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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 computationWed, 17 Dec 2008 08:23:03 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/Dec/17/t1229528168966kmwjfedmns30.htm/, Retrieved Sun, 19 May 2024 05:40:14 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=34409, Retrieved Sun, 19 May 2024 05:40:14 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact154
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Central Tendency ...] [2008-12-17 15:23:03] [d592f629d96b926609f311957d74fcca] [Current]
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Dataseries X:
29.08
28.76
29.59
30.70
30.52
32.67
33.19
37.13
35.54
37.75
41.84
42.94
49.14
44.61
40.22
44.23
45.85
53.38
53.26
51.80
55.30
57.81
63.96
63.77
59.15
56.12
57.42
63.52
61.71
63.01
68.18
72.03
69.75
74.41
74.33
64.24
60.03
59.44
62.50
55.04
58.34
61.92
67.65
67.68
70.30
75.26
71.44
76.36
81.71
92.60
90.60
92.23
94.09
102.79
109.65
124.05
132.69
135.81
116.07
101.42




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 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 & 3 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=34409&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]3 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=34409&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=34409&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 time3 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean64.60966666666673.3216420958324219.4511223071657
Geometric Mean59.9343163941024
Harmonic Mean55.5771279884569
Quadratic Mean69.4649126777925
Winsorized Mean ( 1 / 20 )64.5633.3021297809740119.5519268721644
Winsorized Mean ( 2 / 20 )64.2923.2030588646472720.0720632110768
Winsorized Mean ( 3 / 20 )63.93953.0739595679093220.8003711784300
Winsorized Mean ( 4 / 20 )63.52352.9534682458727321.5081032575074
Winsorized Mean ( 5 / 20 )63.1162.7776940727124622.7224447141388
Winsorized Mean ( 6 / 20 )63.0312.7351755198330123.0445905730570
Winsorized Mean ( 7 / 20 )62.452.4904707312628325.0755807791942
Winsorized Mean ( 8 / 20 )62.46333333333332.4097108351109725.9215057770435
Winsorized Mean ( 9 / 20 )62.50083333333332.3814797101169426.2445374058065
Winsorized Mean ( 10 / 20 )62.64083333333332.2531495507032527.8014538865305
Winsorized Mean ( 11 / 20 )61.3081.8787963420539432.6315304260050
Winsorized Mean ( 12 / 20 )60.4581.6533503017627536.5669634169731
Winsorized Mean ( 13 / 20 )60.49916666666671.5651337606718238.6543106965489
Winsorized Mean ( 14 / 20 )60.38951.5181335073191739.7787807915789
Winsorized Mean ( 15 / 20 )60.67951.4610004780603841.5328406192981
Winsorized Mean ( 16 / 20 )60.94351.2171011411764950.0726668788513
Winsorized Mean ( 17 / 20 )61.531.0708762450458057.4576196686187
Winsorized Mean ( 18 / 20 )61.6260.95116346239928264.7901253950086
Winsorized Mean ( 19 / 20 )61.48983333333330.91875519112770566.9273315972877
Winsorized Mean ( 20 / 20 )61.51983333333330.75824617336073481.1343802246469
Trimmed Mean ( 1 / 20 )64.00017241379313.1441315474421920.3554372481197
Trimmed Mean ( 2 / 20 )63.39714285714292.9455886532091821.5227414011364
Trimmed Mean ( 3 / 20 )62.92.7655006762278422.7445252646967
Trimmed Mean ( 4 / 20 )62.50019230769232.6055930601982523.9869353593292
Trimmed Mean ( 5 / 20 )62.19322.4549545644409425.333747883095
Trimmed Mean ( 6 / 20 )61.96252.3295997072671726.5979171471856
Trimmed Mean ( 7 / 20 )61.73021739130442.1820698299805128.2897533998056
Trimmed Mean ( 8 / 20 )61.592.0719368995836329.7258087407859
Trimmed Mean ( 9 / 20 )61.43404761904761.9519899926535831.472521811207
Trimmed Mean ( 10 / 20 )61.256251.7993387206779034.0437569069385
Trimmed Mean ( 11 / 20 )61.03763157894741.6321126834289837.3979273604508
Trimmed Mean ( 12 / 20 )60.99666666666671.5299483858915239.8684473470804
Trimmed Mean ( 13 / 20 )61.07588235294121.4585925942794441.8731608760933
Trimmed Mean ( 14 / 20 )61.15906251.3846261548099144.1700904518855
Trimmed Mean ( 15 / 20 )61.2691.2918981268331347.4255660933504
Trimmed Mean ( 16 / 20 )61.35321428571431.1748560706142352.2218983416735
Trimmed Mean ( 17 / 20 )61.41230769230771.0956204154151956.0525404859631
Trimmed Mean ( 18 / 20 )61.3951.0314716165034259.5217541788718
Trimmed Mean ( 19 / 20 )61.360.97788002876086662.747983592377
Trimmed Mean ( 20 / 20 )61.33950.89986299395782368.1653767427567
Median61.815
Midrange82.285
Midmean - Weighted Average at Xnp60.7316129032258
Midmean - Weighted Average at X(n+1)p61.269
Midmean - Empirical Distribution Function60.7316129032258
Midmean - Empirical Distribution Function - Averaging61.269
Midmean - Empirical Distribution Function - Interpolation61.269
Midmean - Closest Observation60.7316129032258
