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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 computationSat, 05 Mar 2016 17:48:41 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Mar/05/t14572001946jy29j219jnpqx0.htm/, Retrieved Sat, 27 Apr 2024 11:14:41 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=293531, Retrieved Sat, 27 Apr 2024 11:14:41 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact55
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Central Tendency] [] [2016-03-05 15:33:29] [eb84577074ca016fc26a8bcabc390030]
-    D    [Central Tendency] [] [2016-03-05 17:48:41] [73c24565f080d314e595da727a2003f4] [Current]
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Dataseries X:
89,72
89.95
90.19
90.23
90.32
90.86
90.99
90.98
91.22
91.42
91.55
91.67
92.30
92.92
93.10
93.23
93.36
93.42
93.58
93.68
94.02
94.29
94.54
94.64
96.70
96.83
97.07
97.11
97.42
97.44
97.67
97.84
98.17
98.31
98.42
98.44
98.89
99.26
99.59
99.82
99.95
99.99
100.28
100.38
100.46
100.52
100.43
100.44
101.33
101.43
101.41
101.53
101.58
101.73
102.12
101.86
101.93
101.86
101.92
102.02




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Sir Maurice George Kendall' @ kendall.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 & 'Sir Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=293531&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]'Sir Maurice George Kendall' @ kendall.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=293531&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=293531&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'Sir Maurice George Kendall' @ kendall.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean96.73883333333330.531962791892975181.852631062956
Geometric Mean96.6517908714738
Harmonic Mean96.5640692917592
Quadratic Mean96.825089491309
Winsorized Mean ( 1 / 20 )96.7410.530835217603907182.242995174041
Winsorized Mean ( 2 / 20 )96.7460.528624865653869183.014470725535
Winsorized Mean ( 3 / 20 )96.74750.528122440487897183.191420365742
Winsorized Mean ( 4 / 20 )96.74950.526212424346597183.860158984529
Winsorized Mean ( 5 / 20 )96.79450.517174386493761187.160274228252
Winsorized Mean ( 6 / 20 )96.79350.512714434951767188.786375809969
Winsorized Mean ( 7 / 20 )96.77716666666670.509664511991396189.884059787746
Winsorized Mean ( 8 / 20 )96.80116666666670.502764284812339192.537874289934
Winsorized Mean ( 9 / 20 )96.81616666666670.494787810005784195.672093590048
Winsorized Mean ( 10 / 20 )96.83450.490279029570058197.508957470437
Winsorized Mean ( 11 / 20 )96.84183333333330.483964296417779200.101193518076
Winsorized Mean ( 12 / 20 )96.80583333333330.437072327959771221.486987714865
Winsorized Mean ( 13 / 20 )96.92716666666670.412374486411701235.046468345032
Winsorized Mean ( 14 / 20 )96.96450.404839259794781239.513578918094
Winsorized Mean ( 15 / 20 )96.99450.39924875958968242.942520597144
Winsorized Mean ( 16 / 20 )97.01583333333330.391794530757449247.61916187491
Winsorized Mean ( 17 / 20 )97.00450.385004176732792251.957006864694
Winsorized Mean ( 18 / 20 )96.96550.365058731053846265.61616461023
Winsorized Mean ( 19 / 20 )96.98450.358317192515203270.66661055033
Winsorized Mean ( 20 / 20 )97.05450.334672065226451289.998808040132
Trimmed Mean ( 1 / 20 )96.76706896551720.528526127481101183.088524737081
Trimmed Mean ( 2 / 20 )96.7950.525143208668254184.321149740218
Trimmed Mean ( 3 / 20 )96.82222222222220.521834215105692185.542111688886
Trimmed Mean ( 4 / 20 )96.85096153846150.517370312923902187.198529020947
Trimmed Mean ( 5 / 20 )96.88140.511929524007964189.247533999412
Trimmed Mean ( 6 / 20 )96.9031250.507483724038522190.948242100951
Trimmed Mean ( 7 / 20 )96.92695652173910.502458388169657192.905440139674
Trimmed Mean ( 8 / 20 )96.95613636363640.496108345075766195.433391367019
Trimmed Mean ( 9 / 20 )96.98380952380950.489025905175531198.320392636456
Trimmed Mean ( 10 / 20 )97.011750.481087295173052201.651032927619
Trimmed Mean ( 11 / 20 )97.03973684210530.470955187915455206.048769250474
Trimmed Mean ( 12 / 20 )97.06972222222220.458237043757491211.832988067184
Trimmed Mean ( 13 / 20 )97.10852941176470.452631862461054214.541965481098
Trimmed Mean ( 14 / 20 )97.13468750.450215446717126215.751565629934
Trimmed Mean ( 15 / 20 )97.1590.447021907971966217.347289399725
Trimmed Mean ( 16 / 20 )97.18250.442005597716475219.86712499134
Trimmed Mean ( 17 / 20 )97.20653846153850.434738450921999223.597747692622
Trimmed Mean ( 18 / 20 )97.236250.423587085522846229.55433091162
Trimmed Mean ( 19 / 20 )97.27727272727270.411035110737456236.664144220534
Trimmed Mean ( 20 / 20 )97.32350.39043920950103249.266717152656
Median97.555
Midrange95.92
Midmean - Weighted Average at Xnp97.028064516129
Midmean - Weighted Average at X(n+1)p97.159
Midmean - Empirical Distribution Function97.028064516129
Midmean - Empirical Distribution Function - Averaging97.159
