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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 computationMon, 07 Mar 2016 16:00:05 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Mar/07/t1457366500c5pn3cgm1uy6h8g.htm/, Retrieved Wed, 01 May 2024 10:22:46 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=293585, Retrieved Wed, 01 May 2024 10:22:46 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact105
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2016-03-07 16:00:05] [a1d1814f81d637d5e936c79e282724ec] [Current]
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Dataseries X:
89,65
90,65
89,34
89,15
88,82
88,82
91,97
93,01
93,24
93,2
93,19
92,2
93,39
94,75
94,25
94,37
94,02
92,77
92,64
93,19
92,74
92,52
92,25
91,6
93,73
96,21
96,36
95,69
95,07
95,5
95,22
97,41
98,31
98,54
98,45
98,03
101,45
102,44
102,42
100,98
100,69
100,28
98,06
97,37
97,25
98,93
100,04
100,09
100,79
99,76
99,63
99,26
99,69
99,17
98,79
97,97
98,1
97,91
97,16
96,8
97,46
96,59
96,35
96,12
96,16
95,95
96,06
95,89
95,9
95,82
95,54
95,51




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ fisher.wessa.net

\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 & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=293585&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]'Sir Ronald Aylmer Fisher' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=293585&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=293585&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'Sir Ronald Aylmer Fisher' @ fisher.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean95.95319444444440.394906677947481242.976884926736
Geometric Mean95.8951153428367
Harmonic Mean95.8366550328056
Quadratic Mean96.0108747240529
Winsorized Mean ( 1 / 24 )95.95291666666670.394842505274243.015671780525
Winsorized Mean ( 2 / 24 )95.93513888888890.386725397891877248.070438124447
Winsorized Mean ( 3 / 24 )95.92347222222220.380985674922529251.777110101916
Winsorized Mean ( 4 / 24 )95.93013888888890.374907369522191255.876909037956
Winsorized Mean ( 5 / 24 )95.99263888888890.358123750973826268.043207488644
Winsorized Mean ( 6 / 24 )96.03763888888890.336222251943122285.637367348118
Winsorized Mean ( 7 / 24 )96.05513888888890.326456468796972294.235673267137
Winsorized Mean ( 8 / 24 )96.07513888888890.321064896804244299.239000729085
Winsorized Mean ( 9 / 24 )96.04638888888890.314041709097748305.83959425273
Winsorized Mean ( 10 / 24 )96.07416666666670.306163712253911313.799979623285
Winsorized Mean ( 11 / 24 )96.08333333333330.301669714403716318.505069437457
Winsorized Mean ( 12 / 24 )96.03833333333330.289038866510505332.26788664369
Winsorized Mean ( 13 / 24 )96.02750.285633904339618336.190832184345
Winsorized Mean ( 14 / 24 )96.02750.271088684245829354.229097636994
Winsorized Mean ( 15 / 24 )96.03583333333330.260899397654346368.095266592247
Winsorized Mean ( 16 / 24 )95.98027777777780.252805306846758379.660850379053
Winsorized Mean ( 17 / 24 )95.96138888888890.249429262881002384.72386030612
Winsorized Mean ( 18 / 24 )95.93638888888890.243000794188727394.798663968068
Winsorized Mean ( 19 / 24 )95.92055555555560.229306712555221418.3067930576
Winsorized Mean ( 20 / 24 )96.00388888888890.213372534869788449.93555026881
Winsorized Mean ( 21 / 24 )96.07972222222220.199678240024322481.172721727311
Winsorized Mean ( 22 / 24 )96.13166666666670.187061014541217513.905406225011
Winsorized Mean ( 23 / 24 )96.15083333333330.17900631540428537.136542452036
Winsorized Mean ( 24 / 24 )96.12750.140985763551703681.824161378875
Trimmed Mean ( 1 / 24 )95.96242857142860.381849017657903251.309874148742
Trimmed Mean ( 2 / 24 )95.97250.366368912113119261.955905173439
Trimmed Mean ( 3 / 24 )95.99287878787880.353127073884309271.836644333105
Trimmed Mean ( 4 / 24 )96.018906250.339884296751044282.504685176236
Trimmed Mean ( 5 / 24 )96.04467741935480.326194077651916294.440285705753
Trimmed Mean ( 6 / 24 )96.05716666666670.315209381731335304.740823826557
Trimmed Mean ( 7 / 24 )96.06120689655170.308198135292991311.686528554855
Trimmed Mean ( 8 / 24 )96.06232142857140.302078727920026318.004257002842
Trimmed Mean ( 9 / 24 )96.06018518518520.295739073563972324.813978848169
Trimmed Mean ( 10 / 24 )96.06230769230770.289398348086439331.937995940514
Trimmed Mean ( 11 / 24 )96.06060.283131527811398339.279064901556
Trimmed Mean ( 12 / 24 )96.05750.276084980878473347.927292873214
Trimmed Mean ( 13 / 24 )96.060.269815467446605356.021101788798
Trimmed Mean ( 14 / 24 )96.06409090909090.262328030487543366.198346133859
Trimmed Mean ( 15 / 24 )96.06857142857140.255778870502731375.592288916397
