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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 computationSun, 18 Oct 2009 09:00:46 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Oct/18/t12558781055obymz5ofweckiu.htm/, Retrieved Mon, 29 Apr 2024 13:44:06 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=47349, Retrieved Mon, 29 Apr 2024 13:44:06 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsws3p2b3
Estimated Impact101
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2009-10-18 15:00:46] [9ea4b07b6662a0f40f92decdf1e3b5d5] [Current]
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Dataseries X:
5596.22
8148.91
7449.67
6768.80
6962.11
7982.99
9576.28
8449.08
7774.25
9074.05
10227.48
10191.50
10413.21
8309.06
8980.02
10597.72
10028.35
9324.74
6583.41
7450.08
7818.56
6922.01
6179.63
6471.26
5048.99
5081.70
6393.43
7288.01
7474.38
7711.85
8356.11
8360.59
5915.39
5886.06
5757.45
4812.07
6697.20
9195.60
12103.04
11879.47
12874.59
13374.82
16934.95
15774.40
18257.77
17589.08
18007.95
15967.01
12000.10
9508.20
5849.29
5011.23
4201.50
3223.24
1155.95
1231.21
-750.95
-2277.91
-3852.93
-1905.75




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=47349&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=47349&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=47349&T=0

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean7956.908598.28774333052913.2994668346467
Geometric MeanNaN
Harmonic Mean9861.06385616679
Quadratic Mean9188.65224751795
Winsorized Mean ( 1 / 20 )7978.99466666667588.8086114191813.5510835132578
Winsorized Mean ( 2 / 20 )7977.43766666667581.21681449650713.7254075720045
Winsorized Mean ( 3 / 20 )8002.47116666667556.14251082992114.3892455815412
Winsorized Mean ( 4 / 20 )8065.0685507.08429861582415.9047884582801
Winsorized Mean ( 5 / 20 )8055.28933333333501.42295358213516.0648595677299
Winsorized Mean ( 6 / 20 )8014.53433333333398.76399414342620.0984403081555
Winsorized Mean ( 7 / 20 )8070.3045363.60167777013322.195454513557
Winsorized Mean ( 8 / 20 )8048.8405327.04124605431424.6110868188879
Winsorized Mean ( 9 / 20 )8063.2735318.87357780540525.2867407688469
Winsorized Mean ( 10 / 20 )8049.46183333333313.66878923993725.6622976510933
Winsorized Mean ( 11 / 20 )7820.47116666667267.37450289915529.2491284018069
Winsorized Mean ( 12 / 20 )7886.47316666667243.72198541019632.3584807229982
Winsorized Mean ( 13 / 20 )7881.16483333333231.22119288467234.0849588007457
Winsorized Mean ( 14 / 20 )7894.19883333333226.46942507809534.8576803716931
Winsorized Mean ( 15 / 20 )7862.60383333333218.12031676174236.0470952457027
Winsorized Mean ( 16 / 20 )7749.87316666667197.26702807233439.2862063285352
Winsorized Mean ( 17 / 20 )7805.45183333333182.6732462847842.7290366382659
Winsorized Mean ( 18 / 20 )7814.55383333333164.49907550546347.5051535050956
Winsorized Mean ( 19 / 20 )7798.30566666667154.58558511714350.4465255331357
Winsorized Mean ( 20 / 20 )7795.17233333333143.00449263030254.5099820988531
Trimmed Mean ( 1 / 20 )7982.9248275862555.8677323619914.361194872142
Trimmed Mean ( 2 / 20 )7987.13571428571514.63344917472215.5200477681621
Trimmed Mean ( 3 / 20 )7992.52351851852467.55772919493117.0941961162326
Trimmed Mean ( 4 / 20 )7988.6975420.64304579895918.9916309797217
Trimmed Mean ( 5 / 20 )7965.7862382.72931861830520.8131068420820
Trimmed Mean ( 6 / 20 )7943.41041666667334.56813174009923.742280459746
Trimmed Mean ( 7 / 20 )7927.94869565217311.40636843813425.4585310358776
Trimmed Mean ( 8 / 20 )7900.21704545455292.92801702843226.9698239369427
Trimmed Mean ( 9 / 20 )7873.67714285714280.11586397724328.1086441555371
Trimmed Mean ( 10 / 20 )7842.07775265.36820448042629.5516856111466
Trimmed Mean ( 11 / 20 )7809.33289473684246.90548959013731.6288346107668
Trimmed Mean ( 12 / 20 )7807.64527777778236.53892703446733.0078662977959
Trimmed Mean ( 13 / 20 )7796.05294117647228.95153252851034.0511061667853
Trimmed Mean ( 14 / 20 )7783.7771875221.66283394986335.115391465493
Trimmed Mean ( 15 / 20 )7768.00266666667212.25256526992336.5979212396705
Trimmed Mean ( 16 / 20 )7754.48821428571200.98471069548438.5824781768335
Trimmed Mean ( 17 / 20 )7755.15384615385191.50131753559840.4966083051218
Trimmed Mean ( 18 / 20 )7747.75708333333181.98050542539942.5746541654124
Trimmed Mean ( 19 / 20 )7737.63636363636173.8113671160944.517435723685
Trimmed Mean ( 20 / 20 )7728.057164.04426917772147.1095823020043
Median7743.05
Midrange7202.42
Midmean - Weighted Average at Xnp7706.10870967742
Midmean - Weighted Average at X(n+1)p7768.00266666667
Midmean - Empirical Distribution Function7706.10870967742
Midmean - Empirical Distribution Function - Averaging7768.00266666667
Midmean - Empirical Distribution Function - Interpolation7768.00266666667
Midmean - Closest Observation7706.10870967742
Midmean - True Basic - Statistics Graphics Toolkit7768.00266666667
