Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationWed, 21 Apr 2010 16:52:07 +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/Apr/21/t12718687934bbk5o3tb8m4itg.htm/, Retrieved Thu, 25 Apr 2024 17:43:56 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=74700, Retrieved Thu, 25 Apr 2024 17:43:56 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP1W52
Estimated Impact219
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Taak 5 Eigen reeks] [2010-04-21 16:52:07] [16a17dd935adfa033e8fda163f23b24a] [Current]
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Dataseries X:
93.2
96
95.2
77.1
70.9
64.8
70.1
77.3
79.5
100.6
100.7
107.1
95.9
82.8
83.3
80
80.4
67.5
75.7
71.1
89.3
101.1
105.2
114.1
96.3
84.4
91.2
81.9
80.5
70.4
74.8
75.9
86.3
98.7
100.9
113.8
89.8
84.4
87.2
85.6
72
69.2
77.5
78.1
94.3
97.7
100.2
116.4
97.1
93
96
80.5
76.1
69.9
73.6
92.6
94.2
93.5
108.5
109.4
105.1
92.5
97.1




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'RServer@AstonUniversity' @ vre.aston.ac.uk

\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 & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=74700&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]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=74700&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=74700&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'RServer@AstonUniversity' @ vre.aston.ac.uk







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean88.34126984126981.6380689912439453.9301276768471
Geometric Mean87.3994106792435
Harmonic Mean86.4617422732407
Quadratic Mean89.2778959116572
Winsorized Mean ( 1 / 21 )88.3476190476191.6189195304893954.5719644390924
Winsorized Mean ( 2 / 21 )88.39206349206351.6056739856582655.0498197526857
Winsorized Mean ( 3 / 21 )88.2158730158731.5493771048232156.9363473496909
Winsorized Mean ( 4 / 21 )88.17142857142861.5345540932422957.4573610403885
Winsorized Mean ( 5 / 21 )88.0841269841271.5068561629763158.4555640733123
Winsorized Mean ( 6 / 21 )87.95079365079361.4622224823517460.14870836163
Winsorized Mean ( 7 / 21 )87.96190476190471.4559453629883660.4156632508248
Winsorized Mean ( 8 / 21 )87.5682539682541.3448919603568165.1117387489039
Winsorized Mean ( 9 / 21 )87.7682539682541.2987761094477567.5776627933
Winsorized Mean ( 10 / 21 )87.92698412698411.2608326444224169.7372363540475
Winsorized Mean ( 11 / 21 )88.06666666666671.2320539717266171.4795525907436
Winsorized Mean ( 12 / 21 )88.02857142857141.2134854746940972.5419242869493
Winsorized Mean ( 13 / 21 )87.76031746031751.1581597681467475.7756571019121
Winsorized Mean ( 14 / 21 )87.76031746031751.0892636682072480.5684794433265
Winsorized Mean ( 15 / 21 )87.66507936507941.0609923929083182.62554939228
Winsorized Mean ( 16 / 21 )87.7158730158731.0530165537707183.2996145234133
Winsorized Mean ( 17 / 21 )87.66190476190480.99721945371648487.906332387723
Winsorized Mean ( 18 / 21 )87.97619047619050.92468207482733595.1420957225954
Winsorized Mean ( 19 / 21 )88.12698412698410.90258264688378697.6386865305323
Winsorized Mean ( 20 / 21 )88.22222222222220.87978795926869100.276687459505
Winsorized Mean ( 21 / 21 )88.02222222222220.842537326876961104.472786444364
Trimmed Mean ( 1 / 21 )88.26721311475411.5801911091993855.8585683724519
Trimmed Mean ( 2 / 21 )88.18135593220341.53280792783657.529292699247
Trimmed Mean ( 3 / 21 )88.06491228070171.4832618563529959.3724647495714
Trimmed Mean ( 4 / 21 )88.00727272727271.4491698646474860.7294388837441
Trimmed Mean ( 5 / 21 )87.95849056603771.4122274297095362.2835166033628
Trimmed Mean ( 6 / 21 )87.92745098039221.3750980811546163.9426759337513
Trimmed Mean ( 7 / 21 )87.92244897959181.3416257820262865.5342571359957
Trimmed Mean ( 8 / 21 )87.91489361702131.3002952013917167.6114881627849
Trimmed Mean ( 9 / 21 )87.97555555555561.2768615072285568.89984157053
Trimmed Mean ( 10 / 21 )88.00930232558141.2571823068878370.0052027803743
Trimmed Mean ( 11 / 21 )88.02195121951221.2393079903972571.0250816597234
Trimmed Mean ( 12 / 21 )88.01538461538461.2208298899779972.0947163383846
Trimmed Mean ( 13 / 21 )88.01351351351351.1985862678480573.431104522442
