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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, 10 Oct 2013 14:34:20 -0400
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2013/Oct/10/t1381430079tz2oyi7dgv0p9ek.htm/, Retrieved Thu, 02 May 2024 10:29:29 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=214667, Retrieved Thu, 02 May 2024 10:29:29 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact73
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2013-10-10 18:34:20] [d46004c4f56a1463f2fd3be871dd57bc] [Current]
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Dataseries X:
83,7
86,4
85,9
80,4
81,8
87,5
83,7
87
99,7
101,4
101,9
115,7
123,2
136,9
146,8
149,6
146,5
157
147,9
133,6
128,7
100,8
91,8
89,3
96,7
91,6
93,3
93,3
101
100,4
86,9
83,9
80,3
87,7
92,7
95,5
92
87,4
86,8
83,7
85
81,7
90,9
101,5
113,8
120,1
122,1
132,5
140
149,4
144,3
154,4
151,4
145,5
136,8
146,6
145,1
133,6
131,4
127,5
130,1
131,1
132,3
128,6
125,1
128,7
156,1
163,2
159,8
157,4
156,2
152,5




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gertrude Mary Cox' @ cox.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 & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=214667&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=214667&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=214667&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'Gertrude Mary Cox' @ cox.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean116.3208333333333.1679531223684936.7179780887563
Geometric Mean113.252919459792
Harmonic Mean110.265392229586
Quadratic Mean119.344405329003
Winsorized Mean ( 1 / 24 )116.2753.1582261802527436.8165525088184
Winsorized Mean ( 2 / 24 )116.2444444444443.139914729816737.0215290691127
Winsorized Mean ( 3 / 24 )116.2319444444443.1362056223638837.0613277444595
Winsorized Mean ( 4 / 24 )116.2930555555563.1121759256397837.3671213755851
Winsorized Mean ( 5 / 24 )116.2861111111113.1109229452095337.3799393810697
Winsorized Mean ( 6 / 24 )116.1444444444443.0857850225437937.6385404673135
Winsorized Mean ( 7 / 24 )115.9791666666673.0512048580324438.0109406162441
Winsorized Mean ( 8 / 24 )115.9791666666673.0128817964672238.4944297524911
Winsorized Mean ( 9 / 24 )115.8666666666672.960023156869239.1438379114636
Winsorized Mean ( 10 / 24 )115.9083333333332.9457196540277239.3480530894548
Winsorized Mean ( 11 / 24 )115.7402777777782.9008711522218239.8984552240904
Winsorized Mean ( 12 / 24 )115.5736111111112.8701665453192740.2672142143079
Winsorized Mean ( 13 / 24 )115.5555555555562.8621025524414840.3743588632008
Winsorized Mean ( 14 / 24 )115.6138888888892.8482418495677240.5913173793285
Winsorized Mean ( 15 / 24 )115.4263888888892.8137405927102741.0223988621876
Winsorized Mean ( 16 / 24 )115.3819444444442.7941850293148641.2935948170677
Winsorized Mean ( 17 / 24 )115.5708333333332.7138356439884442.5857894487237
Winsorized Mean ( 18 / 24 )114.8958333333332.5033236416202445.8973148429855
Winsorized Mean ( 19 / 24 )114.26252.3654095033512948.3055893020274
Winsorized Mean ( 20 / 24 )114.2902777777782.3541809773317448.5477874803475
Winsorized Mean ( 21 / 24 )113.4152777777782.2237027479580851.0028950056035
Winsorized Mean ( 22 / 24 )113.6291666666672.1948326688048951.7712207776362
Winsorized Mean ( 23 / 24 )113.4694444444442.1244576210050353.4110180982404
Winsorized Mean ( 24 / 24 )113.4027777777782.1160593674483353.5914915820749
Trimmed Mean ( 1 / 24 )116.1657142857143.1460915222402136.9238191147717
Trimmed Mean ( 2 / 24 )116.053.129582504897537.0816234492597
Trimmed Mean ( 3 / 24 )115.9439393939393.118942897235237.1741141835968
Trimmed Mean ( 4 / 24 )115.83593753.1053001024262537.3026547126619
Trimmed Mean ( 5 / 24 )115.7032258064523.094538072010437.3894982430395
Trimmed Mean ( 6 / 24 )115.5633333333333.0789874396437537.5329018382434
Trimmed Mean ( 7 / 24 )115.4431034482763.0639179059623237.6782626008439
Trimmed Mean ( 8 / 24 )115.3446428571433.0507960634984337.8080476231093
Trimmed Mean ( 9 / 24 )115.2388888888893.039759149340737.9105327847713
Trimmed Mean ( 10 / 24 )115.1423076923083.0334564137517437.9574623753704
Trimmed Mean ( 11 / 24 )115.0323.023918852166838.0407033467758
Trimmed Mean ( 12 / 24 )114.9354166666673.01629805981938.1047941507358
Trimmed Mean ( 13 / 24 )114.8521739130433.0075231582074238.1882924490925
Trimmed Mean ( 14 / 24 )114.7636363636362.9921975543257538.3542978964491
Trimmed Mean ( 15 / 24 )114.6595238095242.9693675334111638.6141232162678
Trimmed Mean ( 16 / 24 )114.56752.9410890785470538.9541074548475
