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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 computationThu, 22 Oct 2009 09:25:33 -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/22/t1256225228rn0kne5hhs56uy2.htm/, Retrieved Thu, 02 May 2024 23:58:42 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=49759, Retrieved Thu, 02 May 2024 23:58:42 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsWS 3 Part 2
Estimated Impact181
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Bivariate Data Series] [Bivariate dataset] [2008-01-05 23:51:08] [74be16979710d4c4e7c6647856088456]
F RMPD  [Univariate Explorative Data Analysis] [Colombia Coffee] [2008-01-07 14:21:11] [74be16979710d4c4e7c6647856088456]
F RMPD    [Univariate Data Series] [] [2009-10-14 08:30:28] [74be16979710d4c4e7c6647856088456]
-           [Univariate Data Series] [WS 3 Part 1/1] [2009-10-21 21:03:12] [9717cb857c153ca3061376906953b329]
- RMPD          [Central Tendency] [WS 3 Part 2] [2009-10-22 15:25:33] [52b85b290d6f50b0921ad6729b8a5af2] [Current]
-    D            [Central Tendency] [WS 3 Part 2] [2009-10-25 17:50:32] [9717cb857c153ca3061376906953b329]
-    D            [Central Tendency] [WS 3 Part 2] [2009-10-25 17:54:25] [9717cb857c153ca3061376906953b329]
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Dataseries X:
8987
8832
8802
8576
8498
8901
8835
8655
8665
8416
8423
8255
8919
9031
8737
8754
8640
8776
8896
8557
8777
8434
8626
8461
8794
8566
8184
8126
8066
8137
8092
7904
7898
7920
8083
8039
8054
8095
7985
7980
7914
7703
7726
7587
7367
7393
7403
7444
7512
7699
7627
7684
7843
7959
8191
8367
8057
8187
8319
8435




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\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 & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=49759&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=49759&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=49759&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'Gwilym Jenkins' @ 72.249.127.135







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean8246.5559.49280650149138.614237332936
Geometric Mean8233.78778834208
Harmonic Mean8220.93383553018
Quadratic Mean8259.20160487683
Winsorized Mean ( 1 / 20 )8246.2559.225923020474139.233794586018
Winsorized Mean ( 2 / 20 )8244.3166666666758.6835403234708140.487718041941
Winsorized Mean ( 3 / 20 )8245.4666666666758.020571389219142.112813942380
Winsorized Mean ( 4 / 20 )8249.6666666666756.9277650461092144.914641563476
Winsorized Mean ( 5 / 20 )8250.8333333333354.6469468015088150.984342516013
Winsorized Mean ( 6 / 20 )8254.5333333333353.7850527755766153.472626823965
Winsorized Mean ( 7 / 20 )8257.6833333333351.873828305693159.187852584751
Winsorized Mean ( 8 / 20 )8258.6166666666751.3123485521367160.947937478936
Winsorized Mean ( 9 / 20 )8256.6666666666750.7543806612676162.678897054646
Winsorized Mean ( 10 / 20 )8260.3333333333350.0239076552383165.127710339285
Winsorized Mean ( 11 / 20 )8277.7545.6318207501273181.403017980099
Winsorized Mean ( 12 / 20 )8285.3543.3072508966569191.3155378939
Winsorized Mean ( 13 / 20 )8271.0540.4390063486144204.531484495375
Winsorized Mean ( 14 / 20 )8271.0539.6977594395424208.350549672618
Winsorized Mean ( 15 / 20 )8268.838.8583317128106212.793489466095
Winsorized Mean ( 16 / 20 )8275.4666666666736.7019563100772225.477535768154
Winsorized Mean ( 17 / 20 )8267.2533.5834454863473246.170393784071
Winsorized Mean ( 18 / 20 )8265.7532.9004715934809251.235000583937
Winsorized Mean ( 19 / 20 )828030.0555794006262275.489615077176
Winsorized Mean ( 20 / 20 )8265.3333333333326.3650456264563313.495885819344
Trimmed Mean ( 1 / 20 )8248.1896551724158.0493795310704142.089195815739
Trimmed Mean ( 2 / 20 )8250.2678571428656.5883316587131145.794505957529
Trimmed Mean ( 3 / 20 )8253.5740740740755.125931693801149.722169230968
Trimmed Mean ( 4 / 20 )8256.6923076923153.6108157131939154.011689578905
Trimmed Mean ( 5 / 20 )8258.852.1327270003191158.418722273045
Trimmed Mean ( 6 / 20 )8260.7916666666751.031687401945161.875730300696
Trimmed Mean ( 7 / 20 )8262.1521739130449.8650058565496165.690388118702
Trimmed Mean ( 8 / 20 )8263.0227272727348.884842121625169.030365419089
Trimmed Mean ( 9 / 20 )8263.8095238095247.7196643165053173.174091690985
Trimmed Mean ( 10 / 20 )826546.294431187502178.531192370094
Trimmed Mean ( 11 / 20 )8265.7368421052644.5595591998949185.498622305150
Trimmed Mean ( 12 / 20 )8263.9166666666743.410761868824190.365621585681
Trimmed Mean ( 13 / 20 )8260.7647058823542.3930143158875194.861461002232
Trimmed Mean ( 14 / 20 )8259.2812541.7082859596451198.024950197936
Trimmed Mean ( 15 / 20 )8257.640.8215516664883202.285304279086
Trimmed Mean ( 16 / 20 )825639.6661331163263208.137253404262
Trimmed Mean ( 17 / 20 )8253.1923076923138.5142938193389214.289072685741
Trimmed Mean ( 18 / 20 )8251.12537.7164435989612218.767312415088
