Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationWed, 26 May 2010 19:38:37 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/May/26/t1274902745jze604zmtx1qyw3.htm/, Retrieved Fri, 03 May 2024 04:04:20 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=76552, Retrieved Fri, 03 May 2024 04:04:20 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP1W52
Estimated Impact119
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Standard Deviation-Mean Plot] [] [2010-05-26 19:08:03] [5a3034bcadf7735f2909fd8cdba599d5]
- RMPD    [Central Tendency] [] [2010-05-26 19:38:37] [ac302f869d0778eba7cafda3b14e71eb] [Current]
Feedback Forum

Post a new message
Dataseries X:
70,5
70,65
70,71
15,80
170,99
15,26
17,21
16,97
16,80
18,37
18,53
18,708
18,73
18,63
19,15
19,76
20,02
20,26
20,32
20,52
20,81
21,26
22,15
23,05
270,01
270,69
70,38
26,33
27,36
28,55
30,10
32,20
36,28
700,91
7070,66
707,83
709,97
52,20
55,67
59,92
65,15
70,17
770,6
78,23
79,27
80,707
81,701
83,97
86,83
89,61
91,79
970,32
96,56
97,98
100,00
101,63
102,60
103,75
106,39
109,02
110,81
112,57
1170,93
118,13
120,7
122,707
127,97
127,87




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=76552&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=76552&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=76552&T=0

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean239.590926470588105.7624311530682.26536893922032
Geometric Mean69.3390111210262
Harmonic Mean41.1465981930549
Quadratic Mean898.245604250496
Winsorized Mean ( 1 / 22 )152.83813235294131.96068226218174.78206726311943
Winsorized Mean ( 2 / 22 )146.9672529.31216070985575.01386613749646
Winsorized Mean ( 3 / 22 )138.16357352941225.8403493181295.34681523954784
Winsorized Mean ( 4 / 22 )134.61122058823524.56382191921055.48006010754217
Winsorized Mean ( 5 / 22 )134.53916176470624.50278226428155.49077081588519
Winsorized Mean ( 6 / 22 )133.94269117647124.28880556952955.51458534233165
Winsorized Mean ( 7 / 22 )89.66563235294129.771949191995049.17581851800798
Winsorized Mean ( 8 / 22 )89.59480882352949.748845232740669.19029963904165
Winsorized Mean ( 9 / 22 )76.49213235294126.423379569194811.9083936312563
Winsorized Mean ( 10 / 22 )70.22742647058825.1753431269107713.5696174627378
Winsorized Mean ( 11 / 22 )70.30992647058835.1581646710882813.6308029995006
Winsorized Mean ( 12 / 22 )69.44469117647065.0031141151828913.8802932688918
Winsorized Mean ( 13 / 22 )69.10688235294124.9359268874407414.000791326302
Winsorized Mean ( 14 / 22 )68.59011764705884.8525037980384714.1349951492640
Winsorized Mean ( 15 / 22 )67.40776470588244.6637497477764414.4535552616263
Winsorized Mean ( 16 / 22 )67.06188235294124.5941443540826914.5972518894286
Winsorized Mean ( 17 / 22 )66.72688235294124.5141420622017414.7817417869201
Winsorized Mean ( 18 / 22 )66.2662941176474.3824781165045515.1207358841305
Winsorized Mean ( 19 / 22 )65.78011764705884.2450407301856115.4957565375781
Winsorized Mean ( 20 / 22 )66.40658823529414.0563127212473216.3711707648798
Winsorized Mean ( 21 / 22 )66.42511764705883.9697250727220416.732926444579
Winsorized Mean ( 22 / 22 )66.28276470588243.8438176434367217.2439930440143
Trimmed Mean ( 1 / 22 )139.48883333333328.91525544610594.82405675416983
Trimmed Mean ( 2 / 22 )125.30520312524.87463427051455.03746916486456
Trimmed Mean ( 3 / 22 )113.42601612903221.57358686353245.25763364462891
Trimmed Mean ( 4 / 22 )104.08071666666719.26470112536845.40266448928242
Trimmed Mean ( 5 / 22 )95.132120689655216.81275477745825.65833035388134
Trimmed Mean ( 6 / 22 )85.561839285714313.33974907294276.41405163004611
