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of Irreproducible Research!

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 08:43:51 -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/t1255877102jka1hqsg73rrn8r.htm/, Retrieved Mon, 29 Apr 2024 10:15:29 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=47337, Retrieved Mon, 29 Apr 2024 10:15:29 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsws3p2.2
Estimated Impact96
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2009-10-18 14:43:51] [9ea4b07b6662a0f40f92decdf1e3b5d5] [Current]
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Dataseries X:
1358.01
996.25
1145.66
1313.59
1363.09
1208.65
1016.06
1109.15
1233.99
1101.63
1037.31
1053.70
1042.82
1361.94
1359.60
1268.87
1449.83
1646.20
2305.04
1939.32
1630.19
1979.47
2413.92
2435.64
3392.23
3470.87
2879.79
2709.70
2712.43
2461.57
2522.68
2638.74
3610.47
3537.09
3067.53
3836.15
2937.24
1832.67
1400.23
1244.17
1075.43
1009.45
878.73
915.92
672.62
522.86
515.57
549.60
402.53
426.79
593.26
724.49
780.60
865.32
3007.16
3420.03
-5485.41
-1882.57
-1365.13
-3132.40




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'RServer@AstonUniversity' @ vre.aston.ac.uk

\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 & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=47337&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]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=47337&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=47337&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'RServer@AstonUniversity' @ vre.aston.ac.uk







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean1391.97233333333201.3755018303416.9123221081086
Geometric MeanNaN
Harmonic Mean1340.56214237546
Quadratic Mean2080.90375757105
Winsorized Mean ( 1 / 20 )1427.42783333333180.7066069723287.89914578802267
Winsorized Mean ( 2 / 20 )1466.64283333333163.9933448567158.94330702636
Winsorized Mean ( 3 / 20 )1489.20383333333154.7453077338859.6235799013325
Winsorized Mean ( 4 / 20 )1603.6585125.01090032469212.8281493520549
Winsorized Mean ( 5 / 20 )1603.3635124.11563301900212.9183041732908
Winsorized Mean ( 6 / 20 )1579.7715115.17055274993113.7168005386772
Winsorized Mean ( 7 / 20 )1573.57883333333113.51225537635413.8626338461523
Winsorized Mean ( 8 / 20 )1567.8215110.98243880190914.1267529973673
Winsorized Mean ( 9 / 20 )1565.753108.18589890499314.4728011307187
Winsorized Mean ( 10 / 20 )1551.08633333333100.59302924371815.4194216537146
Winsorized Mean ( 11 / 20 )1560.0953333333399.111467829026215.7408155434102
Winsorized Mean ( 12 / 20 )1557.1253333333394.76152987745416.4320408856528
Winsorized Mean ( 13 / 20 )1550.33587.46209991280917.7257921036144
Winsorized Mean ( 14 / 20 )1539.20584.382182255350218.2408769109833
Winsorized Mean ( 15 / 20 )1542.0281.963898049362718.8134048855427
Winsorized Mean ( 16 / 20 )1557.6493333333378.19939405781519.9189437731669
Winsorized Mean ( 17 / 20 )1530.5472.068337465410221.2373429695752
Winsorized Mean ( 18 / 20 )1434.85254.575947774353226.2909222563108
Winsorized Mean ( 19 / 20 )1428.86751.563058060147327.7110600836214
Winsorized Mean ( 20 / 20 )1395.1536666666745.435668703817830.7061325708944
Trimmed Mean ( 1 / 20 )1468.40689655172164.9425333968298.90253633378445
Trimmed Mean ( 2 / 20 )1512.31303571429144.23933215565410.4847479055317
Trimmed Mean ( 3 / 20 )1537.68537037037130.06964517061111.8220155698388
Trimmed Mean ( 4 / 20 )1556.33211538462116.89487146056113.3139469331613
Trimmed Mean ( 5 / 20 )1542.1342113.25122828692513.6169313421746
Trimmed Mean ( 6 / 20 )1526.826875108.88135154753914.0228501327279
Trimmed Mean ( 7 / 20 )1515.31717391304106.19168509606714.2696405329871
Trimmed Mean ( 8 / 20 )1503.9675103.13910489567614.5819328325686
Trimmed Mean ( 9 / 20 )1492.56599.81380145669714.9534931864861
Trimmed Mean ( 10 / 20 )1480.36796.133049466044815.3991474131160
Trimmed Mean ( 11 / 20 )1469.2007894736893.309874464605915.7453945566177
Trimmed Mean ( 12 / 20 )1455.4288888888989.714740775112816.2228511871555
Trimmed Mean ( 13 / 20 )1440.4735294117685.895627438138616.7700449065255
Trimmed Mean ( 14 / 20 )1424.62812582.59998280363517.2473174526776
Trimmed Mean ( 15 / 20 )1408.2678.688126004010217.896728153473
Trimmed Mean ( 16 / 20 )1389.1514285714373.451854361776818.9124078710029
Trimmed Mean ( 17 / 20 )1364.8488461538566.319437578405120.5799219051017
Trimmed Mean ( 18 / 20 )1340.482557.646427812860523.2535223926043
Trimmed Mean ( 19 / 20 )1326.1840909090953.377369070203824.8454375704589
Trimmed Mean ( 20 / 20 )1309.97147.341512343819327.6706622823177
Median1291.23
Midrange-824.63
Midmean - Weighted Average at Xnp1391.17838709677
Midmean - Weighted Average at X(n+1)p1408.26
Midmean - Empirical Distribution Function1391.17838709677
Midmean - Empirical Distribution Function - Averaging1408.26
