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Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationThu, 18 Dec 2008 04:31:37 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/Dec/18/t122959994454elingjm9oy0vo.htm/, Retrieved Sat, 11 May 2024 21:05:49 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=34658, Retrieved Sat, 11 May 2024 21:05:49 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact156
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Paper - Central T...] [2008-12-18 11:31:37] [07b7cf1321bc38017c2c7efcf91ca696] [Current]
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Dataseries X:
20,72
21,45
22,09
21,53
23,35
23,57
26,42
25,21
26,44
29,34
29,40
33,05
28,38
26,01
29,31
30,36
35,75
36,15
34,21
37,91
38,70
42,12
42,16
39,80
37,36
38,35
42,60
41,25
42,16
46,94
47,43
47,06
50,18
50,13
43,23
40,04
40,37
42,21
37,00
39,74
42,68
46,29
46,97
48,73
52,37
50,05
54,04
57,78
64,72
63,41
64,36
66,03
72,14
76,60
86,97
93,48
95,59
81,89
70,55
50,38
36,25




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 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 & 4 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=34658&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]4 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=34658&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=34658&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 time4 seconds
R Server'George Udny Yule' @ 72.249.76.132







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean44.76655737704922.2864793000063919.5788159450751
Geometric Mean41.6479650825918
Harmonic Mean38.8650187216551
Quadratic Mean48.1427451933736
Winsorized Mean ( 1 / 20 )44.74393442622952.271816240725119.6952260592822
Winsorized Mean ( 2 / 20 )44.53311475409842.198815261487920.2532316079904
Winsorized Mean ( 3 / 20 )44.31081967213112.1168014495413720.9329125703932
Winsorized Mean ( 4 / 20 )44.04655737704922.0040665745576821.9785899012715
Winsorized Mean ( 5 / 20 )43.69901639344261.9058804127777122.9285195967536
Winsorized Mean ( 6 / 20 )43.70393442622951.8396827250616023.7562346109251
Winsorized Mean ( 7 / 20 )43.27704918032791.7032152709652725.4090307420748
Winsorized Mean ( 8 / 20 )43.15901639344261.6563752265048926.0563039719643
Winsorized Mean ( 9 / 20 )43.10885245901641.6443955173244526.2156227044194
Winsorized Mean ( 10 / 20 )43.27114754098361.5586270597502927.7623484529495
Winsorized Mean ( 11 / 20 )42.42360655737701.3230404425869232.0652379109642
Winsorized Mean ( 12 / 20 )41.69377049180331.1866900554258935.1345073645536
Winsorized Mean ( 13 / 20 )41.35065573770491.1244804232807536.7731219517912
Winsorized Mean ( 14 / 20 )41.1142622950821.0132474023193540.5767260798995
Winsorized Mean ( 15 / 20 )41.72655737704920.89326902810453246.7121953904421
Winsorized Mean ( 16 / 20 )42.01770491803280.84303991937072749.840706178417
Winsorized Mean ( 17 / 20 )42.42459016393440.77542019540440854.7117426336937
Winsorized Mean ( 18 / 20 )42.15311475409840.69580042130143760.5821920533685
Winsorized Mean ( 19 / 20 )41.77934426229510.6289930311781166.4225868831043
Winsorized Mean ( 20 / 20 )41.90393442622950.57534619080393472.8325573298346
Trimmed Mean ( 1 / 20 )44.31271186440682.1596847215426020.5181392554166
Trimmed Mean ( 2 / 20 )43.85122807017542.0187682829727721.7217738360748
Trimmed Mean ( 3 / 20 )43.47309090909091.8930519579069122.9645524136368
Trimmed Mean ( 4 / 20 )43.15169811320751.7772201662406324.2804459081098
Trimmed Mean ( 5 / 20 )42.88411764705881.6792049980885425.5383456432504
Trimmed Mean ( 6 / 20 )42.68122448979591.5917718818552726.8136565146819
Trimmed Mean ( 7 / 20 )42.461.5016393447010228.2757641838785
Trimmed Mean ( 8 / 20 )42.30177777777781.4298168028760729.5854529704
Trimmed Mean ( 9 / 20 )42.14976744186051.3501288847205731.2190694672708
Trimmed Mean ( 10 / 20 )41.99121951219511.2471777014192133.6689947746914
Trimmed Mean ( 11 / 20 )41.79102564102561.1338697901709536.8569883449535
Trimmed Mean ( 12 / 20 )41.69621621621621.0589222204542139.3760895850606
Trimmed Mean ( 13 / 20 )41.69657142857140.9993898090315741.7220298343609
Trimmed Mean ( 14 / 20 )41.74575757575760.93508051734651644.6440245533291
Trimmed Mean ( 15 / 20 )41.83451612903230.87921688502058947.5815658704651
Trimmed Mean ( 16 / 20 )41.84965517241380.83937087670454649.8583597952787
Trimmed Mean ( 17 / 20 )41.82592592592590.79631062731422752.5246361046256
Trimmed Mean ( 18 / 20 )41.740.75322506596634255.4150437710807
Trimmed Mean ( 19 / 20 )41.67913043478260.71711899251400458.1202434601099
Trimmed Mean ( 20 / 20 )41.66380952380950.68602112843711460.7325456851855
Median42.12
Midrange58.155
Midmean - Weighted Average at Xnp41.5563333333333
Midmean - Weighted Average at X(n+1)p41.8345161290323
Midmean - Empirical Distribution Function41.8345161290323
Midmean - Empirical Distribution Function - Averaging41.8345161290323
Midmean - Empirical Distribution Function - Interpolation41.8345161290323
Midmean - Closest Observation41.4759375
