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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationMon, 10 Dec 2007 13:35:56 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2007/Dec/10/t1197318133u8e6coyn9nxvel3.htm/, Retrieved Mon, 06 May 2024 20:01:52 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=3043, Retrieved Mon, 06 May 2024 20:01:52 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact177
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Central Tendency 4] [2007-12-10 20:35:56] [6b5c00822e2ce0f7cf73539c28d95782] [Current]
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Dataseries X:
107,97
108,13
108,54
109,86
109,75
109,99
112,01
111,96
111,41
112,11
111,67
111,95
112,31
113,26
113,5
114,43
115,02
115,1
117,11
117,52
116,1
116,39
116,01
116,74
116,68
117,45
117,8
119,37
118,9
119,05
120,46
120,99
119,86
120,18
119,81
120,15
119,8
120,27
120,71
121,87
121,87
121,92
123,72
124,38
123,21
123,17
122,95
123,46
123,24
123,86
124,28
124,78
125,19
125,46
127,6
127,8
126,63
127,06
126,77
127,05




Summary of compuational 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 compuational 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=3043&T=0

[TABLE]
[ROW][C]Summary of compuational 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=3043&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=3043&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 compuational 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 Mean118.6098333333330.722226567095434164.228012007845
Geometric Mean118.479053161949
Harmonic Mean118.347295429794
Quadratic Mean118.739494798487
Winsorized Mean ( 1 / 20 )118.6091666666670.720853319340187164.539946594450
Winsorized Mean ( 2 / 20 )118.6048333333330.713826463412623166.153595323874
Winsorized Mean ( 3 / 20 )118.6648333333330.699959502124184169.530998540942
Winsorized Mean ( 4 / 20 )118.65350.694637605188758170.813527965791
Winsorized Mean ( 5 / 20 )118.6526666666670.690024476216444171.954286777283
Winsorized Mean ( 6 / 20 )118.6776666666670.639158670461698185.677942193821
Winsorized Mean ( 7 / 20 )118.67650.627763082132213189.046637780789
Winsorized Mean ( 8 / 20 )118.6591666666670.611311098718317194.106023783061
Winsorized Mean ( 9 / 20 )118.6006666666670.601049076587797197.322766619944
Winsorized Mean ( 10 / 20 )118.5923333333330.5967856160826198.718484724537
Winsorized Mean ( 11 / 20 )118.5336666666670.581151835361362203.963335318320
Winsorized Mean ( 12 / 20 )118.5456666666670.569360597198458208.208413525578
Winsorized Mean ( 13 / 20 )118.6951666666670.523417145309328226.769733720741
Winsorized Mean ( 14 / 20 )118.6998333333330.505742419626252234.704127490539
Winsorized Mean ( 15 / 20 )118.9248333333330.465241841713105255.619384738549
Winsorized Mean ( 16 / 20 )119.07150.438342398028761271.640390104786
Winsorized Mean ( 17 / 20 )119.0318333333330.42497932762397280.088525714491
Winsorized Mean ( 18 / 20 )118.9958333333330.335802461745742354.362599710281
Winsorized Mean ( 19 / 20 )119.00850.329185935215196361.523647485734
Winsorized Mean ( 20 / 20 )119.1051666666670.314880076864235378.255645300863
Trimmed Mean ( 1 / 20 )118.6348275862070.706208370551055167.9884189048
Trimmed Mean ( 2 / 20 )118.6623214285710.688031777386008172.466338516219
Trimmed Mean ( 3 / 20 )118.6942592592590.670063860127768177.138727100767
Trimmed Mean ( 4 / 20 )118.7055769230770.654250484401412181.437507121883
Trimmed Mean ( 5 / 20 )118.72120.636277608518515186.587109793830
Trimmed Mean ( 6 / 20 )118.7383333333330.61493075587042193.092201357309
Trimmed Mean ( 7 / 20 )118.7515217391300.603608390131251196.736035616252
Trimmed Mean ( 8 / 20 )118.7661363636360.591777182932784200.694010835369
Trimmed Mean ( 9 / 20 )118.7852380952380.580328538262877204.686191119953
Trimmed Mean ( 10 / 20 )118.8160.567277664568198209.449459094147
Trimmed Mean ( 11 / 20 )118.8513157894740.550306932467817215.972775877077
Trimmed Mean ( 12 / 20 )118.8994444444440.530927751107383223.94656183718
Trimmed Mean ( 13 / 20 )118.9514705882350.507012875258495234.612327206857
Trimmed Mean ( 14 / 20 )118.98843750.487401997877812244.127923188837
Trimmed Mean ( 15 / 20 )119.0296666666670.464127529871558256.458966568104
Trimmed Mean ( 16 / 20 )119.0446428571430.443608484295984268.355198494612
Trimmed Mean ( 17 / 20 )119.0407692307690.421636709493967282.330182714967
Trimmed Mean ( 18 / 20 )119.0420833333330.391817568447925303.820177856968
Trimmed Mean ( 19 / 20 )119.0490909090910.381573927233133311.994825674644
Trimmed Mean ( 20 / 20 )119.05550.364948067682599326.225867576162
Median119.585
Midrange117.885
Midmean - Weighted Average at Xnp118.851290322581
Midmean - Weighted Average at X(n+1)p119.029666666667
Midmean - Empirical Distribution Function118.851290322581
Midmean - Empirical Distribution Function - Averaging119.029666666667
Midmean - Empirical Distribution Function - Interpolation119.029666666667
Midmean - Closest Observation118.851290322581