Trimmed Mean ( 16 / 24 )96.07250.24931335190057385.348394972104
Trimmed Mean ( 17 / 24 )96.08342105263160.242326407288572396.504128987526
Trimmed Mean ( 18 / 24 )96.09777777777780.233403088590679411.724533544221
Trimmed Mean ( 19 / 24 )96.11676470588230.222543921274652431.900202689697
Trimmed Mean ( 20 / 24 )96.140.211041484226481455.550245736646
Trimmed Mean ( 21 / 24 )96.15633333333330.199654001478842481.614856807783
Trimmed Mean ( 22 / 24 )96.16571428571430.187586613907574512.646996939219
Trimmed Mean ( 23 / 24 )96.170.173988505367452552.737663887021
Trimmed Mean ( 24 / 24 )96.17250.155858131794195617.051538427216
Median96.09
Midrange95.63
Midmean - Weighted Average at Xnp96.0194594594595
Midmean - Weighted Average at X(n+1)p96.0977777777778
Midmean - Empirical Distribution Function96.0194594594595
Midmean - Empirical Distribution Function - Averaging96.0977777777778
Midmean - Empirical Distribution Function - Interpolation96.0977777777778
Midmean - Closest Observation96.0194594594595
Midmean - True Basic - Statistics Graphics Toolkit96.0977777777778
Midmean - MS Excel (old versions)96.0834210526316
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 95.9531944444444 & 0.394906677947481 & 242.976884926736 \tabularnewline
Geometric Mean & 95.8951153428367 &  &  \tabularnewline
Harmonic Mean & 95.8366550328056 &  &  \tabularnewline
Quadratic Mean & 96.0108747240529 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 95.9529166666667 & 0.394842505274 & 243.015671780525 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 95.9351388888889 & 0.386725397891877 & 248.070438124447 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 95.9234722222222 & 0.380985674922529 & 251.777110101916 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 95.9301388888889 & 0.374907369522191 & 255.876909037956 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 95.9926388888889 & 0.358123750973826 & 268.043207488644 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 96.0376388888889 & 0.336222251943122 & 285.637367348118 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 96.0551388888889 & 0.326456468796972 & 294.235673267137 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 96.0751388888889 & 0.321064896804244 & 299.239000729085 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 96.0463888888889 & 0.314041709097748 & 305.83959425273 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 96.0741666666667 & 0.306163712253911 & 313.799979623285 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 96.0833333333333 & 0.301669714403716 & 318.505069437457 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 96.0383333333333 & 0.289038866510505 & 332.26788664369 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 96.0275 & 0.285633904339618 & 336.190832184345 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 96.0275 & 0.271088684245829 & 354.229097636994 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 96.0358333333333 & 0.260899397654346 & 368.095266592247 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 95.9802777777778 & 0.252805306846758 & 379.660850379053 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 95.9613888888889 & 0.249429262881002 & 384.72386030612 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 95.9363888888889 & 0.243000794188727 & 394.798663968068 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 95.9205555555556 & 0.229306712555221 & 418.3067930576 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 96.0038888888889 & 0.213372534869788 & 449.93555026881 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 96.0797222222222 & 0.199678240024322 & 481.172721727311 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 96.1316666666667 & 0.187061014541217 & 513.905406225011 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 96.1508333333333 & 0.17900631540428 & 537.136542452036 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 96.1275 & 0.140985763551703 & 681.824161378875 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 95.9624285714286 & 0.381849017657903 & 251.309874148742 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 95.9725 & 0.366368912113119 & 261.955905173439 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 95.9928787878788 & 0.353127073884309 & 271.836644333105 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 96.01890625 & 0.339884296751044 & 282.504685176236 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 96.0446774193548 & 0.326194077651916 & 294.440285705753 