Trimmed Mean ( 7 / 22 )75.40783333333337.4621896873467410.1053224981936
Trimmed Mean ( 8 / 22 )72.74428846153856.6602713112280810.9221208960218
Trimmed Mean ( 9 / 22 )69.87975.5474451039580912.5967357387892
Trimmed Mean ( 10 / 22 )68.83885416666675.2636631872610313.0781267185310
Trimmed Mean ( 11 / 22 )68.63358695652175.2261726098917413.1326674566042
Trimmed Mean ( 12 / 22 )68.39806818181825.1734012929650613.2211023867079
Trimmed Mean ( 13 / 22 )68.25685714285715.1316527074008513.3011450764034
Trimmed Mean ( 14 / 22 )68.14575.0821728589457813.4087725646813
Trimmed Mean ( 15 / 22 )68.08889473684215.0252973036172913.5492271646954
Trimmed Mean ( 16 / 22 )68.17466666666674.9813100324796613.6860918557863
Trimmed Mean ( 17 / 22 )68.31376470588234.9239406968245113.8737992417209
Trimmed Mean ( 18 / 22 )68.5121254.8496333359799114.1272793742368
Trimmed Mean ( 19 / 22 )68.79493333333334.7638741695488814.4409635697510
Trimmed Mean ( 20 / 22 )69.18028571428574.6612211663390114.8416655733632
Trimmed Mean ( 21 / 22 )69.5434.5521176941659215.2770654610112
Trimmed Mean ( 22 / 22 )69.96366666666674.3936560754043115.9237922736655
Median70.68
Midrange3542.96
Midmean - Weighted Average at Xnp66.9565142857143
Midmean - Weighted Average at X(n+1)p68.3137647058823
Midmean - Empirical Distribution Function66.9565142857143
Midmean - Empirical Distribution Function - Averaging68.3137647058823
Midmean - Empirical Distribution Function - Interpolation68.3137647058823
Midmean - Closest Observation66.9565142857143
Midmean - True Basic - Statistics Graphics Toolkit68.3137647058823
Midmean - MS Excel (old versions)68.1746666666667
Number of observations68

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 239.590926470588 & 105.762431153068 & 2.26536893922032 \tabularnewline
Geometric Mean & 69.3390111210262 &  &  \tabularnewline
Harmonic Mean & 41.1465981930549 &  &  \tabularnewline
Quadratic Mean & 898.245604250496 &  &  \tabularnewline
Winsorized Mean ( 1 / 22 ) & 152.838132352941 & 31.9606822621817 & 4.78206726311943 \tabularnewline
Winsorized Mean ( 2 / 22 ) & 146.96725 & 29.3121607098557 & 5.01386613749646 \tabularnewline
Winsorized Mean ( 3 / 22 ) & 138.163573529412 & 25.840349318129 & 5.34681523954784 \tabularnewline
Winsorized Mean ( 4 / 22 ) & 134.611220588235 & 24.5638219192105 & 5.48006010754217 \tabularnewline
Winsorized Mean ( 5 / 22 ) & 134.539161764706 & 24.5027822642815 & 5.49077081588519 \tabularnewline
Winsorized Mean ( 6 / 22 ) & 133.942691176471 & 24.2888055695295 & 5.51458534233165 \tabularnewline
Winsorized Mean ( 7 / 22 ) & 89.6656323529412 & 9.77194919199504 & 9.17581851800798 \tabularnewline
Winsorized Mean ( 8 / 22 ) & 89.5948088235294 & 9.74884523274066 & 9.19029963904165 \tabularnewline
Winsorized Mean ( 9 / 22 ) & 76.4921323529412 & 6.4233795691948 & 11.9083936312563 \tabularnewline
Winsorized Mean ( 10 / 22 ) & 70.2274264705882 & 5.17534312691077 & 13.5696174627378 \tabularnewline
Winsorized Mean ( 11 / 22 ) & 70.3099264705883 & 5.15816467108828 & 13.6308029995006 \tabularnewline
Winsorized Mean ( 12 / 22 ) & 69.4446911764706 & 5.00311411518289 & 13.8802932688918 \tabularnewline
Winsorized Mean ( 13 / 22 ) & 69.1068823529412 & 4.93592688744074 & 14.000791326302 \tabularnewline
Winsorized Mean ( 14 / 22 ) & 68.5901176470588 & 4.85250379803847 & 14.1349951492640 \tabularnewline
Winsorized Mean ( 15 / 22 ) & 67.4077647058824 & 4.66374974777644 & 14.4535552616263 \tabularnewline
Winsorized Mean ( 16 / 22 ) & 67.0618823529412 & 4.59414435408269 & 14.5972518894286 \tabularnewline
