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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationWed, 17 Dec 2014 14:13:42 +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/2014/Dec/17/t1418825663t7vzc0itoenzpa5.htm/, Retrieved Thu, 16 May 2024 04:40:03 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=270300, Retrieved Thu, 16 May 2024 04:40:03 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact49
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [LFM F Central Ten...] [2014-12-17 14:13:42] [ca907db95fc0b179b22bb0898c34dff4] [Current]
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Dataseries X:
109
115
78
118
162
122
100
82
115
90
121
104
110
108
113
115
111
77
89
78
110
117
63
131
77
112
49
56
48
63
162
81
110
104
88
99
76
109
120
91
108
119
158
67
147
165
150
138
149
145
138
109
132
169
172
113
173
158
49
151
141
107
154
154
143
167
137
149
168
140
109
164
126
83
93
117




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=270300&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]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=270300&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=270300&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'Gwilym Jenkins' @ jenkins.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean116.3815789473683.7740093206991330.8376501109989
Geometric Mean111.230508251319
Harmonic Mean105.434465950161
Quadratic Mean120.883861183935
Winsorized Mean ( 1 / 25 )116.3815789473683.768240647940930.8848584314707
Winsorized Mean ( 2 / 25 )116.3026315789473.7530815285969330.9885705100647
Winsorized Mean ( 3 / 25 )116.5394736842113.6823638855740831.6480058205986
Winsorized Mean ( 4 / 25 )116.8552631578953.5953529435300732.5017501739791
Winsorized Mean ( 5 / 25 )116.7236842105263.5712594802340532.6841790288721
Winsorized Mean ( 6 / 25 )116.9605263157893.4952820727712933.4623998523402
Winsorized Mean ( 7 / 25 )117.6052631578953.3136654294035235.490988955715
Winsorized Mean ( 8 / 25 )117.7105263157893.2961868341205135.7111208312915
Winsorized Mean ( 9 / 25 )117.2368421052633.2136697294827836.4806753568083
Winsorized Mean ( 10 / 25 )117.3684210526323.1918669730702336.7710879065037
Winsorized Mean ( 11 / 25 )116.7894736842113.0963088261967337.7189357521762
Winsorized Mean ( 12 / 25 )117.2631578947373.0187930910688738.8443839498842
Winsorized Mean ( 13 / 25 )116.9210526315792.9096791381491940.1834865908792
Winsorized Mean ( 14 / 25 )116.9210526315792.8517008256935641.0004624531898
Winsorized Mean ( 15 / 25 )117.7105263157892.6693724730384344.0967034404923
Winsorized Mean ( 16 / 25 )117.9210526315792.6383649347817444.6947467641863
Winsorized Mean ( 17 / 25 )117.6973684210532.5361263276440246.4083224633331
Winsorized Mean ( 18 / 25 )117.4605263157892.4293845000201548.3499118047454
Winsorized Mean ( 19 / 25 )117.4605263157892.2822304256154351.467426337599
Winsorized Mean ( 20 / 25 )118.5131578947371.9864005550949759.662265795667
Winsorized Mean ( 21 / 25 )118.5131578947371.908843079491862.0863805768095
Winsorized Mean ( 22 / 25 )119.0921052631581.6772133981727471.0059348398385
Winsorized Mean ( 23 / 25 )119.0921052631581.6772133981727471.0059348398385
Winsorized Mean ( 24 / 25 )119.7236842105261.5196489303957178.7837781581243
Winsorized Mean ( 25 / 25 )118.4078947368421.2373114077920295.6977313804462
Trimmed Mean ( 1 / 25 )116.5405405405413.6836787017776331.6369993084092
Trimmed Mean ( 2 / 25 )116.7083333333333.5839713101687532.5639697511525
Trimmed Mean ( 3 / 25 )116.9285714285713.4754579619033133.6440758916665
Trimmed Mean ( 4 / 25 )117.0735294117653.3789954515861134.6474362245176
Trimmed Mean ( 5 / 25 )117.1363636363643.2958889674276635.54014252118
Trimmed Mean ( 6 / 25 )117.2343753.2035556717828936.5950796587078
Trimmed Mean ( 7 / 25 )117.2903225806453.1137764795260437.6681895286518
Trimmed Mean ( 8 / 25 )117.2333333333333.0515687052872538.4173992642574