Midmean - MS Excel (old versions)7783.7771875
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 7956.908 & 598.287743330529 & 13.2994668346467 \tabularnewline
Geometric Mean & NaN &  &  \tabularnewline
Harmonic Mean & 9861.06385616679 &  &  \tabularnewline
Quadratic Mean & 9188.65224751795 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 7978.99466666667 & 588.80861141918 & 13.5510835132578 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 7977.43766666667 & 581.216814496507 & 13.7254075720045 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 8002.47116666667 & 556.142510829921 & 14.3892455815412 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 8065.0685 & 507.084298615824 & 15.9047884582801 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 8055.28933333333 & 501.422953582135 & 16.0648595677299 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 8014.53433333333 & 398.763994143426 & 20.0984403081555 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 8070.3045 & 363.601677770133 & 22.195454513557 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 8048.8405 & 327.041246054314 & 24.6110868188879 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 8063.2735 & 318.873577805405 & 25.2867407688469 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 8049.46183333333 & 313.668789239937 & 25.6622976510933 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 7820.47116666667 & 267.374502899155 & 29.2491284018069 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 7886.47316666667 & 243.721985410196 & 32.3584807229982 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 7881.16483333333 & 231.221192884672 & 34.0849588007457 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 7894.19883333333 & 226.469425078095 & 34.8576803716931 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 7862.60383333333 & 218.120316761742 & 36.0470952457027 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 7749.87316666667 & 197.267028072334 & 39.2862063285352 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 7805.45183333333 & 182.67324628478 & 42.7290366382659 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 7814.55383333333 & 164.499075505463 & 47.5051535050956 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 7798.30566666667 & 154.585585117143 & 50.4465255331357 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 7795.17233333333 & 143.004492630302 & 54.5099820988531 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 7982.9248275862 & 555.86773236199 & 14.361194872142 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 7987.13571428571 & 514.633449174722 & 15.5200477681621 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 7992.52351851852 & 467.557729194931 & 17.0941961162326 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 7988.6975 & 420.643045798959 & 18.9916309797217 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 7965.7862 & 382.729318618305 & 20.8131068420820 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 7943.41041666667 & 334.568131740099 & 23.742280459746 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 7927.94869565217 & 311.406368438134 & 25.4585310358776 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 7900.21704545455 & 292.928017028432 & 26.9698239369427 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 7873.67714285714 & 280.115863977243 & 28.1086441555371 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 7842.07775 & 265.368204480426 & 29.5516856111466 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 7809.33289473684 & 246.905489590137 & 31.6288346107668 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 7807.64527777778 & 236.538927034467 & 33.0078662977959 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 7796.05294117647 & 228.951532528510 & 34.0511061667853 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 7783.7771875 & 221.662833949863 & 35.115391465493 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 7768.00266666667 & 212.252565269923 & 36.5979212396705 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 7754.48821428571 & 200.984710695484 & 38.5824781768335 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 7755.15384615385 & 191.501317535598 & 40.4966083051218 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 7747.75708333333 & 181.980505425399 & 42.5746541654124 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 7737.63636363636 & 173.81136711609 & 44.517435723685 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 7728.057 & 164.044269177721 & 47.1095823020043 \tabularnewline
Median & 7743.05 &  &  \tabularnewline
Midrange & 7202.42 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 7706.10870967742 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 7768.00266666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 7706.10870967742 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 7768.00266666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 7768.00266666667 &  &  \tabularnewline