Winsorized Mean ( 17 / 22 ) & 66.7268823529412 & 4.51414206220174 & 14.7817417869201 \tabularnewline
Winsorized Mean ( 18 / 22 ) & 66.266294117647 & 4.38247811650455 & 15.1207358841305 \tabularnewline
Winsorized Mean ( 19 / 22 ) & 65.7801176470588 & 4.24504073018561 & 15.4957565375781 \tabularnewline
Winsorized Mean ( 20 / 22 ) & 66.4065882352941 & 4.05631272124732 & 16.3711707648798 \tabularnewline
Winsorized Mean ( 21 / 22 ) & 66.4251176470588 & 3.96972507272204 & 16.732926444579 \tabularnewline
Winsorized Mean ( 22 / 22 ) & 66.2827647058824 & 3.84381764343672 & 17.2439930440143 \tabularnewline
Trimmed Mean ( 1 / 22 ) & 139.488833333333 & 28.9152554461059 & 4.82405675416983 \tabularnewline
Trimmed Mean ( 2 / 22 ) & 125.305203125 & 24.8746342705145 & 5.03746916486456 \tabularnewline
Trimmed Mean ( 3 / 22 ) & 113.426016129032 & 21.5735868635324 & 5.25763364462891 \tabularnewline
Trimmed Mean ( 4 / 22 ) & 104.080716666667 & 19.2647011253684 & 5.40266448928242 \tabularnewline
Trimmed Mean ( 5 / 22 ) & 95.1321206896552 & 16.8127547774582 & 5.65833035388134 \tabularnewline
Trimmed Mean ( 6 / 22 ) & 85.5618392857143 & 13.3397490729427 & 6.41405163004611 \tabularnewline
Trimmed Mean ( 7 / 22 ) & 75.4078333333333 & 7.46218968734674 & 10.1053224981936 \tabularnewline
Trimmed Mean ( 8 / 22 ) & 72.7442884615385 & 6.66027131122808 & 10.9221208960218 \tabularnewline
Trimmed Mean ( 9 / 22 ) & 69.8797 & 5.54744510395809 & 12.5967357387892 \tabularnewline
Trimmed Mean ( 10 / 22 ) & 68.8388541666667 & 5.26366318726103 & 13.0781267185310 \tabularnewline
Trimmed Mean ( 11 / 22 ) & 68.6335869565217 & 5.22617260989174 & 13.1326674566042 \tabularnewline
Trimmed Mean ( 12 / 22 ) & 68.3980681818182 & 5.17340129296506 & 13.2211023867079 \tabularnewline
Trimmed Mean ( 13 / 22 ) & 68.2568571428571 & 5.13165270740085 & 13.3011450764034 \tabularnewline
Trimmed Mean ( 14 / 22 ) & 68.1457 & 5.08217285894578 & 13.4087725646813 \tabularnewline
Trimmed Mean ( 15 / 22 ) & 68.0888947368421 & 5.02529730361729 & 13.5492271646954 \tabularnewline
Trimmed Mean ( 16 / 22 ) & 68.1746666666667 & 4.98131003247966 & 13.6860918557863 \tabularnewline
Trimmed Mean ( 17 / 22 ) & 68.3137647058823 & 4.92394069682451 & 13.8737992417209 \tabularnewline
Trimmed Mean ( 18 / 22 ) & 68.512125 & 4.84963333597991 & 14.1272793742368 \tabularnewline
Trimmed Mean ( 19 / 22 ) & 68.7949333333333 & 4.76387416954888 & 14.4409635697510 \tabularnewline
Trimmed Mean ( 20 / 22 ) & 69.1802857142857 & 4.66122116633901 & 14.8416655733632 \tabularnewline
Trimmed Mean ( 21 / 22 ) & 69.543 & 4.55211769416592 & 15.2770654610112 \tabularnewline
Trimmed Mean ( 22 / 22 ) & 69.9636666666667 & 4.39365607540431 & 15.9237922736655 \tabularnewline
Median & 70.68 &  &  \tabularnewline
Midrange & 3542.96 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 66.9565142857143 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 68.3137647058823 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 66.9565142857143 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 68.3137647058823 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 68.3137647058823 &  &  \tabularnewline
Midmean - Closest Observation & 66.9565142857143 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 68.3137647058823 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 68.1746666666667 &  &  \tabularnewline
