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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationSun, 04 Nov 2007 04:21:41 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2007/Nov/04/zjrht4jrpva475x1194175500.htm/, Retrieved Sun, 05 May 2024 15:54:48 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=392, Retrieved Sun, 05 May 2024 15:54:48 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsHuwelijken
Estimated Impact187
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Paper WS2 Q3] [2007-11-04 11:21:41] [d66dce91cbb8b108f7114f1eb0c2faa2] [Current]
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Dataseries X:
1178
2141
2238
2685
4341
5376
4478
6404
4617
3024
1897
2075
1351
2211
2453
3042
4765
4992
4601
6266
4812
3159
1916
2237
1595
2453
2226
3597
4706
4974
5756
5493
5004
3225
2006
2291
1588
2105
2191
3591
4668
4885
5822
5599
5340
3082
2010
2301
1514
1979
2480
3499
4676
5585
5610
5796
6199
3030
1930
2552




Summary of compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\begin{tabular}{lllllllll}
\hline
Summary of compuational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=392&T=0

[TABLE]
[ROW][C]Summary of compuational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=392&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=392&T=0

As an alternative you can also use a QR Code:  

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

Summary of compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean3560.28333333333199.9331527999117.8073685303028
Geometric Mean3218.91790245011
Harmonic Mean2894.98391890294
Quadratic Mean3877.37541171001
Winsorized Mean ( 1 / 20 )3560.86666666667198.82790512620217.9092902699271
Winsorized Mean ( 2 / 20 )3564.06666666667197.32738987461118.0616926465778
Winsorized Mean ( 3 / 20 )3548.91666666667192.66160183116618.4204669375513
Winsorized Mean ( 4 / 20 )3547.65192.23606577818818.4546535825045
Winsorized Mean ( 5 / 20 )3569.48333333333187.50422291540819.0368156931788
Winsorized Mean ( 6 / 20 )3556.78333333333184.39626038168319.2888040460860
Winsorized Mean ( 7 / 20 )3557.13333333333183.90877968902019.3418353346059
Winsorized Mean ( 8 / 20 )3561.8182.58799720453719.5073063647773
Winsorized Mean ( 9 / 20 )3552.05179.43353021533319.7959099157069
Winsorized Mean ( 10 / 20 )3533.21666666667175.81568432323920.0961403430356
Winsorized Mean ( 11 / 20 )3538.53333333333172.91684992162420.4637855416474
Winsorized Mean ( 12 / 20 )3477.33333333333160.68962725966921.6400609836134
Winsorized Mean ( 13 / 20 )3482.53333333333159.14954674693621.8821442128950
Winsorized Mean ( 14 / 20 )3490156.82265344257022.2544378850092
Winsorized Mean ( 15 / 20 )3472.75152.59129086557522.7585072535975
Winsorized Mean ( 16 / 20 )3457.28333333333149.00382600719823.202648052583
Winsorized Mean ( 17 / 20 )3447.08333333333146.52626168207423.5253618959628
Winsorized Mean ( 18 / 20 )3429.68333333333143.80355694363823.8497809527587
Winsorized Mean ( 19 / 20 )3436.96666666667140.03382958233824.5438311365025
Winsorized Mean ( 20 / 20 )3437.63333333333139.17220152057324.7005745096673
Trimmed Mean ( 1 / 20 )3552.3275862069196.56740559227318.0718037942428
Trimmed Mean ( 2 / 20 )3543.17857142857193.67024308495718.2949043435356
Trimmed Mean ( 3 / 20 )3531.57407407407190.94355179827818.4953827495835
Trimmed Mean ( 4 / 20 )3524.90384615385189.58662712657318.5925763835680
Trimmed Mean ( 5 / 20 )3518.08187.83007700730818.7301206284610
Trimmed Mean ( 6 / 20 )3505.22916666667186.88400524943418.7561753184187
Trimmed Mean ( 7 / 20 )3494.02173913043186.28161240426518.7566646757801
Trimmed Mean ( 8 / 20 )3481.72727272727185.27590523574918.7921212329096
Trimmed Mean ( 9 / 20 )3467.42857142857183.9312227631618.8517670862952
Trimmed Mean ( 10 / 20 )3453.325182.59136591594718.9128603243468
Trimmed Mean ( 11 / 20 )3440.71052631579181.31782846363818.9761291289996
Trimmed Mean ( 12 / 20 )3425.88888888889179.82244231012319.0515090601460
Trimmed Mean ( 13 / 20 )3418.32352941176180.37980192423218.9507000947236
Trimmed Mean ( 14 / 20 )3409.0625180.71211587938718.8646039774960
Trimmed Mean ( 15 / 20 )3397.5180.86286638440118.7849505424682
Trimmed Mean ( 16 / 20 )3386.75181.24796386376818.6857271541301
Trimmed Mean ( 17 / 20 )3376.57692307692181.6753416490918.5857744503316
Trimmed Mean ( 18 / 20 )3366.20833333333181.70349293507518.5258317215516
Trimmed Mean ( 19 / 20 )3356.59090909091181.11600476548618.5328232777501
Trimmed Mean ( 20 / 20 )3343.9179.73257766382918.6048630886184
Median3120.5
Midrange3791
Midmean - Weighted Average at Xnp3358.58064516129
Midmean - Weighted Average at X(n+1)p3397.5
Midmean - Empirical Distribution Function3358.58064516129
Midmean - Empirical Distribution Function - Averaging3397.5
Midmean - Empirical Distribution Function - Interpolation3397.5
Midmean - Closest Observation3358.58064516129
