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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 computationTue, 14 Oct 2008 11:44:38 -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/14/t1224006448ctmeats26rlndgt.htm/, Retrieved Sat, 18 May 2024 03:43:18 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=16260, Retrieved Sat, 18 May 2024 03:43:18 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact150
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
F       [Central Tendency] [Investeringen] [2008-10-14 17:44:38] [701cc898ddafddb72d72f8df86ee2872] [Current]
Feedback Forum
2008-10-22 12:40:35 [Kim Wester] [reply
Correct. Geen toevoegingen.
2008-10-25 18:11:30 [Kevin Neelen] [reply
Deze computation is correct uitgevoerd door de student.
2008-10-27 08:07:53 [Siem Van Opstal] [reply
de student maakt juiste berekeningen en trekt de correctie conclusies

Post a new message
Dataseries X:
72.50
59.40
85.70
88.20
62.80
87.00
79.20
112.00
79.20
132.10
40.10
69.00
59.40
73.80
57.40
81.10
46.60
41.40
71.20
67.90
72.00
14.50
39.70
51.90
73.70
70.90
60.80
61.00
54.50
39.10
66.60
58.50
59.80
80.90
37.30
44.60
48.70
54.00
49.50
61.60
35.00
35.70
51.30
49.00
41.50
72.50
42.10
44.10
45.10
50.30
40.90
47.20
36.90
40.90
38.30
46.30
28.40
78.40
36.80
50.70
42.80




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 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 & 2 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=16260&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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=16260&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=16260&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'George Udny Yule' @ 72.249.76.132







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean57.70163934426232.5937024318406222.2468231651826
Geometric Mean54.3582010291127
Harmonic Mean50.8165218546228
Quadratic Mean61.0992366671751
Winsorized Mean ( 1 / 20 )57.62.3968706830027924.031334025847
Winsorized Mean ( 2 / 20 )57.03606557377052.1088870407748327.0455763969297
Winsorized Mean ( 3 / 20 )57.0114754098362.0886318610878127.2960862428591
Winsorized Mean ( 4 / 20 )56.99836065573772.0564764972215227.7165145007724
Winsorized Mean ( 5 / 20 )56.62950819672131.9721813174691328.714148995891
Winsorized Mean ( 6 / 20 )56.64918032786891.9616063771731128.8789743890955
Winsorized Mean ( 7 / 20 )56.56885245901641.9035551165851829.7174754574462
Winsorized Mean ( 8 / 20 )56.67377049180331.8870205237478530.0334679875354
Winsorized Mean ( 9 / 20 )56.6442622950821.8500827401231130.6171508260829
Winsorized Mean ( 10 / 20 )55.9557377049181.6997806425339532.9193875402075
Winsorized Mean ( 11 / 20 )56.08196721311481.6745058943300333.4916511210927
Winsorized Mean ( 12 / 20 )55.84590163934431.633746864853334.1827138834992
Winsorized Mean ( 13 / 20 )55.95245901639341.6176343899161034.5890637372612
Winsorized Mean ( 14 / 20 )55.86065573770491.5947305281188935.0282726471644
Winsorized Mean ( 15 / 20 )55.8114754098361.5397290556498336.2475951239883
Winsorized Mean ( 16 / 20 )55.9163934426231.4996123002202837.2872331297958
Winsorized Mean ( 17 / 20 )55.74918032786881.3601924947161240.9862431563437
Winsorized Mean ( 18 / 20 )55.5721311475411.2869036231328543.1828228226256
Winsorized Mean ( 19 / 20 )55.32295081967211.2007520262936146.0735852267839
Winsorized Mean ( 20 / 20 )54.47049180327870.95606589234442756.9735749799716
Trimmed Mean ( 1 / 20 )57.17288135593222.242195152727225.4986196390588
Trimmed Mean ( 2 / 20 )56.71578947368422.045694772434427.7244632180351
Trimmed Mean ( 3 / 20 )56.53818181818182.0011385495105828.2530071853393
Trimmed Mean ( 4 / 20 )56.35660377358491.9546407682493728.8322052261600
Trimmed Mean ( 5 / 20 )56.16470588235291.9081102930456529.4347271680533
Trimmed Mean ( 6 / 20 )56.04897959183671.8774872900304929.8531872303256
Trimmed Mean ( 7 / 20 )55.91914893617021.8401439791481330.3884639299025
Trimmed Mean ( 8 / 20 )55.79333333333331.8073458412542430.870313838006
Trimmed Mean ( 9 / 20 )55.63720930232561.7671921633958831.4833952157255
Trimmed Mean ( 10 / 20 )55.47073170731711.7226618791944532.2005916409181
Trimmed Mean ( 11 / 20 )55.39487179487181.7022567727432332.5420187376324
Trimmed Mean ( 12 / 20 )55.29189189189191.6776188723176832.9585538195005
Trimmed Mean ( 13 / 20 )55.21142857142861.6514102525807833.4328968135843
Trimmed Mean ( 14 / 20 )55.10606060606061.6152970185753934.1151255604132
Trimmed Mean ( 15 / 20 )551.5672796787420735.0926517749174
Trimmed Mean ( 16 / 20 )54.88620689655171.5115297778764336.31169408628
Trimmed Mean ( 17 / 20 )54.74074074074071.4382370822719738.0609994106585
Trimmed Mean ( 18 / 20 )54.5961.3753966700555939.6947303920646
Trimmed Mean ( 19 / 20 )54.45217391304351.3018969068007841.8252579206533
Trimmed Mean ( 20 / 20 )54.31904761904761.2171711748699344.6272872218260
Median54
Midrange73.3
Midmean - Weighted Average at Xnp54.46
Midmean - Weighted Average at X(n+1)p55