Trimmed Mean ( 19 / 20 )8248.9090909090936.4899268013695226.059896908302
Trimmed Mean ( 20 / 20 )824435.3812320156798233.004887911945
Median8189
Midrange8199
Midmean - Weighted Average at Xnp8246.51612903226
Midmean - Weighted Average at X(n+1)p8257.6
Midmean - Empirical Distribution Function8246.51612903226
Midmean - Empirical Distribution Function - Averaging8257.6
Midmean - Empirical Distribution Function - Interpolation8257.6
Midmean - Closest Observation8246.51612903226
Midmean - True Basic - Statistics Graphics Toolkit8257.6
Midmean - MS Excel (old versions)8259.28125
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 8246.55 & 59.49280650149 & 138.614237332936 \tabularnewline
Geometric Mean & 8233.78778834208 &  &  \tabularnewline
Harmonic Mean & 8220.93383553018 &  &  \tabularnewline
Quadratic Mean & 8259.20160487683 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 8246.25 & 59.225923020474 & 139.233794586018 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 8244.31666666667 & 58.6835403234708 & 140.487718041941 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 8245.46666666667 & 58.020571389219 & 142.112813942380 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 8249.66666666667 & 56.9277650461092 & 144.914641563476 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 8250.83333333333 & 54.6469468015088 & 150.984342516013 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 8254.53333333333 & 53.7850527755766 & 153.472626823965 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 8257.68333333333 & 51.873828305693 & 159.187852584751 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 8258.61666666667 & 51.3123485521367 & 160.947937478936 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 8256.66666666667 & 50.7543806612676 & 162.678897054646 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 8260.33333333333 & 50.0239076552383 & 165.127710339285 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 8277.75 & 45.6318207501273 & 181.403017980099 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 8285.35 & 43.3072508966569 & 191.3155378939 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 8271.05 & 40.4390063486144 & 204.531484495375 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 8271.05 & 39.6977594395424 & 208.350549672618 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 8268.8 & 38.8583317128106 & 212.793489466095 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 8275.46666666667 & 36.7019563100772 & 225.477535768154 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 8267.25 & 33.5834454863473 & 246.170393784071 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 8265.75 & 32.9004715934809 & 251.235000583937 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 8280 & 30.0555794006262 & 275.489615077176 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 8265.33333333333 & 26.3650456264563 & 313.495885819344 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 8248.18965517241 & 58.0493795310704 & 142.089195815739 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 8250.26785714286 & 56.5883316587131 & 145.794505957529 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 8253.57407407407 & 55.125931693801 & 149.722169230968 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 8256.69230769231 & 53.6108157131939 & 154.011689578905 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 8258.8 & 52.1327270003191 & 158.418722273045 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 8260.79166666667 & 51.031687401945 & 161.875730300696 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 8262.15217391304 & 49.8650058565496 & 165.690388118702 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 8263.02272727273 & 48.884842121625 & 169.030365419089 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 8263.80952380952 & 47.7196643165053 & 173.174091690985 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 8265 & 46.294431187502 & 178.531192370094 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 8265.73684210526 & 44.5595591998949 & 185.498622305150 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 8263.91666666667 & 43.410761868824 & 190.365621585681 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 8260.76470588235 & 42.3930143158875 & 194.861461002232 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 8259.28125 & 41.7082859596451 & 198.024950197936 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 8257.6 & 40.8215516664883 & 202.285304279086 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 8256 & 39.6661331163263 & 208.137253404262 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 8253.19230769231 & 38.5142938193389 & 214.289072685741 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 8251.125 & 37.7164435989612 & 218.767312415088 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 8248.90909090909 & 36.4899268013695 & 226.059896908302 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 8244 & 35.3812320156798 & 233.004887911945 \tabularnewline
