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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, 16 Oct 2008 08:30:25 -0600
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/Oct/16/t1224167448125cc5nkigtqs4l.htm/, Retrieved Wed, 15 May 2024 16:55:10 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=16350, Retrieved Wed, 15 May 2024 16:55:10 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact221
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
F     [Central Tendency] [Q1 central tenden...] [2007-10-18 09:35:57] [b731da8b544846036771bbf9bf2f34ce]
-    D  [Central Tendency] [] [2008-10-16 14:20:24] [7c33e759a6f7358dc2f6505c3a7a1eae]
-    D      [Central Tendency] [] [2008-10-16 14:30:25] [1e28c3a908c2cc51d131d1d2a5af4149] [Current]
-    D        [Central Tendency] [] [2008-10-16 14:31:36] [7c33e759a6f7358dc2f6505c3a7a1eae]
-    D          [Central Tendency] [] [2008-10-16 14:32:46] [7c33e759a6f7358dc2f6505c3a7a1eae]
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Dataseries X:
11.9
11.1
7.3
5.4
2.7
4.9
3.6
5.8
3.9
3.9
3.7
0.9
3.5
3
3.8
2.6
5.9
5.5
7.5
8.6
5.8
6.1
6.1
6.1
4.6
4.3
5.1
6
4.6
3.9
2.4
0.1
3.3
4.2
5.1
2.7
4.7
7.1
5.1
5.8
4.9
4.6
6
3.7
4.2
4.7
5
5.9
6.2
2.9
4.3
4.9
4.8
6.2
6.5
9.9
8.8
9.2
8
9.1
7.5
6.9
8.8
4.9
6.4
6.8
4.9
3.7
5.3
4.7
5.9
4.6
4.4
5.5
4.8
7.9
6.7
7.6
7.1
6.7




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'George Udny Yule' @ 72.249.76.132

\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 & 1 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=16350&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]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=16350&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=16350&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 time1 seconds
R Server'George Udny Yule' @ 72.249.76.132







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean5.493750.23197926406404623.6820735774180
Geometric Mean4.94420245659846
Harmonic Mean3.00074241647570
Quadratic Mean5.86793191848713
Winsorized Mean ( 1 / 26 )5.493750.22589725281444624.3196848635986
Winsorized Mean ( 2 / 26 )5.501250.20875227392076126.3530063489904
Winsorized Mean ( 3 / 26 )5.48250.20077992706922727.3060164929221
Winsorized Mean ( 4 / 26 )5.48250.19872039226963527.5890155880985
Winsorized Mean ( 5 / 26 )5.463750.19452346633683128.0878708512172
Winsorized Mean ( 6 / 26 )5.478750.1918983590902228.5502701845626
Winsorized Mean ( 7 / 26 )5.470.18664594520310229.3068247158957
Winsorized Mean ( 8 / 26 )5.440.16960117028495232.0752503703842
Winsorized Mean ( 9 / 26 )5.451250.16396968064519133.2454754961424
Winsorized Mean ( 10 / 26 )5.426250.15522282625676934.9578095622605
Winsorized Mean ( 11 / 26 )5.426250.15078637489650835.9863416288394
Winsorized Mean ( 12 / 26 )5.426250.15078637489650835.9863416288394
Winsorized Mean ( 13 / 26 )5.393750.14525559914261037.1328198832770
Winsorized Mean ( 14 / 26 )5.376250.13699121922798439.2452160824462
Winsorized Mean ( 15 / 26 )5.3950.13430434925142340.1699574888700
Winsorized Mean ( 16 / 26 )5.3550.12803159222471241.8256143421327
Winsorized Mean ( 17 / 26 )5.333750.12482828395313142.7286976243513
Winsorized Mean ( 18 / 26 )5.378750.11205352685099648.0016127216812
Winsorized Mean ( 19 / 26 )5.378750.11205352685099648.0016127216812
Winsorized Mean ( 20 / 26 )5.353750.10142877637640752.7833440495425
