41 )[/C][C]3.27906976744186[/C][C]0.069211517129567[/C][C]47.3775161047734[/C][/ROW]
[ROW][C]Median[/C][C]3[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]3[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]3.14782608695652[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]3.14782608695652[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]3.14782608695652[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]3.14782608695652[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]3.14782608695652[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]3.14782608695652[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]3.14782608695652[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]3.14782608695652[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]125[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=94355&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=94355&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 Mean3.1680.085561522856646237.0259889519243
Geometric Mean3.00066268317862
Harmonic Mean2.80164363093015
Quadratic Mean3.30817170050165
Winsorized Mean ( 1 / 41 )3.1680.085561522856646237.0259889519243
Winsorized Mean ( 2 / 41 )3.1680.085561522856646237.0259889519243
Winsorized Mean ( 3 / 41 )3.1680.085561522856646237.0259889519243
Winsorized Mean ( 4 / 41 )3.20.080321932890249939.839678713564
Winsorized Mean ( 5 / 41 )3.20.080321932890249939.839678713564
Winsorized Mean ( 6 / 41 )3.1520.073665328650331142.7881074821735
Winsorized Mean ( 7 / 41 )3.1520.073665328650331142.7881074821735
Winsorized Mean ( 8 / 41 )3.1520.073665328650331142.7881074821735
Winsorized Mean ( 9 / 41 )3.1520.073665328650331142.7881074821735
Winsorized Mean ( 10 / 41 )3.1520.073665328650331142.7881074821735
Winsorized Mean ( 11 / 41 )3.1520.073665328650331142.7881074821735
Winsorized Mean ( 12 / 41 )3.1520.073665328650331142.7881074821735
Winsorized Mean ( 13 / 41 )3.1520.073665328650331142.7881074821735
Winsorized Mean ( 14 / 41 )3.1520.073665328650331142.7881074821735
Winsorized Mean ( 15 / 41 )3.1520.073665328650331142.7881074821735
Winsorized Mean ( 16 / 41 )3.1520.073665328650331142.7881074821735
Winsorized Mean ( 17 / 41 )3.1520.073665328650331142.7881074821735
Winsorized Mean ( 18 / 41 )3.1520.073665328650331142.7881074821735
Winsorized Mean ( 19 / 41 )3.1520.073665328650331142.7881074821735
Winsorized Mean ( 20 / 41 )3.1520.073665328650331142.7881074821735
Winsorized Mean ( 21 / 41 )3.1520.073665328650331142.7881074821735
Winsorized Mean ( 22 / 41 )3.1520.073665328650331142.7881074821735
Winsorized Mean ( 23 / 41 )3.1520.073665328650331142.7881074821735
Winsorized Mean ( 24 / 41 )3.1520.073665328650331142.7881074821735
Winsorized Mean ( 25 / 41 )3.1520.073665328650331142.7881074821735
Winsorized Mean ( 26 / 41 )3.1520.073665328650331142.7881074821735
Winsorized Mean ( 27 / 41 )3.1520.073665328650331142.7881074821735
Winsorized Mean ( 28 / 41 )3.1520.073665328650331142.7881074821735
Winsorized Mean ( 29 / 41 )3.1520.073665328650331142.7881074821735
Winsorized Mean ( 30 / 41 )3.1520.073665328650331142.7881074821735
Winsorized Mean ( 31 / 41 )3.1520.073665328650331142.7881074821735
Winsorized Mean ( 32 / 41 )3.1520.073665328650331142.7881074821735
Winsorized Mean ( 33 / 41 )3.1520.073665328650331142.7881074821735
Winsorized Mean ( 34 / 41 )3.4240.044379594264670577.1525755638952
Winsorized Mean ( 35 / 41 )3.4240.044379594264670577.1525755638952
Winsorized Mean ( 36 / 41 )3.4240.044379594264670577.1525755638952
Winsorized Mean ( 37 / 41 )3.4240.044379594264670577.1525755638952
Winsorized Mean ( 38 / 41 )3.4240.044379594264670577.1525755638952
Winsorized Mean ( 39 / 41 )3.4240.044379594264670577.1525755638952