Trimmed Mean ( 17 / 24 )114.4710526315792.9018508536589339.4476003090383
Trimmed Mean ( 18 / 24 )114.3416666666672.8612916802320439.9615556346895
Trimmed Mean ( 19 / 24 )114.2764705882352.8490860992838440.1098691320561
Trimmed Mean ( 20 / 24 )114.2781252.854247451715640.0379178516253
Trimmed Mean ( 21 / 24 )114.2766666666672.8504997881328840.0900456623151
Trimmed Mean ( 22 / 24 )114.3821428571432.8635413637838939.9442956556416
Trimmed Mean ( 23 / 24 )114.4769230769232.8714579930615739.8671766585264
Trimmed Mean ( 24 / 24 )114.6083333333332.8822665991875739.7632659538289
Median117.9
Midrange121.75
Midmean - Weighted Average at Xnp113.664864864865
Midmean - Weighted Average at X(n+1)p114.341666666667
Midmean - Empirical Distribution Function113.664864864865
Midmean - Empirical Distribution Function - Averaging114.341666666667
Midmean - Empirical Distribution Function - Interpolation114.341666666667
Midmean - Closest Observation113.664864864865
Midmean - True Basic - Statistics Graphics Toolkit114.341666666667
Midmean - MS Excel (old versions)114.471052631579
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 116.320833333333 & 3.16795312236849 & 36.7179780887563 \tabularnewline
Geometric Mean & 113.252919459792 &  &  \tabularnewline
Harmonic Mean & 110.265392229586 &  &  \tabularnewline
Quadratic Mean & 119.344405329003 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 116.275 & 3.15822618025274 & 36.8165525088184 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 116.244444444444 & 3.1399147298167 & 37.0215290691127 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 116.231944444444 & 3.13620562236388 & 37.0613277444595 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 116.293055555556 & 3.11217592563978 & 37.3671213755851 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 116.286111111111 & 3.11092294520953 & 37.3799393810697 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 116.144444444444 & 3.08578502254379 & 37.6385404673135 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 115.979166666667 & 3.05120485803244 & 38.0109406162441 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 115.979166666667 & 3.01288179646722 & 38.4944297524911 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 115.866666666667 & 2.9600231568692 & 39.1438379114636 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 115.908333333333 & 2.94571965402772 & 39.3480530894548 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 115.740277777778 & 2.90087115222182 & 39.8984552240904 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 115.573611111111 & 2.87016654531927 & 40.2672142143079 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 115.555555555556 & 2.86210255244148 & 40.3743588632008 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 115.613888888889 & 2.84824184956772 & 40.5913173793285 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 115.426388888889 & 2.81374059271027 & 41.0223988621876 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 115.381944444444 & 2.79418502931486 & 41.2935948170677 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 115.570833333333 & 2.71383564398844 & 42.5857894487237 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 114.895833333333 & 2.50332364162024 & 45.8973148429855 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 114.2625 & 2.36540950335129 & 48.3055893020274 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 114.290277777778 & 2.35418097733174 & 48.5477874803475 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 113.415277777778 & 2.22370274795808 & 51.0028950056035 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 113.629166666667 & 2.19483266880489 & 51.7712207776362 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 113.469444444444 & 2.12445762100503 & 53.4110180982404 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 113.402777777778 & 2.11605936744833 & 53.5914915820749 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 116.165714285714 & 3.14609152224021 & 36.9238191147717 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 116.05 & 3.1295825048975 & 37.0816234492597 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 115.943939393939 & 3.1189428972352 & 37.1741141835968 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 115.8359375 & 3.10530010242625 & 37.3026547126619 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 115.703225806452 & 3.0945380720104 & 37.3894982430395 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 