Number of observations & 68 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=76552&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]239.590926470588[/C][C]105.762431153068[/C][C]2.26536893922032[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]69.3390111210262[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]41.1465981930549[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]898.245604250496[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 22 )[/C][C]152.838132352941[/C][C]31.9606822621817[/C][C]4.78206726311943[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 22 )[/C][C]146.96725[/C][C]29.3121607098557[/C][C]5.01386613749646[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 22 )[/C][C]138.163573529412[/C][C]25.840349318129[/C][C]5.34681523954784[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 22 )[/C][C]134.611220588235[/C][C]24.5638219192105[/C][C]5.48006010754217[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 22 )[/C][C]134.539161764706[/C][C]24.5027822642815[/C][C]5.49077081588519[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 22 )[/C][C]133.942691176471[/C][C]24.2888055695295[/C][C]5.51458534233165[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 22 )[/C][C]89.6656323529412[/C][C]9.77194919199504[/C][C]9.17581851800798[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 22 )[/C][C]89.5948088235294[/C][C]9.74884523274066[/C][C]9.19029963904165[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 22 )[/C][C]76.4921323529412[/C][C]6.4233795691948[/C][C]11.9083936312563[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 22 )[/C][C]70.2274264705882[/C][C]5.17534312691077[/C][C]13.5696174627378[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 22 )[/C][C]70.3099264705883[/C][C]5.15816467108828[/C][C]13.6308029995006[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 22 )[/C][C]69.4446911764706[/C][C]5.00311411518289[/C][C]13.8802932688918[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 22 )[/C][C]69.1068823529412[/C][C]4.93592688744074[/C][C]14.000791326302[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 22 )[/C][C]68.5901176470588[/C][C]4.85250379803847[/C][C]14.1349951492640[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 22 )[/C][C]67.4077647058824[/C][C]4.66374974777644[/C][C]14.4535552616263[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 22 )[/C][C]67.0618823529412[/C][C]4.59414435408269[/C][C]14.5972518894286[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 22 )[/C][C]66.7268823529412[/C][C]4.51414206220174[/C][C]14.7817417869201[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 22 )[/C][C]66.266294117647[/C][C]4.38247811650455[/C][C]15.1207358841305[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 22 )[/C][C]65.7801176470588[/C][C]4.24504073018561[/C][C]15.4957565375781[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 22 )[/C][C]66.4065882352941[/C][C]4.05631272124732[/C][C]16.3711707648798[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 22 )[/C][C]66.4251176470588[/C][C]3.96972507272204[/C][C]16.732926444579[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 22 )[/C][C]66.2827647058824[/C][C]3.84381764343672[/C][C]17.2439930440143[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 22 )[/C][C]139.488833333333[/C][C]28.9152554461059[/C][C]4.82405675416983[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 22 )[/C][C]125.305203125[/C][C]24.8746342705145[/C][C]5.03746916486456[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 22 )[/C][C]113.426016129032[/C][C]21.5735868635324[/C][C]5.25763364462891[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 22 )[/C][C]104.080716666667[/C][C]19.2647011253684[/C][C]5.40266448928242[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 