Trimmed Mean ( 9 / 25 )117.1551724137932.9791371487938639.3252027558465
Trimmed Mean ( 10 / 25 )117.1428571428572.908834346293140.2714088178102
Trimmed Mean ( 11 / 25 )117.1111111111112.8261614331647741.4382242064526
Trimmed Mean ( 12 / 25 )117.1538461538462.7440302151319442.6940802283452
Trimmed Mean ( 13 / 25 )117.142.6576051825134744.0772770804176
Trimmed Mean ( 14 / 25 )117.1666666666672.5718975894078545.5565054958674
Trimmed Mean ( 15 / 25 )117.1956521739132.4747262699783947.3570162468662
Trimmed Mean ( 16 / 25 )117.1363636363642.3906510363234848.9976838344858
Trimmed Mean ( 17 / 25 )117.0476190476192.2868996152255851.181791394929
Trimmed Mean ( 18 / 25 )116.9752.1745873466488153.79181488399
Trimmed Mean ( 19 / 25 )116.9210526315792.0513956595766656.9958564968922
Trimmed Mean ( 20 / 25 )116.8611111111111.9240139827965160.7381818198932
Trimmed Mean ( 21 / 25 )116.6764705882351.8309678086421863.7239333414392
Trimmed Mean ( 22 / 25 )116.468751.7209480080382967.6770881258421
Trimmed Mean ( 23 / 25 )116.1666666666671.6316435077548271.1961075532452
Trimmed Mean ( 24 / 25 )115.8214285714291.4943045058354977.508585511941
Trimmed Mean ( 25 / 25 )115.3461538461541.3335231620293186.4973006322772
Median114
Midrange110.5
Midmean - Weighted Average at Xnp116.25641025641
Midmean - Weighted Average at X(n+1)p116.921052631579
Midmean - Empirical Distribution Function116.25641025641
Midmean - Empirical Distribution Function - Averaging116.921052631579
Midmean - Empirical Distribution Function - Interpolation116.921052631579
Midmean - Closest Observation116.25641025641
Midmean - True Basic - Statistics Graphics Toolkit116.921052631579
Midmean - MS Excel (old versions)116.975
Number of observations76

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 116.381578947368 & 3.77400932069913 & 30.8376501109989 \tabularnewline
Geometric Mean & 111.230508251319 &  &  \tabularnewline
Harmonic Mean & 105.434465950161 &  &  \tabularnewline
Quadratic Mean & 120.883861183935 &  &  \tabularnewline
Winsorized Mean ( 1 / 25 ) & 116.381578947368 & 3.7682406479409 & 30.8848584314707 \tabularnewline
Winsorized Mean ( 2 / 25 ) & 116.302631578947 & 3.75308152859693 & 30.9885705100647 \tabularnewline
Winsorized Mean ( 3 / 25 ) & 116.539473684211 & 3.68236388557408 & 31.6480058205986 \tabularnewline
Winsorized Mean ( 4 / 25 ) & 116.855263157895 & 3.59535294353007 & 32.5017501739791 \tabularnewline
Winsorized Mean ( 5 / 25 ) & 116.723684210526 & 3.57125948023405 & 32.6841790288721 \tabularnewline
Winsorized Mean ( 6 / 25 ) & 116.960526315789 & 3.49528207277129 & 33.4623998523402 \tabularnewline
Winsorized Mean ( 7 / 25 ) & 117.605263157895 & 3.31366542940352 & 35.490988955715 \tabularnewline
Winsorized Mean ( 8 / 25 ) & 117.710526315789 & 3.29618683412051 & 35.7111208312915 \tabularnewline
Winsorized Mean ( 9 / 25 ) & 117.236842105263 & 3.21366972948278 & 36.4806753568083 \tabularnewline
Winsorized Mean ( 10 / 25 ) & 117.368421052632 & 3.19186697307023 & 36.7710879065037 \tabularnewline
Winsorized Mean ( 11 / 25 ) & 116.789473684211 & 3.09630882619673 & 37.7189357521762 \tabularnewline
Winsorized Mean ( 12 / 25 ) & 117.263157894737 & 3.01879309106887 & 38.8443839498842 \tabularnewline
Winsorized Mean ( 13 / 25 ) & 116.921052631579 & 2.90967913814919 & 40.1834865908792 \tabularnewline
Winsorized Mean ( 14 / 25 ) & 116.921052631579 & 2.85170082569356 & 41.0004624531898 \tabularnewline
Winsorized Mean ( 15 / 25 ) & 117.710526315789 & 2.66937247303843 & 44.0967034404923 \tabularnewline
Winsorized Mean ( 16 / 25 ) & 117.921052631579 & 2.63836493478174 & 44.6947467641863 \tabularnewline
Winsorized Mean ( 17 / 25 ) & 117.697368421053 & 2.53612632764402 & 46.4083224633331 \tabularnewline
Winsorized Mean ( 18 / 25 ) & 117.460526315789 & 2.42938450002015 & 48.3499118047454 \tabularnewline
Winsorized Mean ( 19 / 25 ) & 117.460526315789 & 2.28223042561543 & 51.467426337599 \tabularnewline
