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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 computationMon, 20 Oct 2008 15:17:29 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/Oct/20/t1224537494i8m37ukrvllp7nl.htm/, Retrieved Sun, 19 May 2024 15:57:14 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=18167, Retrieved Sun, 19 May 2024 15:57:14 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact122
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
F     [Univariate Data Series] [uitvoer van belgi...] [2008-10-13 19:23:12] [1e1d8320a8a1170c475bf6e4ce119de6]
- RMP   [Central Tendency] [Central Tendency ...] [2008-10-18 10:47:17] [1e1d8320a8a1170c475bf6e4ce119de6]
F    D    [Central Tendency] [Central Tendency ...] [2008-10-20 21:11:22] [3754dd41128068acfc463ebbabce5a9c]
-    D        [Central Tendency] [] [2008-10-20 21:17:29] [02e7fb326979b65614900650d62c19a6] [Current]
-    D          [Central Tendency] [Central Tendency ...] [2008-10-20 21:22:30] [3754dd41128068acfc463ebbabce5a9c]
-    D            [Central Tendency] [Central Tendency ...] [2008-10-20 21:26:01] [3754dd41128068acfc463ebbabce5a9c]
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Dataseries X:
117
122.2
116.8
115
105.3
114.1
102.1
91
123.2
125.8
108.1
117.2
111
114.5
141.9
135.5
128.3
142.7
135.4
174.3
186
154.9
146.2
135.9
118
113.3
138
138
116.7
303
111.6
110.1
132.8
133.2
135.9
153.7
132.7
141.1
168
136
134.7
146.4
135.5
134.8
145
156.4
161.7
144.1
147.7
152.2
170.7
225.8
151.3
162.3
132.6
130.1
149.1
340.7
243.4
238.1




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=18167&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=18167&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=18167&T=0

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean145.8183333333335.6997038735976725.5834928563214
Geometric Mean141.044804844896
Harmonic Mean137.429779966145
Quadratic Mean152.248800214211
Winsorized Mean ( 1 / 20 )145.3755.3315051377540927.2671593187734
Winsorized Mean ( 2 / 20 )143.4954.4278691263405732.4072360554595
Winsorized Mean ( 3 / 20 )143.374.3078409000726833.2811734058194
Winsorized Mean ( 4 / 20 )142.6833333333333.9915391921426235.7464442824980
Winsorized Mean ( 5 / 20 )139.4416666666672.9266313637627347.6457911280594
Winsorized Mean ( 6 / 20 )138.3316666666672.6215485694664552.7671576555306
Winsorized Mean ( 7 / 20 )138.112.4922305259245755.4162219599504
Winsorized Mean ( 8 / 20 )137.8566666666672.3959610160032157.53710755137
Winsorized Mean ( 9 / 20 )137.0616666666672.2115517108736561.9753388504408
Winsorized Mean ( 10 / 20 )137.0452.1779330181707662.9243410410773
Winsorized Mean ( 11 / 20 )136.3851.9460953591467970.0813551396548
Winsorized Mean ( 12 / 20 )136.1051.8912247922151671.9665904128629
Winsorized Mean ( 13 / 20 )135.8883333333331.8404787691825473.833143641037
Winsorized Mean ( 14 / 20 )135.5851.7758531410370376.3492187877788
Winsorized Mean ( 15 / 20 )135.561.7054088099454579.48827237754
Winsorized Mean ( 16 / 20 )136.0933333333331.4231993612440995.6249258110738
Winsorized Mean ( 17 / 20 )135.981.31573656628689103.348955622436
Winsorized Mean ( 18 / 20 )136.371.13079468081942120.596605478530
Winsorized Mean ( 19 / 20 )137.0983333333330.999136609387552137.216805034670
Winsorized Mean ( 20 / 20 )137.2983333333330.84951462268872161.619741045520
Trimmed Mean ( 1 / 20 )143.4034482758624.7209005912774530.3762906045556
Trimmed Mean ( 2 / 20 )141.2910714285713.8752287546938436.4600596177539
Trimmed Mean ( 3 / 20 )140.0666666666673.4694957010042840.3709007698504
Trimmed Mean ( 4 / 20 )138.7961538461542.9916108968595246.3951224378334
Trimmed Mean ( 5 / 20 )137.632.4968196096765455.1221239478449
Trimmed Mean ( 6 / 20 )137.1770833333332.3268880833281458.953021555351
Trimmed Mean ( 7 / 20 )136.9260869565222.217596372065361.7452700957475
Trimmed Mean ( 8 / 20 )136.6954545454552.1168930785416064.573622508903
Trimmed Mean ( 9 / 20 )136.4880952380952.0142010413199267.7628957775999
Trimmed Mean ( 10 / 20 )136.39251.9341843424329670.5168049434396
Trimmed Mean ( 11 / 20 )136.2894736842111.8356273010963774.2468112142417
Trimmed Mean ( 12 / 20 )136.2751.7704289454235876.9728716604302
Trimmed Mean ( 13 / 20 )136.31.6949069140856580.4173957090322
Trimmed Mean ( 14 / 20 )136.3593751.6026116498710585.0857255474035
Trimmed Mean ( 15 / 20 )136.471.4892113935612591.6391054957283
Trimmed Mean ( 16 / 20 )136.61.34513625123685101.551050961861
Trimmed Mean ( 17 / 20 )136.6730769230771.24291911603052109.961360446017
Trimmed Mean ( 18 / 20 )136.7751.12673778825344121.390266152354
Trimmed Mean ( 19 / 20 )136.8363636363641.02734359790780133.194350862782
Trimmed Mean ( 20 / 20 )136.7950.927687418998674147.458073914222
Median135.7
Midrange215.85
Midmean - Weighted Average at Xnp135.848387096774
Midmean - Weighted Average at X(n+1)p136.47