Midmean - Empirical Distribution Function - Interpolation97.159
Midmean - Closest Observation97.028064516129
Midmean - True Basic - Statistics Graphics Toolkit97.159
Midmean - MS Excel (old versions)97.1346875
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 96.7388333333333 & 0.531962791892975 & 181.852631062956 \tabularnewline
Geometric Mean & 96.6517908714738 &  &  \tabularnewline
Harmonic Mean & 96.5640692917592 &  &  \tabularnewline
Quadratic Mean & 96.825089491309 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 96.741 & 0.530835217603907 & 182.242995174041 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 96.746 & 0.528624865653869 & 183.014470725535 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 96.7475 & 0.528122440487897 & 183.191420365742 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 96.7495 & 0.526212424346597 & 183.860158984529 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 96.7945 & 0.517174386493761 & 187.160274228252 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 96.7935 & 0.512714434951767 & 188.786375809969 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 96.7771666666667 & 0.509664511991396 & 189.884059787746 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 96.8011666666667 & 0.502764284812339 & 192.537874289934 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 96.8161666666667 & 0.494787810005784 & 195.672093590048 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 96.8345 & 0.490279029570058 & 197.508957470437 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 96.8418333333333 & 0.483964296417779 & 200.101193518076 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 96.8058333333333 & 0.437072327959771 & 221.486987714865 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 96.9271666666667 & 0.412374486411701 & 235.046468345032 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 96.9645 & 0.404839259794781 & 239.513578918094 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 96.9945 & 0.39924875958968 & 242.942520597144 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 97.0158333333333 & 0.391794530757449 & 247.61916187491 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 97.0045 & 0.385004176732792 & 251.957006864694 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 96.9655 & 0.365058731053846 & 265.61616461023 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 96.9845 & 0.358317192515203 & 270.66661055033 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 97.0545 & 0.334672065226451 & 289.998808040132 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 96.7670689655172 & 0.528526127481101 & 183.088524737081 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 96.795 & 0.525143208668254 & 184.321149740218 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 96.8222222222222 & 0.521834215105692 & 185.542111688886 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 96.8509615384615 & 0.517370312923902 & 187.198529020947 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 96.8814 & 0.511929524007964 & 189.247533999412 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 96.903125 & 0.507483724038522 & 190.948242100951 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 96.9269565217391 & 0.502458388169657 & 192.905440139674 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 96.9561363636364 & 0.496108345075766 & 195.433391367019 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 96.9838095238095 & 0.489025905175531 & 198.320392636456 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 97.01175 & 0.481087295173052 & 201.651032927619 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 97.0397368421053 & 0.470955187915455 & 206.048769250474 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 97.0697222222222 & 0.458237043757491 & 211.832988067184 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 97.1085294117647 & 0.452631862461054 & 214.541965481098 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 97.1346875 & 0.450215446717126 & 215.751565629934 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 97.159 & 0.447021907971966 & 217.347289399725 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 97.1825 & 0.442005597716475 & 219.86712499134 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 97.2065384615385 & 0.434738450921999 & 223.597747692622 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 97.23625 & 0.423587085522846 & 229.55433091162 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 97.2772727272727 & 0.411035110737456 & 236.664144220534 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 97.3235 & 0.39043920950103 & 249.266717152656 \tabularnewline
Median & 97.555 &  &  \tabularnewline