22 )[/C][C]95.1321206896552[/C][C]16.8127547774582[/C][C]5.65833035388134[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 22 )[/C][C]85.5618392857143[/C][C]13.3397490729427[/C][C]6.41405163004611[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 22 )[/C][C]75.4078333333333[/C][C]7.46218968734674[/C][C]10.1053224981936[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 22 )[/C][C]72.7442884615385[/C][C]6.66027131122808[/C][C]10.9221208960218[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 22 )[/C][C]69.8797[/C][C]5.54744510395809[/C][C]12.5967357387892[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 22 )[/C][C]68.8388541666667[/C][C]5.26366318726103[/C][C]13.0781267185310[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 22 )[/C][C]68.6335869565217[/C][C]5.22617260989174[/C][C]13.1326674566042[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 22 )[/C][C]68.3980681818182[/C][C]5.17340129296506[/C][C]13.2211023867079[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 22 )[/C][C]68.2568571428571[/C][C]5.13165270740085[/C][C]13.3011450764034[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 22 )[/C][C]68.1457[/C][C]5.08217285894578[/C][C]13.4087725646813[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 22 )[/C][C]68.0888947368421[/C][C]5.02529730361729[/C][C]13.5492271646954[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 22 )[/C][C]68.1746666666667[/C][C]4.98131003247966[/C][C]13.6860918557863[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 22 )[/C][C]68.3137647058823[/C][C]4.92394069682451[/C][C]13.8737992417209[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 22 )[/C][C]68.512125[/C][C]4.84963333597991[/C][C]14.1272793742368[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 22 )[/C][C]68.7949333333333[/C][C]4.76387416954888[/C][C]14.4409635697510[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 22 )[/C][C]69.1802857142857[/C][C]4.66122116633901[/C][C]14.8416655733632[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 22 )[/C][C]69.543[/C][C]4.55211769416592[/C][C]15.2770654610112[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 22 )[/C][C]69.9636666666667[/C][C]4.39365607540431[/C][C]15.9237922736655[/C][/ROW]
[ROW][C]Median[/C][C]70.68[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]3542.96[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]66.9565142857143[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]68.3137647058823[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]66.9565142857143[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]68.3137647058823[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]68.3137647058823[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]66.9565142857143[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]68.3137647058823[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]68.1746666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]68[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=76552&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=76552&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 Mean239.590926470588105.7624311530682.26536893922032
Geometric Mean69.3390111210262
Harmonic Mean41.1465981930549
Quadratic Mean898.245604250496
Winsorized Mean ( 1 / 22 )152.83813235294131.96068226218174.78206726311943
Winsorized Mean ( 2 / 22 )146.9672529.31216070985575.01386613749646
Winsorized Mean ( 3 / 22 )138.16357352941225.8403493181295.34681523954784
