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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationFri, 09 Oct 2015 10:10:05 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2015/Oct/09/t1444381830ihko9fygnf4z1uw.htm/, Retrieved Tue, 14 May 2024 20:43:02 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=281761, Retrieved Tue, 14 May 2024 20:43:02 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact58
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2015-10-09 09:10:05] [e7bd1b63287b3004f428c98394187272] [Current]
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Dataseries X:
62239,3
64816,6
62625,3
67923
64363,7
67342
64411,2
69174,5
66290,2
69336,8
66712,2
72225,9
68229,5
71096,3
68407,9
74522,4
71798,4
75074,3
72694,6
78789,4
74814,5
78303,2
75431,6
82600,7
78830,5
82168,1
79493,2
86876,6
83478,5
87003,2
83672,7
90914,2
86448
90577,7
86621,1
91418,5
84275,4
87677,9
85149,6
92600
87111,3
92293,9
89060
97281,6
91812
95980,4
92043,7
100079,2
94384,8
97900,5
93630,8
102255,2
95251,8
100001,8
95689,8
104298
97435,1
101220,2
97537
105834,9




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

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=281761&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' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=281761&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=281761&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' @ jenkins.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean83292.17833333331594.7521976023752.2289158519794
Geometric Mean82371.1373279327
Harmonic Mean81436.9607290496
Quadratic Mean84188.1096785377
Winsorized Mean ( 1 / 20 )83272.99666666671587.3791359763952.4594249599015
Winsorized Mean ( 2 / 20 )83262.851560.3674916859153.36105144695
Winsorized Mean ( 3 / 20 )83213.4751549.4439288036153.7053800096224
Winsorized Mean ( 4 / 20 )83164.4351529.2925574106354.3809845912102
Winsorized Mean ( 5 / 20 )83280.7851503.8306966439155.3790963210535
Winsorized Mean ( 6 / 20 )83112.8551457.8767590618157.0095205122041
Winsorized Mean ( 7 / 20 )83143.92333333331436.7762298602257.8683873002426
Winsorized Mean ( 8 / 20 )83207.80333333331420.182547242258.5895126615319
Winsorized Mean ( 9 / 20 )83230.75333333331407.9356439722759.1154529609825
Winsorized Mean ( 10 / 20 )83043.621366.8022883626860.7575950867626
Winsorized Mean ( 11 / 20 )83130.88666666671333.0480283019462.3615090392205
Winsorized Mean ( 12 / 20 )83075.74666666671313.4134083954463.251788154164
Winsorized Mean ( 13 / 20 )83269.12166666671217.977389950268.366722037485
Winsorized Mean ( 14 / 20 )83257.01166666671163.5172621579471.5563183929499
Winsorized Mean ( 15 / 20 )83106.18666666671107.4877818674575.0402740575003
Winsorized Mean ( 16 / 20 )83149.54666666671074.963388556677.3510498606978
Winsorized Mean ( 17 / 20 )83596.5333333333981.32143018623185.1877180726286
Winsorized Mean ( 18 / 20 )83614.6533333333957.51469740299587.3246682898089
Winsorized Mean ( 19 / 20 )83572.315926.7306421078490.1797255887812
Winsorized Mean ( 20 / 20 )83523.315884.26703333435994.4548556617039
Trimmed Mean ( 1 / 20 )83266.49137931031560.594428163653.3556251878284
Trimmed Mean ( 2 / 20 )83259.52142857141527.1597726518154.519194991626
Trimmed Mean ( 3 / 20 )83257.67222222221503.006562310455.3940843040896
Trimmed Mean ( 4 / 20 )83274.67115384621477.2639997908156.3708796570133
Trimmed Mean ( 5 / 20 )83307.7421451.8582048044157.3800814186418
Trimmed Mean ( 6 / 20 )83314.481251427.3241461985558.3711005463579
Trimmed Mean ( 7 / 20 )83358.31304347831408.663575799359.175458552039
Trimmed Mean ( 8 / 20 )83400.07727272731388.9352965417560.0460492870915
Trimmed Mean ( 9 / 20 )83434.41190476191366.0399041178561.0775802765744
Trimmed Mean ( 10 / 20 )83468.3551337.4257502273462.4097113322455
Trimmed Mean ( 11 / 20 )83535.41842105261308.3723272602863.8468245472412
Trimmed Mean ( 12 / 20 )83596.71111111111276.3863363354365.4948339161337
Trimmed Mean ( 13 / 20 )83673.32352941181235.7416735051967.7110154358327
Trimmed Mean ( 14 / 20 )83731.6218751204.9680800277569.4886638599351
Trimmed Mean ( 15 / 20 )83799.42333333331174.3421079670371.3586124220678
Trimmed Mean ( 16 / 20 )83898.45714285711143.2617514316173.3851692648672
Trimmed Mean ( 17 / 20 )84006.47307692311103.7102669361476.1127948099299
Trimmed Mean ( 18 / 20 )84066.75833333331074.3912562219978.2459442465565
Trimmed Mean ( 19 / 20 )84135.25909090911031.4182046091281.5724007147948
Trimmed Mean ( 20 / 20 )84224.145968.15324883797586.9946417068682
Median84712.5
Midrange84037.1
Midmean - Weighted Average at Xnp83412.2935483871
Midmean - Weighted Average at X(n+1)p83799.4233333333
Midmean - Empirical Distribution Function83412.2935483871
Midmean - Empirical Distribution Function - Averaging83799.4233333333
Midmean - Empirical Distribution Function - Interpolation83799.4233333333
Midmean - Closest Observation83412.2935483871