Midmean - True Basic - Statistics Graphics Toolkit3397.5
Midmean - MS Excel (old versions)3409.0625
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 3560.28333333333 & 199.93315279991 & 17.8073685303028 \tabularnewline
Geometric Mean & 3218.91790245011 &  &  \tabularnewline
Harmonic Mean & 2894.98391890294 &  &  \tabularnewline
Quadratic Mean & 3877.37541171001 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 3560.86666666667 & 198.827905126202 & 17.9092902699271 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 3564.06666666667 & 197.327389874611 & 18.0616926465778 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 3548.91666666667 & 192.661601831166 & 18.4204669375513 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 3547.65 & 192.236065778188 & 18.4546535825045 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 3569.48333333333 & 187.504222915408 & 19.0368156931788 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 3556.78333333333 & 184.396260381683 & 19.2888040460860 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 3557.13333333333 & 183.908779689020 & 19.3418353346059 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 3561.8 & 182.587997204537 & 19.5073063647773 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 3552.05 & 179.433530215333 & 19.7959099157069 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 3533.21666666667 & 175.815684323239 & 20.0961403430356 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 3538.53333333333 & 172.916849921624 & 20.4637855416474 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 3477.33333333333 & 160.689627259669 & 21.6400609836134 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 3482.53333333333 & 159.149546746936 & 21.8821442128950 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 3490 & 156.822653442570 & 22.2544378850092 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 3472.75 & 152.591290865575 & 22.7585072535975 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 3457.28333333333 & 149.003826007198 & 23.202648052583 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 3447.08333333333 & 146.526261682074 & 23.5253618959628 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 3429.68333333333 & 143.803556943638 & 23.8497809527587 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 3436.96666666667 & 140.033829582338 & 24.5438311365025 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 3437.63333333333 & 139.172201520573 & 24.7005745096673 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 3552.3275862069 & 196.567405592273 & 18.0718037942428 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 3543.17857142857 & 193.670243084957 & 18.2949043435356 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 3531.57407407407 & 190.943551798278 & 18.4953827495835 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 3524.90384615385 & 189.586627126573 & 18.5925763835680 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 3518.08 & 187.830077007308 & 18.7301206284610 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 3505.22916666667 & 186.884005249434 & 18.7561753184187 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 3494.02173913043 & 186.281612404265 & 18.7566646757801 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 3481.72727272727 & 185.275905235749 & 18.7921212329096 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 3467.42857142857 & 183.93122276316 & 18.8517670862952 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 3453.325 & 182.591365915947 & 18.9128603243468 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 3440.71052631579 & 181.317828463638 & 18.9761291289996 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 3425.88888888889 & 179.822442310123 & 19.0515090601460 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 3418.32352941176 & 180.379801924232 & 18.9507000947236 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 3409.0625 & 180.712115879387 & 18.8646039774960 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 3397.5 & 180.862866384401 & 18.7849505424682 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 3386.75 & 181.247963863768 & 18.6857271541301 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 3376.57692307692 & 181.67534164909 & 18.5857744503316 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 3366.20833333333 & 181.703492935075 & 18.5258317215516 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 3356.59090909091 & 181.116004765486 & 18.5328232777501 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 3343.9 & 179.732577663829 & 18.6048630886184 \tabularnewline
Median & 3120.5 &  &  \tabularnewline