Midmean - Empirical Distribution Function55
Midmean - Empirical Distribution Function - Averaging55
Midmean - Empirical Distribution Function - Interpolation55
Midmean - Closest Observation54.578125
Midmean - True Basic - Statistics Graphics Toolkit55
Midmean - MS Excel (old versions)55
Number of observations61

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 57.7016393442623 & 2.59370243184062 & 22.2468231651826 \tabularnewline
Geometric Mean & 54.3582010291127 &  &  \tabularnewline
Harmonic Mean & 50.8165218546228 &  &  \tabularnewline
Quadratic Mean & 61.0992366671751 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 57.6 & 2.39687068300279 & 24.031334025847 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 57.0360655737705 & 2.10888704077483 & 27.0455763969297 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 57.011475409836 & 2.08863186108781 & 27.2960862428591 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 56.9983606557377 & 2.05647649722152 & 27.7165145007724 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 56.6295081967213 & 1.97218131746913 & 28.714148995891 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 56.6491803278689 & 1.96160637717311 & 28.8789743890955 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 56.5688524590164 & 1.90355511658518 & 29.7174754574462 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 56.6737704918033 & 1.88702052374785 & 30.0334679875354 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 56.644262295082 & 1.85008274012311 & 30.6171508260829 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 55.955737704918 & 1.69978064253395 & 32.9193875402075 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 56.0819672131148 & 1.67450589433003 & 33.4916511210927 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 55.8459016393443 & 1.6337468648533 & 34.1827138834992 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 55.9524590163934 & 1.61763438991610 & 34.5890637372612 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 55.8606557377049 & 1.59473052811889 & 35.0282726471644 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 55.811475409836 & 1.53972905564983 & 36.2475951239883 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 55.916393442623 & 1.49961230022028 & 37.2872331297958 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 55.7491803278688 & 1.36019249471612 & 40.9862431563437 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 55.572131147541 & 1.28690362313285 & 43.1828228226256 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 55.3229508196721 & 1.20075202629361 & 46.0735852267839 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 54.4704918032787 & 0.956065892344427 & 56.9735749799716 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 57.1728813559322 & 2.2421951527272 & 25.4986196390588 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 56.7157894736842 & 2.0456947724344 & 27.7244632180351 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 56.5381818181818 & 2.00113854951058 & 28.2530071853393 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 56.3566037735849 & 1.95464076824937 & 28.8322052261600 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 56.1647058823529 & 1.90811029304565 & 29.4347271680533 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 56.0489795918367 & 1.87748729003049 & 29.8531872303256 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 55.9191489361702 & 1.84014397914813 & 30.3884639299025 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 55.7933333333333 & 1.80734584125424 & 30.870313838006 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 55.6372093023256 & 1.76719216339588 & 31.4833952157255 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 55.4707317073171 & 1.72266187919445 & 32.2005916409181 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 55.3948717948718 & 1.70225677274323 & 32.5420187376324 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 55.2918918918919 & 1.67761887231768 & 32.9585538195005 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 55.2114285714286 & 1.65141025258078 & 33.4328968135843 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 55.1060606060606 & 1.61529701857539 & 34.1151255604132 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 55 & 1.56727967874207 & 35.0926517749174 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 54.8862068965517 & 1.51152977787643 & 36.31169408628 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 54.7407407407407 & 1.43823708227197 & 38.0609994106585 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 54.596 & 1.37539667005559 & 39.6947303920646 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 54.4521739130435 & 1.30189690680078 & 41.8252579206533 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 54.3190476190476 & 1.21717117486993 & 44.6272872218260 \tabularnewline
Median & 54 &  &  \tabularnewline
