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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 computationThu, 26 Feb 2015 12:50:21 +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/2015/Feb/26/t1424955049r7azw5168xcticp.htm/, Retrieved Sat, 18 May 2024 05:07:18 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=277580, Retrieved Sat, 18 May 2024 05:07:18 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact76
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2015-02-26 12:50:21] [d95fe07e11cd60b998b93c9c7758de3b] [Current]
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Dataseries X:
95
98
95
81
83
106
114
80
82
76
78
70
82
86
87
74
79
110
117
82
71
67
66
57
71
77
76
69
74
101
105
73
68
65
70
65
80
92
93
90
96
125
134
100
97
97
101
90
108
113
112
103
103
125
128
91
84
83
83
69
77
83
78
70
75
101
117
80
87
81
78
73




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ jenkins.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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=277580&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' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=277580&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=277580&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' @ jenkins.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean88.15277777777782.0340085581533243.3394330738765
Geometric Mean86.5736752263054
Harmonic Mean85.0824000998342
Quadratic Mean89.8034118381801
Winsorized Mean ( 1 / 24 )88.18055555555561.9878667946190544.3593885637867
Winsorized Mean ( 2 / 24 )88.09722222222221.9650864705020444.831219157351
Winsorized Mean ( 3 / 24 )88.13888888888891.9583201533424845.0073951077165
Winsorized Mean ( 4 / 24 )87.751.8405481169727747.6760151993886
Winsorized Mean ( 5 / 24 )87.81944444444441.8297368039873347.9956703352471
Winsorized Mean ( 6 / 24 )87.65277777777781.7627425328663749.7252299433922
Winsorized Mean ( 7 / 24 )87.55555555555561.7425101164197250.2467989887215
Winsorized Mean ( 8 / 24 )87.55555555555561.7034542014125951.3988315523541
Winsorized Mean ( 9 / 24 )87.30555555555561.6540175976029752.7839339086114
Winsorized Mean ( 10 / 24 )87.02777777777781.6015412449393554.3400165639029
Winsorized Mean ( 11 / 24 )86.8751.5236704997676857.0169206618139
Winsorized Mean ( 12 / 24 )86.70833333333331.4945699184051558.0155750932413
Winsorized Mean ( 13 / 24 )86.70833333333331.381387213565762.7690284677803
Winsorized Mean ( 14 / 24 )86.70833333333331.381387213565762.7690284677803
Winsorized Mean ( 15 / 24 )86.51.2847668964021367.3273885264596
Winsorized Mean ( 16 / 24 )86.51.2847668964021367.3273885264596
Winsorized Mean ( 17 / 24 )86.73611111111111.2530078140162369.222322591188
Winsorized Mean ( 18 / 24 )86.73611111111111.1806660171096573.463714424039
Winsorized Mean ( 19 / 24 )86.20833333333331.0989640697511878.4450881572973
Winsorized Mean ( 20 / 24 )86.20833333333331.0214708893442784.396270351546
Winsorized Mean ( 21 / 24 )86.20833333333331.0214708893442784.396270351546
Winsorized Mean ( 22 / 24 )86.20833333333330.93801172783976791.9053896392856
Winsorized Mean ( 23 / 24 )85.88888888888890.89152582266072196.3392048842255
Winsorized Mean ( 24 / 24 )85.88888888888890.89152582266072196.3392048842255
Trimmed Mean ( 1 / 24 )87.94285714285711.934420239304345.4621262515766
Trimmed Mean ( 2 / 24 )87.69117647058821.8703895441712746.8839107574473
Trimmed Mean ( 3 / 24 )87.4696969696971.808323116248848.3706126320748
Trimmed Mean ( 4 / 24 )87.218751.7362653701309250.2335365897572
Trimmed Mean ( 5 / 24 )87.06451612903231.6943728949090951.3845071475271
Trimmed Mean ( 6 / 24 )86.88333333333331.6464465531422752.7702118040305
Trimmed Mean ( 7 / 24 )86.72413793103451.6071891391139553.9601318976347
Trimmed Mean ( 8 / 24 )86.57142857142861.5639728679633255.3535360777492
Trimmed Mean ( 9 / 24 )86.40740740740741.5198473843255456.8526868543137
Trimmed Mean ( 10 / 24 )86.26923076923081.4768488386319258.414394562646
Trimmed Mean ( 11 / 24 )86.161.4352301955734260.0321817822237
Trimmed Mean ( 12 / 24 )86.06251.4001666092604661.4658994371079
Trimmed Mean ( 13 / 24 )85.97826086956521.3614744530876963.1508440533534
Trimmed Mean ( 14 / 24 )85.88636363636361.3362785996444664.2727973487078
Trimmed Mean ( 15 / 24 )85.78571428571431.3019844205005565.8884337899634
Trimmed Mean ( 16 / 24 )85.71.2781196123953967.0516273820297
Trimmed Mean ( 17 / 24 )85.60526315789471.244355376876168.7948674058072