Trimmed Mean ( 14 / 21 )88.04857142857141.1801536107719274.6077210838511
Trimmed Mean ( 15 / 21 )88.08787878787881.1694967641507475.3211821426853
Trimmed Mean ( 16 / 21 )88.14516129032261.1577772429505376.1330919458128
Trimmed Mean ( 17 / 21 )88.20344827586211.1387756232739977.4546332685592
Trimmed Mean ( 18 / 21 )88.27777777777781.1229455230211878.6126984506555
Trimmed Mean ( 19 / 21 )88.321.1169153951844379.0749240101717
Trimmed Mean ( 20 / 21 )88.34782608695651.1071786878578179.7954540272932
Trimmed Mean ( 21 / 21 )88.36666666666671.0911621880522380.9839890295367
Median89.3
Midrange90.6
Midmean - Weighted Average at Xnp88.0878787878788
Midmean - Weighted Average at X(n+1)p88.0878787878788
Midmean - Empirical Distribution Function88.0878787878788
Midmean - Empirical Distribution Function - Averaging88.0878787878788
Midmean - Empirical Distribution Function - Interpolation88.425
Midmean - Closest Observation88.0878787878788
Midmean - True Basic - Statistics Graphics Toolkit88.0878787878788
Midmean - MS Excel (old versions)88.0878787878788
Number of observations63

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 88.3412698412698 & 1.63806899124394 & 53.9301276768471 \tabularnewline
Geometric Mean & 87.3994106792435 &  &  \tabularnewline
Harmonic Mean & 86.4617422732407 &  &  \tabularnewline
Quadratic Mean & 89.2778959116572 &  &  \tabularnewline
Winsorized Mean ( 1 / 21 ) & 88.347619047619 & 1.61891953048939 & 54.5719644390924 \tabularnewline
Winsorized Mean ( 2 / 21 ) & 88.3920634920635 & 1.60567398565826 & 55.0498197526857 \tabularnewline
Winsorized Mean ( 3 / 21 ) & 88.215873015873 & 1.54937710482321 & 56.9363473496909 \tabularnewline
Winsorized Mean ( 4 / 21 ) & 88.1714285714286 & 1.53455409324229 & 57.4573610403885 \tabularnewline
Winsorized Mean ( 5 / 21 ) & 88.084126984127 & 1.50685616297631 & 58.4555640733123 \tabularnewline
Winsorized Mean ( 6 / 21 ) & 87.9507936507936 & 1.46222248235174 & 60.14870836163 \tabularnewline
Winsorized Mean ( 7 / 21 ) & 87.9619047619047 & 1.45594536298836 & 60.4156632508248 \tabularnewline
Winsorized Mean ( 8 / 21 ) & 87.568253968254 & 1.34489196035681 & 65.1117387489039 \tabularnewline
Winsorized Mean ( 9 / 21 ) & 87.768253968254 & 1.29877610944775 & 67.5776627933 \tabularnewline
Winsorized Mean ( 10 / 21 ) & 87.9269841269841 & 1.26083264442241 & 69.7372363540475 \tabularnewline
Winsorized Mean ( 11 / 21 ) & 88.0666666666667 & 1.23205397172661 & 71.4795525907436 \tabularnewline
Winsorized Mean ( 12 / 21 ) & 88.0285714285714 & 1.21348547469409 & 72.5419242869493 \tabularnewline
Winsorized Mean ( 13 / 21 ) & 87.7603174603175 & 1.15815976814674 & 75.7756571019121 \tabularnewline
Winsorized Mean ( 14 / 21 ) & 87.7603174603175 & 1.08926366820724 & 80.5684794433265 \tabularnewline
Winsorized Mean ( 15 / 21 ) & 87.6650793650794 & 1.06099239290831 & 82.62554939228 \tabularnewline
Winsorized Mean ( 16 / 21 ) & 87.715873015873 & 1.05301655377071 & 83.2996145234133 \tabularnewline
Winsorized Mean ( 17 / 21 ) & 87.6619047619048 & 0.997219453716484 & 87.906332387723 \tabularnewline
Winsorized Mean ( 18 / 21 ) & 87.9761904761905 & 0.924682074827335 & 95.1420957225954 \tabularnewline
Winsorized Mean ( 19 / 21 ) & 88.1269841269841 & 0.902582646883786 & 97.6386865305323 \tabularnewline
Winsorized Mean ( 20 / 21 ) & 88.2222222222222 & 0.87978795926869 & 100.276687459505 \tabularnewline
Winsorized Mean ( 21 / 21 ) & 88.0222222222222 & 0.842537326876961 & 104.472786444364 \tabularnewline
Trimmed Mean ( 1 / 21 ) & 88.2672131147541 & 1.58019110919938 & 55.8585683724519 \tabularnewline
Trimmed Mean ( 2 / 21 ) & 88.1813559322034 & 1.532807927836 & 57.529292699247 \tabularnewline
Trimmed Mean ( 3 / 21 ) & 88.0649122807017 & 1.48326185635299 & 59.3724647495714 \tabularnewline
Trimmed Mean ( 4 / 21 ) & 88.0072727272727 & 1.44916986464748 & 60.7294388837441 \tabularnewline
Trimmed Mean ( 5 / 21 ) & 87.9584905660377 & 1.41222742970953 & 62.2835166033628 \tabularnewline
Trimmed Mean ( 6 / 21 ) & 87.9274509803922 & 1.37509808115461 & 63.9426759337513 \tabularnewline
Trimmed Mean ( 7 / 21 ) & 87.9224489795918 & 1.34162578202628 & 65.5342571359957 \tabularnewline