115.563333333333 & 3.07898743964375 & 37.5329018382434 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 115.443103448276 & 3.06391790596232 & 37.6782626008439 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 115.344642857143 & 3.05079606349843 & 37.8080476231093 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 115.238888888889 & 3.0397591493407 & 37.9105327847713 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 115.142307692308 & 3.03345641375174 & 37.9574623753704 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 115.032 & 3.0239188521668 & 38.0407033467758 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 114.935416666667 & 3.016298059819 & 38.1047941507358 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 114.852173913043 & 3.00752315820742 & 38.1882924490925 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 114.763636363636 & 2.99219755432575 & 38.3542978964491 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 114.659523809524 & 2.96936753341116 & 38.6141232162678 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 114.5675 & 2.94108907854705 & 38.9541074548475 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 114.471052631579 & 2.90185085365893 & 39.4476003090383 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 114.341666666667 & 2.86129168023204 & 39.9615556346895 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 114.276470588235 & 2.84908609928384 & 40.1098691320561 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 114.278125 & 2.8542474517156 & 40.0379178516253 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 114.276666666667 & 2.85049978813288 & 40.0900456623151 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 114.382142857143 & 2.86354136378389 & 39.9442956556416 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 114.476923076923 & 2.87145799306157 & 39.8671766585264 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 114.608333333333 & 2.88226659918757 & 39.7632659538289 \tabularnewline
Median & 117.9 &  &  \tabularnewline
Midrange & 121.75 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 113.664864864865 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 114.341666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 113.664864864865 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 114.341666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 114.341666666667 &  &  \tabularnewline
Midmean - Closest Observation & 113.664864864865 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 114.341666666667 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 114.471052631579 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=214667&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]116.320833333333[/C][C]3.16795312236849[/C][C]36.7179780887563[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]113.252919459792[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]110.265392229586[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]119.344405329003[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]116.275[/C][C]3.15822618025274[/C][C]36.8165525088184[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]116.244444444444[/C][C]3.1399147298167[/C][C]37.0215290691127[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]116.231944444444[/C][C]3.13620562236388[/C][C]37.0613277444595[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]116.293055555556[/C][C]3.11217592563978[/C][C]37.3671213755851[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]116.286111111111[/C][C]3.11092294520953[/C][C]37.3799393810697[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]116.144444444444[/C][C]3.08578502254379[/C][C]37.6385404673135[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]115.979166666667[/C][C]3.05120485803244[/C][C]38.0109406162441[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]115.979166666667[/C][C]3.01288179646722[/C][C]38.4944297524911[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]115.866666666667[/C][C]2.9600231568692[/C][C]39.1438379114636[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]115.908333333333[/C][C]2.94571965402772[/C][C]39.3480530894548[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]115.740277777778[/C][C]2.90087115222182[/C][C]39.8984552240904[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]115.573611111111[/C][C]2.87016654531927[/C][C]40.2672142143079[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]115.555555555556[/C][C]2.86210255244148[/C][C]40.3743588632008[