Midrange & 73.3 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 54.46 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 55 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 55 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 55 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 55 &  &  \tabularnewline
Midmean - Closest Observation & 54.578125 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 55 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 55 &  &  \tabularnewline
Number of observations & 61 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=16260&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]57.7016393442623[/C][C]2.59370243184062[/C][C]22.2468231651826[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]54.3582010291127[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]50.8165218546228[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]61.0992366671751[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]57.6[/C][C]2.39687068300279[/C][C]24.031334025847[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]57.0360655737705[/C][C]2.10888704077483[/C][C]27.0455763969297[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]57.011475409836[/C][C]2.08863186108781[/C][C]27.2960862428591[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]56.9983606557377[/C][C]2.05647649722152[/C][C]27.7165145007724[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]56.6295081967213[/C][C]1.97218131746913[/C][C]28.714148995891[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]56.6491803278689[/C][C]1.96160637717311[/C][C]28.8789743890955[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]56.5688524590164[/C][C]1.90355511658518[/C][C]29.7174754574462[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]56.6737704918033[/C][C]1.88702052374785[/C][C]30.0334679875354[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]56.644262295082[/C][C]1.85008274012311[/C][C]30.6171508260829[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]55.955737704918[/C][C]1.69978064253395[/C][C]32.9193875402075[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]56.0819672131148[/C][C]1.67450589433003[/C][C]33.4916511210927[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]55.8459016393443[/C][C]1.6337468648533[/C][C]34.1827138834992[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]55.9524590163934[/C][C]1.61763438991610[/C][C]34.5890637372612[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]55.8606557377049[/C][C]1.59473052811889[/C][C]35.0282726471644[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]55.811475409836[/C][C]1.53972905564983[/C][C]36.2475951239883[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]55.916393442623[/C][C]1.49961230022028[/C][C]37.2872331297958[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]55.7491803278688[/C][C]1.36019249471612[/C][C]40.9862431563437[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]55.572131147541[/C][C]1.28690362313285[/C][C]43.1828228226256[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]55.3229508196721[/C][C]1.20075202629361[/C][C]46.0735852267839[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]54.4704918032787[/C][C]0.956065892344427[/C][C]56.9735749799716[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]57.1728813559322[/C][C]2.2421951527272[/C][C]25.4986196390588[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]56.7157894736842[/C][C]2.0456947724344[/C][C]27.7244632180351[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]56.5381818181818[/C][C]2.00113854951058[/C][C]28.2530071853393[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]56.3566037735849[/C][C]1.95464076824937[/C][C]28.8322052261600[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]56.1647058823529[/C][C]1.90811029304565[/C][C]29.4347271680533[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]56.0489795918367[/C][C]1.87748729003049[/C][C]29.8531872303256[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]55.9191489361702[/C][C]1.84014397914813[/C][C]30.3884639299025[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]55.7933333333333[/C][C]1.80734584125424[/C][C]30.870313838006[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]55.6372093023256[/C][C]1.76719216339588[/C][C]31.4833952157255[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]55.4707317073171[/C][C]1.72266187919445[/C][C]32.2005916409181[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]55.3948717948718[/C][C]1.70225677274323[/C][C]32.5420187376324[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]55.2918918918919[/C][C]1.67761887231768[/C][C]32.9585538195005[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]55.2114285714286[/C][C]1.65141025258078[/C][C]33.4328968135843[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]55.1060606060606[/C][C]1.61529701857539[/C][C]34.1151255604132[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]55[/C][C]1.56727967874207[/C][C]35.0926517749174[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]54.8862068965517[/C][C]1.51152977787643[/C][C]36.31169408628[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]54.7407407407407[/C][C]1.43823708227197[/C][C]38.0609994106585[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]54.596[/C][C]1.37539667005559[/C][C]39.6947303920646[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]54.4521739130435[/C][C]1.30189690680078[/C][C]41.8252579206533[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]54.3190476190476[/C][C]1.21717117486993[/C][C]44.6272872218260[/C][/ROW]