Trimmed Mean ( 18 / 24 )85.47222222222221.2041503038012470.9813566897795
Trimmed Mean ( 19 / 24 )85.32352941176471.1660073932274773.1758048082282
Trimmed Mean ( 20 / 24 )85.218751.1347999459546675.095835441117
Trimmed Mean ( 21 / 24 )85.11.1093645276339176.7105832935761
Trimmed Mean ( 22 / 24 )84.96428571428571.0684040202169479.5244908354366
Trimmed Mean ( 23 / 24 )84.80769230769231.0318306819498182.1914814041333
Trimmed Mean ( 24 / 24 )84.66666666666670.99029103222356685.4967518756168
Median83
Midrange95.5
Midmean - Weighted Average at Xnp85.1891891891892
Midmean - Weighted Average at X(n+1)p85.4722222222222
Midmean - Empirical Distribution Function85.1891891891892
Midmean - Empirical Distribution Function - Averaging85.4722222222222
Midmean - Empirical Distribution Function - Interpolation85.4722222222222
Midmean - Closest Observation85.1891891891892
Midmean - True Basic - Statistics Graphics Toolkit85.4722222222222
Midmean - MS Excel (old versions)86.375
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 88.1527777777778 & 2.03400855815332 & 43.3394330738765 \tabularnewline
Geometric Mean & 86.5736752263054 &  &  \tabularnewline
Harmonic Mean & 85.0824000998342 &  &  \tabularnewline
Quadratic Mean & 89.8034118381801 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 88.1805555555556 & 1.98786679461905 & 44.3593885637867 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 88.0972222222222 & 1.96508647050204 & 44.831219157351 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 88.1388888888889 & 1.95832015334248 & 45.0073951077165 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 87.75 & 1.84054811697277 & 47.6760151993886 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 87.8194444444444 & 1.82973680398733 & 47.9956703352471 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 87.6527777777778 & 1.76274253286637 & 49.7252299433922 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 87.5555555555556 & 1.74251011641972 & 50.2467989887215 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 87.5555555555556 & 1.70345420141259 & 51.3988315523541 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 87.3055555555556 & 1.65401759760297 & 52.7839339086114 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 87.0277777777778 & 1.60154124493935 & 54.3400165639029 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 86.875 & 1.52367049976768 & 57.0169206618139 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 86.7083333333333 & 1.49456991840515 & 58.0155750932413 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 86.7083333333333 & 1.3813872135657 & 62.7690284677803 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 86.7083333333333 & 1.3813872135657 & 62.7690284677803 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 86.5 & 1.28476689640213 & 67.3273885264596 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 86.5 & 1.28476689640213 & 67.3273885264596 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 86.7361111111111 & 1.25300781401623 & 69.222322591188 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 86.7361111111111 & 1.18066601710965 & 73.463714424039 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 86.2083333333333 & 1.09896406975118 & 78.4450881572973 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 86.2083333333333 & 1.02147088934427 & 84.396270351546 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 86.2083333333333 & 1.02147088934427 & 84.396270351546 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 86.2083333333333 & 0.938011727839767 & 91.9053896392856 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 85.8888888888889 & 0.891525822660721 & 96.3392048842255 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 85.8888888888889 & 0.891525822660721 & 96.3392048842255 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 87.9428571428571 & 1.9344202393043 & 45.4621262515766 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 87.6911764705882 & 1.87038954417127 & 46.8839107574473 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 87.469696969697 & 1.8083231162488 & 48.3706126320748 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 87.21875 & 1.73626537013092 & 50.2335365897572 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 87.0645161290323 & 1.69437289490909 & 51.3845071475271 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 86.8833333333333 & 1.64644655314227 & 52.7702118040305 