Midmean - True Basic - Statistics Graphics Toolkit83799.4233333333
Midmean - MS Excel (old versions)83731.621875
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 83292.1783333333 & 1594.75219760237 & 52.2289158519794 \tabularnewline
Geometric Mean & 82371.1373279327 &  &  \tabularnewline
Harmonic Mean & 81436.9607290496 &  &  \tabularnewline
Quadratic Mean & 84188.1096785377 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 83272.9966666667 & 1587.37913597639 & 52.4594249599015 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 83262.85 & 1560.36749168591 & 53.36105144695 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 83213.475 & 1549.44392880361 & 53.7053800096224 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 83164.435 & 1529.29255741063 & 54.3809845912102 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 83280.785 & 1503.83069664391 & 55.3790963210535 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 83112.855 & 1457.87675906181 & 57.0095205122041 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 83143.9233333333 & 1436.77622986022 & 57.8683873002426 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 83207.8033333333 & 1420.1825472422 & 58.5895126615319 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 83230.7533333333 & 1407.93564397227 & 59.1154529609825 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 83043.62 & 1366.80228836268 & 60.7575950867626 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 83130.8866666667 & 1333.04802830194 & 62.3615090392205 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 83075.7466666667 & 1313.41340839544 & 63.251788154164 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 83269.1216666667 & 1217.9773899502 & 68.366722037485 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 83257.0116666667 & 1163.51726215794 & 71.5563183929499 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 83106.1866666667 & 1107.48778186745 & 75.0402740575003 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 83149.5466666667 & 1074.9633885566 & 77.3510498606978 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 83596.5333333333 & 981.321430186231 & 85.1877180726286 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 83614.6533333333 & 957.514697402995 & 87.3246682898089 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 83572.315 & 926.73064210784 & 90.1797255887812 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 83523.315 & 884.267033334359 & 94.4548556617039 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 83266.4913793103 & 1560.5944281636 & 53.3556251878284 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 83259.5214285714 & 1527.15977265181 & 54.519194991626 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 83257.6722222222 & 1503.0065623104 & 55.3940843040896 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 83274.6711538462 & 1477.26399979081 & 56.3708796570133 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 83307.742 & 1451.85820480441 & 57.3800814186418 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 83314.48125 & 1427.32414619855 & 58.3711005463579 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 83358.3130434783 & 1408.6635757993 & 59.175458552039 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 83400.0772727273 & 1388.93529654175 & 60.0460492870915 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 83434.4119047619 & 1366.03990411785 & 61.0775802765744 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 83468.355 & 1337.42575022734 & 62.4097113322455 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 83535.4184210526 & 1308.37232726028 & 63.8468245472412 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 83596.7111111111 & 1276.38633633543 & 65.4948339161337 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 83673.3235294118 & 1235.74167350519 & 67.7110154358327 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 83731.621875 & 1204.96808002775 & 69.4886638599351 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 83799.4233333333 & 1174.34210796703 & 71.3586124220678 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 83898.4571428571 & 1143.26175143161 & 73.3851692648672 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 84006.4730769231 & 1103.71026693614 & 76.1127948099299 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 84066.7583333333 & 1074.39125622199 & 78.2459442465565 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 84135.2590909091 & 1031.41820460912 & 81.5724007147948 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 84224.145 & 968.153248837975 & 86.9946417068682 \tabularnewline
Median & 84712.5 &  &  \tabularnewline