Midmean - Empirical Distribution Function135.848387096774
Midmean - Empirical Distribution Function - Averaging136.47
Midmean - Empirical Distribution Function - Interpolation136.47
Midmean - Closest Observation135.848387096774
Midmean - True Basic - Statistics Graphics Toolkit136.47
Midmean - MS Excel (old versions)136.359375
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 145.818333333333 & 5.69970387359767 & 25.5834928563214 \tabularnewline
Geometric Mean & 141.044804844896 &  &  \tabularnewline
Harmonic Mean & 137.429779966145 &  &  \tabularnewline
Quadratic Mean & 152.248800214211 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 145.375 & 5.33150513775409 & 27.2671593187734 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 143.495 & 4.42786912634057 & 32.4072360554595 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 143.37 & 4.30784090007268 & 33.2811734058194 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 142.683333333333 & 3.99153919214262 & 35.7464442824980 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 139.441666666667 & 2.92663136376273 & 47.6457911280594 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 138.331666666667 & 2.62154856946645 & 52.7671576555306 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 138.11 & 2.49223052592457 & 55.4162219599504 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 137.856666666667 & 2.39596101600321 & 57.53710755137 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 137.061666666667 & 2.21155171087365 & 61.9753388504408 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 137.045 & 2.17793301817076 & 62.9243410410773 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 136.385 & 1.94609535914679 & 70.0813551396548 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 136.105 & 1.89122479221516 & 71.9665904128629 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 135.888333333333 & 1.84047876918254 & 73.833143641037 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 135.585 & 1.77585314103703 & 76.3492187877788 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 135.56 & 1.70540880994545 & 79.48827237754 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 136.093333333333 & 1.42319936124409 & 95.6249258110738 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 135.98 & 1.31573656628689 & 103.348955622436 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 136.37 & 1.13079468081942 & 120.596605478530 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 137.098333333333 & 0.999136609387552 & 137.216805034670 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 137.298333333333 & 0.84951462268872 & 161.619741045520 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 143.403448275862 & 4.72090059127745 & 30.3762906045556 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 141.291071428571 & 3.87522875469384 & 36.4600596177539 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 140.066666666667 & 3.46949570100428 & 40.3709007698504 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 138.796153846154 & 2.99161089685952 & 46.3951224378334 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 137.63 & 2.49681960967654 & 55.1221239478449 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 137.177083333333 & 2.32688808332814 & 58.953021555351 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 136.926086956522 & 2.2175963720653 & 61.7452700957475 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 136.695454545455 & 2.11689307854160 & 64.573622508903 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 136.488095238095 & 2.01420104131992 & 67.7628957775999 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 136.3925 & 1.93418434243296 & 70.5168049434396 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 136.289473684211 & 1.83562730109637 & 74.2468112142417 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 136.275 & 1.77042894542358 & 76.9728716604302 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 136.3 & 1.69490691408565 & 80.4173957090322 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 136.359375 & 1.60261164987105 & 85.0857255474035 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 136.47 & 1.48921139356125 & 91.6391054957283 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 136.6 & 1.34513625123685 & 101.551050961861 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 136.673076923077 & 1.24291911603052 & 109.961360446017 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 136.775 & 1.12673778825344 & 121.390266152354 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 136.836363636364 & 1.02734359790780 & 133.194350862782 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 136.795 & 0.927687418998674 & 147.458073914222 \tabularnewline
Median & 135.7 &  &  \tabularnewline