Midmean - Empirical Distribution Function - Interpolation1408.26
Midmean - Closest Observation1391.17838709677
Midmean - True Basic - Statistics Graphics Toolkit1408.26
Midmean - MS Excel (old versions)1424.628125
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 1391.97233333333 & 201.375501830341 & 6.9123221081086 \tabularnewline
Geometric Mean & NaN &  &  \tabularnewline
Harmonic Mean & 1340.56214237546 &  &  \tabularnewline
Quadratic Mean & 2080.90375757105 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 1427.42783333333 & 180.706606972328 & 7.89914578802267 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 1466.64283333333 & 163.993344856715 & 8.94330702636 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 1489.20383333333 & 154.745307733885 & 9.6235799013325 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 1603.6585 & 125.010900324692 & 12.8281493520549 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 1603.3635 & 124.115633019002 & 12.9183041732908 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 1579.7715 & 115.170552749931 & 13.7168005386772 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 1573.57883333333 & 113.512255376354 & 13.8626338461523 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 1567.8215 & 110.982438801909 & 14.1267529973673 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 1565.753 & 108.185898904993 & 14.4728011307187 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 1551.08633333333 & 100.593029243718 & 15.4194216537146 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 1560.09533333333 & 99.1114678290262 & 15.7408155434102 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 1557.12533333333 & 94.761529877454 & 16.4320408856528 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 1550.335 & 87.462099912809 & 17.7257921036144 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 1539.205 & 84.3821822553502 & 18.2408769109833 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 1542.02 & 81.9638980493627 & 18.8134048855427 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 1557.64933333333 & 78.199394057815 & 19.9189437731669 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 1530.54 & 72.0683374654102 & 21.2373429695752 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 1434.852 & 54.5759477743532 & 26.2909222563108 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 1428.867 & 51.5630580601473 & 27.7110600836214 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 1395.15366666667 & 45.4356687038178 & 30.7061325708944 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 1468.40689655172 & 164.942533396829 & 8.90253633378445 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 1512.31303571429 & 144.239332155654 & 10.4847479055317 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 1537.68537037037 & 130.069645170611 & 11.8220155698388 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 1556.33211538462 & 116.894871460561 & 13.3139469331613 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 1542.1342 & 113.251228286925 & 13.6169313421746 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 1526.826875 & 108.881351547539 & 14.0228501327279 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 1515.31717391304 & 106.191685096067 & 14.2696405329871 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 1503.9675 & 103.139104895676 & 14.5819328325686 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 1492.565 & 99.813801456697 & 14.9534931864861 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 1480.367 & 96.1330494660448 & 15.3991474131160 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 1469.20078947368 & 93.3098744646059 & 15.7453945566177 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 1455.42888888889 & 89.7147407751128 & 16.2228511871555 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 1440.47352941176 & 85.8956274381386 & 16.7700449065255 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 1424.628125 & 82.599982803635 & 17.2473174526776 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 1408.26 & 78.6881260040102 & 17.896728153473 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 1389.15142857143 & 73.4518543617768 & 18.9124078710029 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 1364.84884615385 & 66.3194375784051 & 20.5799219051017 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 1340.4825 & 57.6464278128605 & 23.2535223926043 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 1326.18409090909 & 53.3773690702038 & 24.8454375704589 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 1309.971 & 47.3415123438193 & 27.6706622823177 \tabularnewline
Median & 1291.23 &  &  \tabularnewline