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 86.7241379310345 & 1.60718913911395 & 53.9601318976347 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 86.5714285714286 & 1.56397286796332 & 55.3535360777492 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 86.4074074074074 & 1.51984738432554 & 56.8526868543137 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 86.2692307692308 & 1.47684883863192 & 58.414394562646 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 86.16 & 1.43523019557342 & 60.0321817822237 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 86.0625 & 1.40016660926046 & 61.4658994371079 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 85.9782608695652 & 1.36147445308769 & 63.1508440533534 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 85.8863636363636 & 1.33627859964446 & 64.2727973487078 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 85.7857142857143 & 1.30198442050055 & 65.8884337899634 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 85.7 & 1.27811961239539 & 67.0516273820297 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 85.6052631578947 & 1.2443553768761 & 68.7948674058072 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 85.4722222222222 & 1.20415030380124 & 70.9813566897795 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 85.3235294117647 & 1.16600739322747 & 73.1758048082282 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 85.21875 & 1.13479994595466 & 75.095835441117 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 85.1 & 1.10936452763391 & 76.7105832935761 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 84.9642857142857 & 1.06840402021694 & 79.5244908354366 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 84.8076923076923 & 1.03183068194981 & 82.1914814041333 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 84.6666666666667 & 0.990291032223566 & 85.4967518756168 \tabularnewline
Median & 83 &  &  \tabularnewline
Midrange & 95.5 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 85.1891891891892 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 85.4722222222222 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 85.1891891891892 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 85.4722222222222 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 85.4722222222222 &  &  \tabularnewline
Midmean - Closest Observation & 85.1891891891892 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 85.4722222222222 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 86.375 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=277580&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]88.1527777777778[/C][C]2.03400855815332[/C][C]43.3394330738765[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]86.5736752263054[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]85.0824000998342[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]89.8034118381801[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]88.1805555555556[/C][C]1.98786679461905[/C][C]44.3593885637867[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]88.0972222222222[/C][C]1.96508647050204[/C][C]44.831219157351[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]88.1388888888889[/C][C]1.95832015334248[/C][C]45.0073951077165[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]87.75[/C][C]1.84054811697277[/C][C]47.6760151993886[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]87.8194444444444[/C][C]1.82973680398733[/C][C]47.9956703352471[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]87.6527777777778[/C][C]1.76274253286637[/C][C]49.7252299433922[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]87.5555555555556[/C][C]1.74251011641972[/C][C]50.2467989887215[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]87.5555555555556[/C][C]1.70345420141259[/C][C]51.3988315523541[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]87.3055555555556[/C][C]1.65401759760297[/C][C]52.7839339086114[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]87.0277777777778[/C][C]1.60154124493935[/C][C]54.3400165639029[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]86.875[/C][C]1.52367049976768[/C][C]57.0169206618139[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]86.7083333333333[/C][C]1.49456991840515[/C][C]58.0155750932413[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]86.7083333333333[/C][C]1.3813872135657[/C][C]62.7690284677803[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