Midmean - Closest Observation & 7706.10870967742 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 7768.00266666667 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 7783.7771875 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=47349&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]7956.908[/C][C]598.287743330529[/C][C]13.2994668346467[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]NaN[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]9861.06385616679[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]9188.65224751795[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]7978.99466666667[/C][C]588.80861141918[/C][C]13.5510835132578[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]7977.43766666667[/C][C]581.216814496507[/C][C]13.7254075720045[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]8002.47116666667[/C][C]556.142510829921[/C][C]14.3892455815412[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]8065.0685[/C][C]507.084298615824[/C][C]15.9047884582801[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]8055.28933333333[/C][C]501.422953582135[/C][C]16.0648595677299[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]8014.53433333333[/C][C]398.763994143426[/C][C]20.0984403081555[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]8070.3045[/C][C]363.601677770133[/C][C]22.195454513557[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]8048.8405[/C][C]327.041246054314[/C][C]24.6110868188879[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]8063.2735[/C][C]318.873577805405[/C][C]25.2867407688469[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]8049.46183333333[/C][C]313.668789239937[/C][C]25.6622976510933[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]7820.47116666667[/C][C]267.374502899155[/C][C]29.2491284018069[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]7886.47316666667[/C][C]243.721985410196[/C][C]32.3584807229982[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]7881.16483333333[/C][C]231.221192884672[/C][C]34.0849588007457[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]7894.19883333333[/C][C]226.469425078095[/C][C]34.8576803716931[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]7862.60383333333[/C][C]218.120316761742[/C][C]36.0470952457027[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]7749.87316666667[/C][C]197.267028072334[/C][C]39.2862063285352[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]7805.45183333333[/C][C]182.67324628478[/C][C]42.7290366382659[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]7814.55383333333[/C][C]164.499075505463[/C][C]47.5051535050956[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]7798.30566666667[/C][C]154.585585117143[/C][C]50.4465255331357[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]7795.17233333333[/C][C]143.004492630302[/C][C]54.5099820988531[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]7982.9248275862[/C][C]555.86773236199[/C][C]14.361194872142[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]7987.13571428571[/C][C]514.633449174722[/C][C]15.5200477681621[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]7992.52351851852[/C][C]467.557729194931[/C][C]17.0941961162326[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]7988.6975[/C][C]420.643045798959[/C][C]18.9916309797217[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]7965.7862[/C][C]382.729318618305[/C][C]20.8131068420820[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]7943.41041666667[/C][C]334.568131740099[/C][C]23.742280459746[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]7927.94869565217[/C][C]311.406368438134[/C][C]25.4585310358776[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]7900.21704545455[/C][C]292.928017028432[/C][C]26.9698239369427[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]7873.67714285714[/C][C]280.115863977243[/C][C]28.1086441555371[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]7842.07775[/C][C]265.368204480426[/C][C]29.5516856111466[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]7809.33289473684[/C][C]246.905489590137[/C][C]31.6288346107668[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]7807.64527777778[/C][C]236.538927034467[/C][C]33.0078662977959[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]7796.05294117647[/C][C]228.951532528510[/C][C]34.0511061667853[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]7783.7771875[/C][C]221.662833949863[/C][C]35.115391465493[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]7768.00266666667[/C][C]212.252565269923[/C][C]36.5979212396705[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]7754.48821428571[/C][C]200.984710695484[/C][C]38.5824781768335[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]7755.15384615385[/C][C]191.501317535598[/C][C]40.4966083051218[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]7747.75708333333[/C][C]181.980505425399[/C][C]42.5746541654124[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]7737.63636363636[/C][C]173.81136711609[/C][C]44.517435723685[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]7728.057[/C][C]164.044269177721[/C][C]47.1095823020043[/C][/ROW]