Winsorized Mean ( 21 / 26 )5.32750.097726934861727654.5141419562355
Winsorized Mean ( 22 / 26 )5.30.08663907382886861.1733224488146
Winsorized Mean ( 23 / 26 )5.35750.079372040959496367.4985792885677
Winsorized Mean ( 24 / 26 )5.32750.075409745701967770.6473672654353
Winsorized Mean ( 25 / 26 )5.32750.075409745701967770.6473672654353
Winsorized Mean ( 26 / 26 )5.32750.075409745701967770.6473672654354
Trimmed Mean ( 1 / 26 )5.480769230769230.2120107946873525.8513687421042
Trimmed Mean ( 2 / 26 )5.467105263157890.1952900511106227.9947966220825
Trimmed Mean ( 3 / 26 )5.448648648648650.18670393881030829.1833620831347
Trimmed Mean ( 4 / 26 )5.436111111111110.18025917651574930.1571948579060
Trimmed Mean ( 5 / 26 )5.422857142857140.17337439506354431.2783046243339
Trimmed Mean ( 6 / 26 )5.413235294117650.16653658913690832.5047806141118
Trimmed Mean ( 7 / 26 )5.40.15907658943213933.9459125901339
Trimmed Mean ( 8 / 26 )5.38750.15150534329725535.559801936686
Trimmed Mean ( 9 / 26 )5.379032258064520.14667362504319436.6734800239678
Trimmed Mean ( 10 / 26 )5.368333333333330.14208876963273337.7815456296036
Trimmed Mean ( 11 / 26 )5.360344827586210.138436950278838.7204775660757
Trimmed Mean ( 12 / 26 )5.351785714285710.13486383396068539.6828827797218
Trimmed Mean ( 13 / 26 )5.342592592592590.13040821388677740.9682215050590
Trimmed Mean ( 14 / 26 )5.336538461538460.12605598741013742.3346686752408
Trimmed Mean ( 15 / 26 )5.3320.12233910716879243.5837740146608
Trimmed Mean ( 16 / 26 )5.3250.11814539065631545.0715848533644
Trimmed Mean ( 17 / 26 )5.321739130434780.11416206141048146.6156537879948
Trimmed Mean ( 18 / 26 )5.320454545454550.10970744998390948.4967479075933
Trimmed Mean ( 19 / 26 )5.314285714285710.10671808947971349.7974217885145
Trimmed Mean ( 20 / 26 )5.30750.10268120318334651.6891099388759
Trimmed Mean ( 21 / 26 )5.302631578947370.099821094737313353.1213526850376
Trimmed Mean ( 22 / 26 )5.30.096773340156674254.7671496242602
Trimmed Mean ( 23 / 26 )5.30.09525273633322155.6414461570857
Trimmed Mean ( 24 / 26 )5.293750.094606304349026655.9555733249025
Trimmed Mean ( 25 / 26 )5.290.094364175941664656.0594096987638
Trimmed Mean ( 26 / 26 )5.285714285714290.09353638424499156.5097136090905
Median5.1
Midrange6
Midmean - Weighted Average at Xnp5.2547619047619
Midmean - Weighted Average at X(n+1)p5.3075
Midmean - Empirical Distribution Function5.2547619047619
Midmean - Empirical Distribution Function - Averaging5.3075
Midmean - Empirical Distribution Function - Interpolation5.3075
Midmean - Closest Observation5.2547619047619
Midmean - True Basic - Statistics Graphics Toolkit5.3075
Midmean - MS Excel (old versions)5.32045454545455
Number of observations80

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 5.49375 & 0.231979264064046 & 23.6820735774180 \tabularnewline
Geometric Mean & 4.94420245659846 &  &  \tabularnewline
Harmonic Mean & 3.00074241647570 &  &  \tabularnewline
Quadratic Mean & 5.86793191848713 &  &  \tabularnewline
Winsorized Mean ( 1 / 26 ) & 5.49375 & 0.225897252814446 & 24.3196848635986 \tabularnewline
Winsorized Mean ( 2 / 26 ) & 5.50125 & 0.208752273920761 & 26.3530063489904 \tabularnewline
Winsorized Mean ( 3 / 26 ) & 5.4825 & 0.200779927069227 & 27.3060164929221 \tabularnewline
Winsorized Mean ( 4 / 26 ) & 5.4825 & 0.198720392269635 & 27.5890155880985 \tabularnewline