Midrange & 3791 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 3358.58064516129 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 3397.5 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 3358.58064516129 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 3397.5 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 3397.5 &  &  \tabularnewline
Midmean - Closest Observation & 3358.58064516129 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 3397.5 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 3409.0625 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=392&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]3560.28333333333[/C][C]199.93315279991[/C][C]17.8073685303028[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]3218.91790245011[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]2894.98391890294[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]3877.37541171001[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]3560.86666666667[/C][C]198.827905126202[/C][C]17.9092902699271[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]3564.06666666667[/C][C]197.327389874611[/C][C]18.0616926465778[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]3548.91666666667[/C][C]192.661601831166[/C][C]18.4204669375513[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]3547.65[/C][C]192.236065778188[/C][C]18.4546535825045[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]3569.48333333333[/C][C]187.504222915408[/C][C]19.0368156931788[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]3556.78333333333[/C][C]184.396260381683[/C][C]19.2888040460860[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]3557.13333333333[/C][C]183.908779689020[/C][C]19.3418353346059[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]3561.8[/C][C]182.587997204537[/C][C]19.5073063647773[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]3552.05[/C][C]179.433530215333[/C][C]19.7959099157069[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]3533.21666666667[/C][C]175.815684323239[/C][C]20.0961403430356[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]3538.53333333333[/C][C]172.916849921624[/C][C]20.4637855416474[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]3477.33333333333[/C][C]160.689627259669[/C][C]21.6400609836134[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]3482.53333333333[/C][C]159.149546746936[/C][C]21.8821442128950[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]3490[/C][C]156.822653442570[/C][C]22.2544378850092[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]3472.75[/C][C]152.591290865575[/C][C]22.7585072535975[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]3457.28333333333[/C][C]149.003826007198[/C][C]23.202648052583[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]3447.08333333333[/C][C]146.526261682074[/C][C]23.5253618959628[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]3429.68333333333[/C][C]143.803556943638[/C][C]23.8497809527587[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]3436.96666666667[/C][C]140.033829582338[/C][C]24.5438311365025[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]3437.63333333333[/C][C]139.172201520573[/C][C]24.7005745096673[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]3552.3275862069[/C][C]196.567405592273[/C][C]18.0718037942428[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]3543.17857142857[/C][C]193.670243084957[/C][C]18.2949043435356[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]3531.57407407407[/C][C]190.943551798278[/C][C]18.4953827495835[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]3524.90384615385[/C][C]189.586627126573[/C][C]18.5925763835680[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]3518.08[/C][C]187.830077007308[/C][C]18.7301206284610[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]3505.22916666667[/C][C]186.884005249434[/C][C]18.7561753184187[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]3494.02173913043[/C][C]186.281612404265[/C][C]18.7566646757801[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]3481.72727272727[/C][C]185.275905235749[/C][C]18.7921212329096[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]3467.42857142857[/C][C]183.93122276316[/C][C]18.8517670862952[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]3453.325[/C][C]182.591365915947[/C][C]18.9128603243468[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]3440.71052631579[/C][C]181.317828463638[/C][C]18.9761291289996[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]3425.88888888889[/C][C]179.822442310123[/C][C]19.0515090601460[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]3418.32352941176[/C][C]180.379801924232[/C][C]18.9507000947236[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]3409.0625[/C][C]180.712115879387[/C][C]18.8646039774960[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]3397.5[/C][C]180.862866384401[/C][C]18.7849505424682[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]3386.75[/C][C]181.247963863768[/C][C]18.6857271541301[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]3376.57692307692[/C][C]181.67534164909[/C][C]18.5857744503316[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]3366.20833333333[/C][C]181.703492935075[/C][C]18.5258317215516[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]3356.59090909091[/C][C]181.116004765486[/C][C]18.5328232777501[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]3343.9[/C][C]179.732577663829[/C][C]18.6048630886184[/C][/ROW]