Midmean - True Basic - Statistics Graphics Toolkit61.269
Midmean - MS Excel (old versions)61.1590625
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 64.6096666666667 & 3.32164209583242 & 19.4511223071657 \tabularnewline
Geometric Mean & 59.9343163941024 &  &  \tabularnewline
Harmonic Mean & 55.5771279884569 &  &  \tabularnewline
Quadratic Mean & 69.4649126777925 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 64.563 & 3.30212978097401 & 19.5519268721644 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 64.292 & 3.20305886464727 & 20.0720632110768 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 63.9395 & 3.07395956790932 & 20.8003711784300 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 63.5235 & 2.95346824587273 & 21.5081032575074 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 63.116 & 2.77769407271246 & 22.7224447141388 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 63.031 & 2.73517551983301 & 23.0445905730570 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 62.45 & 2.49047073126283 & 25.0755807791942 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 62.4633333333333 & 2.40971083511097 & 25.9215057770435 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 62.5008333333333 & 2.38147971011694 & 26.2445374058065 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 62.6408333333333 & 2.25314955070325 & 27.8014538865305 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 61.308 & 1.87879634205394 & 32.6315304260050 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 60.458 & 1.65335030176275 & 36.5669634169731 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 60.4991666666667 & 1.56513376067182 & 38.6543106965489 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 60.3895 & 1.51813350731917 & 39.7787807915789 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 60.6795 & 1.46100047806038 & 41.5328406192981 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 60.9435 & 1.21710114117649 & 50.0726668788513 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 61.53 & 1.07087624504580 & 57.4576196686187 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 61.626 & 0.951163462399282 & 64.7901253950086 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 61.4898333333333 & 0.918755191127705 & 66.9273315972877 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 61.5198333333333 & 0.758246173360734 & 81.1343802246469 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 64.0001724137931 & 3.14413154744219 & 20.3554372481197 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 63.3971428571429 & 2.94558865320918 & 21.5227414011364 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 62.9 & 2.76550067622784 & 22.7445252646967 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 62.5001923076923 & 2.60559306019825 & 23.9869353593292 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 62.1932 & 2.45495456444094 & 25.333747883095 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 61.9625 & 2.32959970726717 & 26.5979171471856 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 61.7302173913044 & 2.18206982998051 & 28.2897533998056 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 61.59 & 2.07193689958363 & 29.7258087407859 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 61.4340476190476 & 1.95198999265358 & 31.472521811207 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 61.25625 & 1.79933872067790 & 34.0437569069385 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 61.0376315789474 & 1.63211268342898 & 37.3979273604508 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 60.9966666666667 & 1.52994838589152 & 39.8684473470804 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 61.0758823529412 & 1.45859259427944 & 41.8731608760933 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 61.1590625 & 1.38462615480991 & 44.1700904518855 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 61.269 & 1.29189812683313 & 47.4255660933504 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 61.3532142857143 & 1.17485607061423 & 52.2218983416735 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 61.4123076923077 & 1.09562041541519 & 56.0525404859631 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 61.395 & 1.03147161650342 & 59.5217541788718 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 61.36 & 0.977880028760866 & 62.747983592377 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 61.3395 & 0.899862993957823 & 68.1653767427567 \tabularnewline
Median & 61.815 &  &  \tabularnewline