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 96.0571666666667 & 0.315209381731335 & 304.740823826557 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 96.0612068965517 & 0.308198135292991 & 311.686528554855 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 96.0623214285714 & 0.302078727920026 & 318.004257002842 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 96.0601851851852 & 0.295739073563972 & 324.813978848169 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 96.0623076923077 & 0.289398348086439 & 331.937995940514 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 96.0606 & 0.283131527811398 & 339.279064901556 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 96.0575 & 0.276084980878473 & 347.927292873214 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 96.06 & 0.269815467446605 & 356.021101788798 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 96.0640909090909 & 0.262328030487543 & 366.198346133859 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 96.0685714285714 & 0.255778870502731 & 375.592288916397 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 96.0725 & 0.24931335190057 & 385.348394972104 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 96.0834210526316 & 0.242326407288572 & 396.504128987526 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 96.0977777777778 & 0.233403088590679 & 411.724533544221 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 96.1167647058823 & 0.222543921274652 & 431.900202689697 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 96.14 & 0.211041484226481 & 455.550245736646 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 96.1563333333333 & 0.199654001478842 & 481.614856807783 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 96.1657142857143 & 0.187586613907574 & 512.646996939219 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 96.17 & 0.173988505367452 & 552.737663887021 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 96.1725 & 0.155858131794195 & 617.051538427216 \tabularnewline
Median & 96.09 &  &  \tabularnewline
Midrange & 95.63 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 96.0194594594595 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 96.0977777777778 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 96.0194594594595 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 96.0977777777778 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 96.0977777777778 &  &  \tabularnewline
Midmean - Closest Observation & 96.0194594594595 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 96.0977777777778 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 96.0834210526316 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=293585&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]95.9531944444444[/C][C]0.394906677947481[/C][C]242.976884926736[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]95.8951153428367[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]95.8366550328056[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]96.0108747240529[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]95.9529166666667[/C][C]0.394842505274[/C][C]243.015671780525[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]95.9351388888889[/C][C]0.386725397891877[/C][C]248.070438124447[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]95.9234722222222[/C][C]0.380985674922529[/C][C]251.777110101916[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]95.9301388888889[/C][C]0.374907369522191[/C][C]255.876909037956[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]95.9926388888889[/C][C]0.358123750973826[/C][C]268.043207488644[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]96.0376388888889[/C][C]0.336222251943122[/C][C]285.637367348118[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]96.0551388888889[/C][C]0.326456468796972[/C][C]294.235673267137[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]96.0751388888889[/C][C]0.321064896804244[/C][C]299.239000729085[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]96.0463888888889[/C][C]0.314041709097748[/C][C]305.83959425273[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]96.0741666666667[/C][C]0.306163712253911[/C][C]313.799979623285[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]96.0833333333333[/C][C]0.301669714403716[/C][C]318.505069437457[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]96.0383333333333[/C][C]0.289038866510505[/C][C]332.26788664369[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]96.0275[/C][C]0.285633904339618[/C][C]336.190832184345[