Winsorized Mean ( 20 / 25 ) & 118.513157894737 & 1.98640055509497 & 59.662265795667 \tabularnewline
Winsorized Mean ( 21 / 25 ) & 118.513157894737 & 1.9088430794918 & 62.0863805768095 \tabularnewline
Winsorized Mean ( 22 / 25 ) & 119.092105263158 & 1.67721339817274 & 71.0059348398385 \tabularnewline
Winsorized Mean ( 23 / 25 ) & 119.092105263158 & 1.67721339817274 & 71.0059348398385 \tabularnewline
Winsorized Mean ( 24 / 25 ) & 119.723684210526 & 1.51964893039571 & 78.7837781581243 \tabularnewline
Winsorized Mean ( 25 / 25 ) & 118.407894736842 & 1.23731140779202 & 95.6977313804462 \tabularnewline
Trimmed Mean ( 1 / 25 ) & 116.540540540541 & 3.68367870177763 & 31.6369993084092 \tabularnewline
Trimmed Mean ( 2 / 25 ) & 116.708333333333 & 3.58397131016875 & 32.5639697511525 \tabularnewline
Trimmed Mean ( 3 / 25 ) & 116.928571428571 & 3.47545796190331 & 33.6440758916665 \tabularnewline
Trimmed Mean ( 4 / 25 ) & 117.073529411765 & 3.37899545158611 & 34.6474362245176 \tabularnewline
Trimmed Mean ( 5 / 25 ) & 117.136363636364 & 3.29588896742766 & 35.54014252118 \tabularnewline
Trimmed Mean ( 6 / 25 ) & 117.234375 & 3.20355567178289 & 36.5950796587078 \tabularnewline
Trimmed Mean ( 7 / 25 ) & 117.290322580645 & 3.11377647952604 & 37.6681895286518 \tabularnewline
Trimmed Mean ( 8 / 25 ) & 117.233333333333 & 3.05156870528725 & 38.4173992642574 \tabularnewline
Trimmed Mean ( 9 / 25 ) & 117.155172413793 & 2.97913714879386 & 39.3252027558465 \tabularnewline
Trimmed Mean ( 10 / 25 ) & 117.142857142857 & 2.9088343462931 & 40.2714088178102 \tabularnewline
Trimmed Mean ( 11 / 25 ) & 117.111111111111 & 2.82616143316477 & 41.4382242064526 \tabularnewline
Trimmed Mean ( 12 / 25 ) & 117.153846153846 & 2.74403021513194 & 42.6940802283452 \tabularnewline
Trimmed Mean ( 13 / 25 ) & 117.14 & 2.65760518251347 & 44.0772770804176 \tabularnewline
Trimmed Mean ( 14 / 25 ) & 117.166666666667 & 2.57189758940785 & 45.5565054958674 \tabularnewline
Trimmed Mean ( 15 / 25 ) & 117.195652173913 & 2.47472626997839 & 47.3570162468662 \tabularnewline
Trimmed Mean ( 16 / 25 ) & 117.136363636364 & 2.39065103632348 & 48.9976838344858 \tabularnewline
Trimmed Mean ( 17 / 25 ) & 117.047619047619 & 2.28689961522558 & 51.181791394929 \tabularnewline
Trimmed Mean ( 18 / 25 ) & 116.975 & 2.17458734664881 & 53.79181488399 \tabularnewline
Trimmed Mean ( 19 / 25 ) & 116.921052631579 & 2.05139565957666 & 56.9958564968922 \tabularnewline
Trimmed Mean ( 20 / 25 ) & 116.861111111111 & 1.92401398279651 & 60.7381818198932 \tabularnewline
Trimmed Mean ( 21 / 25 ) & 116.676470588235 & 1.83096780864218 & 63.7239333414392 \tabularnewline
Trimmed Mean ( 22 / 25 ) & 116.46875 & 1.72094800803829 & 67.6770881258421 \tabularnewline
Trimmed Mean ( 23 / 25 ) & 116.166666666667 & 1.63164350775482 & 71.1961075532452 \tabularnewline
Trimmed Mean ( 24 / 25 ) & 115.821428571429 & 1.49430450583549 & 77.508585511941 \tabularnewline
Trimmed Mean ( 25 / 25 ) & 115.346153846154 & 1.33352316202931 & 86.4973006322772 \tabularnewline
Median & 114 &  &  \tabularnewline
Midrange & 110.5 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 116.25641025641 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 116.921052631579 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 116.25641025641 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 116.921052631579 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 116.921052631579 &  &  \tabularnewline
Midmean - Closest Observation & 116.25641025641 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 116.921052631579 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 116.975 &  &  \tabularnewline
