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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 computationTue, 13 Dec 2011 16:46:45 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Dec/13/t1323812818zfwr3rbdjse0ouz.htm/, Retrieved Thu, 02 May 2024 21:57:52 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=154743, Retrieved Thu, 02 May 2024 21:57:52 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact82
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Histogram] [] [2011-12-13 20:06:04] [0fa8c500575976cf9d2f7efbe256ddfb]
- RMP     [Central Tendency] [] [2011-12-13 21:46:45] [2e63149daec6ba44c7d6fab36a0b0c34] [Current]
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Dataseries X:
94
85,5
86
94
109
118
72
140
102,8
99,8
80
106
122
161
135
140
140
135
109
135
135
90
90
81
104
104
135
81
126
140
120
120
110
108
120
118
85
94
72,6
78
65
130
70
78,5
93,5
80
78,8
90,3
87,7
107
90
103
126
98
128
132
94
111
95
155




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=154743&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]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=154743&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=154743&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'Herman Ole Andreas Wold' @ wold.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean106.4752.9923477027262935.5824291084195
Geometric Mean104.006688652658
Harmonic Mean101.574887750757
Quadratic Mean108.927591392937
Winsorized Mean ( 1 / 20 )106.4583333333332.9443811198463636.1564379746085
Winsorized Mean ( 2 / 20 )106.0252.808993451227637.7448370175674
Winsorized Mean ( 3 / 20 )106.0552.8028792954090637.8378762773379
Winsorized Mean ( 4 / 20 )106.4152.7347066534138538.9127659696727
Winsorized Mean ( 5 / 20 )106.4566666666672.7274181896378939.0320292909686
Winsorized Mean ( 6 / 20 )105.9866666666672.623095452929440.405188666811
Winsorized Mean ( 7 / 20 )106.1266666666672.5988696659297240.8357017891088
Winsorized Mean ( 8 / 20 )106.1266666666672.5988696659297240.8357017891088
Winsorized Mean ( 9 / 20 )106.2766666666672.573603912767441.294880746582
Winsorized Mean ( 10 / 20 )106.2766666666672.573603912767441.294880746582
Winsorized Mean ( 11 / 20 )106.462.3530160955171445.2440594022382
Winsorized Mean ( 12 / 20 )106.162.2650640728768146.8684313486851
Winsorized Mean ( 13 / 20 )105.8352.172157958745248.7234363292521
Winsorized Mean ( 14 / 20 )105.7652.0317714085243952.0555607566177
Winsorized Mean ( 15 / 20 )106.341.9475092016202354.6030796216676
Winsorized Mean ( 16 / 20 )105.2733333333331.7705801447447259.4569715727337
Winsorized Mean ( 17 / 20 )104.7066666666671.6814925886843462.2700732499765
Winsorized Mean ( 18 / 20 )104.7966666666671.6681935943328862.8204466332191
Winsorized Mean ( 19 / 20 )105.811.5239624607978169.4308440803769
Winsorized Mean ( 20 / 20 )105.311.3971433729291375.375227797285
Trimmed Mean ( 1 / 20 )106.252.8578748360175637.1779752776224
Trimmed Mean ( 2 / 20 )106.0267857142862.7509248634522838.5422325134781
Trimmed Mean ( 3 / 20 )106.0277777777782.7085397169120339.1457349197222
Trimmed Mean ( 4 / 20 )106.0173076923082.6571735075876639.8985265318849
Trimmed Mean ( 5 / 20 )105.8982.6173775471814940.4595814287609
Trimmed Mean ( 6 / 20 )105.7583333333332.5673202515914741.1940556569732
Trimmed Mean ( 7 / 20 )105.7086956521742.5336056796531341.7226313080599
Trimmed Mean ( 8 / 20 )105.6272727272732.4940147457826842.3523048153128
Trimmed Mean ( 9 / 20 )105.5380952380952.4395834462432543.2607031338136
Trimmed Mean ( 10 / 20 )105.4152.3720962005398144.4395973384263
Trimmed Mean ( 11 / 20 )105.2789473684212.2795090618870746.1849216257411
Trimmed Mean ( 12 / 20 )105.12.214562194720647.4585903482652
Trimmed Mean ( 13 / 20 )104.9441176470592.1475027622013848.8679779575611
Trimmed Mean ( 14 / 20 )104.8156252.0779715866244550.4413177132354
Trimmed Mean ( 15 / 20 )104.682.0174947478175251.8861325974903
Trimmed Mean ( 16 / 20 )104.4428571428571.9482486272367453.6085875707719
Trimmed Mean ( 17 / 20 )104.3230769230771.9023492172518454.839077902733
Trimmed Mean ( 18 / 20 )104.2666666666671.8559116930932956.1808339559967
Trimmed Mean ( 19 / 20 )104.1863636363641.776814302986258.6366079231031
Trimmed Mean ( 20 / 20 )103.931.6959564914975461.2810532115888
Median104
Midrange113
Midmean - Weighted Average at Xnp104.815625
Midmean - Weighted Average at X(n+1)p105.367741935484
Midmean - Empirical Distribution Function104.815625
Midmean - Empirical Distribution Function - Averaging105.367741935484
Midmean - Empirical Distribution Function - Interpolation105.367741935484
Midmean - Closest Observation104.815625
Midmean - True Basic - Statistics Graphics Toolkit105.367741935484
Midmean - MS Excel (old versions)104.815625