Winsorized Mean ( 5 / 26 ) & 5.46375 & 0.194523466336831 & 28.0878708512172 \tabularnewline
Winsorized Mean ( 6 / 26 ) & 5.47875 & 0.19189835909022 & 28.5502701845626 \tabularnewline
Winsorized Mean ( 7 / 26 ) & 5.47 & 0.186645945203102 & 29.3068247158957 \tabularnewline
Winsorized Mean ( 8 / 26 ) & 5.44 & 0.169601170284952 & 32.0752503703842 \tabularnewline
Winsorized Mean ( 9 / 26 ) & 5.45125 & 0.163969680645191 & 33.2454754961424 \tabularnewline
Winsorized Mean ( 10 / 26 ) & 5.42625 & 0.155222826256769 & 34.9578095622605 \tabularnewline
Winsorized Mean ( 11 / 26 ) & 5.42625 & 0.150786374896508 & 35.9863416288394 \tabularnewline
Winsorized Mean ( 12 / 26 ) & 5.42625 & 0.150786374896508 & 35.9863416288394 \tabularnewline
Winsorized Mean ( 13 / 26 ) & 5.39375 & 0.145255599142610 & 37.1328198832770 \tabularnewline
Winsorized Mean ( 14 / 26 ) & 5.37625 & 0.136991219227984 & 39.2452160824462 \tabularnewline
Winsorized Mean ( 15 / 26 ) & 5.395 & 0.134304349251423 & 40.1699574888700 \tabularnewline
Winsorized Mean ( 16 / 26 ) & 5.355 & 0.128031592224712 & 41.8256143421327 \tabularnewline
Winsorized Mean ( 17 / 26 ) & 5.33375 & 0.124828283953131 & 42.7286976243513 \tabularnewline
Winsorized Mean ( 18 / 26 ) & 5.37875 & 0.112053526850996 & 48.0016127216812 \tabularnewline
Winsorized Mean ( 19 / 26 ) & 5.37875 & 0.112053526850996 & 48.0016127216812 \tabularnewline
Winsorized Mean ( 20 / 26 ) & 5.35375 & 0.101428776376407 & 52.7833440495425 \tabularnewline
Winsorized Mean ( 21 / 26 ) & 5.3275 & 0.0977269348617276 & 54.5141419562355 \tabularnewline
Winsorized Mean ( 22 / 26 ) & 5.3 & 0.086639073828868 & 61.1733224488146 \tabularnewline
Winsorized Mean ( 23 / 26 ) & 5.3575 & 0.0793720409594963 & 67.4985792885677 \tabularnewline
Winsorized Mean ( 24 / 26 ) & 5.3275 & 0.0754097457019677 & 70.6473672654353 \tabularnewline
Winsorized Mean ( 25 / 26 ) & 5.3275 & 0.0754097457019677 & 70.6473672654353 \tabularnewline
Winsorized Mean ( 26 / 26 ) & 5.3275 & 0.0754097457019677 & 70.6473672654354 \tabularnewline
Trimmed Mean ( 1 / 26 ) & 5.48076923076923 & 0.21201079468735 & 25.8513687421042 \tabularnewline
Trimmed Mean ( 2 / 26 ) & 5.46710526315789 & 0.19529005111062 & 27.9947966220825 \tabularnewline
Trimmed Mean ( 3 / 26 ) & 5.44864864864865 & 0.186703938810308 & 29.1833620831347 \tabularnewline
Trimmed Mean ( 4 / 26 ) & 5.43611111111111 & 0.180259176515749 & 30.1571948579060 \tabularnewline
Trimmed Mean ( 5 / 26 ) & 5.42285714285714 & 0.173374395063544 & 31.2783046243339 \tabularnewline
Trimmed Mean ( 6 / 26 ) & 5.41323529411765 & 0.166536589136908 & 32.5047806141118 \tabularnewline
Trimmed Mean ( 7 / 26 ) & 5.4 & 0.159076589432139 & 33.9459125901339 \tabularnewline
Trimmed Mean ( 8 / 26 ) & 5.3875 & 0.151505343297255 & 35.559801936686 \tabularnewline
Trimmed Mean ( 9 / 26 ) & 5.37903225806452 & 0.146673625043194 & 36.6734800239678 \tabularnewline
Trimmed Mean ( 10 / 26 ) & 5.36833333333333 & 0.142088769632733 & 37.7815456296036 \tabularnewline
Trimmed Mean ( 11 / 26 ) & 5.36034482758621 & 0.1384369502788 & 38.7204775660757 \tabularnewline
Trimmed Mean ( 12 / 26 ) & 5.35178571428571 & 0.134863833960685 & 39.6828827797218 \tabularnewline
Trimmed Mean ( 13 / 26 ) & 5.34259259259259 & 0.130408213886777 & 40.9682215050590 \tabularnewline
Trimmed Mean ( 14 / 26 ) & 5.33653846153846 & 0.126055987410137 & 42.3346686752408 \tabularnewline