Median & 8189 &  &  \tabularnewline
Midrange & 8199 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 8246.51612903226 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 8257.6 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 8246.51612903226 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 8257.6 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 8257.6 &  &  \tabularnewline
Midmean - Closest Observation & 8246.51612903226 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 8257.6 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 8259.28125 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=49759&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]8246.55[/C][C]59.49280650149[/C][C]138.614237332936[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]8233.78778834208[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]8220.93383553018[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]8259.20160487683[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]8246.25[/C][C]59.225923020474[/C][C]139.233794586018[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]8244.31666666667[/C][C]58.6835403234708[/C][C]140.487718041941[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]8245.46666666667[/C][C]58.020571389219[/C][C]142.112813942380[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]8249.66666666667[/C][C]56.9277650461092[/C][C]144.914641563476[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]8250.83333333333[/C][C]54.6469468015088[/C][C]150.984342516013[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]8254.53333333333[/C][C]53.7850527755766[/C][C]153.472626823965[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]8257.68333333333[/C][C]51.873828305693[/C][C]159.187852584751[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]8258.61666666667[/C][C]51.3123485521367[/C][C]160.947937478936[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]8256.66666666667[/C][C]50.7543806612676[/C][C]162.678897054646[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]8260.33333333333[/C][C]50.0239076552383[/C][C]165.127710339285[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]8277.75[/C][C]45.6318207501273[/C][C]181.403017980099[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]8285.35[/C][C]43.3072508966569[/C][C]191.3155378939[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]8271.05[/C][C]40.4390063486144[/C][C]204.531484495375[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]8271.05[/C][C]39.6977594395424[/C][C]208.350549672618[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]8268.8[/C][C]38.8583317128106[/C][C]212.793489466095[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]8275.46666666667[/C][C]36.7019563100772[/C][C]225.477535768154[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]8267.25[/C][C]33.5834454863473[/C][C]246.170393784071[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]8265.75[/C][C]32.9004715934809[/C][C]251.235000583937[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]8280[/C][C]30.0555794006262[/C][C]275.489615077176[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]8265.33333333333[/C][C]26.3650456264563[/C][C]313.495885819344[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]8248.18965517241[/C][C]58.0493795310704[/C][C]142.089195815739[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]8250.26785714286[/C][C]56.5883316587131[/C][C]145.794505957529[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]8253.57407407407[/C][C]55.125931693801[/C][C]149.722169230968[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]8256.69230769231[/C][C]53.6108157131939[/C][C]154.011689578905[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]8258.8[/C][C]52.1327270003191[/C][C]158.418722273045[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]8260.79166666667[/C][C]51.031687401945[/C][C]161.875730300696[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]8262.15217391304[/C][C]49.8650058565496[/C][C]165.690388118702[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]8263.02272727273[/C][C]48.884842121625[/C][C]169.030365419089[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]8263.80952380952[/C][C]47.7196643165053[/C][C]173.174091690985[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]8265[/C][C]46.294431187502[/C][C]178.531192370094[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]8265.73684210526[/C][C]44.5595591998949[/C][C]185.498622305150[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]8263.91666666667[/C][C]43.410761868824[/C][C]190.365621585681[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]8260.76470588235[/C][C]42.3930143158875[/C][C]194.861461002232[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]8259.28125[/C][C]41.7082859596451[/C][C]198.024950197936[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]8257.6[/C][C]40.8215516664883[/C][C]202.285304279086[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]8256[/C][C]39.6661331163263[/C][C]208.137253404262[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]8253.19230769231[/C][C]38.5142938193389[/C][C]214.289072685741[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]8251.125[/C][C]37.7164435989612[/C][C]218.767312415088[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]8248.90909090909[/C][C]36.4899268013695[/C][C]226.059896908302[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]8244[/C][C]35.3812320156798[/C][C]233.004887911945[/C][/ROW]