Midrange & 84037.1 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 83412.2935483871 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 83799.4233333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 83412.2935483871 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 83799.4233333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 83799.4233333333 &  &  \tabularnewline
Midmean - Closest Observation & 83412.2935483871 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 83799.4233333333 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 83731.621875 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=281761&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]83292.1783333333[/C][C]1594.75219760237[/C][C]52.2289158519794[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]82371.1373279327[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]81436.9607290496[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]84188.1096785377[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]83272.9966666667[/C][C]1587.37913597639[/C][C]52.4594249599015[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]83262.85[/C][C]1560.36749168591[/C][C]53.36105144695[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]83213.475[/C][C]1549.44392880361[/C][C]53.7053800096224[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]83164.435[/C][C]1529.29255741063[/C][C]54.3809845912102[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]83280.785[/C][C]1503.83069664391[/C][C]55.3790963210535[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]83112.855[/C][C]1457.87675906181[/C][C]57.0095205122041[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]83143.9233333333[/C][C]1436.77622986022[/C][C]57.8683873002426[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]83207.8033333333[/C][C]1420.1825472422[/C][C]58.5895126615319[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]83230.7533333333[/C][C]1407.93564397227[/C][C]59.1154529609825[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]83043.62[/C][C]1366.80228836268[/C][C]60.7575950867626[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]83130.8866666667[/C][C]1333.04802830194[/C][C]62.3615090392205[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]83075.7466666667[/C][C]1313.41340839544[/C][C]63.251788154164[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]83269.1216666667[/C][C]1217.9773899502[/C][C]68.366722037485[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]83257.0116666667[/C][C]1163.51726215794[/C][C]71.5563183929499[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]83106.1866666667[/C][C]1107.48778186745[/C][C]75.0402740575003[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]83149.5466666667[/C][C]1074.9633885566[/C][C]77.3510498606978[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]83596.5333333333[/C][C]981.321430186231[/C][C]85.1877180726286[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]83614.6533333333[/C][C]957.514697402995[/C][C]87.3246682898089[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]83572.315[/C][C]926.73064210784[/C][C]90.1797255887812[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]83523.315[/C][C]884.267033334359[/C][C]94.4548556617039[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]83266.4913793103[/C][C]1560.5944281636[/C][C]53.3556251878284[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]83259.5214285714[/C][C]1527.15977265181[/C][C]54.519194991626[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]83257.6722222222[/C][C]1503.0065623104[/C][C]55.3940843040896[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]83274.6711538462[/C][C]1477.26399979081[/C][C]56.3708796570133[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]83307.742[/C][C]1451.85820480441[/C][C]57.3800814186418[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]83314.48125[/C][C]1427.32414619855[/C][C]58.3711005463579[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]83358.3130434783[/C][C]1408.6635757993[/C][C]59.175458552039[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]83400.0772727273[/C][C]1388.93529654175[/C][C]60.0460492870915[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]83434.4119047619[/C][C]1366.03990411785[/C][C]61.0775802765744[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]83468.355[/C][C]1337.42575022734[/C][C]62.4097113322455[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]83535.4184210526[/C][C]1308.37232726028[/C][C]63.8468245472412[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]83596.7111111111[/C][C]1276.38633633543[/C][C]65.4948339161337[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]83673.3235294118[/C][C]1235.74167350519[/C][C]67.7110154358327[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]83731.621875[/C][C]1204.96808002775[/C][C]69.4886638599351[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]83799.4233333333[/C][C]1174.34210796703[/C][C]71.3586124220678[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]83898.4571428571[/C][C]1143.26175143161[/C][C]73.3851692648672[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]84006.4730769231[/C][C]1103.71026693614[/C][C]76.1127948099299[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]84066.7583333333[/C][C]1074.39125622199[/C][C]78.2459442465565[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]84135.2590909091[/C][C]1031.41820460912[/C][C]81.5724007147948[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]84224.145[/C][C]968.153248837975[/C][C]86.9946417068682[/C][/ROW]