[ROW][C]Median[/C][C]54[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]73.3[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]54.46[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]55[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]55[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]55[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]55[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]54.578125[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]55[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]55[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]61[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=16260&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=16260&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 Mean57.70163934426232.5937024318406222.2468231651826
Geometric Mean54.3582010291127
Harmonic Mean50.8165218546228
Quadratic Mean61.0992366671751
Winsorized Mean ( 1 / 20 )57.62.3968706830027924.031334025847
Winsorized Mean ( 2 / 20 )57.03606557377052.1088870407748327.0455763969297
Winsorized Mean ( 3 / 20 )57.0114754098362.0886318610878127.2960862428591
Winsorized Mean ( 4 / 20 )56.99836065573772.0564764972215227.7165145007724
Winsorized Mean ( 5 / 20 )56.62950819672131.9721813174691328.714148995891
Winsorized Mean ( 6 / 20 )56.64918032786891.9616063771731128.8789743890955
Winsorized Mean ( 7 / 20 )56.56885245901641.9035551165851829.7174754574462
Winsorized Mean ( 8 / 20 )56.67377049180331.8870205237478530.0334679875354
Winsorized Mean ( 9 / 20 )56.6442622950821.8500827401231130.6171508260829
Winsorized Mean ( 10 / 20 )55.9557377049181.6997806425339532.9193875402075
Winsorized Mean ( 11 / 20 )56.08196721311481.6745058943300333.4916511210927
Winsorized Mean ( 12 / 20 )55.84590163934431.633746864853334.1827138834992
Winsorized Mean ( 13 / 20 )55.95245901639341.6176343899161034.5890637372612
Winsorized Mean ( 14 / 20 )55.86065573770491.5947305281188935.0282726471644
Winsorized Mean ( 15 / 20 )55.8114754098361.5397290556498336.2475951239883
Winsorized Mean ( 16 / 20 )55.9163934426231.4996123002202837.2872331297958
Winsorized Mean ( 17 / 20 )55.74918032786881.3601924947161240.9862431563437
Winsorized Mean ( 18 / 20 )55.5721311475411.2869036231328543.1828228226256
Winsorized Mean ( 19 / 20 )55.32295081967211.2007520262936146.0735852267839
Winsorized Mean ( 20 / 20 )54.47049180327870.95606589234442756.9735749799716
Trimmed Mean ( 1 / 20 )57.17288135593222.242195152727225.4986196390588
Trimmed Mean ( 2 / 20 )56.71578947368422.045694772434427.7244632180351
Trimmed Mean ( 3 / 20 )56.53818181818182.0011385495105828.2530071853393
Trimmed Mean ( 4 / 20 )56.35660377358491.9546407682493728.8322052261600
Trimmed Mean ( 5 / 20 )56.16470588235291.9081102930456529.4347271680533
Trimmed Mean ( 6 / 20 )56.04897959183671.8774872900304929.8531872303256
Trimmed Mean ( 7 / 20 )55.91914893617021.8401439791481330.3884639299025
Trimmed Mean ( 8 / 20 )55.79333333333331.8073458412542430.870313838006
Trimmed Mean ( 9 / 20 )55.63720930232561.7671921633958831.4833952157255
Trimmed Mean ( 10 / 20 )55.47073170731711.7226618791944532.2005916409181
Trimmed Mean ( 11 / 20 )55.39487179487181.7022567727432332.5420187376324
Trimmed Mean ( 12 / 20 )55.29189189189191.6776188723176832.9585538195005
Trimmed Mean ( 13 / 20 )55.21142857142861.6514102525807833.4328968135843
Trimmed Mean ( 14 / 20 )55.10606060606061.6152970185753934.1151255604132
Trimmed Mean ( 15 / 20 )551.5672796787420735.0926517749174
Trimmed Mean ( 16 / 20 )54.88620689655171.5115297778764336.31169408628
Trimmed Mean ( 17 / 20 )54.74074074074071.4382370822719738.0609994106585
Trimmed Mean ( 18 / 20 )54.5961.3753966700555939.6947303920646
Trimmed Mean ( 19 / 20 )54.45217391304351.3018969068007841.8252579206533
Trimmed Mean ( 20 / 20 )54.31904761904761.2171711748699344.6272872218260
Median54
Midrange73.3
Midmean - Weighted Average at Xnp54.46
Midmean - Weighted Average at X(n+1)p55
Midmean - Empirical Distribution Function55
Midmean - Empirical Distribution Function - Averaging55
Midmean - Empirical Distribution Function - Interpolation55
Midmean - Closest Observation54.578125
Midmean - True Basic - Statistics Graphics Toolkit55
Midmean - MS Excel (old versions)55
Number of observations61



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')