Midmean - True Basic - Statistics Graphics Toolkit119.029666666667
Midmean - MS Excel (old versions)118.9884375
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 118.609833333333 & 0.722226567095434 & 164.228012007845 \tabularnewline
Geometric Mean & 118.479053161949 &  &  \tabularnewline
Harmonic Mean & 118.347295429794 &  &  \tabularnewline
Quadratic Mean & 118.739494798487 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 118.609166666667 & 0.720853319340187 & 164.539946594450 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 118.604833333333 & 0.713826463412623 & 166.153595323874 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 118.664833333333 & 0.699959502124184 & 169.530998540942 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 118.6535 & 0.694637605188758 & 170.813527965791 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 118.652666666667 & 0.690024476216444 & 171.954286777283 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 118.677666666667 & 0.639158670461698 & 185.677942193821 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 118.6765 & 0.627763082132213 & 189.046637780789 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 118.659166666667 & 0.611311098718317 & 194.106023783061 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 118.600666666667 & 0.601049076587797 & 197.322766619944 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 118.592333333333 & 0.5967856160826 & 198.718484724537 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 118.533666666667 & 0.581151835361362 & 203.963335318320 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 118.545666666667 & 0.569360597198458 & 208.208413525578 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 118.695166666667 & 0.523417145309328 & 226.769733720741 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 118.699833333333 & 0.505742419626252 & 234.704127490539 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 118.924833333333 & 0.465241841713105 & 255.619384738549 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 119.0715 & 0.438342398028761 & 271.640390104786 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 119.031833333333 & 0.42497932762397 & 280.088525714491 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 118.995833333333 & 0.335802461745742 & 354.362599710281 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 119.0085 & 0.329185935215196 & 361.523647485734 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 119.105166666667 & 0.314880076864235 & 378.255645300863 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 118.634827586207 & 0.706208370551055 & 167.9884189048 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 118.662321428571 & 0.688031777386008 & 172.466338516219 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 118.694259259259 & 0.670063860127768 & 177.138727100767 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 118.705576923077 & 0.654250484401412 & 181.437507121883 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 118.7212 & 0.636277608518515 & 186.587109793830 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 118.738333333333 & 0.61493075587042 & 193.092201357309 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 118.751521739130 & 0.603608390131251 & 196.736035616252 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 118.766136363636 & 0.591777182932784 & 200.694010835369 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 118.785238095238 & 0.580328538262877 & 204.686191119953 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 118.816 & 0.567277664568198 & 209.449459094147 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 118.851315789474 & 0.550306932467817 & 215.972775877077 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 118.899444444444 & 0.530927751107383 & 223.94656183718 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 118.951470588235 & 0.507012875258495 & 234.612327206857 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 118.9884375 & 0.487401997877812 & 244.127923188837 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 119.029666666667 & 0.464127529871558 & 256.458966568104 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 119.044642857143 & 0.443608484295984 & 268.355198494612 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 119.040769230769 & 0.421636709493967 & 282.330182714967 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 119.042083333333 & 0.391817568447925 & 303.820177856968 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 119.049090909091 & 0.381573927233133 & 311.994825674644 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 119.0555 & 0.364948067682599 & 326.225867576162 \tabularnewline
Median & 119.585 &  &  \tabularnewline