Winsorized Mean ( 4 / 22 )134.61122058823524.56382191921055.48006010754217
Winsorized Mean ( 5 / 22 )134.53916176470624.50278226428155.49077081588519
Winsorized Mean ( 6 / 22 )133.94269117647124.28880556952955.51458534233165
Winsorized Mean ( 7 / 22 )89.66563235294129.771949191995049.17581851800798
Winsorized Mean ( 8 / 22 )89.59480882352949.748845232740669.19029963904165
Winsorized Mean ( 9 / 22 )76.49213235294126.423379569194811.9083936312563
Winsorized Mean ( 10 / 22 )70.22742647058825.1753431269107713.5696174627378
Winsorized Mean ( 11 / 22 )70.30992647058835.1581646710882813.6308029995006
Winsorized Mean ( 12 / 22 )69.44469117647065.0031141151828913.8802932688918
Winsorized Mean ( 13 / 22 )69.10688235294124.9359268874407414.000791326302
Winsorized Mean ( 14 / 22 )68.59011764705884.8525037980384714.1349951492640
Winsorized Mean ( 15 / 22 )67.40776470588244.6637497477764414.4535552616263
Winsorized Mean ( 16 / 22 )67.06188235294124.5941443540826914.5972518894286
Winsorized Mean ( 17 / 22 )66.72688235294124.5141420622017414.7817417869201
Winsorized Mean ( 18 / 22 )66.2662941176474.3824781165045515.1207358841305
Winsorized Mean ( 19 / 22 )65.78011764705884.2450407301856115.4957565375781
Winsorized Mean ( 20 / 22 )66.40658823529414.0563127212473216.3711707648798
Winsorized Mean ( 21 / 22 )66.42511764705883.9697250727220416.732926444579
Winsorized Mean ( 22 / 22 )66.28276470588243.8438176434367217.2439930440143
Trimmed Mean ( 1 / 22 )139.48883333333328.91525544610594.82405675416983
Trimmed Mean ( 2 / 22 )125.30520312524.87463427051455.03746916486456
Trimmed Mean ( 3 / 22 )113.42601612903221.57358686353245.25763364462891
Trimmed Mean ( 4 / 22 )104.08071666666719.26470112536845.40266448928242
Trimmed Mean ( 5 / 22 )95.132120689655216.81275477745825.65833035388134
Trimmed Mean ( 6 / 22 )85.561839285714313.33974907294276.41405163004611
Trimmed Mean ( 7 / 22 )75.40783333333337.4621896873467410.1053224981936
Trimmed Mean ( 8 / 22 )72.74428846153856.6602713112280810.9221208960218
Trimmed Mean ( 9 / 22 )69.87975.5474451039580912.5967357387892
Trimmed Mean ( 10 / 22 )68.83885416666675.2636631872610313.0781267185310
Trimmed Mean ( 11 / 22 )68.63358695652175.2261726098917413.1326674566042
Trimmed Mean ( 12 / 22 )68.39806818181825.1734012929650613.2211023867079
Trimmed Mean ( 13 / 22 )68.25685714285715.1316527074008513.3011450764034
Trimmed Mean ( 14 / 22 )68.14575.0821728589457813.4087725646813
Trimmed Mean ( 15 / 22 )68.08889473684215.0252973036172913.5492271646954
Trimmed Mean ( 16 / 22 )68.17466666666674.9813100324796613.6860918557863
Trimmed Mean ( 17 / 22 )68.31376470588234.9239406968245113.8737992417209
Trimmed Mean ( 18 / 22 )68.5121254.8496333359799114.1272793742368
Trimmed Mean ( 19 / 22 )68.79493333333334.7638741695488814.4409635697510
Trimmed Mean ( 20 / 22 )69.18028571428574.6612211663390114.8416655733632
Trimmed Mean ( 21 / 22 )69.5434.5521176941659215.2770654610112
Trimmed Mean ( 22 / 22 )69.96366666666674.3936560754043115.9237922736655
Median70.68
Midrange3542.96
Midmean - Weighted Average at Xnp66.9565142857143
Midmean - Weighted Average at X(n+1)p68.3137647058823
Midmean - Empirical Distribution Function66.9565142857143
Midmean - Empirical Distribution Function - Averaging68.3137647058823
Midmean - Empirical Distribution Function - Interpolation68.3137647058823
Midmean - Closest Observation66.9565142857143
Midmean - True Basic - Statistics Graphics Toolkit68.3137647058823
Midmean - MS Excel (old versions)68.1746666666667
Number of observations68



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')