[ROW][C]Median[/C][C]7743.05[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]7202.42[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]7706.10870967742[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]7768.00266666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]7706.10870967742[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]7768.00266666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]7768.00266666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]7706.10870967742[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]7768.00266666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]7783.7771875[/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=47349&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=47349&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 Mean7956.908598.28774333052913.2994668346467
Geometric MeanNaN
Harmonic Mean9861.06385616679
Quadratic Mean9188.65224751795
Winsorized Mean ( 1 / 20 )7978.99466666667588.8086114191813.5510835132578
Winsorized Mean ( 2 / 20 )7977.43766666667581.21681449650713.7254075720045
Winsorized Mean ( 3 / 20 )8002.47116666667556.14251082992114.3892455815412
Winsorized Mean ( 4 / 20 )8065.0685507.08429861582415.9047884582801
Winsorized Mean ( 5 / 20 )8055.28933333333501.42295358213516.0648595677299
Winsorized Mean ( 6 / 20 )8014.53433333333398.76399414342620.0984403081555
Winsorized Mean ( 7 / 20 )8070.3045363.60167777013322.195454513557
Winsorized Mean ( 8 / 20 )8048.8405327.04124605431424.6110868188879
Winsorized Mean ( 9 / 20 )8063.2735318.87357780540525.2867407688469
Winsorized Mean ( 10 / 20 )8049.46183333333313.66878923993725.6622976510933
Winsorized Mean ( 11 / 20 )7820.47116666667267.37450289915529.2491284018069
Winsorized Mean ( 12 / 20 )7886.47316666667243.72198541019632.3584807229982
Winsorized Mean ( 13 / 20 )7881.16483333333231.22119288467234.0849588007457
Winsorized Mean ( 14 / 20 )7894.19883333333226.46942507809534.8576803716931
Winsorized Mean ( 15 / 20 )7862.60383333333218.12031676174236.0470952457027
Winsorized Mean ( 16 / 20 )7749.87316666667197.26702807233439.2862063285352
Winsorized Mean ( 17 / 20 )7805.45183333333182.6732462847842.7290366382659
Winsorized Mean ( 18 / 20 )7814.55383333333164.49907550546347.5051535050956
Winsorized Mean ( 19 / 20 )7798.30566666667154.58558511714350.4465255331357
Winsorized Mean ( 20 / 20 )7795.17233333333143.00449263030254.5099820988531
Trimmed Mean ( 1 / 20 )7982.9248275862555.8677323619914.361194872142
Trimmed Mean ( 2 / 20 )7987.13571428571514.63344917472215.5200477681621
Trimmed Mean ( 3 / 20 )7992.52351851852467.55772919493117.0941961162326
Trimmed Mean ( 4 / 20 )7988.6975420.64304579895918.9916309797217
Trimmed Mean ( 5 / 20 )7965.7862382.72931861830520.8131068420820
Trimmed Mean ( 6 / 20 )7943.41041666667334.56813174009923.742280459746
Trimmed Mean ( 7 / 20 )7927.94869565217311.40636843813425.4585310358776
Trimmed Mean ( 8 / 20 )7900.21704545455292.92801702843226.9698239369427
Trimmed Mean ( 9 / 20 )7873.67714285714280.11586397724328.1086441555371
Trimmed Mean ( 10 / 20 )7842.07775265.36820448042629.5516856111466
Trimmed Mean ( 11 / 20 )7809.33289473684246.90548959013731.6288346107668
Trimmed Mean ( 12 / 20 )7807.64527777778236.53892703446733.0078662977959
Trimmed Mean ( 13 / 20 )7796.05294117647228.95153252851034.0511061667853
Trimmed Mean ( 14 / 20 )7783.7771875221.66283394986335.115391465493
Trimmed Mean ( 15 / 20 )7768.00266666667212.25256526992336.5979212396705
Trimmed Mean ( 16 / 20 )7754.48821428571200.98471069548438.5824781768335
Trimmed Mean ( 17 / 20 )7755.15384615385191.50131753559840.4966083051218
Trimmed Mean ( 18 / 20 )7747.75708333333181.98050542539942.5746541654124
Trimmed Mean ( 19 / 20 )7737.63636363636173.8113671160944.517435723685
Trimmed Mean ( 20 / 20 )7728.057164.04426917772147.1095823020043
Median7743.05
Midrange7202.42
Midmean - Weighted Average at Xnp7706.10870967742
Midmean - Weighted Average at X(n+1)p7768.00266666667
Midmean - Empirical Distribution Function7706.10870967742
Midmean - Empirical Distribution Function - Averaging7768.00266666667
Midmean - Empirical Distribution Function - Interpolation7768.00266666667
Midmean - Closest Observation7706.10870967742
Midmean - True Basic - Statistics Graphics Toolkit7768.00266666667
Midmean - MS Excel (old versions)7783.7771875
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')