Midrange & 215.85 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 135.848387096774 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 136.47 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 135.848387096774 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 136.47 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 136.47 &  &  \tabularnewline
Midmean - Closest Observation & 135.848387096774 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 136.47 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 136.359375 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=18167&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]145.818333333333[/C][C]5.69970387359767[/C][C]25.5834928563214[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]141.044804844896[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]137.429779966145[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]152.248800214211[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]145.375[/C][C]5.33150513775409[/C][C]27.2671593187734[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]143.495[/C][C]4.42786912634057[/C][C]32.4072360554595[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]143.37[/C][C]4.30784090007268[/C][C]33.2811734058194[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]142.683333333333[/C][C]3.99153919214262[/C][C]35.7464442824980[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]139.441666666667[/C][C]2.92663136376273[/C][C]47.6457911280594[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]138.331666666667[/C][C]2.62154856946645[/C][C]52.7671576555306[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]138.11[/C][C]2.49223052592457[/C][C]55.4162219599504[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]137.856666666667[/C][C]2.39596101600321[/C][C]57.53710755137[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]137.061666666667[/C][C]2.21155171087365[/C][C]61.9753388504408[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]137.045[/C][C]2.17793301817076[/C][C]62.9243410410773[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]136.385[/C][C]1.94609535914679[/C][C]70.0813551396548[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]136.105[/C][C]1.89122479221516[/C][C]71.9665904128629[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]135.888333333333[/C][C]1.84047876918254[/C][C]73.833143641037[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]135.585[/C][C]1.77585314103703[/C][C]76.3492187877788[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]135.56[/C][C]1.70540880994545[/C][C]79.48827237754[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]136.093333333333[/C][C]1.42319936124409[/C][C]95.6249258110738[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]135.98[/C][C]1.31573656628689[/C][C]103.348955622436[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]136.37[/C][C]1.13079468081942[/C][C]120.596605478530[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]137.098333333333[/C][C]0.999136609387552[/C][C]137.216805034670[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]137.298333333333[/C][C]0.84951462268872[/C][C]161.619741045520[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]143.403448275862[/C][C]4.72090059127745[/C][C]30.3762906045556[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]141.291071428571[/C][C]3.87522875469384[/C][C]36.4600596177539[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]140.066666666667[/C][C]3.46949570100428[/C][C]40.3709007698504[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]138.796153846154[/C][C]2.99161089685952[/C][C]46.3951224378334[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]137.63[/C][C]2.49681960967654[/C][C]55.1221239478449[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]137.177083333333[/C][C]2.32688808332814[/C][C]58.953021555351[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]136.926086956522[/C][C]2.2175963720653[/C][C]61.7452700957475[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]136.695454545455[/C][C]2.11689307854160[/C][C]64.573622508903[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]136.488095238095[/C][C]2.01420104131992[/C][C]67.7628957775999[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]136.3925[/C][C]1.93418434243296[/C][C]70.5168049434396[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]136.289473684211[/C][C]1.83562730109637[/C][C]74.2468112142417[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]136.275[/C][C]1.77042894542358[/C][C]76.9728716604302[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]136.3[/C][C]1.69490691408565[/C][C]80.4173957090322[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]136.359375[/C][C]1.60261164987105[/C][C]85.0857255474035[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]136.47[/C][C]1.48921139356125[/C][C]91.6391054957283[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]136.6[/C][C]1.34513625123685[/C][C]101.551050961861[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]136.673076923077[/C][C]1.24291911603052[/C][C]109.961360446017[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]136.775[/C][C]1.12673778825344[/C][C]121.390266152354[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]136.836363636364[/C][C]1.02734359790780[/C][C]133.194350862782[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]136.795[/C][C]0.927687418998674[/C][C]147.458073914222[/C][/ROW]