Trimmed Mean ( 8 / 21 ) & 87.9148936170213 & 1.30029520139171 & 67.6114881627849 \tabularnewline
Trimmed Mean ( 9 / 21 ) & 87.9755555555556 & 1.27686150722855 & 68.89984157053 \tabularnewline
Trimmed Mean ( 10 / 21 ) & 88.0093023255814 & 1.25718230688783 & 70.0052027803743 \tabularnewline
Trimmed Mean ( 11 / 21 ) & 88.0219512195122 & 1.23930799039725 & 71.0250816597234 \tabularnewline
Trimmed Mean ( 12 / 21 ) & 88.0153846153846 & 1.22082988997799 & 72.0947163383846 \tabularnewline
Trimmed Mean ( 13 / 21 ) & 88.0135135135135 & 1.19858626784805 & 73.431104522442 \tabularnewline
Trimmed Mean ( 14 / 21 ) & 88.0485714285714 & 1.18015361077192 & 74.6077210838511 \tabularnewline
Trimmed Mean ( 15 / 21 ) & 88.0878787878788 & 1.16949676415074 & 75.3211821426853 \tabularnewline
Trimmed Mean ( 16 / 21 ) & 88.1451612903226 & 1.15777724295053 & 76.1330919458128 \tabularnewline
Trimmed Mean ( 17 / 21 ) & 88.2034482758621 & 1.13877562327399 & 77.4546332685592 \tabularnewline
Trimmed Mean ( 18 / 21 ) & 88.2777777777778 & 1.12294552302118 & 78.6126984506555 \tabularnewline
Trimmed Mean ( 19 / 21 ) & 88.32 & 1.11691539518443 & 79.0749240101717 \tabularnewline
Trimmed Mean ( 20 / 21 ) & 88.3478260869565 & 1.10717868785781 & 79.7954540272932 \tabularnewline
Trimmed Mean ( 21 / 21 ) & 88.3666666666667 & 1.09116218805223 & 80.9839890295367 \tabularnewline
Median & 89.3 &  &  \tabularnewline
Midrange & 90.6 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 88.0878787878788 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 88.0878787878788 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 88.0878787878788 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 88.0878787878788 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 88.425 &  &  \tabularnewline
Midmean - Closest Observation & 88.0878787878788 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 88.0878787878788 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 88.0878787878788 &  &  \tabularnewline
Number of observations & 63 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=74700&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]88.3412698412698[/C][C]1.63806899124394[/C][C]53.9301276768471[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]87.3994106792435[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]86.4617422732407[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]89.2778959116572[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 21 )[/C][C]88.347619047619[/C][C]1.61891953048939[/C][C]54.5719644390924[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 21 )[/C][C]88.3920634920635[/C][C]1.60567398565826[/C][C]55.0498197526857[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 21 )[/C][C]88.215873015873[/C][C]1.54937710482321[/C][C]56.9363473496909[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 21 )[/C][C]88.1714285714286[/C][C]1.53455409324229[/C][C]57.4573610403885[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 21 )[/C][C]88.084126984127[/C][C]1.50685616297631[/C][C]58.4555640733123[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 21 )[/C][C]87.9507936507936[/C][C]1.46222248235174[/C][C]60.14870836163[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 21 )[/C][C]87.9619047619047[/C][C]1.45594536298836[/C][C]60.4156632508248[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 21 )[/C][C]87.568253968254[/C][C]1.34489196035681[/C][C]65.1117387489039[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 21 )[/C][C]87.768253968254[/C][C]1.29877610944775[/C][C]67.5776627933[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 21 )[/C][C]87.9269841269841[/C][C]1.26083264442241[/C][C]69.7372363540475[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 21 )[/C][C]88.0666666666667[/C][C]1.23205397172661[/C][C]71.4795525907436[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 21 )[/C][C]88.0285714285714[/C][C]1.21348547469409[/C][C]72.5419242869493[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 21 )[/C][C]87.7603174603175[/C][C]1.15815976814674[/C][C]75.7756571019121[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 21 )[/C][C]87.7603174603175[/C][C]1.08926366820724[/C][C]80.5684794433265[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 21 )[/C][C]87.6650793650794[/C][C]1.06099239290831[/C][C]82.62554939228[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 21 )[/C][C]87.715873015873[/C][C]1.05301655377071[/C][C]83.2996145234133[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 21 )[/C][C]87.6619047619048[/C][C]0.997219453716484[/C][C]87.906332387723[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 21 )[/C][C]87.9761904761905[/C][C]0.924682074827335[/C][C]95.1420957225954[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 21 )[/C][C]88.1269841269841[/C][C]0.902582646883786[/C][C]97.6386865305323[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 21 )[/C][C]88.2222222222222[/C][C]0.87978795926869[/C][C]100.276687459505[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 21 )[/C][C]88.0222222222222[/C][C]0.842537326876961[/C][C]104.472786444364[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 21 )[/C][C]88.2672131147541[/C][C]1.58019110919938[/C][C]55.8585683724519[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 21 )[/C][C]88.1813559322034[/C][C]1.532807927836[/C][C]57.529292699247[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 21 )[/C][C]88.0649122807017[/C][C]1.48326185635299[/C][C]59.3724647495714[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 21 )[/C][C]88.0072727272727[/C][C]1.44916986464748[/C][C]60.7294388837441[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 21 )[/C][C]87.9584905660377[/C][C]1.41222742970953[/C][C]62.2835166033628[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 21 )[/C][C]87.9274509803922[/C][C]1.37509808115461[/C][C]63.9426759337513[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 21 )[/C][C]87.9224489795918[/C][C]1.34162578202628[/C][C]65.5342571359957[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 21 )[/C][C]87.9148936170213[/C][C]1.30029520139171[/C][C]67.6114881627849[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 21 )[/C][C]87.9755555555556[/C][C]1.27686150722855[/C][C]68.89984157053[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 21 )[/C][C]88.0093023255814[/C][C]1.25718230688783[/C][C]70.0052027803743[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 21 )[/C][C]88.0219512195122[/C][C]1.23930799039725[/C][C]71.0250816597234[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 21 )[/C][C]88.0153846153846[/C][C]1.22082988997799[/C][C]72.0947163383846[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 21 )[/C][C]88.0135135135135[/C][C]1.19858626784805[/C][C]73.431104522442[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 21 )[/C][C]88.0485714285714[/C][C]1.18015361077192[/C][C]74.6077210838511[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 21 )[/C][C]88.0878787878788[/C][C]1.16949676415074[/C][C]75.3211821426853[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 21 )[/C][C]88.1451612903226[/C][C]1.15777724295053[/C][C]76.1330919458128[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 21 )[/C][C]88.2034482758621[/C][C]1.13877562327399[/C][C]77.4546332685592[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 21 )[/C][C]88.2777777777778[/C][C]1.12294552302118[/C][C]78.6126984506555[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 21 )[/C][C]88.32[/C][C]1.11691539518443[/C][C]79.0749240101717[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 21 )[/C][C]88.3478260869565[/C][C]1.10717868785781[/C][C]79.7954540272932[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 21 )[/C][C]88.3666666666667[/C][C]1.09116218805223[/C][C]80.9839890295367[/C][/ROW]
[ROW][C]Median[/C][C]89.3[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]90.6[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]88.0878787878788[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]88.0878787878788[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]88.0878787878788[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]88.0878787878788[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]88.425[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]88.0878787878788[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]88.0878787878788[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]88.0878787878788[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]63[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=74700&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=74700&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 Mean88.34126984126981.6380689912439453.9301276768471