Midrange & 82.285 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 60.7316129032258 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 61.269 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 60.7316129032258 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 61.269 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 61.269 &  &  \tabularnewline
Midmean - Closest Observation & 60.7316129032258 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 61.269 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 61.1590625 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=34409&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]64.6096666666667[/C][C]3.32164209583242[/C][C]19.4511223071657[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]59.9343163941024[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]55.5771279884569[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]69.4649126777925[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]64.563[/C][C]3.30212978097401[/C][C]19.5519268721644[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]64.292[/C][C]3.20305886464727[/C][C]20.0720632110768[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]63.9395[/C][C]3.07395956790932[/C][C]20.8003711784300[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]63.5235[/C][C]2.95346824587273[/C][C]21.5081032575074[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]63.116[/C][C]2.77769407271246[/C][C]22.7224447141388[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]63.031[/C][C]2.73517551983301[/C][C]23.0445905730570[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]62.45[/C][C]2.49047073126283[/C][C]25.0755807791942[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]62.4633333333333[/C][C]2.40971083511097[/C][C]25.9215057770435[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]62.5008333333333[/C][C]2.38147971011694[/C][C]26.2445374058065[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]62.6408333333333[/C][C]2.25314955070325[/C][C]27.8014538865305[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]61.308[/C][C]1.87879634205394[/C][C]32.6315304260050[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]60.458[/C][C]1.65335030176275[/C][C]36.5669634169731[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]60.4991666666667[/C][C]1.56513376067182[/C][C]38.6543106965489[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]60.3895[/C][C]1.51813350731917[/C][C]39.7787807915789[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]60.6795[/C][C]1.46100047806038[/C][C]41.5328406192981[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]60.9435[/C][C]1.21710114117649[/C][C]50.0726668788513[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]61.53[/C][C]1.07087624504580[/C][C]57.4576196686187[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]61.626[/C][C]0.951163462399282[/C][C]64.7901253950086[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]61.4898333333333[/C][C]0.918755191127705[/C][C]66.9273315972877[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]61.5198333333333[/C][C]0.758246173360734[/C][C]81.1343802246469[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]64.0001724137931[/C][C]3.14413154744219[/C][C]20.3554372481197[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]63.3971428571429[/C][C]2.94558865320918[/C][C]21.5227414011364[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]62.9[/C][C]2.76550067622784[/C][C]22.7445252646967[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]62.5001923076923[/C][C]2.60559306019825[/C][C]23.9869353593292[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]62.1932[/C][C]2.45495456444094[/C][C]25.333747883095[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]61.9625[/C][C]2.32959970726717[/C][C]26.5979171471856[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]61.7302173913044[/C][C]2.18206982998051[/C][C]28.2897533998056[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]61.59[/C][C]2.07193689958363[/C][C]29.7258087407859[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]61.4340476190476[/C][C]1.95198999265358[/C][C]31.472521811207[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]61.25625[/C][C]1.79933872067790[/C][C]34.0437569069385[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]61.0376315789474[/C][C]1.63211268342898[/C][C]37.3979273604508[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]60.9966666666667[/C][C]1.52994838589152[/C][C]39.8684473470804[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]61.0758823529412[/C][C]1.45859259427944[/C][C]41.8731608760933[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]61.1590625[/C][C]1.38462615480991[/C][C]44.1700904518855[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]61.269[/C][C]1.29189812683313[/C][C]47.4255660933504[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]61.3532142857143[/C][C]1.17485607061423[/C][C]52.2218983416735[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]61.4123076923077[/C][C]1.09562041541519[/C][C]56.0525404859631[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]61.395[/C][C]1.03147161650342[/C][C]59.5217541788718[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]61.36[/C][C]0.977880028760866[/C][C]62.747983592377[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]61.3395[/C][C]0.899862993957823[/C][C]68.1653767427567[/C][/ROW]