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]115.613888888889[/C][C]2.84824184956772[/C][C]40.5913173793285[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]115.426388888889[/C][C]2.81374059271027[/C][C]41.0223988621876[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]115.381944444444[/C][C]2.79418502931486[/C][C]41.2935948170677[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]115.570833333333[/C][C]2.71383564398844[/C][C]42.5857894487237[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]114.895833333333[/C][C]2.50332364162024[/C][C]45.8973148429855[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]114.2625[/C][C]2.36540950335129[/C][C]48.3055893020274[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]114.290277777778[/C][C]2.35418097733174[/C][C]48.5477874803475[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]113.415277777778[/C][C]2.22370274795808[/C][C]51.0028950056035[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]113.629166666667[/C][C]2.19483266880489[/C][C]51.7712207776362[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]113.469444444444[/C][C]2.12445762100503[/C][C]53.4110180982404[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]113.402777777778[/C][C]2.11605936744833[/C][C]53.5914915820749[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]116.165714285714[/C][C]3.14609152224021[/C][C]36.9238191147717[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]116.05[/C][C]3.1295825048975[/C][C]37.0816234492597[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]115.943939393939[/C][C]3.1189428972352[/C][C]37.1741141835968[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]115.8359375[/C][C]3.10530010242625[/C][C]37.3026547126619[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]115.703225806452[/C][C]3.0945380720104[/C][C]37.3894982430395[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]115.563333333333[/C][C]3.07898743964375[/C][C]37.5329018382434[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]115.443103448276[/C][C]3.06391790596232[/C][C]37.6782626008439[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]115.344642857143[/C][C]3.05079606349843[/C][C]37.8080476231093[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]115.238888888889[/C][C]3.0397591493407[/C][C]37.9105327847713[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]115.142307692308[/C][C]3.03345641375174[/C][C]37.9574623753704[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]115.032[/C][C]3.0239188521668[/C][C]38.0407033467758[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]114.935416666667[/C][C]3.016298059819[/C][C]38.1047941507358[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]114.852173913043[/C][C]3.00752315820742[/C][C]38.1882924490925[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]114.763636363636[/C][C]2.99219755432575[/C][C]38.3542978964491[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]114.659523809524[/C][C]2.96936753341116[/C][C]38.6141232162678[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]114.5675[/C][C]2.94108907854705[/C][C]38.9541074548475[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]114.471052631579[/C][C]2.90185085365893[/C][C]39.4476003090383[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]114.341666666667[/C][C]2.86129168023204[/C][C]39.9615556346895[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]114.276470588235[/C][C]2.84908609928384[/C][C]40.1098691320561[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]114.278125[/C][C]2.8542474517156[/C][C]40.0379178516253[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]114.276666666667[/C][C]2.85049978813288[/C][C]40.0900456623151[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]114.382142857143[/C][C]2.86354136378389[/C][C]39.9442956556416[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]114.476923076923[/C][C]2.87145799306157[/C][C]39.8671766585264[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]114.608333333333[/C][C]2.88226659918757[/C][C]39.7632659538289[/C][/ROW]
[ROW][C]Median[/C][C]117.9[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]121.75[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]113.664864864865[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]114.341666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]113.664864864865[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]114.341666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]114.341666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]113.664864864865[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]114.341666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]114.471052631579[/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=214667&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=214667&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 Mean116.3208333333333.1679531223684936.7179780887563