Trimmed Mean ( 15 / 26 ) & 5.332 & 0.122339107168792 & 43.5837740146608 \tabularnewline
Trimmed Mean ( 16 / 26 ) & 5.325 & 0.118145390656315 & 45.0715848533644 \tabularnewline
Trimmed Mean ( 17 / 26 ) & 5.32173913043478 & 0.114162061410481 & 46.6156537879948 \tabularnewline
Trimmed Mean ( 18 / 26 ) & 5.32045454545455 & 0.109707449983909 & 48.4967479075933 \tabularnewline
Trimmed Mean ( 19 / 26 ) & 5.31428571428571 & 0.106718089479713 & 49.7974217885145 \tabularnewline
Trimmed Mean ( 20 / 26 ) & 5.3075 & 0.102681203183346 & 51.6891099388759 \tabularnewline
Trimmed Mean ( 21 / 26 ) & 5.30263157894737 & 0.0998210947373133 & 53.1213526850376 \tabularnewline
Trimmed Mean ( 22 / 26 ) & 5.3 & 0.0967733401566742 & 54.7671496242602 \tabularnewline
Trimmed Mean ( 23 / 26 ) & 5.3 & 0.095252736333221 & 55.6414461570857 \tabularnewline
Trimmed Mean ( 24 / 26 ) & 5.29375 & 0.0946063043490266 & 55.9555733249025 \tabularnewline
Trimmed Mean ( 25 / 26 ) & 5.29 & 0.0943641759416646 & 56.0594096987638 \tabularnewline
Trimmed Mean ( 26 / 26 ) & 5.28571428571429 & 0.093536384244991 & 56.5097136090905 \tabularnewline
Median & 5.1 &  &  \tabularnewline
Midrange & 6 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 5.2547619047619 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 5.3075 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 5.2547619047619 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 5.3075 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 5.3075 &  &  \tabularnewline
Midmean - Closest Observation & 5.2547619047619 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 5.3075 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 5.32045454545455 &  &  \tabularnewline
Number of observations & 80 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=16350&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]5.49375[/C][C]0.231979264064046[/C][C]23.6820735774180[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]4.94420245659846[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]3.00074241647570[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]5.86793191848713[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 26 )[/C][C]5.49375[/C][C]0.225897252814446[/C][C]24.3196848635986[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 26 )[/C][C]5.50125[/C][C]0.208752273920761[/C][C]26.3530063489904[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 26 )[/C][C]5.4825[/C][C]0.200779927069227[/C][C]27.3060164929221[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 26 )[/C][C]5.4825[/C][C]0.198720392269635[/C][C]27.5890155880985[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 26 )[/C][C]5.46375[/C][C]0.194523466336831[/C][C]28.0878708512172[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 26 )[/C][C]5.47875[/C][C]0.19189835909022[/C][C]28.5502701845626[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 26 )[/C][C]5.47[/C][C]0.186645945203102[/C][C]29.3068247158957[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 26 )[/C][C]5.44[/C][C]0.169601170284952[/C][C]32.0752503703842[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 26 )[/C][C]5.45125[/C][C]0.163969680645191[/C][C]33.2454754961424[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 26 )[/C][C]5.42625[/C][C]0.155222826256769[/C][C]34.9578095622605[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 26 )[/C][C]5.42625[/C][C]0.150786374896508[/C][C]35.9863416288394[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 26 )[/C][C]5.42625[/C][C]0.150786374896508[/C][C]35.9863416288394[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 26 )[/C][C]5.39375[/C][C]0.145255599142610[/C][C]37.1328198832770[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 26 )[/C][C]5.37625[/C][C]0.136991219227984[/C][C]39.2452160824462[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 26 )[/C][C]5.395[/C][C]0.134304349251423[/C][C]40.1699574888700[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 26 )[/C][C]5.355[/C][C]0.128031592224712[/C][C]41.8256143421327[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 26 )[/C][C]5.33375[/C][C]0.124828283953131[/C][C]42.7286976243513[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 26 )[/C][C]5.37875[/C][C]0.112053526850996[/C][C]48.0016127216812[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 26 )[/C][C]5.37875[/C][C]0.112053526850996[/C][C]48.0016127216812[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 26 )[/C][C]5.35375[/C][C]0.101428776376407[/C][C]52.7833440495425[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 26 )[/C][C]5.3275[/C][C]0.0977269348617276[/C][C]54.5141419562355[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 26 )[/C][C]5.3[/C][C]0.086639073828868[/C][C]61.1733224488146[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 26 )[/C][C]5.3575[/C][C]0.0793720409594963[/C][C]67.4985792885677[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 26 )[/C][C]5.3275[/C][C]0.0754097457019677[/C][C]70.6473672654353[/C][/ROW]
[ROW][C]Winsorized Mean ( 25 / 26 )[/C][C]5.3275[/C][C]0.0754097457019677[/C][C]70.6473672654353[/C][/ROW]
[ROW][C]Winsorized Mean ( 26 / 26 )[/C][C]5.3275[/C][C]0.0754097457019677[/C][C]70.6473672654354[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 26 )[/C][C]5.48076923076923[/C][C]0.21201079468735[/C][C]25.8513687421042[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 26 )[/C][C]5.46710526315789[/C][C]0.19529005111062[/C][C]27.9947966220825[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 26 )[/C][C]5.44864864864865[/C][C]0.186703938810308[/C][C]29.1833620831347[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 26 )[/C][C]5.43611111111111[/C][C]0.180259176515749[/C][C]30.1571948579060[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 26 )[/C][C]5.42285714285714[/C][C]0.173374395063544[/C][C]31.2783046243339[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 26 )[/C][C]5.41323529411765[/C][C]0.166536589136908[/C][C]32.5047806141118[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 26 )[/C][C]5.4[/C][C]0.159076589432139[/C][C]33.9459125901339[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 26 )[/C][C]5.3875[/C][C]0.151505343297255[/C][C]35.559801936686[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 26 )[/C][C]5.37903225806452[/C][C]0.146673625043194[/C][C]36.6734800239678[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 26 )[/C][C]5.36833333333333[/C][C]0.142088769632733[/C][C]37.7815456296036[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 26 )[/C][C]5.36034482758621[/C][C]0.1384369502788[/C][C]38.7204775660757[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 26 )[/C][C]5.35178571428571[/C][C]0.134863833960685[/C][C]39.6828827797218[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 