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]96.0275[/C][C]0.271088684245829[/C][C]354.229097636994[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]96.0358333333333[/C][C]0.260899397654346[/C][C]368.095266592247[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]95.9802777777778[/C][C]0.252805306846758[/C][C]379.660850379053[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]95.9613888888889[/C][C]0.249429262881002[/C][C]384.72386030612[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]95.9363888888889[/C][C]0.243000794188727[/C][C]394.798663968068[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]95.9205555555556[/C][C]0.229306712555221[/C][C]418.3067930576[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]96.0038888888889[/C][C]0.213372534869788[/C][C]449.93555026881[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]96.0797222222222[/C][C]0.199678240024322[/C][C]481.172721727311[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]96.1316666666667[/C][C]0.187061014541217[/C][C]513.905406225011[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]96.1508333333333[/C][C]0.17900631540428[/C][C]537.136542452036[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]96.1275[/C][C]0.140985763551703[/C][C]681.824161378875[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]95.9624285714286[/C][C]0.381849017657903[/C][C]251.309874148742[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]95.9725[/C][C]0.366368912113119[/C][C]261.955905173439[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]95.9928787878788[/C][C]0.353127073884309[/C][C]271.836644333105[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]96.01890625[/C][C]0.339884296751044[/C][C]282.504685176236[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]96.0446774193548[/C][C]0.326194077651916[/C][C]294.440285705753[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]96.0571666666667[/C][C]0.315209381731335[/C][C]304.740823826557[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]96.0612068965517[/C][C]0.308198135292991[/C][C]311.686528554855[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]96.0623214285714[/C][C]0.302078727920026[/C][C]318.004257002842[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]96.0601851851852[/C][C]0.295739073563972[/C][C]324.813978848169[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]96.0623076923077[/C][C]0.289398348086439[/C][C]331.937995940514[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]96.0606[/C][C]0.283131527811398[/C][C]339.279064901556[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]96.0575[/C][C]0.276084980878473[/C][C]347.927292873214[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]96.06[/C][C]0.269815467446605[/C][C]356.021101788798[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]96.0640909090909[/C][C]0.262328030487543[/C][C]366.198346133859[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]96.0685714285714[/C][C]0.255778870502731[/C][C]375.592288916397[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]96.0725[/C][C]0.24931335190057[/C][C]385.348394972104[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]96.0834210526316[/C][C]0.242326407288572[/C][C]396.504128987526[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]96.0977777777778[/C][C]0.233403088590679[/C][C]411.724533544221[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]96.1167647058823[/C][C]0.222543921274652[/C][C]431.900202689697[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]96.14[/C][C]0.211041484226481[/C][C]455.550245736646[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]96.1563333333333[/C][C]0.199654001478842[/C][C]481.614856807783[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]96.1657142857143[/C][C]0.187586613907574[/C][C]512.646996939219[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]96.17[/C][C]0.173988505367452[/C][C]552.737663887021[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]96.1725[/C][C]0.155858131794195[/C][C]617.051538427216[/C][/ROW]
[ROW][C]Median[/C][C]96.09[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]95.63[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]96.0194594594595[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]96.0977777777778[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]96.0194594594595[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]96.0977777777778[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]96.0977777777778[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]96.0194594594595[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]96.0977777777778[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]96.0834210526316[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]72[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=293585&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=293585&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 Mean95.95319444444440.394906677947481242.976884926736