Midrange & 95.92 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 97.028064516129 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 97.159 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 97.028064516129 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 97.159 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 97.159 &  &  \tabularnewline
Midmean - Closest Observation & 97.028064516129 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 97.159 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 97.1346875 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=293531&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]96.7388333333333[/C][C]0.531962791892975[/C][C]181.852631062956[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]96.6517908714738[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]96.5640692917592[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]96.825089491309[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]96.741[/C][C]0.530835217603907[/C][C]182.242995174041[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]96.746[/C][C]0.528624865653869[/C][C]183.014470725535[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]96.7475[/C][C]0.528122440487897[/C][C]183.191420365742[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]96.7495[/C][C]0.526212424346597[/C][C]183.860158984529[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]96.7945[/C][C]0.517174386493761[/C][C]187.160274228252[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]96.7935[/C][C]0.512714434951767[/C][C]188.786375809969[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]96.7771666666667[/C][C]0.509664511991396[/C][C]189.884059787746[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]96.8011666666667[/C][C]0.502764284812339[/C][C]192.537874289934[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]96.8161666666667[/C][C]0.494787810005784[/C][C]195.672093590048[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]96.8345[/C][C]0.490279029570058[/C][C]197.508957470437[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]96.8418333333333[/C][C]0.483964296417779[/C][C]200.101193518076[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]96.8058333333333[/C][C]0.437072327959771[/C][C]221.486987714865[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]96.9271666666667[/C][C]0.412374486411701[/C][C]235.046468345032[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]96.9645[/C][C]0.404839259794781[/C][C]239.513578918094[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]96.9945[/C][C]0.39924875958968[/C][C]242.942520597144[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]97.0158333333333[/C][C]0.391794530757449[/C][C]247.61916187491[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]97.0045[/C][C]0.385004176732792[/C][C]251.957006864694[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]96.9655[/C][C]0.365058731053846[/C][C]265.61616461023[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]96.9845[/C][C]0.358317192515203[/C][C]270.66661055033[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]97.0545[/C][C]0.334672065226451[/C][C]289.998808040132[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]96.7670689655172[/C][C]0.528526127481101[/C][C]183.088524737081[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]96.795[/C][C]0.525143208668254[/C][C]184.321149740218[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]96.8222222222222[/C][C]0.521834215105692[/C][C]185.542111688886[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]96.8509615384615[/C][C]0.517370312923902[/C][C]187.198529020947[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]96.8814[/C][C]0.511929524007964[/C][C]189.247533999412[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]96.903125[/C][C]0.507483724038522[/C][C]190.948242100951[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]96.9269565217391[/C][C]0.502458388169657[/C][C]192.905440139674[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]96.9561363636364[/C][C]0.496108345075766[/C][C]195.433391367019[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]96.9838095238095[/C][C]0.489025905175531[/C][C]198.320392636456[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]97.01175[/C][C]0.481087295173052[/C][C]201.651032927619[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]97.0397368421053[/C][C]0.470955187915455[/C][C]206.048769250474[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]97.0697222222222[/C][C]0.458237043757491[/C][C]211.832988067184[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]97.1085294117647[/C][C]0.452631862461054[/C][C]214.541965481098[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]97.1346875[/C][C]0.450215446717126[/C][C]215.751565629934[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]97.159[/C][C]0.447021907971966[/C][C]217.347289399725[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]97.1825[/C][C]0.442005597716475[/C][C]219.86712499134[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]97.2065384615385[/C][C]0.434738450921999[/C][C]223.597747692622[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]97.23625[/C][C]0.423587085522846[/C][C]229.55433091162[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]97.2772727272727[/C][C]0.411035110737456[/C][C]236.664144220534[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]97.3235[/C][C]0.39043920950103[/C][C]249.266717152656[/C][/ROW]