Midmean - True Basic - Statistics Graphics Toolkit41.8345161290323
Midmean - MS Excel (old versions)41.8345161290323
Number of observations61

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 44.7665573770492 & 2.28647930000639 & 19.5788159450751 \tabularnewline
Geometric Mean & 41.6479650825918 &  &  \tabularnewline
Harmonic Mean & 38.8650187216551 &  &  \tabularnewline
Quadratic Mean & 48.1427451933736 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 44.7439344262295 & 2.2718162407251 & 19.6952260592822 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 44.5331147540984 & 2.1988152614879 & 20.2532316079904 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 44.3108196721311 & 2.11680144954137 & 20.9329125703932 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 44.0465573770492 & 2.00406657455768 & 21.9785899012715 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 43.6990163934426 & 1.90588041277771 & 22.9285195967536 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 43.7039344262295 & 1.83968272506160 & 23.7562346109251 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 43.2770491803279 & 1.70321527096527 & 25.4090307420748 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 43.1590163934426 & 1.65637522650489 & 26.0563039719643 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 43.1088524590164 & 1.64439551732445 & 26.2156227044194 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 43.2711475409836 & 1.55862705975029 & 27.7623484529495 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 42.4236065573770 & 1.32304044258692 & 32.0652379109642 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 41.6937704918033 & 1.18669005542589 & 35.1345073645536 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 41.3506557377049 & 1.12448042328075 & 36.7731219517912 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 41.114262295082 & 1.01324740231935 & 40.5767260798995 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 41.7265573770492 & 0.893269028104532 & 46.7121953904421 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 42.0177049180328 & 0.843039919370727 & 49.840706178417 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 42.4245901639344 & 0.775420195404408 & 54.7117426336937 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 42.1531147540984 & 0.695800421301437 & 60.5821920533685 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 41.7793442622951 & 0.62899303117811 & 66.4225868831043 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 41.9039344262295 & 0.575346190803934 & 72.8325573298346 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 44.3127118644068 & 2.15968472154260 & 20.5181392554166 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 43.8512280701754 & 2.01876828297277 & 21.7217738360748 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 43.4730909090909 & 1.89305195790691 & 22.9645524136368 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 43.1516981132075 & 1.77722016624063 & 24.2804459081098 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 42.8841176470588 & 1.67920499808854 & 25.5383456432504 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 42.6812244897959 & 1.59177188185527 & 26.8136565146819 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 42.46 & 1.50163934470102 & 28.2757641838785 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 42.3017777777778 & 1.42981680287607 & 29.5854529704 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 42.1497674418605 & 1.35012888472057 & 31.2190694672708 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 41.9912195121951 & 1.24717770141921 & 33.6689947746914 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 41.7910256410256 & 1.13386979017095 & 36.8569883449535 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 41.6962162162162 & 1.05892222045421 & 39.3760895850606 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 41.6965714285714 & 0.99938980903157 & 41.7220298343609 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 41.7457575757576 & 0.935080517346516 & 44.6440245533291 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 41.8345161290323 & 0.879216885020589 & 47.5815658704651 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 41.8496551724138 & 0.839370876704546 & 49.8583597952787 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 41.8259259259259 & 0.796310627314227 & 52.5246361046256 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 41.74 & 0.753225065966342 & 55.4150437710807 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 41.6791304347826 & 0.717118992514004 & 58.1202434601099 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 41.6638095238095 & 0.686021128437114 & 60.7325456851855 \tabularnewline
Median & 42.12 &  &  \tabularnewline