[ROW][C]Median[/C][C]3120.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]3791[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]3358.58064516129[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]3397.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]3358.58064516129[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]3397.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]3397.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]3358.58064516129[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]3397.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]3409.0625[/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=392&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=392&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 Mean3560.28333333333199.9331527999117.8073685303028
Geometric Mean3218.91790245011
Harmonic Mean2894.98391890294
Quadratic Mean3877.37541171001
Winsorized Mean ( 1 / 20 )3560.86666666667198.82790512620217.9092902699271
Winsorized Mean ( 2 / 20 )3564.06666666667197.32738987461118.0616926465778
Winsorized Mean ( 3 / 20 )3548.91666666667192.66160183116618.4204669375513
Winsorized Mean ( 4 / 20 )3547.65192.23606577818818.4546535825045
Winsorized Mean ( 5 / 20 )3569.48333333333187.50422291540819.0368156931788
Winsorized Mean ( 6 / 20 )3556.78333333333184.39626038168319.2888040460860
Winsorized Mean ( 7 / 20 )3557.13333333333183.90877968902019.3418353346059
Winsorized Mean ( 8 / 20 )3561.8182.58799720453719.5073063647773
Winsorized Mean ( 9 / 20 )3552.05179.43353021533319.7959099157069
Winsorized Mean ( 10 / 20 )3533.21666666667175.81568432323920.0961403430356
Winsorized Mean ( 11 / 20 )3538.53333333333172.91684992162420.4637855416474
Winsorized Mean ( 12 / 20 )3477.33333333333160.68962725966921.6400609836134
Winsorized Mean ( 13 / 20 )3482.53333333333159.14954674693621.8821442128950
Winsorized Mean ( 14 / 20 )3490156.82265344257022.2544378850092
Winsorized Mean ( 15 / 20 )3472.75152.59129086557522.7585072535975
Winsorized Mean ( 16 / 20 )3457.28333333333149.00382600719823.202648052583
Winsorized Mean ( 17 / 20 )3447.08333333333146.52626168207423.5253618959628
Winsorized Mean ( 18 / 20 )3429.68333333333143.80355694363823.8497809527587
Winsorized Mean ( 19 / 20 )3436.96666666667140.03382958233824.5438311365025
Winsorized Mean ( 20 / 20 )3437.63333333333139.17220152057324.7005745096673
Trimmed Mean ( 1 / 20 )3552.3275862069196.56740559227318.0718037942428
Trimmed Mean ( 2 / 20 )3543.17857142857193.67024308495718.2949043435356
Trimmed Mean ( 3 / 20 )3531.57407407407190.94355179827818.4953827495835
Trimmed Mean ( 4 / 20 )3524.90384615385189.58662712657318.5925763835680
Trimmed Mean ( 5 / 20 )3518.08187.83007700730818.7301206284610
Trimmed Mean ( 6 / 20 )3505.22916666667186.88400524943418.7561753184187
Trimmed Mean ( 7 / 20 )3494.02173913043186.28161240426518.7566646757801
Trimmed Mean ( 8 / 20 )3481.72727272727185.27590523574918.7921212329096
Trimmed Mean ( 9 / 20 )3467.42857142857183.9312227631618.8517670862952
Trimmed Mean ( 10 / 20 )3453.325182.59136591594718.9128603243468
Trimmed Mean ( 11 / 20 )3440.71052631579181.31782846363818.9761291289996
Trimmed Mean ( 12 / 20 )3425.88888888889179.82244231012319.0515090601460
Trimmed Mean ( 13 / 20 )3418.32352941176180.37980192423218.9507000947236
Trimmed Mean ( 14 / 20 )3409.0625180.71211587938718.8646039774960
Trimmed Mean ( 15 / 20 )3397.5180.86286638440118.7849505424682
Trimmed Mean ( 16 / 20 )3386.75181.24796386376818.6857271541301
Trimmed Mean ( 17 / 20 )3376.57692307692181.6753416490918.5857744503316
Trimmed Mean ( 18 / 20 )3366.20833333333181.70349293507518.5258317215516
Trimmed Mean ( 19 / 20 )3356.59090909091181.11600476548618.5328232777501
Trimmed Mean ( 20 / 20 )3343.9179.73257766382918.6048630886184
Median3120.5
Midrange3791
Midmean - Weighted Average at Xnp3358.58064516129
Midmean - Weighted Average at X(n+1)p3397.5
Midmean - Empirical Distribution Function3358.58064516129
Midmean - Empirical Distribution Function - Averaging3397.5
Midmean - Empirical Distribution Function - Interpolation3397.5
Midmean - Closest Observation3358.58064516129
Midmean - True Basic - Statistics Graphics Toolkit3397.5
Midmean - MS Excel (old versions)3409.0625
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')