[ROW][C]Median[/C][C]8189[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]8199[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]8246.51612903226[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]8257.6[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]8246.51612903226[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]8257.6[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]8257.6[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]8246.51612903226[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]8257.6[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]8259.28125[/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=49759&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=49759&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 Mean8246.5559.49280650149138.614237332936
Geometric Mean8233.78778834208
Harmonic Mean8220.93383553018
Quadratic Mean8259.20160487683
Winsorized Mean ( 1 / 20 )8246.2559.225923020474139.233794586018
Winsorized Mean ( 2 / 20 )8244.3166666666758.6835403234708140.487718041941
Winsorized Mean ( 3 / 20 )8245.4666666666758.020571389219142.112813942380
Winsorized Mean ( 4 / 20 )8249.6666666666756.9277650461092144.914641563476
Winsorized Mean ( 5 / 20 )8250.8333333333354.6469468015088150.984342516013
Winsorized Mean ( 6 / 20 )8254.5333333333353.7850527755766153.472626823965
Winsorized Mean ( 7 / 20 )8257.6833333333351.873828305693159.187852584751
Winsorized Mean ( 8 / 20 )8258.6166666666751.3123485521367160.947937478936
Winsorized Mean ( 9 / 20 )8256.6666666666750.7543806612676162.678897054646
Winsorized Mean ( 10 / 20 )8260.3333333333350.0239076552383165.127710339285
Winsorized Mean ( 11 / 20 )8277.7545.6318207501273181.403017980099
Winsorized Mean ( 12 / 20 )8285.3543.3072508966569191.3155378939
Winsorized Mean ( 13 / 20 )8271.0540.4390063486144204.531484495375
Winsorized Mean ( 14 / 20 )8271.0539.6977594395424208.350549672618
Winsorized Mean ( 15 / 20 )8268.838.8583317128106212.793489466095
Winsorized Mean ( 16 / 20 )8275.4666666666736.7019563100772225.477535768154
Winsorized Mean ( 17 / 20 )8267.2533.5834454863473246.170393784071
Winsorized Mean ( 18 / 20 )8265.7532.9004715934809251.235000583937
Winsorized Mean ( 19 / 20 )828030.0555794006262275.489615077176
Winsorized Mean ( 20 / 20 )8265.3333333333326.3650456264563313.495885819344
Trimmed Mean ( 1 / 20 )8248.1896551724158.0493795310704142.089195815739
Trimmed Mean ( 2 / 20 )8250.2678571428656.5883316587131145.794505957529
Trimmed Mean ( 3 / 20 )8253.5740740740755.125931693801149.722169230968
Trimmed Mean ( 4 / 20 )8256.6923076923153.6108157131939154.011689578905
Trimmed Mean ( 5 / 20 )8258.852.1327270003191158.418722273045
Trimmed Mean ( 6 / 20 )8260.7916666666751.031687401945161.875730300696
Trimmed Mean ( 7 / 20 )8262.1521739130449.8650058565496165.690388118702
Trimmed Mean ( 8 / 20 )8263.0227272727348.884842121625169.030365419089
Trimmed Mean ( 9 / 20 )8263.8095238095247.7196643165053173.174091690985
Trimmed Mean ( 10 / 20 )826546.294431187502178.531192370094
Trimmed Mean ( 11 / 20 )8265.7368421052644.5595591998949185.498622305150
Trimmed Mean ( 12 / 20 )8263.9166666666743.410761868824190.365621585681
Trimmed Mean ( 13 / 20 )8260.7647058823542.3930143158875194.861461002232
Trimmed Mean ( 14 / 20 )8259.2812541.7082859596451198.024950197936
Trimmed Mean ( 15 / 20 )8257.640.8215516664883202.285304279086
Trimmed Mean ( 16 / 20 )825639.6661331163263208.137253404262
Trimmed Mean ( 17 / 20 )8253.1923076923138.5142938193389214.289072685741
Trimmed Mean ( 18 / 20 )8251.12537.7164435989612218.767312415088
Trimmed Mean ( 19 / 20 )8248.9090909090936.4899268013695226.059896908302
Trimmed Mean ( 20 / 20 )824435.3812320156798233.004887911945
Median8189
Midrange8199
Midmean - Weighted Average at Xnp8246.51612903226
Midmean - Weighted Average at X(n+1)p8257.6
Midmean - Empirical Distribution Function8246.51612903226
Midmean - Empirical Distribution Function - Averaging8257.6
Midmean - Empirical Distribution Function - Interpolation8257.6
Midmean - Closest Observation8246.51612903226
Midmean - True Basic - Statistics Graphics Toolkit8257.6
Midmean - MS Excel (old versions)8259.28125
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')