Geometric Mean113.252919459792
Harmonic Mean110.265392229586
Quadratic Mean119.344405329003
Winsorized Mean ( 1 / 24 )116.2753.1582261802527436.8165525088184
Winsorized Mean ( 2 / 24 )116.2444444444443.139914729816737.0215290691127
Winsorized Mean ( 3 / 24 )116.2319444444443.1362056223638837.0613277444595
Winsorized Mean ( 4 / 24 )116.2930555555563.1121759256397837.3671213755851
Winsorized Mean ( 5 / 24 )116.2861111111113.1109229452095337.3799393810697
Winsorized Mean ( 6 / 24 )116.1444444444443.0857850225437937.6385404673135
Winsorized Mean ( 7 / 24 )115.9791666666673.0512048580324438.0109406162441
Winsorized Mean ( 8 / 24 )115.9791666666673.0128817964672238.4944297524911
Winsorized Mean ( 9 / 24 )115.8666666666672.960023156869239.1438379114636
Winsorized Mean ( 10 / 24 )115.9083333333332.9457196540277239.3480530894548
Winsorized Mean ( 11 / 24 )115.7402777777782.9008711522218239.8984552240904
Winsorized Mean ( 12 / 24 )115.5736111111112.8701665453192740.2672142143079
Winsorized Mean ( 13 / 24 )115.5555555555562.8621025524414840.3743588632008
Winsorized Mean ( 14 / 24 )115.6138888888892.8482418495677240.5913173793285
Winsorized Mean ( 15 / 24 )115.4263888888892.8137405927102741.0223988621876
Winsorized Mean ( 16 / 24 )115.3819444444442.7941850293148641.2935948170677
Winsorized Mean ( 17 / 24 )115.5708333333332.7138356439884442.5857894487237
Winsorized Mean ( 18 / 24 )114.8958333333332.5033236416202445.8973148429855
Winsorized Mean ( 19 / 24 )114.26252.3654095033512948.3055893020274
Winsorized Mean ( 20 / 24 )114.2902777777782.3541809773317448.5477874803475
Winsorized Mean ( 21 / 24 )113.4152777777782.2237027479580851.0028950056035
Winsorized Mean ( 22 / 24 )113.6291666666672.1948326688048951.7712207776362
Winsorized Mean ( 23 / 24 )113.4694444444442.1244576210050353.4110180982404
Winsorized Mean ( 24 / 24 )113.4027777777782.1160593674483353.5914915820749
Trimmed Mean ( 1 / 24 )116.1657142857143.1460915222402136.9238191147717
Trimmed Mean ( 2 / 24 )116.053.129582504897537.0816234492597
Trimmed Mean ( 3 / 24 )115.9439393939393.118942897235237.1741141835968
Trimmed Mean ( 4 / 24 )115.83593753.1053001024262537.3026547126619
Trimmed Mean ( 5 / 24 )115.7032258064523.094538072010437.3894982430395
Trimmed Mean ( 6 / 24 )115.5633333333333.0789874396437537.5329018382434
Trimmed Mean ( 7 / 24 )115.4431034482763.0639179059623237.6782626008439
Trimmed Mean ( 8 / 24 )115.3446428571433.0507960634984337.8080476231093
Trimmed Mean ( 9 / 24 )115.2388888888893.039759149340737.9105327847713
Trimmed Mean ( 10 / 24 )115.1423076923083.0334564137517437.9574623753704
Trimmed Mean ( 11 / 24 )115.0323.023918852166838.0407033467758
Trimmed Mean ( 12 / 24 )114.9354166666673.01629805981938.1047941507358
Trimmed Mean ( 13 / 24 )114.8521739130433.0075231582074238.1882924490925
Trimmed Mean ( 14 / 24 )114.7636363636362.9921975543257538.3542978964491
Trimmed Mean ( 15 / 24 )114.6595238095242.9693675334111638.6141232162678
Trimmed Mean ( 16 / 24 )114.56752.9410890785470538.9541074548475
Trimmed Mean ( 17 / 24 )114.4710526315792.9018508536589339.4476003090383
Trimmed Mean ( 18 / 24 )114.3416666666672.8612916802320439.9615556346895
Trimmed Mean ( 19 / 24 )114.2764705882352.8490860992838440.1098691320561
Trimmed Mean ( 20 / 24 )114.2781252.854247451715640.0379178516253
Trimmed Mean ( 21 / 24 )114.2766666666672.8504997881328840.0900456623151
Trimmed Mean ( 22 / 24 )114.3821428571432.8635413637838939.9442956556416
Trimmed Mean ( 23 / 24 )114.4769230769232.8714579930615739.8671766585264
Trimmed Mean ( 24 / 24 )114.6083333333332.8822665991875739.7632659538289
Median117.9
Midrange121.75
Midmean - Weighted Average at Xnp113.664864864865
Midmean - Weighted Average at X(n+1)p114.341666666667
Midmean - Empirical Distribution Function113.664864864865
Midmean - Empirical Distribution Function - Averaging114.341666666667
Midmean - Empirical Distribution Function - Interpolation114.341666666667
Midmean - Closest Observation113.664864864865
Midmean - True Basic - Statistics Graphics Toolkit114.341666666667
Midmean - MS Excel (old versions)114.471052631579
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')