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 106.475 & 2.99234770272629 & 35.5824291084195 \tabularnewline
Geometric Mean & 104.006688652658 &  &  \tabularnewline
Harmonic Mean & 101.574887750757 &  &  \tabularnewline
Quadratic Mean & 108.927591392937 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 106.458333333333 & 2.94438111984636 & 36.1564379746085 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 106.025 & 2.8089934512276 & 37.7448370175674 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 106.055 & 2.80287929540906 & 37.8378762773379 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 106.415 & 2.73470665341385 & 38.9127659696727 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 106.456666666667 & 2.72741818963789 & 39.0320292909686 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 105.986666666667 & 2.6230954529294 & 40.405188666811 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 106.126666666667 & 2.59886966592972 & 40.8357017891088 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 106.126666666667 & 2.59886966592972 & 40.8357017891088 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 106.276666666667 & 2.5736039127674 & 41.294880746582 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 106.276666666667 & 2.5736039127674 & 41.294880746582 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 106.46 & 2.35301609551714 & 45.2440594022382 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 106.16 & 2.26506407287681 & 46.8684313486851 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 105.835 & 2.1721579587452 & 48.7234363292521 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 105.765 & 2.03177140852439 & 52.0555607566177 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 106.34 & 1.94750920162023 & 54.6030796216676 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 105.273333333333 & 1.77058014474472 & 59.4569715727337 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 104.706666666667 & 1.68149258868434 & 62.2700732499765 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 104.796666666667 & 1.66819359433288 & 62.8204466332191 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 105.81 & 1.52396246079781 & 69.4308440803769 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 105.31 & 1.39714337292913 & 75.375227797285 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 106.25 & 2.85787483601756 & 37.1779752776224 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 106.026785714286 & 2.75092486345228 & 38.5422325134781 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 106.027777777778 & 2.70853971691203 & 39.1457349197222 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 106.017307692308 & 2.65717350758766 & 39.8985265318849 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 105.898 & 2.61737754718149 & 40.4595814287609 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 105.758333333333 & 2.56732025159147 & 41.1940556569732 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 105.708695652174 & 2.53360567965313 & 41.7226313080599 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 105.627272727273 & 2.49401474578268 & 42.3523048153128 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 105.538095238095 & 2.43958344624325 & 43.2607031338136 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 105.415 & 2.37209620053981 & 44.4395973384263 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 105.278947368421 & 2.27950906188707 & 46.1849216257411 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 105.1 & 2.2145621947206 & 47.4585903482652 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 104.944117647059 & 2.14750276220138 & 48.8679779575611 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 104.815625 & 2.07797158662445 & 50.4413177132354 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 104.68 & 2.01749474781752 & 51.8861325974903 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 104.442857142857 & 1.94824862723674 & 53.6085875707719 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 104.323076923077 & 1.90234921725184 & 54.839077902733 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 104.266666666667 & 1.85591169309329 & 56.1808339559967 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 104.186363636364 & 1.7768143029862 & 58.6366079231031 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 103.93 & 1.69595649149754 & 61.2810532115888 \tabularnewline
Median & 104 &  &  \tabularnewline
Midrange & 113 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 104.815625 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 105.367741935484 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 104.815625 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 105.367741935484 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 105.367741935484 &  &  \tabularnewline