Midrange & 117.885 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 118.851290322581 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 119.029666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 118.851290322581 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 119.029666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 119.029666666667 &  &  \tabularnewline
Midmean - Closest Observation & 118.851290322581 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 119.029666666667 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 118.9884375 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=3043&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]118.609833333333[/C][C]0.722226567095434[/C][C]164.228012007845[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]118.479053161949[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]118.347295429794[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]118.739494798487[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]118.609166666667[/C][C]0.720853319340187[/C][C]164.539946594450[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]118.604833333333[/C][C]0.713826463412623[/C][C]166.153595323874[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]118.664833333333[/C][C]0.699959502124184[/C][C]169.530998540942[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]118.6535[/C][C]0.694637605188758[/C][C]170.813527965791[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]118.652666666667[/C][C]0.690024476216444[/C][C]171.954286777283[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]118.677666666667[/C][C]0.639158670461698[/C][C]185.677942193821[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]118.6765[/C][C]0.627763082132213[/C][C]189.046637780789[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]118.659166666667[/C][C]0.611311098718317[/C][C]194.106023783061[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]118.600666666667[/C][C]0.601049076587797[/C][C]197.322766619944[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]118.592333333333[/C][C]0.5967856160826[/C][C]198.718484724537[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]118.533666666667[/C][C]0.581151835361362[/C][C]203.963335318320[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]118.545666666667[/C][C]0.569360597198458[/C][C]208.208413525578[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]118.695166666667[/C][C]0.523417145309328[/C][C]226.769733720741[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]118.699833333333[/C][C]0.505742419626252[/C][C]234.704127490539[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]118.924833333333[/C][C]0.465241841713105[/C][C]255.619384738549[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]119.0715[/C][C]0.438342398028761[/C][C]271.640390104786[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]119.031833333333[/C][C]0.42497932762397[/C][C]280.088525714491[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]118.995833333333[/C][C]0.335802461745742[/C][C]354.362599710281[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]119.0085[/C][C]0.329185935215196[/C][C]361.523647485734[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]119.105166666667[/C][C]0.314880076864235[/C][C]378.255645300863[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]118.634827586207[/C][C]0.706208370551055[/C][C]167.9884189048[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]118.662321428571[/C][C]0.688031777386008[/C][C]172.466338516219[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]118.694259259259[/C][C]0.670063860127768[/C][C]177.138727100767[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]118.705576923077[/C][C]0.654250484401412[/C][C]181.437507121883[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]118.7212[/C][C]0.636277608518515[/C][C]186.587109793830[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]118.738333333333[/C][C]0.61493075587042[/C][C]193.092201357309[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]118.751521739130[/C][C]0.603608390131251[/C][C]196.736035616252[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]118.766136363636[/C][C]0.591777182932784[/C][C]200.694010835369[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]118.785238095238[/C][C]0.580328538262877[/C][C]204.686191119953[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]118.816[/C][C]0.567277664568198[/C][C]209.449459094147[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]118.851315789474[/C][C]0.550306932467817[/C][C]215.972775877077[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]118.899444444444[/C][C]0.530927751107383[/C][C]223.94656183718[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]118.951470588235[/C][C]0.507012875258495[/C][C]234.612327206857[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]118.9884375[/C][C]0.487401997877812[/C][C]244.127923188837[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]119.029666666667[/C][C]0.464127529871558[/C][C]256.458966568104[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]119.044642857143[/C][C]0.443608484295984[/C][C]268.355198494612[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]119.040769230769[/C][C]0.421636709493967[/C][C]282.330182714967[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]119.042083333333[/C][C]0.391817568447925[/C][C]303.820177856968[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]119.049090909091[/C][C]0.381573927233133[/C][C]311.994825674644[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]119.0555[/C][C]0.364948067682599[/C][C]326.225867576162[/C][/ROW]