[ROW][C]Median[/C][C]135.7[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]215.85[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]135.848387096774[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]136.47[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]135.848387096774[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]136.47[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]136.47[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]135.848387096774[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]136.47[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]136.359375[/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=18167&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=18167&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 Mean145.8183333333335.6997038735976725.5834928563214
Geometric Mean141.044804844896
Harmonic Mean137.429779966145
Quadratic Mean152.248800214211
Winsorized Mean ( 1 / 20 )145.3755.3315051377540927.2671593187734
Winsorized Mean ( 2 / 20 )143.4954.4278691263405732.4072360554595
Winsorized Mean ( 3 / 20 )143.374.3078409000726833.2811734058194
Winsorized Mean ( 4 / 20 )142.6833333333333.9915391921426235.7464442824980
Winsorized Mean ( 5 / 20 )139.4416666666672.9266313637627347.6457911280594
Winsorized Mean ( 6 / 20 )138.3316666666672.6215485694664552.7671576555306
Winsorized Mean ( 7 / 20 )138.112.4922305259245755.4162219599504
Winsorized Mean ( 8 / 20 )137.8566666666672.3959610160032157.53710755137
Winsorized Mean ( 9 / 20 )137.0616666666672.2115517108736561.9753388504408
Winsorized Mean ( 10 / 20 )137.0452.1779330181707662.9243410410773
Winsorized Mean ( 11 / 20 )136.3851.9460953591467970.0813551396548
Winsorized Mean ( 12 / 20 )136.1051.8912247922151671.9665904128629
Winsorized Mean ( 13 / 20 )135.8883333333331.8404787691825473.833143641037
Winsorized Mean ( 14 / 20 )135.5851.7758531410370376.3492187877788
Winsorized Mean ( 15 / 20 )135.561.7054088099454579.48827237754
Winsorized Mean ( 16 / 20 )136.0933333333331.4231993612440995.6249258110738
Winsorized Mean ( 17 / 20 )135.981.31573656628689103.348955622436
Winsorized Mean ( 18 / 20 )136.371.13079468081942120.596605478530
Winsorized Mean ( 19 / 20 )137.0983333333330.999136609387552137.216805034670
Winsorized Mean ( 20 / 20 )137.2983333333330.84951462268872161.619741045520
Trimmed Mean ( 1 / 20 )143.4034482758624.7209005912774530.3762906045556
Trimmed Mean ( 2 / 20 )141.2910714285713.8752287546938436.4600596177539
Trimmed Mean ( 3 / 20 )140.0666666666673.4694957010042840.3709007698504
Trimmed Mean ( 4 / 20 )138.7961538461542.9916108968595246.3951224378334
Trimmed Mean ( 5 / 20 )137.632.4968196096765455.1221239478449
Trimmed Mean ( 6 / 20 )137.1770833333332.3268880833281458.953021555351
Trimmed Mean ( 7 / 20 )136.9260869565222.217596372065361.7452700957475
Trimmed Mean ( 8 / 20 )136.6954545454552.1168930785416064.573622508903
Trimmed Mean ( 9 / 20 )136.4880952380952.0142010413199267.7628957775999
Trimmed Mean ( 10 / 20 )136.39251.9341843424329670.5168049434396
Trimmed Mean ( 11 / 20 )136.2894736842111.8356273010963774.2468112142417
Trimmed Mean ( 12 / 20 )136.2751.7704289454235876.9728716604302
Trimmed Mean ( 13 / 20 )136.31.6949069140856580.4173957090322
Trimmed Mean ( 14 / 20 )136.3593751.6026116498710585.0857255474035
Trimmed Mean ( 15 / 20 )136.471.4892113935612591.6391054957283
Trimmed Mean ( 16 / 20 )136.61.34513625123685101.551050961861
Trimmed Mean ( 17 / 20 )136.6730769230771.24291911603052109.961360446017
Trimmed Mean ( 18 / 20 )136.7751.12673778825344121.390266152354
Trimmed Mean ( 19 / 20 )136.8363636363641.02734359790780133.194350862782
Trimmed Mean ( 20 / 20 )136.7950.927687418998674147.458073914222
Median135.7
Midrange215.85
Midmean - Weighted Average at Xnp135.848387096774
Midmean - Weighted Average at X(n+1)p136.47
Midmean - Empirical Distribution Function135.848387096774
Midmean - Empirical Distribution Function - Averaging136.47
Midmean - Empirical Distribution Function - Interpolation136.47
Midmean - Closest Observation135.848387096774
Midmean - True Basic - Statistics Graphics Toolkit136.47
Midmean - MS Excel (old versions)136.359375
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')