Midrange & -824.63 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 1391.17838709677 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 1408.26 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 1391.17838709677 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 1408.26 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 1408.26 &  &  \tabularnewline
Midmean - Closest Observation & 1391.17838709677 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 1408.26 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 1424.628125 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=47337&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]1391.97233333333[/C][C]201.375501830341[/C][C]6.9123221081086[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]NaN[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]1340.56214237546[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]2080.90375757105[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]1427.42783333333[/C][C]180.706606972328[/C][C]7.89914578802267[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]1466.64283333333[/C][C]163.993344856715[/C][C]8.94330702636[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]1489.20383333333[/C][C]154.745307733885[/C][C]9.6235799013325[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]1603.6585[/C][C]125.010900324692[/C][C]12.8281493520549[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]1603.3635[/C][C]124.115633019002[/C][C]12.9183041732908[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]1579.7715[/C][C]115.170552749931[/C][C]13.7168005386772[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]1573.57883333333[/C][C]113.512255376354[/C][C]13.8626338461523[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]1567.8215[/C][C]110.982438801909[/C][C]14.1267529973673[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]1565.753[/C][C]108.185898904993[/C][C]14.4728011307187[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]1551.08633333333[/C][C]100.593029243718[/C][C]15.4194216537146[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]1560.09533333333[/C][C]99.1114678290262[/C][C]15.7408155434102[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]1557.12533333333[/C][C]94.761529877454[/C][C]16.4320408856528[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]1550.335[/C][C]87.462099912809[/C][C]17.7257921036144[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]1539.205[/C][C]84.3821822553502[/C][C]18.2408769109833[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]1542.02[/C][C]81.9638980493627[/C][C]18.8134048855427[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]1557.64933333333[/C][C]78.199394057815[/C][C]19.9189437731669[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]1530.54[/C][C]72.0683374654102[/C][C]21.2373429695752[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]1434.852[/C][C]54.5759477743532[/C][C]26.2909222563108[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]1428.867[/C][C]51.5630580601473[/C][C]27.7110600836214[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]1395.15366666667[/C][C]45.4356687038178[/C][C]30.7061325708944[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]1468.40689655172[/C][C]164.942533396829[/C][C]8.90253633378445[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]1512.31303571429[/C][C]144.239332155654[/C][C]10.4847479055317[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]1537.68537037037[/C][C]130.069645170611[/C][C]11.8220155698388[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]1556.33211538462[/C][C]116.894871460561[/C][C]13.3139469331613[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]1542.1342[/C][C]113.251228286925[/C][C]13.6169313421746[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]1526.826875[/C][C]108.881351547539[/C][C]14.0228501327279[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]1515.31717391304[/C][C]106.191685096067[/C][C]14.2696405329871[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]1503.9675[/C][C]103.139104895676[/C][C]14.5819328325686[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]1492.565[/C][C]99.813801456697[/C][C]14.9534931864861[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]1480.367[/C][C]96.1330494660448[/C][C]15.3991474131160[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]1469.20078947368[/C][C]93.3098744646059[/C][C]15.7453945566177[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]1455.42888888889[/C][C]89.7147407751128[/C][C]16.2228511871555[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]1440.47352941176[/C][C]85.8956274381386[/C][C]16.7700449065255[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]1424.628125[/C][C]82.599982803635[/C][C]17.2473174526776[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]1408.26[/C][C]78.6881260040102[/C][C]17.896728153473[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]1389.15142857143[/C][C]73.4518543617768[/C][C]18.9124078710029[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]1364.84884615385[/C][C]66.3194375784051[/C][C]20.5799219051017[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]1340.4825[/C][C]57.6464278128605[/C][C]23.2535223926043[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]1326.18409090909[/C][C]53.3773690702038[/C][C]24.8454375704589[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]1309.971[/C][C]47.3415123438193[/C][C]27.6706622823177[/C][/ROW]