Midmean - Closest Observation & 104.815625 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 105.367741935484 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 104.815625 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=154743&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]106.475[/C][C]2.99234770272629[/C][C]35.5824291084195[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]104.006688652658[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]101.574887750757[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]108.927591392937[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]106.458333333333[/C][C]2.94438111984636[/C][C]36.1564379746085[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]106.025[/C][C]2.8089934512276[/C][C]37.7448370175674[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]106.055[/C][C]2.80287929540906[/C][C]37.8378762773379[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]106.415[/C][C]2.73470665341385[/C][C]38.9127659696727[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]106.456666666667[/C][C]2.72741818963789[/C][C]39.0320292909686[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]105.986666666667[/C][C]2.6230954529294[/C][C]40.405188666811[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]106.126666666667[/C][C]2.59886966592972[/C][C]40.8357017891088[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]106.126666666667[/C][C]2.59886966592972[/C][C]40.8357017891088[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]106.276666666667[/C][C]2.5736039127674[/C][C]41.294880746582[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]106.276666666667[/C][C]2.5736039127674[/C][C]41.294880746582[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]106.46[/C][C]2.35301609551714[/C][C]45.2440594022382[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]106.16[/C][C]2.26506407287681[/C][C]46.8684313486851[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]105.835[/C][C]2.1721579587452[/C][C]48.7234363292521[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]105.765[/C][C]2.03177140852439[/C][C]52.0555607566177[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]106.34[/C][C]1.94750920162023[/C][C]54.6030796216676[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]105.273333333333[/C][C]1.77058014474472[/C][C]59.4569715727337[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]104.706666666667[/C][C]1.68149258868434[/C][C]62.2700732499765[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]104.796666666667[/C][C]1.66819359433288[/C][C]62.8204466332191[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]105.81[/C][C]1.52396246079781[/C][C]69.4308440803769[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]105.31[/C][C]1.39714337292913[/C][C]75.375227797285[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]106.25[/C][C]2.85787483601756[/C][C]37.1779752776224[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]106.026785714286[/C][C]2.75092486345228[/C][C]38.5422325134781[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]106.027777777778[/C][C]2.70853971691203[/C][C]39.1457349197222[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]106.017307692308[/C][C]2.65717350758766[/C][C]39.8985265318849[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]105.898[/C][C]2.61737754718149[/C][C]40.4595814287609[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]105.758333333333[/C][C]2.56732025159147[/C][C]41.1940556569732[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]105.708695652174[/C][C]2.53360567965313[/C][C]41.7226313080599[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]105.627272727273[/C][C]2.49401474578268[/C][C]42.3523048153128[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]105.538095238095[/C][C]2.43958344624325[/C][C]43.2607031338136[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]105.415[/C][C]2.37209620053981[/C][C]44.4395973384263[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]105.278947368421[/C][C]2.27950906188707[/C][C]46.1849216257411[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]105.1[/C][C]2.2145621947206[/C][C]47.4585903482652[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]104.944117647059[/C][C]2.14750276220138[/C][C]48.8679779575611[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]104.815625[/C][C]2.07797158662445[/C][C]50.4413177132354[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]104.68[/C][C]2.01749474781752[/C][C]51.8861325974903[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]104.442857142857[/C][C]1.94824862723674[/C][C]53.6085875707719[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]104.323076923077[/C][C]1.90234921725184[/C][C]54.839077902733[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]104.266666666667[/C][C]1.85591169309329[/C][C]56.1808339559967[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]104.186363636364[/C][C]1.7768143029862[/C][C]58.6366079231031[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]103.93[/C][C]1.69595649149754[/C][C]61.2810532115888[/C][/ROW]