]86.7083333333333[/C][C]1.3813872135657[/C][C]62.7690284677803[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]86.5[/C][C]1.28476689640213[/C][C]67.3273885264596[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]86.5[/C][C]1.28476689640213[/C][C]67.3273885264596[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]86.7361111111111[/C][C]1.25300781401623[/C][C]69.222322591188[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]86.7361111111111[/C][C]1.18066601710965[/C][C]73.463714424039[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]86.2083333333333[/C][C]1.09896406975118[/C][C]78.4450881572973[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]86.2083333333333[/C][C]1.02147088934427[/C][C]84.396270351546[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]86.2083333333333[/C][C]1.02147088934427[/C][C]84.396270351546[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]86.2083333333333[/C][C]0.938011727839767[/C][C]91.9053896392856[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]85.8888888888889[/C][C]0.891525822660721[/C][C]96.3392048842255[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]85.8888888888889[/C][C]0.891525822660721[/C][C]96.3392048842255[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]87.9428571428571[/C][C]1.9344202393043[/C][C]45.4621262515766[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]87.6911764705882[/C][C]1.87038954417127[/C][C]46.8839107574473[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]87.469696969697[/C][C]1.8083231162488[/C][C]48.3706126320748[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]87.21875[/C][C]1.73626537013092[/C][C]50.2335365897572[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]87.0645161290323[/C][C]1.69437289490909[/C][C]51.3845071475271[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]86.8833333333333[/C][C]1.64644655314227[/C][C]52.7702118040305[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]86.7241379310345[/C][C]1.60718913911395[/C][C]53.9601318976347[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]86.5714285714286[/C][C]1.56397286796332[/C][C]55.3535360777492[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]86.4074074074074[/C][C]1.51984738432554[/C][C]56.8526868543137[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]86.2692307692308[/C][C]1.47684883863192[/C][C]58.414394562646[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]86.16[/C][C]1.43523019557342[/C][C]60.0321817822237[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]86.0625[/C][C]1.40016660926046[/C][C]61.4658994371079[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]85.9782608695652[/C][C]1.36147445308769[/C][C]63.1508440533534[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]85.8863636363636[/C][C]1.33627859964446[/C][C]64.2727973487078[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]85.7857142857143[/C][C]1.30198442050055[/C][C]65.8884337899634[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]85.7[/C][C]1.27811961239539[/C][C]67.0516273820297[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]85.6052631578947[/C][C]1.2443553768761[/C][C]68.7948674058072[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]85.4722222222222[/C][C]1.20415030380124[/C][C]70.9813566897795[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]85.3235294117647[/C][C]1.16600739322747[/C][C]73.1758048082282[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]85.21875[/C][C]1.13479994595466[/C][C]75.095835441117[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]85.1[/C][C]1.10936452763391[/C][C]76.7105832935761[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]84.9642857142857[/C][C]1.06840402021694[/C][C]79.5244908354366[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]84.8076923076923[/C][C]1.03183068194981[/C][C]82.1914814041333[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]84.6666666666667[/C][C]0.990291032223566[/C][C]85.4967518756168[/C][/ROW]
[ROW][C]Median[/C][C]83[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]95.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]85.1891891891892[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]85.4722222222222[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]85.1891891891892[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]85.4722222222222[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]85.4722222222222[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]85.1891891891892[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]85.4722222222222[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]86.375[/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=277580&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=277580&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 Mean88.15277777777782.0340085581533243.3394330738765