26 )[/C][C]5.34259259259259[/C][C]0.130408213886777[/C][C]40.9682215050590[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 26 )[/C][C]5.33653846153846[/C][C]0.126055987410137[/C][C]42.3346686752408[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 26 )[/C][C]5.332[/C][C]0.122339107168792[/C][C]43.5837740146608[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 26 )[/C][C]5.325[/C][C]0.118145390656315[/C][C]45.0715848533644[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 26 )[/C][C]5.32173913043478[/C][C]0.114162061410481[/C][C]46.6156537879948[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 26 )[/C][C]5.32045454545455[/C][C]0.109707449983909[/C][C]48.4967479075933[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 26 )[/C][C]5.31428571428571[/C][C]0.106718089479713[/C][C]49.7974217885145[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 26 )[/C][C]5.3075[/C][C]0.102681203183346[/C][C]51.6891099388759[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 26 )[/C][C]5.30263157894737[/C][C]0.0998210947373133[/C][C]53.1213526850376[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 26 )[/C][C]5.3[/C][C]0.0967733401566742[/C][C]54.7671496242602[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 26 )[/C][C]5.3[/C][C]0.095252736333221[/C][C]55.6414461570857[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 26 )[/C][C]5.29375[/C][C]0.0946063043490266[/C][C]55.9555733249025[/C][/ROW]
[ROW][C]Trimmed Mean ( 25 / 26 )[/C][C]5.29[/C][C]0.0943641759416646[/C][C]56.0594096987638[/C][/ROW]
[ROW][C]Trimmed Mean ( 26 / 26 )[/C][C]5.28571428571429[/C][C]0.093536384244991[/C][C]56.5097136090905[/C][/ROW]
[ROW][C]Median[/C][C]5.1[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]6[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]5.2547619047619[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]5.3075[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]5.2547619047619[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]5.3075[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]5.3075[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]5.2547619047619[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]5.3075[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]5.32045454545455[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]80[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=16350&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=16350&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 Mean5.493750.23197926406404623.6820735774180
Geometric Mean4.94420245659846
Harmonic Mean3.00074241647570
Quadratic Mean5.86793191848713
Winsorized Mean ( 1 / 26 )5.493750.22589725281444624.3196848635986
Winsorized Mean ( 2 / 26 )5.501250.20875227392076126.3530063489904
Winsorized Mean ( 3 / 26 )5.48250.20077992706922727.3060164929221
Winsorized Mean ( 4 / 26 )5.48250.19872039226963527.5890155880985
Winsorized Mean ( 5 / 26 )5.463750.19452346633683128.0878708512172
Winsorized Mean ( 6 / 26 )5.478750.1918983590902228.5502701845626
Winsorized Mean ( 7 / 26 )5.470.18664594520310229.3068247158957
Winsorized Mean ( 8 / 26 )5.440.16960117028495232.0752503703842
Winsorized Mean ( 9 / 26 )5.451250.16396968064519133.2454754961424
Winsorized Mean ( 10 / 26 )5.426250.15522282625676934.9578095622605
Winsorized Mean ( 11 / 26 )5.426250.15078637489650835.9863416288394