[ROW][C]Median[/C][C]1291.23[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]-824.63[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]1391.17838709677[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]1408.26[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]1391.17838709677[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]1408.26[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]1408.26[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]1391.17838709677[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]1408.26[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]1424.628125[/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=47337&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=47337&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 Mean1391.97233333333201.3755018303416.9123221081086
Geometric MeanNaN
Harmonic Mean1340.56214237546
Quadratic Mean2080.90375757105
Winsorized Mean ( 1 / 20 )1427.42783333333180.7066069723287.89914578802267
Winsorized Mean ( 2 / 20 )1466.64283333333163.9933448567158.94330702636
Winsorized Mean ( 3 / 20 )1489.20383333333154.7453077338859.6235799013325
Winsorized Mean ( 4 / 20 )1603.6585125.01090032469212.8281493520549
Winsorized Mean ( 5 / 20 )1603.3635124.11563301900212.9183041732908
Winsorized Mean ( 6 / 20 )1579.7715115.17055274993113.7168005386772
Winsorized Mean ( 7 / 20 )1573.57883333333113.51225537635413.8626338461523
Winsorized Mean ( 8 / 20 )1567.8215110.98243880190914.1267529973673
Winsorized Mean ( 9 / 20 )1565.753108.18589890499314.4728011307187
Winsorized Mean ( 10 / 20 )1551.08633333333100.59302924371815.4194216537146
Winsorized Mean ( 11 / 20 )1560.0953333333399.111467829026215.7408155434102
Winsorized Mean ( 12 / 20 )1557.1253333333394.76152987745416.4320408856528
Winsorized Mean ( 13 / 20 )1550.33587.46209991280917.7257921036144
Winsorized Mean ( 14 / 20 )1539.20584.382182255350218.2408769109833
Winsorized Mean ( 15 / 20 )1542.0281.963898049362718.8134048855427
Winsorized Mean ( 16 / 20 )1557.6493333333378.19939405781519.9189437731669
Winsorized Mean ( 17 / 20 )1530.5472.068337465410221.2373429695752
Winsorized Mean ( 18 / 20 )1434.85254.575947774353226.2909222563108
Winsorized Mean ( 19 / 20 )1428.86751.563058060147327.7110600836214
Winsorized Mean ( 20 / 20 )1395.1536666666745.435668703817830.7061325708944
Trimmed Mean ( 1 / 20 )1468.40689655172164.9425333968298.90253633378445
Trimmed Mean ( 2 / 20 )1512.31303571429144.23933215565410.4847479055317
Trimmed Mean ( 3 / 20 )1537.68537037037130.06964517061111.8220155698388
Trimmed Mean ( 4 / 20 )1556.33211538462116.89487146056113.3139469331613
Trimmed Mean ( 5 / 20 )1542.1342113.25122828692513.6169313421746
Trimmed Mean ( 6 / 20 )1526.826875108.88135154753914.0228501327279
Trimmed Mean ( 7 / 20 )1515.31717391304106.19168509606714.2696405329871
Trimmed Mean ( 8 / 20 )1503.9675103.13910489567614.5819328325686
Trimmed Mean ( 9 / 20 )1492.56599.81380145669714.9534931864861
Trimmed Mean ( 10 / 20 )1480.36796.133049466044815.3991474131160
Trimmed Mean ( 11 / 20 )1469.2007894736893.309874464605915.7453945566177
Trimmed Mean ( 12 / 20 )1455.4288888888989.714740775112816.2228511871555
Trimmed Mean ( 13 / 20 )1440.4735294117685.895627438138616.7700449065255
Trimmed Mean ( 14 / 20 )1424.62812582.59998280363517.2473174526776
Trimmed Mean ( 15 / 20 )1408.2678.688126004010217.896728153473
Trimmed Mean ( 16 / 20 )1389.1514285714373.451854361776818.9124078710029
Trimmed Mean ( 17 / 20 )1364.8488461538566.319437578405120.5799219051017
Trimmed Mean ( 18 / 20 )1340.482557.646427812860523.2535223926043
Trimmed Mean ( 19 / 20 )1326.1840909090953.377369070203824.8454375704589
Trimmed Mean ( 20 / 20 )1309.97147.341512343819327.6706622823177
Median1291.23
Midrange-824.63
Midmean - Weighted Average at Xnp1391.17838709677
Midmean - Weighted Average at X(n+1)p1408.26
Midmean - Empirical Distribution Function1391.17838709677
Midmean - Empirical Distribution Function - Averaging1408.26
Midmean - Empirical Distribution Function - Interpolation1408.26
Midmean - Closest Observation1391.17838709677
Midmean - True Basic - Statistics Graphics Toolkit1408.26
Midmean - MS Excel (old versions)1424.628125
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')