[ROW][C]Median[/C][C]84712.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]84037.1[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]83412.2935483871[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]83799.4233333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]83412.2935483871[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]83799.4233333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]83799.4233333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]83412.2935483871[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]83799.4233333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]83731.621875[/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=281761&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=281761&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 Mean83292.17833333331594.7521976023752.2289158519794
Geometric Mean82371.1373279327
Harmonic Mean81436.9607290496
Quadratic Mean84188.1096785377
Winsorized Mean ( 1 / 20 )83272.99666666671587.3791359763952.4594249599015
Winsorized Mean ( 2 / 20 )83262.851560.3674916859153.36105144695
Winsorized Mean ( 3 / 20 )83213.4751549.4439288036153.7053800096224
Winsorized Mean ( 4 / 20 )83164.4351529.2925574106354.3809845912102
Winsorized Mean ( 5 / 20 )83280.7851503.8306966439155.3790963210535
Winsorized Mean ( 6 / 20 )83112.8551457.8767590618157.0095205122041
Winsorized Mean ( 7 / 20 )83143.92333333331436.7762298602257.8683873002426
Winsorized Mean ( 8 / 20 )83207.80333333331420.182547242258.5895126615319
Winsorized Mean ( 9 / 20 )83230.75333333331407.9356439722759.1154529609825
Winsorized Mean ( 10 / 20 )83043.621366.8022883626860.7575950867626
Winsorized Mean ( 11 / 20 )83130.88666666671333.0480283019462.3615090392205
Winsorized Mean ( 12 / 20 )83075.74666666671313.4134083954463.251788154164
Winsorized Mean ( 13 / 20 )83269.12166666671217.977389950268.366722037485
Winsorized Mean ( 14 / 20 )83257.01166666671163.5172621579471.5563183929499
Winsorized Mean ( 15 / 20 )83106.18666666671107.4877818674575.0402740575003
Winsorized Mean ( 16 / 20 )83149.54666666671074.963388556677.3510498606978
Winsorized Mean ( 17 / 20 )83596.5333333333981.32143018623185.1877180726286
Winsorized Mean ( 18 / 20 )83614.6533333333957.51469740299587.3246682898089
Winsorized Mean ( 19 / 20 )83572.315926.7306421078490.1797255887812
Winsorized Mean ( 20 / 20 )83523.315884.26703333435994.4548556617039
Trimmed Mean ( 1 / 20 )83266.49137931031560.594428163653.3556251878284
Trimmed Mean ( 2 / 20 )83259.52142857141527.1597726518154.519194991626
Trimmed Mean ( 3 / 20 )83257.67222222221503.006562310455.3940843040896
Trimmed Mean ( 4 / 20 )83274.67115384621477.2639997908156.3708796570133
Trimmed Mean ( 5 / 20 )83307.7421451.8582048044157.3800814186418
Trimmed Mean ( 6 / 20 )83314.481251427.3241461985558.3711005463579
Trimmed Mean ( 7 / 20 )83358.31304347831408.663575799359.175458552039
Trimmed Mean ( 8 / 20 )83400.07727272731388.9352965417560.0460492870915
Trimmed Mean ( 9 / 20 )83434.41190476191366.0399041178561.0775802765744
Trimmed Mean ( 10 / 20 )83468.3551337.4257502273462.4097113322455
Trimmed Mean ( 11 / 20 )83535.41842105261308.3723272602863.8468245472412
Trimmed Mean ( 12 / 20 )83596.71111111111276.3863363354365.4948339161337
Trimmed Mean ( 13 / 20 )83673.32352941181235.7416735051967.7110154358327
Trimmed Mean ( 14 / 20 )83731.6218751204.9680800277569.4886638599351
Trimmed Mean ( 15 / 20 )83799.42333333331174.3421079670371.3586124220678
Trimmed Mean ( 16 / 20 )83898.45714285711143.2617514316173.3851692648672
Trimmed Mean ( 17 / 20 )84006.47307692311103.7102669361476.1127948099299
Trimmed Mean ( 18 / 20 )84066.75833333331074.3912562219978.2459442465565
Trimmed Mean ( 19 / 20 )84135.25909090911031.4182046091281.5724007147948
Trimmed Mean ( 20 / 20 )84224.145968.15324883797586.9946417068682
Median84712.5
Midrange84037.1
Midmean - Weighted Average at Xnp83412.2935483871
Midmean - Weighted Average at X(n+1)p83799.4233333333
Midmean - Empirical Distribution Function83412.2935483871
Midmean - Empirical Distribution Function - Averaging83799.4233333333
Midmean - Empirical Distribution Function - Interpolation83799.4233333333
Midmean - Closest Observation83412.2935483871
Midmean - True Basic - Statistics Graphics Toolkit83799.4233333333
Midmean - MS Excel (old versions)83731.621875
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')