Geometric Mean86.5736752263054
Harmonic Mean85.0824000998342
Quadratic Mean89.8034118381801
Winsorized Mean ( 1 / 24 )88.18055555555561.9878667946190544.3593885637867
Winsorized Mean ( 2 / 24 )88.09722222222221.9650864705020444.831219157351
Winsorized Mean ( 3 / 24 )88.13888888888891.9583201533424845.0073951077165
Winsorized Mean ( 4 / 24 )87.751.8405481169727747.6760151993886
Winsorized Mean ( 5 / 24 )87.81944444444441.8297368039873347.9956703352471
Winsorized Mean ( 6 / 24 )87.65277777777781.7627425328663749.7252299433922
Winsorized Mean ( 7 / 24 )87.55555555555561.7425101164197250.2467989887215
Winsorized Mean ( 8 / 24 )87.55555555555561.7034542014125951.3988315523541
Winsorized Mean ( 9 / 24 )87.30555555555561.6540175976029752.7839339086114
Winsorized Mean ( 10 / 24 )87.02777777777781.6015412449393554.3400165639029
Winsorized Mean ( 11 / 24 )86.8751.5236704997676857.0169206618139
Winsorized Mean ( 12 / 24 )86.70833333333331.4945699184051558.0155750932413
Winsorized Mean ( 13 / 24 )86.70833333333331.381387213565762.7690284677803
Winsorized Mean ( 14 / 24 )86.70833333333331.381387213565762.7690284677803
Winsorized Mean ( 15 / 24 )86.51.2847668964021367.3273885264596
Winsorized Mean ( 16 / 24 )86.51.2847668964021367.3273885264596
Winsorized Mean ( 17 / 24 )86.73611111111111.2530078140162369.222322591188
Winsorized Mean ( 18 / 24 )86.73611111111111.1806660171096573.463714424039
Winsorized Mean ( 19 / 24 )86.20833333333331.0989640697511878.4450881572973
Winsorized Mean ( 20 / 24 )86.20833333333331.0214708893442784.396270351546
Winsorized Mean ( 21 / 24 )86.20833333333331.0214708893442784.396270351546
Winsorized Mean ( 22 / 24 )86.20833333333330.93801172783976791.9053896392856
Winsorized Mean ( 23 / 24 )85.88888888888890.89152582266072196.3392048842255
Winsorized Mean ( 24 / 24 )85.88888888888890.89152582266072196.3392048842255
Trimmed Mean ( 1 / 24 )87.94285714285711.934420239304345.4621262515766
Trimmed Mean ( 2 / 24 )87.69117647058821.8703895441712746.8839107574473
Trimmed Mean ( 3 / 24 )87.4696969696971.808323116248848.3706126320748
Trimmed Mean ( 4 / 24 )87.218751.7362653701309250.2335365897572
Trimmed Mean ( 5 / 24 )87.06451612903231.6943728949090951.3845071475271
Trimmed Mean ( 6 / 24 )86.88333333333331.6464465531422752.7702118040305
Trimmed Mean ( 7 / 24 )86.72413793103451.6071891391139553.9601318976347
Trimmed Mean ( 8 / 24 )86.57142857142861.5639728679633255.3535360777492
Trimmed Mean ( 9 / 24 )86.40740740740741.5198473843255456.8526868543137
Trimmed Mean ( 10 / 24 )86.26923076923081.4768488386319258.414394562646
Trimmed Mean ( 11 / 24 )86.161.4352301955734260.0321817822237
Trimmed Mean ( 12 / 24 )86.06251.4001666092604661.4658994371079
Trimmed Mean ( 13 / 24 )85.97826086956521.3614744530876963.1508440533534
Trimmed Mean ( 14 / 24 )85.88636363636361.3362785996444664.2727973487078
Trimmed Mean ( 15 / 24 )85.78571428571431.3019844205005565.8884337899634
Trimmed Mean ( 16 / 24 )85.71.2781196123953967.0516273820297
Trimmed Mean ( 17 / 24 )85.60526315789471.244355376876168.7948674058072
Trimmed Mean ( 18 / 24 )85.47222222222221.2041503038012470.9813566897795
Trimmed Mean ( 19 / 24 )85.32352941176471.1660073932274773.1758048082282
Trimmed Mean ( 20 / 24 )85.218751.1347999459546675.095835441117
Trimmed Mean ( 21 / 24 )85.11.1093645276339176.7105832935761
Trimmed Mean ( 22 / 24 )84.96428571428571.0684040202169479.5244908354366
Trimmed Mean ( 23 / 24 )84.80769230769231.0318306819498182.1914814041333
Trimmed Mean ( 24 / 24 )84.66666666666670.99029103222356685.4967518756168
Median83
Midrange95.5
Midmean - Weighted Average at Xnp85.1891891891892
Midmean - Weighted Average at X(n+1)p85.4722222222222
Midmean - Empirical Distribution Function85.1891891891892
Midmean - Empirical Distribution Function - Averaging85.4722222222222
Midmean - Empirical Distribution Function - Interpolation85.4722222222222
Midmean - Closest Observation85.1891891891892
Midmean - True Basic - Statistics Graphics Toolkit85.4722222222222
Midmean - MS Excel (old versions)86.375
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')