Number of observations & 76 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=270300&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]116.381578947368[/C][C]3.77400932069913[/C][C]30.8376501109989[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]111.230508251319[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]105.434465950161[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]120.883861183935[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 25 )[/C][C]116.381578947368[/C][C]3.7682406479409[/C][C]30.8848584314707[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 25 )[/C][C]116.302631578947[/C][C]3.75308152859693[/C][C]30.9885705100647[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 25 )[/C][C]116.539473684211[/C][C]3.68236388557408[/C][C]31.6480058205986[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 25 )[/C][C]116.855263157895[/C][C]3.59535294353007[/C][C]32.5017501739791[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 25 )[/C][C]116.723684210526[/C][C]3.57125948023405[/C][C]32.6841790288721[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 25 )[/C][C]116.960526315789[/C][C]3.49528207277129[/C][C]33.4623998523402[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 25 )[/C][C]117.605263157895[/C][C]3.31366542940352[/C][C]35.490988955715[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 25 )[/C][C]117.710526315789[/C][C]3.29618683412051[/C][C]35.7111208312915[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 25 )[/C][C]117.236842105263[/C][C]3.21366972948278[/C][C]36.4806753568083[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 25 )[/C][C]117.368421052632[/C][C]3.19186697307023[/C][C]36.7710879065037[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 25 )[/C][C]116.789473684211[/C][C]3.09630882619673[/C][C]37.7189357521762[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 25 )[/C][C]117.263157894737[/C][C]3.01879309106887[/C][C]38.8443839498842[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 25 )[/C][C]116.921052631579[/C][C]2.90967913814919[/C][C]40.1834865908792[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 25 )[/C][C]116.921052631579[/C][C]2.85170082569356[/C][C]41.0004624531898[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 25 )[/C][C]117.710526315789[/C][C]2.66937247303843[/C][C]44.0967034404923[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 25 )[/C][C]117.921052631579[/C][C]2.63836493478174[/C][C]44.6947467641863[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 25 )[/C][C]117.697368421053[/C][C]2.53612632764402[/C][C]46.4083224633331[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 25 )[/C][C]117.460526315789[/C][C]2.42938450002015[/C][C]48.3499118047454[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 25 )[/C][C]117.460526315789[/C][C]2.28223042561543[/C][C]51.467426337599[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 25 )[/C][C]118.513157894737[/C][C]1.98640055509497[/C][C]59.662265795667[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 25 )[/C][C]118.513157894737[/C][C]1.9088430794918[/C][C]62.0863805768095[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 25 )[/C][C]119.092105263158[/C][C]1.67721339817274[/C][C]71.0059348398385[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 25 )[/C][C]119.092105263158[/C][C]1.67721339817274[/C][C]71.0059348398385[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 25 )[/C][C]119.723684210526[/C][C]1.51964893039571[/C][C]78.7837781581243[/C][/ROW]
[ROW][C]Winsorized Mean ( 25 / 25 )[/C][C]118.407894736842[/C][C]1.23731140779202[/C][C]95.6977313804462[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 25 )[/C][C]116.540540540541[/C][C]3.68367870177763[/C][C]31.6369993084092[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 25 )[/C][C]116.708333333333[/C][C]3.58397131016875[/C][C]32.5639697511525[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 25 )[/C][C]116.928571428571[/C][C]3.47545796190331[/C][C]33.6440758916665[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 25 )[/C][C]117.073529411765[/C][C]3.37899545158611[/C][C]34.6474362245176[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 25 )[/C][C]117.136363636364[/C][C]3.29588896742766[/C][C]35.54014252118[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 25 )[/C][C]117.234375[/C][C]3.20355567178289[/C][C]36.5950796587078[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 25 )[/C][C]117.290322580645[/C][C]3.11377647952604[/C][C]37.6681895286518[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 25 )[/C][C]117.233333333333[/C][C]3.05156870528725[/C][C]38.4173992642574[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 25 )[/C][C]117.155172413793[/C][C]2.97913714879386[/C][C]39.3252027558465[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 25 )[/C][C]117.142857142857[/C][C]2.9088343462931[/C][C]40.2714088178102[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 25 )[/C][C]117.111111111111[/C][C]2.82616143316477[/C][C]41.4382242064526[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 25 )[/C][C]117.153846153846[/C][C]2.74403021513194[/C][C]42.6940802283452[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 25 )[/C][C]117.14[/C][C]2.65760518251347[/C][C]44.0772770804176[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 25 )[/C][C]117.166666666667[/C][C]2.57189758940785[/C][C]45.5565054958674[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 25 )[/C][C]117.195652173913[/C][C]2.47472626997839[/C][C]47.3570162468662[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 25 )[/C][C]117.136363636364[/C][C]2.39065103632348[/C][C]48.9976838344858[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 25 )[/C][C]117.047619047619[/C][C]2.28689961522558[/C][C]51.181791394929[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 25 )[/C][C]116.975[/C][C]2.17458734664881[/C][C]53.79181488399[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 25 )[/C][C]116.921052631579[/C][C]2.05139565957666[/C][C]56.9958564968922[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 25 )[/C][C]116.861111111111[/C][C]1.92401398279651[/C][C]60.7381818198932[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 25 )[/C][C]116.676470588235[/C][C]1.83096780864218[/C][C]63.7239333414392[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 25 )[/C][C]116.46875[/C][C]1.72094800803829[/C][C]67.6770881258421[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 25 )[/C][C]116.166666666667[/C][C]1.63164350775482[/C][C]71.1961075532452[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 25 )[/C][C]115.821428571429[/C][C]1.49430450583549[/C][C]77.508585511941[/C][/ROW]
[ROW][C]Trimmed Mean ( 25 / 25 )[/C][C]115.346153846154[/C][C]1.33352316202931[/C][C]86.4973006322772[/C][/ROW]
[ROW][C]Median[/C][C]114[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]110.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]116.25641025641[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]116.921052631579[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]116.25641025641[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]116.921052631579[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]116.921052631579[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]116.25641025641[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]116.921052631579[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]116.975[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]76[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=270300&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=270300&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 Mean116.3815789473683.7740093206991330.8376501109989
Geometric Mean111.230508251319
Harmonic Mean105.434465950161
Quadratic Mean120.883861183935
Winsorized Mean ( 1 / 25 )116.3815789473683.768240647940930.8848584314707
Winsorized Mean ( 2 / 25 )116.3026315789473.7530815285969330.9885705100647
Winsorized Mean ( 3 / 25 )116.5394736842113.6823638855740831.6480058205986
Winsorized Mean ( 4 / 25 )116.8552631578953.5953529435300732.5017501739791