Geometric Mean87.3994106792435
Harmonic Mean86.4617422732407
Quadratic Mean89.2778959116572
Winsorized Mean ( 1 / 21 )88.3476190476191.6189195304893954.5719644390924
Winsorized Mean ( 2 / 21 )88.39206349206351.6056739856582655.0498197526857
Winsorized Mean ( 3 / 21 )88.2158730158731.5493771048232156.9363473496909
Winsorized Mean ( 4 / 21 )88.17142857142861.5345540932422957.4573610403885
Winsorized Mean ( 5 / 21 )88.0841269841271.5068561629763158.4555640733123
Winsorized Mean ( 6 / 21 )87.95079365079361.4622224823517460.14870836163
Winsorized Mean ( 7 / 21 )87.96190476190471.4559453629883660.4156632508248
Winsorized Mean ( 8 / 21 )87.5682539682541.3448919603568165.1117387489039
Winsorized Mean ( 9 / 21 )87.7682539682541.2987761094477567.5776627933
Winsorized Mean ( 10 / 21 )87.92698412698411.2608326444224169.7372363540475
Winsorized Mean ( 11 / 21 )88.06666666666671.2320539717266171.4795525907436
Winsorized Mean ( 12 / 21 )88.02857142857141.2134854746940972.5419242869493
Winsorized Mean ( 13 / 21 )87.76031746031751.1581597681467475.7756571019121
Winsorized Mean ( 14 / 21 )87.76031746031751.0892636682072480.5684794433265
Winsorized Mean ( 15 / 21 )87.66507936507941.0609923929083182.62554939228
Winsorized Mean ( 16 / 21 )87.7158730158731.0530165537707183.2996145234133
Winsorized Mean ( 17 / 21 )87.66190476190480.99721945371648487.906332387723
Winsorized Mean ( 18 / 21 )87.97619047619050.92468207482733595.1420957225954
Winsorized Mean ( 19 / 21 )88.12698412698410.90258264688378697.6386865305323
Winsorized Mean ( 20 / 21 )88.22222222222220.87978795926869100.276687459505
Winsorized Mean ( 21 / 21 )88.02222222222220.842537326876961104.472786444364
Trimmed Mean ( 1 / 21 )88.26721311475411.5801911091993855.8585683724519
Trimmed Mean ( 2 / 21 )88.18135593220341.53280792783657.529292699247
Trimmed Mean ( 3 / 21 )88.06491228070171.4832618563529959.3724647495714
Trimmed Mean ( 4 / 21 )88.00727272727271.4491698646474860.7294388837441
Trimmed Mean ( 5 / 21 )87.95849056603771.4122274297095362.2835166033628
Trimmed Mean ( 6 / 21 )87.92745098039221.3750980811546163.9426759337513
Trimmed Mean ( 7 / 21 )87.92244897959181.3416257820262865.5342571359957
Trimmed Mean ( 8 / 21 )87.91489361702131.3002952013917167.6114881627849
Trimmed Mean ( 9 / 21 )87.97555555555561.2768615072285568.89984157053
Trimmed Mean ( 10 / 21 )88.00930232558141.2571823068878370.0052027803743
Trimmed Mean ( 11 / 21 )88.02195121951221.2393079903972571.0250816597234
Trimmed Mean ( 12 / 21 )88.01538461538461.2208298899779972.0947163383846
Trimmed Mean ( 13 / 21 )88.01351351351351.1985862678480573.431104522442
Trimmed Mean ( 14 / 21 )88.04857142857141.1801536107719274.6077210838511
Trimmed Mean ( 15 / 21 )88.08787878787881.1694967641507475.3211821426853
Trimmed Mean ( 16 / 21 )88.14516129032261.1577772429505376.1330919458128
Trimmed Mean ( 17 / 21 )88.20344827586211.1387756232739977.4546332685592
Trimmed Mean ( 18 / 21 )88.27777777777781.1229455230211878.6126984506555
Trimmed Mean ( 19 / 21 )88.321.1169153951844379.0749240101717
Trimmed Mean ( 20 / 21 )88.34782608695651.1071786878578179.7954540272932
Trimmed Mean ( 21 / 21 )88.36666666666671.0911621880522380.9839890295367
Median89.3
Midrange90.6
Midmean - Weighted Average at Xnp88.0878787878788
Midmean - Weighted Average at X(n+1)p88.0878787878788
Midmean - Empirical Distribution Function88.0878787878788
Midmean - Empirical Distribution Function - Averaging88.0878787878788
Midmean - Empirical Distribution Function - Interpolation88.425
Midmean - Closest Observation88.0878787878788
Midmean - True Basic - Statistics Graphics Toolkit88.0878787878788
Midmean - MS Excel (old versions)88.0878787878788
Number of observations63



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')