[ROW][C]Median[/C][C]97.555[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]95.92[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]97.028064516129[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]97.159[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]97.028064516129[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]97.159[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]97.159[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]97.028064516129[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]97.159[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]97.1346875[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]60[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=293531&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=293531&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 Mean96.73883333333330.531962791892975181.852631062956
Geometric Mean96.6517908714738
Harmonic Mean96.5640692917592
Quadratic Mean96.825089491309
Winsorized Mean ( 1 / 20 )96.7410.530835217603907182.242995174041
Winsorized Mean ( 2 / 20 )96.7460.528624865653869183.014470725535
Winsorized Mean ( 3 / 20 )96.74750.528122440487897183.191420365742
Winsorized Mean ( 4 / 20 )96.74950.526212424346597183.860158984529
Winsorized Mean ( 5 / 20 )96.79450.517174386493761187.160274228252
Winsorized Mean ( 6 / 20 )96.79350.512714434951767188.786375809969
Winsorized Mean ( 7 / 20 )96.77716666666670.509664511991396189.884059787746
Winsorized Mean ( 8 / 20 )96.80116666666670.502764284812339192.537874289934
Winsorized Mean ( 9 / 20 )96.81616666666670.494787810005784195.672093590048
Winsorized Mean ( 10 / 20 )96.83450.490279029570058197.508957470437
Winsorized Mean ( 11 / 20 )96.84183333333330.483964296417779200.101193518076
Winsorized Mean ( 12 / 20 )96.80583333333330.437072327959771221.486987714865
Winsorized Mean ( 13 / 20 )96.92716666666670.412374486411701235.046468345032
Winsorized Mean ( 14 / 20 )96.96450.404839259794781239.513578918094
Winsorized Mean ( 15 / 20 )96.99450.39924875958968242.942520597144
Winsorized Mean ( 16 / 20 )97.01583333333330.391794530757449247.61916187491
Winsorized Mean ( 17 / 20 )97.00450.385004176732792251.957006864694
Winsorized Mean ( 18 / 20 )96.96550.365058731053846265.61616461023
Winsorized Mean ( 19 / 20 )96.98450.358317192515203270.66661055033
Winsorized Mean ( 20 / 20 )97.05450.334672065226451289.998808040132
Trimmed Mean ( 1 / 20 )96.76706896551720.528526127481101183.088524737081
Trimmed Mean ( 2 / 20 )96.7950.525143208668254184.321149740218
Trimmed Mean ( 3 / 20 )96.82222222222220.521834215105692185.542111688886
Trimmed Mean ( 4 / 20 )96.85096153846150.517370312923902187.198529020947
Trimmed Mean ( 5 / 20 )96.88140.511929524007964189.247533999412
Trimmed Mean ( 6 / 20 )96.9031250.507483724038522190.948242100951
Trimmed Mean ( 7 / 20 )96.92695652173910.502458388169657192.905440139674
Trimmed Mean ( 8 / 20 )96.95613636363640.496108345075766195.433391367019
Trimmed Mean ( 9 / 20 )96.98380952380950.489025905175531198.320392636456
Trimmed Mean ( 10 / 20 )97.011750.481087295173052201.651032927619
Trimmed Mean ( 11 / 20 )97.03973684210530.470955187915455206.048769250474
Trimmed Mean ( 12 / 20 )97.06972222222220.458237043757491211.832988067184
Trimmed Mean ( 13 / 20 )97.10852941176470.452631862461054214.541965481098
Trimmed Mean ( 14 / 20 )97.13468750.450215446717126215.751565629934
Trimmed Mean ( 15 / 20 )97.1590.447021907971966217.347289399725
Trimmed Mean ( 16 / 20 )97.18250.442005597716475219.86712499134
Trimmed Mean ( 17 / 20 )97.20653846153850.434738450921999223.597747692622
Trimmed Mean ( 18 / 20 )97.236250.423587085522846229.55433091162
Trimmed Mean ( 19 / 20 )97.27727272727270.411035110737456236.664144220534
Trimmed Mean ( 20 / 20 )97.32350.39043920950103249.266717152656
Median97.555
Midrange95.92
Midmean - Weighted Average at Xnp97.028064516129
Midmean - Weighted Average at X(n+1)p97.159
Midmean - Empirical Distribution Function97.028064516129
Midmean - Empirical Distribution Function - Averaging97.159
Midmean - Empirical Distribution Function - Interpolation97.159
Midmean - Closest Observation97.028064516129
Midmean - True Basic - Statistics Graphics Toolkit97.159
Midmean - MS Excel (old versions)97.1346875
Number of observations60



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')