[ROW][C]Median[/C][C]119.585[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]117.885[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]118.851290322581[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]119.029666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]118.851290322581[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]119.029666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]119.029666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]118.851290322581[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]119.029666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]118.9884375[/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=3043&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=3043&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 Mean118.6098333333330.722226567095434164.228012007845
Geometric Mean118.479053161949
Harmonic Mean118.347295429794
Quadratic Mean118.739494798487
Winsorized Mean ( 1 / 20 )118.6091666666670.720853319340187164.539946594450
Winsorized Mean ( 2 / 20 )118.6048333333330.713826463412623166.153595323874
Winsorized Mean ( 3 / 20 )118.6648333333330.699959502124184169.530998540942
Winsorized Mean ( 4 / 20 )118.65350.694637605188758170.813527965791
Winsorized Mean ( 5 / 20 )118.6526666666670.690024476216444171.954286777283
Winsorized Mean ( 6 / 20 )118.6776666666670.639158670461698185.677942193821
Winsorized Mean ( 7 / 20 )118.67650.627763082132213189.046637780789
Winsorized Mean ( 8 / 20 )118.6591666666670.611311098718317194.106023783061
Winsorized Mean ( 9 / 20 )118.6006666666670.601049076587797197.322766619944
Winsorized Mean ( 10 / 20 )118.5923333333330.5967856160826198.718484724537
Winsorized Mean ( 11 / 20 )118.5336666666670.581151835361362203.963335318320
Winsorized Mean ( 12 / 20 )118.5456666666670.569360597198458208.208413525578
Winsorized Mean ( 13 / 20 )118.6951666666670.523417145309328226.769733720741
Winsorized Mean ( 14 / 20 )118.6998333333330.505742419626252234.704127490539
Winsorized Mean ( 15 / 20 )118.9248333333330.465241841713105255.619384738549
Winsorized Mean ( 16 / 20 )119.07150.438342398028761271.640390104786
Winsorized Mean ( 17 / 20 )119.0318333333330.42497932762397280.088525714491
Winsorized Mean ( 18 / 20 )118.9958333333330.335802461745742354.362599710281
Winsorized Mean ( 19 / 20 )119.00850.329185935215196361.523647485734
Winsorized Mean ( 20 / 20 )119.1051666666670.314880076864235378.255645300863
Trimmed Mean ( 1 / 20 )118.6348275862070.706208370551055167.9884189048
Trimmed Mean ( 2 / 20 )118.6623214285710.688031777386008172.466338516219
Trimmed Mean ( 3 / 20 )118.6942592592590.670063860127768177.138727100767
Trimmed Mean ( 4 / 20 )118.7055769230770.654250484401412181.437507121883
Trimmed Mean ( 5 / 20 )118.72120.636277608518515186.587109793830
Trimmed Mean ( 6 / 20 )118.7383333333330.61493075587042193.092201357309
Trimmed Mean ( 7 / 20 )118.7515217391300.603608390131251196.736035616252
Trimmed Mean ( 8 / 20 )118.7661363636360.591777182932784200.694010835369
Trimmed Mean ( 9 / 20 )118.7852380952380.580328538262877204.686191119953
Trimmed Mean ( 10 / 20 )118.8160.567277664568198209.449459094147
Trimmed Mean ( 11 / 20 )118.8513157894740.550306932467817215.972775877077
Trimmed Mean ( 12 / 20 )118.8994444444440.530927751107383223.94656183718
Trimmed Mean ( 13 / 20 )118.9514705882350.507012875258495234.612327206857
Trimmed Mean ( 14 / 20 )118.98843750.487401997877812244.127923188837
Trimmed Mean ( 15 / 20 )119.0296666666670.464127529871558256.458966568104
Trimmed Mean ( 16 / 20 )119.0446428571430.443608484295984268.355198494612
Trimmed Mean ( 17 / 20 )119.0407692307690.421636709493967282.330182714967
Trimmed Mean ( 18 / 20 )119.0420833333330.391817568447925303.820177856968
Trimmed Mean ( 19 / 20 )119.0490909090910.381573927233133311.994825674644
Trimmed Mean ( 20 / 20 )119.05550.364948067682599326.225867576162
Median119.585
Midrange117.885
Midmean - Weighted Average at Xnp118.851290322581
Midmean - Weighted Average at X(n+1)p119.029666666667
Midmean - Empirical Distribution Function118.851290322581
Midmean - Empirical Distribution Function - Averaging119.029666666667
Midmean - Empirical Distribution Function - Interpolation119.029666666667
Midmean - Closest Observation118.851290322581
Midmean - True Basic - Statistics Graphics Toolkit119.029666666667
Midmean - MS Excel (old versions)118.9884375
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')