Midrange & 58.155 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 41.5563333333333 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 41.8345161290323 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 41.8345161290323 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 41.8345161290323 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 41.8345161290323 &  &  \tabularnewline
Midmean - Closest Observation & 41.4759375 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 41.8345161290323 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 41.8345161290323 &  &  \tabularnewline
Number of observations & 61 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=34658&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]44.7665573770492[/C][C]2.28647930000639[/C][C]19.5788159450751[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]41.6479650825918[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]38.8650187216551[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]48.1427451933736[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]44.7439344262295[/C][C]2.2718162407251[/C][C]19.6952260592822[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]44.5331147540984[/C][C]2.1988152614879[/C][C]20.2532316079904[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]44.3108196721311[/C][C]2.11680144954137[/C][C]20.9329125703932[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]44.0465573770492[/C][C]2.00406657455768[/C][C]21.9785899012715[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]43.6990163934426[/C][C]1.90588041277771[/C][C]22.9285195967536[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]43.7039344262295[/C][C]1.83968272506160[/C][C]23.7562346109251[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]43.2770491803279[/C][C]1.70321527096527[/C][C]25.4090307420748[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]43.1590163934426[/C][C]1.65637522650489[/C][C]26.0563039719643[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]43.1088524590164[/C][C]1.64439551732445[/C][C]26.2156227044194[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]43.2711475409836[/C][C]1.55862705975029[/C][C]27.7623484529495[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]42.4236065573770[/C][C]1.32304044258692[/C][C]32.0652379109642[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]41.6937704918033[/C][C]1.18669005542589[/C][C]35.1345073645536[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]41.3506557377049[/C][C]1.12448042328075[/C][C]36.7731219517912[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]41.114262295082[/C][C]1.01324740231935[/C][C]40.5767260798995[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]41.7265573770492[/C][C]0.893269028104532[/C][C]46.7121953904421[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]42.0177049180328[/C][C]0.843039919370727[/C][C]49.840706178417[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]42.4245901639344[/C][C]0.775420195404408[/C][C]54.7117426336937[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]42.1531147540984[/C][C]0.695800421301437[/C][C]60.5821920533685[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]41.7793442622951[/C][C]0.62899303117811[/C][C]66.4225868831043[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]41.9039344262295[/C][C]0.575346190803934[/C][C]72.8325573298346[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]44.3127118644068[/C][C]2.15968472154260[/C][C]20.5181392554166[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]43.8512280701754[/C][C]2.01876828297277[/C][C]21.7217738360748[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]43.4730909090909[/C][C]1.89305195790691[/C][C]22.9645524136368[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]43.1516981132075[/C][C]1.77722016624063[/C][C]24.2804459081098[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]42.8841176470588[/C][C]1.67920499808854[/C][C]25.5383456432504[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]42.6812244897959[/C][C]1.59177188185527[/C][C]26.8136565146819[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]42.46[/C][C]1.50163934470102[/C][C]28.2757641838785[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]42.3017777777778[/C][C]1.42981680287607[/C][C]29.5854529704[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]42.1497674418605[/C][C]1.35012888472057[/C][C]31.2190694672708[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]41.9912195121951[/C][C]1.24717770141921[/C][C]33.6689947746914[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]41.7910256410256[/C][C]1.13386979017095[/C][C]36.8569883449535[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]41.6962162162162[/C][C]1.05892222045421[/C][C]39.3760895850606[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]41.6965714285714[/C][C]0.99938980903157[/C][C]41.7220298343609[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]41.7457575757576[/C][C]0.935080517346516[/C][C]44.6440245533291[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]41.8345161290323[/C][C]0.879216885020589[/C][C]47.5815658704651[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]41.8496551724138[/C][C]0.839370876704546[/C][C]49.8583597952787[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]41.8259259259259[/C][C]0.796310627314227[/C][C]52.5246361046256[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]41.74[/C][C]0.753225065966342[/C][C]55.4150437710807[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]41.6791304347826[/C][C]0.717118992514004[/C][C]58.1202434601099[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]41.6638095238095[/C][C]0.686021128437114[/C][C]60.7325456851855[/C][/ROW]