[ROW][C]Median[/C][C]61.815[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]82.285[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]60.7316129032258[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]61.269[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]60.7316129032258[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]61.269[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]61.269[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]60.7316129032258[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]61.269[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]61.1590625[/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=34409&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=34409&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 Mean64.60966666666673.3216420958324219.4511223071657
Geometric Mean59.9343163941024
Harmonic Mean55.5771279884569
Quadratic Mean69.4649126777925
Winsorized Mean ( 1 / 20 )64.5633.3021297809740119.5519268721644
Winsorized Mean ( 2 / 20 )64.2923.2030588646472720.0720632110768
Winsorized Mean ( 3 / 20 )63.93953.0739595679093220.8003711784300
Winsorized Mean ( 4 / 20 )63.52352.9534682458727321.5081032575074
Winsorized Mean ( 5 / 20 )63.1162.7776940727124622.7224447141388
Winsorized Mean ( 6 / 20 )63.0312.7351755198330123.0445905730570
Winsorized Mean ( 7 / 20 )62.452.4904707312628325.0755807791942
Winsorized Mean ( 8 / 20 )62.46333333333332.4097108351109725.9215057770435
Winsorized Mean ( 9 / 20 )62.50083333333332.3814797101169426.2445374058065
Winsorized Mean ( 10 / 20 )62.64083333333332.2531495507032527.8014538865305
Winsorized Mean ( 11 / 20 )61.3081.8787963420539432.6315304260050
Winsorized Mean ( 12 / 20 )60.4581.6533503017627536.5669634169731
Winsorized Mean ( 13 / 20 )60.49916666666671.5651337606718238.6543106965489
Winsorized Mean ( 14 / 20 )60.38951.5181335073191739.7787807915789
Winsorized Mean ( 15 / 20 )60.67951.4610004780603841.5328406192981
Winsorized Mean ( 16 / 20 )60.94351.2171011411764950.0726668788513
Winsorized Mean ( 17 / 20 )61.531.0708762450458057.4576196686187
Winsorized Mean ( 18 / 20 )61.6260.95116346239928264.7901253950086
Winsorized Mean ( 19 / 20 )61.48983333333330.91875519112770566.9273315972877
Winsorized Mean ( 20 / 20 )61.51983333333330.75824617336073481.1343802246469
Trimmed Mean ( 1 / 20 )64.00017241379313.1441315474421920.3554372481197
Trimmed Mean ( 2 / 20 )63.39714285714292.9455886532091821.5227414011364
Trimmed Mean ( 3 / 20 )62.92.7655006762278422.7445252646967
Trimmed Mean ( 4 / 20 )62.50019230769232.6055930601982523.9869353593292
Trimmed Mean ( 5 / 20 )62.19322.4549545644409425.333747883095
Trimmed Mean ( 6 / 20 )61.96252.3295997072671726.5979171471856
Trimmed Mean ( 7 / 20 )61.73021739130442.1820698299805128.2897533998056
Trimmed Mean ( 8 / 20 )61.592.0719368995836329.7258087407859
Trimmed Mean ( 9 / 20 )61.43404761904761.9519899926535831.472521811207
Trimmed Mean ( 10 / 20 )61.256251.7993387206779034.0437569069385
Trimmed Mean ( 11 / 20 )61.03763157894741.6321126834289837.3979273604508
Trimmed Mean ( 12 / 20 )60.99666666666671.5299483858915239.8684473470804
Trimmed Mean ( 13 / 20 )61.07588235294121.4585925942794441.8731608760933
Trimmed Mean ( 14 / 20 )61.15906251.3846261548099144.1700904518855
Trimmed Mean ( 15 / 20 )61.2691.2918981268331347.4255660933504
Trimmed Mean ( 16 / 20 )61.35321428571431.1748560706142352.2218983416735
Trimmed Mean ( 17 / 20 )61.41230769230771.0956204154151956.0525404859631
Trimmed Mean ( 18 / 20 )61.3951.0314716165034259.5217541788718
Trimmed Mean ( 19 / 20 )61.360.97788002876086662.747983592377
Trimmed Mean ( 20 / 20 )61.33950.89986299395782368.1653767427567
Median61.815
Midrange82.285
Midmean - Weighted Average at Xnp60.7316129032258
Midmean - Weighted Average at X(n+1)p61.269
Midmean - Empirical Distribution Function60.7316129032258
Midmean - Empirical Distribution Function - Averaging61.269
Midmean - Empirical Distribution Function - Interpolation61.269
Midmean - Closest Observation60.7316129032258
Midmean - True Basic - Statistics Graphics Toolkit61.269
Midmean - MS Excel (old versions)61.1590625
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')