[ROW][C]Median[/C][C]104[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]113[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]104.815625[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]105.367741935484[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]104.815625[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]105.367741935484[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]105.367741935484[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]104.815625[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]105.367741935484[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]104.815625[/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=154743&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=154743&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 Mean106.4752.9923477027262935.5824291084195
Geometric Mean104.006688652658
Harmonic Mean101.574887750757
Quadratic Mean108.927591392937
Winsorized Mean ( 1 / 20 )106.4583333333332.9443811198463636.1564379746085
Winsorized Mean ( 2 / 20 )106.0252.808993451227637.7448370175674
Winsorized Mean ( 3 / 20 )106.0552.8028792954090637.8378762773379
Winsorized Mean ( 4 / 20 )106.4152.7347066534138538.9127659696727
Winsorized Mean ( 5 / 20 )106.4566666666672.7274181896378939.0320292909686
Winsorized Mean ( 6 / 20 )105.9866666666672.623095452929440.405188666811
Winsorized Mean ( 7 / 20 )106.1266666666672.5988696659297240.8357017891088
Winsorized Mean ( 8 / 20 )106.1266666666672.5988696659297240.8357017891088
Winsorized Mean ( 9 / 20 )106.2766666666672.573603912767441.294880746582
Winsorized Mean ( 10 / 20 )106.2766666666672.573603912767441.294880746582
Winsorized Mean ( 11 / 20 )106.462.3530160955171445.2440594022382
Winsorized Mean ( 12 / 20 )106.162.2650640728768146.8684313486851
Winsorized Mean ( 13 / 20 )105.8352.172157958745248.7234363292521
Winsorized Mean ( 14 / 20 )105.7652.0317714085243952.0555607566177
Winsorized Mean ( 15 / 20 )106.341.9475092016202354.6030796216676
Winsorized Mean ( 16 / 20 )105.2733333333331.7705801447447259.4569715727337
Winsorized Mean ( 17 / 20 )104.7066666666671.6814925886843462.2700732499765
Winsorized Mean ( 18 / 20 )104.7966666666671.6681935943328862.8204466332191
Winsorized Mean ( 19 / 20 )105.811.5239624607978169.4308440803769
Winsorized Mean ( 20 / 20 )105.311.3971433729291375.375227797285
Trimmed Mean ( 1 / 20 )106.252.8578748360175637.1779752776224
Trimmed Mean ( 2 / 20 )106.0267857142862.7509248634522838.5422325134781
Trimmed Mean ( 3 / 20 )106.0277777777782.7085397169120339.1457349197222
Trimmed Mean ( 4 / 20 )106.0173076923082.6571735075876639.8985265318849
Trimmed Mean ( 5 / 20 )105.8982.6173775471814940.4595814287609
Trimmed Mean ( 6 / 20 )105.7583333333332.5673202515914741.1940556569732
Trimmed Mean ( 7 / 20 )105.7086956521742.5336056796531341.7226313080599
Trimmed Mean ( 8 / 20 )105.6272727272732.4940147457826842.3523048153128
Trimmed Mean ( 9 / 20 )105.5380952380952.4395834462432543.2607031338136
Trimmed Mean ( 10 / 20 )105.4152.3720962005398144.4395973384263
Trimmed Mean ( 11 / 20 )105.2789473684212.2795090618870746.1849216257411
Trimmed Mean ( 12 / 20 )105.12.214562194720647.4585903482652
Trimmed Mean ( 13 / 20 )104.9441176470592.1475027622013848.8679779575611
Trimmed Mean ( 14 / 20 )104.8156252.0779715866244550.4413177132354
Trimmed Mean ( 15 / 20 )104.682.0174947478175251.8861325974903
Trimmed Mean ( 16 / 20 )104.4428571428571.9482486272367453.6085875707719
Trimmed Mean ( 17 / 20 )104.3230769230771.9023492172518454.839077902733
Trimmed Mean ( 18 / 20 )104.2666666666671.8559116930932956.1808339559967
Trimmed Mean ( 19 / 20 )104.1863636363641.776814302986258.6366079231031
Trimmed Mean ( 20 / 20 )103.931.6959564914975461.2810532115888
Median104
Midrange113
Midmean - Weighted Average at Xnp104.815625
Midmean - Weighted Average at X(n+1)p105.367741935484
Midmean - Empirical Distribution Function104.815625
Midmean - Empirical Distribution Function - Averaging105.367741935484
Midmean - Empirical Distribution Function - Interpolation105.367741935484
Midmean - Closest Observation104.815625
Midmean - True Basic - Statistics Graphics Toolkit105.367741935484
Midmean - MS Excel (old versions)104.815625
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')