Winsorized Mean ( 5 / 25 )116.7236842105263.5712594802340532.6841790288721
Winsorized Mean ( 6 / 25 )116.9605263157893.4952820727712933.4623998523402
Winsorized Mean ( 7 / 25 )117.6052631578953.3136654294035235.490988955715
Winsorized Mean ( 8 / 25 )117.7105263157893.2961868341205135.7111208312915
Winsorized Mean ( 9 / 25 )117.2368421052633.2136697294827836.4806753568083
Winsorized Mean ( 10 / 25 )117.3684210526323.1918669730702336.7710879065037
Winsorized Mean ( 11 / 25 )116.7894736842113.0963088261967337.7189357521762
Winsorized Mean ( 12 / 25 )117.2631578947373.0187930910688738.8443839498842
Winsorized Mean ( 13 / 25 )116.9210526315792.9096791381491940.1834865908792
Winsorized Mean ( 14 / 25 )116.9210526315792.8517008256935641.0004624531898
Winsorized Mean ( 15 / 25 )117.7105263157892.6693724730384344.0967034404923
Winsorized Mean ( 16 / 25 )117.9210526315792.6383649347817444.6947467641863
Winsorized Mean ( 17 / 25 )117.6973684210532.5361263276440246.4083224633331
Winsorized Mean ( 18 / 25 )117.4605263157892.4293845000201548.3499118047454
Winsorized Mean ( 19 / 25 )117.4605263157892.2822304256154351.467426337599
Winsorized Mean ( 20 / 25 )118.5131578947371.9864005550949759.662265795667
Winsorized Mean ( 21 / 25 )118.5131578947371.908843079491862.0863805768095
Winsorized Mean ( 22 / 25 )119.0921052631581.6772133981727471.0059348398385
Winsorized Mean ( 23 / 25 )119.0921052631581.6772133981727471.0059348398385
Winsorized Mean ( 24 / 25 )119.7236842105261.5196489303957178.7837781581243
Winsorized Mean ( 25 / 25 )118.4078947368421.2373114077920295.6977313804462
Trimmed Mean ( 1 / 25 )116.5405405405413.6836787017776331.6369993084092
Trimmed Mean ( 2 / 25 )116.7083333333333.5839713101687532.5639697511525
Trimmed Mean ( 3 / 25 )116.9285714285713.4754579619033133.6440758916665
Trimmed Mean ( 4 / 25 )117.0735294117653.3789954515861134.6474362245176
Trimmed Mean ( 5 / 25 )117.1363636363643.2958889674276635.54014252118
Trimmed Mean ( 6 / 25 )117.2343753.2035556717828936.5950796587078
Trimmed Mean ( 7 / 25 )117.2903225806453.1137764795260437.6681895286518
Trimmed Mean ( 8 / 25 )117.2333333333333.0515687052872538.4173992642574
Trimmed Mean ( 9 / 25 )117.1551724137932.9791371487938639.3252027558465
Trimmed Mean ( 10 / 25 )117.1428571428572.908834346293140.2714088178102
Trimmed Mean ( 11 / 25 )117.1111111111112.8261614331647741.4382242064526
Trimmed Mean ( 12 / 25 )117.1538461538462.7440302151319442.6940802283452
Trimmed Mean ( 13 / 25 )117.142.6576051825134744.0772770804176
Trimmed Mean ( 14 / 25 )117.1666666666672.5718975894078545.5565054958674
Trimmed Mean ( 15 / 25 )117.1956521739132.4747262699783947.3570162468662
Trimmed Mean ( 16 / 25 )117.1363636363642.3906510363234848.9976838344858
Trimmed Mean ( 17 / 25 )117.0476190476192.2868996152255851.181791394929
Trimmed Mean ( 18 / 25 )116.9752.1745873466488153.79181488399
Trimmed Mean ( 19 / 25 )116.9210526315792.0513956595766656.9958564968922
Trimmed Mean ( 20 / 25 )116.8611111111111.9240139827965160.7381818198932
Trimmed Mean ( 21 / 25 )116.6764705882351.8309678086421863.7239333414392
Trimmed Mean ( 22 / 25 )116.468751.7209480080382967.6770881258421
Trimmed Mean ( 23 / 25 )116.1666666666671.6316435077548271.1961075532452
Trimmed Mean ( 24 / 25 )115.8214285714291.4943045058354977.508585511941
Trimmed Mean ( 25 / 25 )115.3461538461541.3335231620293186.4973006322772
Median114
Midrange110.5
Midmean - Weighted Average at Xnp116.25641025641
Midmean - Weighted Average at X(n+1)p116.921052631579
Midmean - Empirical Distribution Function116.25641025641
Midmean - Empirical Distribution Function - Averaging116.921052631579
Midmean - Empirical Distribution Function - Interpolation116.921052631579
Midmean - Closest Observation116.25641025641
Midmean - True Basic - Statistics Graphics Toolkit116.921052631579
Midmean - MS Excel (old versions)116.975
Number of observations76



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')