Winsorized Mean ( 12 / 26 )5.426250.15078637489650835.9863416288394
Winsorized Mean ( 13 / 26 )5.393750.14525559914261037.1328198832770
Winsorized Mean ( 14 / 26 )5.376250.13699121922798439.2452160824462
Winsorized Mean ( 15 / 26 )5.3950.13430434925142340.1699574888700
Winsorized Mean ( 16 / 26 )5.3550.12803159222471241.8256143421327
Winsorized Mean ( 17 / 26 )5.333750.12482828395313142.7286976243513
Winsorized Mean ( 18 / 26 )5.378750.11205352685099648.0016127216812
Winsorized Mean ( 19 / 26 )5.378750.11205352685099648.0016127216812
Winsorized Mean ( 20 / 26 )5.353750.10142877637640752.7833440495425
Winsorized Mean ( 21 / 26 )5.32750.097726934861727654.5141419562355
Winsorized Mean ( 22 / 26 )5.30.08663907382886861.1733224488146
Winsorized Mean ( 23 / 26 )5.35750.079372040959496367.4985792885677
Winsorized Mean ( 24 / 26 )5.32750.075409745701967770.6473672654353
Winsorized Mean ( 25 / 26 )5.32750.075409745701967770.6473672654353
Winsorized Mean ( 26 / 26 )5.32750.075409745701967770.6473672654354
Trimmed Mean ( 1 / 26 )5.480769230769230.2120107946873525.8513687421042
Trimmed Mean ( 2 / 26 )5.467105263157890.1952900511106227.9947966220825
Trimmed Mean ( 3 / 26 )5.448648648648650.18670393881030829.1833620831347
Trimmed Mean ( 4 / 26 )5.436111111111110.18025917651574930.1571948579060
Trimmed Mean ( 5 / 26 )5.422857142857140.17337439506354431.2783046243339
Trimmed Mean ( 6 / 26 )5.413235294117650.16653658913690832.5047806141118
Trimmed Mean ( 7 / 26 )5.40.15907658943213933.9459125901339
Trimmed Mean ( 8 / 26 )5.38750.15150534329725535.559801936686
Trimmed Mean ( 9 / 26 )5.379032258064520.14667362504319436.6734800239678
Trimmed Mean ( 10 / 26 )5.368333333333330.14208876963273337.7815456296036
Trimmed Mean ( 11 / 26 )5.360344827586210.138436950278838.7204775660757
Trimmed Mean ( 12 / 26 )5.351785714285710.13486383396068539.6828827797218
Trimmed Mean ( 13 / 26 )5.342592592592590.13040821388677740.9682215050590
Trimmed Mean ( 14 / 26 )5.336538461538460.12605598741013742.3346686752408
Trimmed Mean ( 15 / 26 )5.3320.12233910716879243.5837740146608
Trimmed Mean ( 16 / 26 )5.3250.11814539065631545.0715848533644
Trimmed Mean ( 17 / 26 )5.321739130434780.11416206141048146.6156537879948
Trimmed Mean ( 18 / 26 )5.320454545454550.10970744998390948.4967479075933
Trimmed Mean ( 19 / 26 )5.314285714285710.10671808947971349.7974217885145
Trimmed Mean ( 20 / 26 )5.30750.10268120318334651.6891099388759
Trimmed Mean ( 21 / 26 )5.302631578947370.099821094737313353.1213526850376
Trimmed Mean ( 22 / 26 )5.30.096773340156674254.7671496242602
Trimmed Mean ( 23 / 26 )5.30.09525273633322155.6414461570857
Trimmed Mean ( 24 / 26 )5.293750.094606304349026655.9555733249025
Trimmed Mean ( 25 / 26 )5.290.094364175941664656.0594096987638
Trimmed Mean ( 26 / 26 )5.285714285714290.09353638424499156.5097136090905
Median5.1
Midrange6
Midmean - Weighted Average at Xnp5.2547619047619
Midmean - Weighted Average at X(n+1)p5.3075
Midmean - Empirical Distribution Function5.2547619047619
Midmean - Empirical Distribution Function - Averaging5.3075
Midmean - Empirical Distribution Function - Interpolation5.3075
Midmean - Closest Observation5.2547619047619
Midmean - True Basic - Statistics Graphics Toolkit5.3075
Midmean - MS Excel (old versions)5.32045454545455
Number of observations80



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')