Geometric Mean95.8951153428367
Harmonic Mean95.8366550328056
Quadratic Mean96.0108747240529
Winsorized Mean ( 1 / 24 )95.95291666666670.394842505274243.015671780525
Winsorized Mean ( 2 / 24 )95.93513888888890.386725397891877248.070438124447
Winsorized Mean ( 3 / 24 )95.92347222222220.380985674922529251.777110101916
Winsorized Mean ( 4 / 24 )95.93013888888890.374907369522191255.876909037956
Winsorized Mean ( 5 / 24 )95.99263888888890.358123750973826268.043207488644
Winsorized Mean ( 6 / 24 )96.03763888888890.336222251943122285.637367348118
Winsorized Mean ( 7 / 24 )96.05513888888890.326456468796972294.235673267137
Winsorized Mean ( 8 / 24 )96.07513888888890.321064896804244299.239000729085
Winsorized Mean ( 9 / 24 )96.04638888888890.314041709097748305.83959425273
Winsorized Mean ( 10 / 24 )96.07416666666670.306163712253911313.799979623285
Winsorized Mean ( 11 / 24 )96.08333333333330.301669714403716318.505069437457
Winsorized Mean ( 12 / 24 )96.03833333333330.289038866510505332.26788664369
Winsorized Mean ( 13 / 24 )96.02750.285633904339618336.190832184345
Winsorized Mean ( 14 / 24 )96.02750.271088684245829354.229097636994
Winsorized Mean ( 15 / 24 )96.03583333333330.260899397654346368.095266592247
Winsorized Mean ( 16 / 24 )95.98027777777780.252805306846758379.660850379053
Winsorized Mean ( 17 / 24 )95.96138888888890.249429262881002384.72386030612
Winsorized Mean ( 18 / 24 )95.93638888888890.243000794188727394.798663968068
Winsorized Mean ( 19 / 24 )95.92055555555560.229306712555221418.3067930576
Winsorized Mean ( 20 / 24 )96.00388888888890.213372534869788449.93555026881
Winsorized Mean ( 21 / 24 )96.07972222222220.199678240024322481.172721727311
Winsorized Mean ( 22 / 24 )96.13166666666670.187061014541217513.905406225011
Winsorized Mean ( 23 / 24 )96.15083333333330.17900631540428537.136542452036
Winsorized Mean ( 24 / 24 )96.12750.140985763551703681.824161378875
Trimmed Mean ( 1 / 24 )95.96242857142860.381849017657903251.309874148742
Trimmed Mean ( 2 / 24 )95.97250.366368912113119261.955905173439
Trimmed Mean ( 3 / 24 )95.99287878787880.353127073884309271.836644333105
Trimmed Mean ( 4 / 24 )96.018906250.339884296751044282.504685176236
Trimmed Mean ( 5 / 24 )96.04467741935480.326194077651916294.440285705753
Trimmed Mean ( 6 / 24 )96.05716666666670.315209381731335304.740823826557
Trimmed Mean ( 7 / 24 )96.06120689655170.308198135292991311.686528554855
Trimmed Mean ( 8 / 24 )96.06232142857140.302078727920026318.004257002842
Trimmed Mean ( 9 / 24 )96.06018518518520.295739073563972324.813978848169
Trimmed Mean ( 10 / 24 )96.06230769230770.289398348086439331.937995940514
Trimmed Mean ( 11 / 24 )96.06060.283131527811398339.279064901556
Trimmed Mean ( 12 / 24 )96.05750.276084980878473347.927292873214
Trimmed Mean ( 13 / 24 )96.060.269815467446605356.021101788798
Trimmed Mean ( 14 / 24 )96.06409090909090.262328030487543366.198346133859
Trimmed Mean ( 15 / 24 )96.06857142857140.255778870502731375.592288916397
Trimmed Mean ( 16 / 24 )96.07250.24931335190057385.348394972104
Trimmed Mean ( 17 / 24 )96.08342105263160.242326407288572396.504128987526
Trimmed Mean ( 18 / 24 )96.09777777777780.233403088590679411.724533544221
Trimmed Mean ( 19 / 24 )96.11676470588230.222543921274652431.900202689697
Trimmed Mean ( 20 / 24 )96.140.211041484226481455.550245736646
Trimmed Mean ( 21 / 24 )96.15633333333330.199654001478842481.614856807783
Trimmed Mean ( 22 / 24 )96.16571428571430.187586613907574512.646996939219
Trimmed Mean ( 23 / 24 )96.170.173988505367452552.737663887021
Trimmed Mean ( 24 / 24 )96.17250.155858131794195617.051538427216
Median96.09
Midrange95.63
Midmean - Weighted Average at Xnp96.0194594594595
Midmean - Weighted Average at X(n+1)p96.0977777777778
Midmean - Empirical Distribution Function96.0194594594595
Midmean - Empirical Distribution Function - Averaging96.0977777777778
Midmean - Empirical Distribution Function - Interpolation96.0977777777778
Midmean - Closest Observation96.0194594594595
Midmean - True Basic - Statistics Graphics Toolkit96.0977777777778
Midmean - MS Excel (old versions)96.0834210526316
Number of observations72



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')