Winsorized Mean ( 40 / 41 )3.4240.044379594264670577.1525755638952
Winsorized Mean ( 41 / 41 )3.4240.044379594264670577.1525755638952
Trimmed Mean ( 1 / 41 )3.170731707317070.083814272910318637.8304505571475
Trimmed Mean ( 2 / 41 )3.173553719008260.081883547921222338.7569151505434
Trimmed Mean ( 3 / 41 )3.176470588235290.079743802507712439.8334477206311
Trimmed Mean ( 4 / 41 )3.179487179487180.077363900457037541.0978138473363
Trimmed Mean ( 5 / 41 )3.173913043478260.076399597409909541.5435833575032
Trimmed Mean ( 6 / 41 )3.168141592920350.075323422823176942.0605101862886
Trimmed Mean ( 7 / 41 )3.171171171171170.07558006518181141.9577723774488
Trimmed Mean ( 8 / 41 )3.17431192660550.075828235422789341.8618725453224
Trimmed Mean ( 9 / 41 )3.177570093457940.076066547019106241.7735551037936
Trimmed Mean ( 10 / 41 )3.180952380952380.07629342861124241.6936614182216
Trimmed Mean ( 11 / 41 )3.184466019417480.07650709622638541.6231457797669
Trimmed Mean ( 12 / 41 )3.188118811881190.076705520587115141.5630946440213
Trimmed Mean ( 13 / 41 )3.191919191919190.076886388483447241.5147499431109
Trimmed Mean ( 14 / 41 )3.195876288659790.077047056929331441.4795375194031
Trimmed Mean ( 15 / 41 )3.20.07718449849879641.4591020507818
Trimmed Mean ( 16 / 41 )3.204301075268820.077295235813192741.4553502755717
Trimmed Mean ( 17 / 41 )3.208791208791210.077375262595073241.4705049284773
Trimmed Mean ( 18 / 41 )3.213483146067420.077419947967556641.5071726399771
Trimmed Mean ( 19 / 41 )3.21839080459770.077423919691329141.5684302400171
Trimmed Mean ( 20 / 41 )3.223529411764710.07738092069406341.6579356106321
Trimmed Mean ( 21 / 41 )3.22891566265060.077283631410856741.7800717138275
Trimmed Mean ( 22 / 41 )3.234567901234570.077123447896965341.9401360991518
Trimmed Mean ( 23 / 41 )3.240506329113920.076890202055643342.1445937516052
Trimmed Mean ( 24 / 41 )3.246753246753250.076571805113191642.401419712566
Trimmed Mean ( 25 / 41 )3.253333333333330.076153787820432142.720571444254
Trimmed Mean ( 26 / 41 )3.260273972602740.075618699368398243.1146528548366
Trimmed Mean ( 27 / 41 )3.267605633802820.074945309312034743.5998685414473
Trimmed Mean ( 28 / 41 )3.275362318840580.074107528759544844.1974300542133
Trimmed Mean ( 29 / 41 )3.283582089552240.073072921173295244.9356894021672
Trimmed Mean ( 30 / 41 )3.292307692307690.071800595009978745.8534875908777
Trimmed Mean ( 31 / 41 )3.30158730158730.070238131398592347.0056255177294
Trimmed Mean ( 32 / 41 )3.311475409836070.068316939016533348.4722450611357
Trimmed Mean ( 33 / 41 )3.322033898305080.065944905391606650.3758990717714
Trimmed Mean ( 34 / 41 )3.333333333333330.062994078834871252.9150262212918
Trimmed Mean ( 35 / 41 )3.327272727272730.063852446986986352.1087739668122
Trimmed Mean ( 36 / 41 )3.320754716981130.064728891497758451.3025117554521
Trimmed Mean ( 37 / 41 )3.313725490196080.065620394237966750.4984087443781
Trimmed Mean ( 38 / 41 )3.306122448979590.06652247352247649.6993312773096
Trimmed Mean ( 39 / 41 )3.297872340425530.06742861107915648.909094932329
Trimmed Mean ( 40 / 41 )3.288888888888890.068329432425405148.1328290335113
Trimmed Mean ( 41 / 41 )3.279069767441860.06921151712956747.3775161047734
Median3
Midrange3
Midmean - Weighted Average at Xnp3.14782608695652
Midmean - Weighted Average at X(n+1)p3.14782608695652
Midmean - Empirical Distribution Function3.14782608695652
Midmean - Empirical Distribution Function - Averaging3.14782608695652
Midmean - Empirical Distribution Function - Interpolation3.14782608695652
Midmean - Closest Observation3.14782608695652
Midmean - True Basic - Statistics Graphics Toolkit3.14782608695652
Midmean - MS Excel (old versions)3.14782608695652
Number of observations125



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')