[ROW][C]Median[/C][C]42.12[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]58.155[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]41.5563333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]41.8345161290323[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]41.8345161290323[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]41.8345161290323[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]41.8345161290323[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]41.4759375[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]41.8345161290323[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]41.8345161290323[/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=34658&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=34658&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 Mean44.76655737704922.2864793000063919.5788159450751
Geometric Mean41.6479650825918
Harmonic Mean38.8650187216551
Quadratic Mean48.1427451933736
Winsorized Mean ( 1 / 20 )44.74393442622952.271816240725119.6952260592822
Winsorized Mean ( 2 / 20 )44.53311475409842.198815261487920.2532316079904
Winsorized Mean ( 3 / 20 )44.31081967213112.1168014495413720.9329125703932
Winsorized Mean ( 4 / 20 )44.04655737704922.0040665745576821.9785899012715
Winsorized Mean ( 5 / 20 )43.69901639344261.9058804127777122.9285195967536
Winsorized Mean ( 6 / 20 )43.70393442622951.8396827250616023.7562346109251
Winsorized Mean ( 7 / 20 )43.27704918032791.7032152709652725.4090307420748
Winsorized Mean ( 8 / 20 )43.15901639344261.6563752265048926.0563039719643
Winsorized Mean ( 9 / 20 )43.10885245901641.6443955173244526.2156227044194
Winsorized Mean ( 10 / 20 )43.27114754098361.5586270597502927.7623484529495
Winsorized Mean ( 11 / 20 )42.42360655737701.3230404425869232.0652379109642
Winsorized Mean ( 12 / 20 )41.69377049180331.1866900554258935.1345073645536
Winsorized Mean ( 13 / 20 )41.35065573770491.1244804232807536.7731219517912
Winsorized Mean ( 14 / 20 )41.1142622950821.0132474023193540.5767260798995
Winsorized Mean ( 15 / 20 )41.72655737704920.89326902810453246.7121953904421
Winsorized Mean ( 16 / 20 )42.01770491803280.84303991937072749.840706178417
Winsorized Mean ( 17 / 20 )42.42459016393440.77542019540440854.7117426336937
Winsorized Mean ( 18 / 20 )42.15311475409840.69580042130143760.5821920533685
Winsorized Mean ( 19 / 20 )41.77934426229510.6289930311781166.4225868831043
Winsorized Mean ( 20 / 20 )41.90393442622950.57534619080393472.8325573298346
Trimmed Mean ( 1 / 20 )44.31271186440682.1596847215426020.5181392554166
Trimmed Mean ( 2 / 20 )43.85122807017542.0187682829727721.7217738360748
Trimmed Mean ( 3 / 20 )43.47309090909091.8930519579069122.9645524136368
Trimmed Mean ( 4 / 20 )43.15169811320751.7772201662406324.2804459081098
Trimmed Mean ( 5 / 20 )42.88411764705881.6792049980885425.5383456432504
Trimmed Mean ( 6 / 20 )42.68122448979591.5917718818552726.8136565146819
Trimmed Mean ( 7 / 20 )42.461.5016393447010228.2757641838785
Trimmed Mean ( 8 / 20 )42.30177777777781.4298168028760729.5854529704
Trimmed Mean ( 9 / 20 )42.14976744186051.3501288847205731.2190694672708
Trimmed Mean ( 10 / 20 )41.99121951219511.2471777014192133.6689947746914
Trimmed Mean ( 11 / 20 )41.79102564102561.1338697901709536.8569883449535
Trimmed Mean ( 12 / 20 )41.69621621621621.0589222204542139.3760895850606
Trimmed Mean ( 13 / 20 )41.69657142857140.9993898090315741.7220298343609
Trimmed Mean ( 14 / 20 )41.74575757575760.93508051734651644.6440245533291
Trimmed Mean ( 15 / 20 )41.83451612903230.87921688502058947.5815658704651
Trimmed Mean ( 16 / 20 )41.84965517241380.83937087670454649.8583597952787
Trimmed Mean ( 17 / 20 )41.82592592592590.79631062731422752.5246361046256
Trimmed Mean ( 18 / 20 )41.740.75322506596634255.4150437710807
Trimmed Mean ( 19 / 20 )41.67913043478260.71711899251400458.1202434601099
Trimmed Mean ( 20 / 20 )41.66380952380950.68602112843711460.7325456851855
Median42.12
Midrange58.155
Midmean - Weighted Average at Xnp41.5563333333333
Midmean - Weighted Average at X(n+1)p41.8345161290323
Midmean - Empirical Distribution Function41.8345161290323
Midmean - Empirical Distribution Function - Averaging41.8345161290323
Midmean - Empirical Distribution Function - Interpolation41.8345161290323
Midmean - Closest Observation41.4759375
Midmean - True Basic - Statistics Graphics Toolkit41.8345161290323
Midmean - MS Excel (old versions)41.8345161290323
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')