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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 computationTue, 21 Oct 2008 01:12:47 -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/2008/Oct/21/t1224573218uqxmqx9k69mtqte.htm/, Retrieved Sun, 19 May 2024 20:59:04 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=18345, Retrieved Sun, 19 May 2024 20:59:04 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact135
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Q9 Tijdreeks2] [2008-10-21 07:12:47] [d7f41258beeebb8716e3f5d39f3cdc01] [Current]
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Dataseries X:
6,1
9
9,1
8,3
10,3
8,7
7
9,7
7,3
5,3
6,2
5,5
6,4
8,2
7,6
7,4
8,9
7,5
8,1
11,2
8,8
6,2
7,5
5,6
7,4
8,7
9,2
10
10,7
8,3
8
10,2
8,9
7,3
6,8
7,3
7,8
10
9,6
9,4
9,7
8,2
8,5
10,5
10,2
7
7,2
6,9
9
9,1
8,8
7,7
6,6
6,7
8
7,9
8,5
4,8
4,3
5,2




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=18345&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=18345&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=18345&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 Mean8.0050.20113273858592439.7995873584761
Geometric Mean7.84486129000795
Harmonic Mean7.6720468076057
Quadratic Mean8.15271938271724
Winsorized Mean ( 1 / 20 )8.0050.1965870517774640.7198741098260
Winsorized Mean ( 2 / 20 )8.011666666666670.19157526683401441.8199426213416
Winsorized Mean ( 3 / 20 )8.006666666666670.18820992406855442.5411502942337
Winsorized Mean ( 4 / 20 )8.013333333333330.18367661748757343.627400389576
Winsorized Mean ( 5 / 20 )8.021666666666670.18176926559066944.1310396485338
Winsorized Mean ( 6 / 20 )8.051666666666670.16713761146913748.1738765792608
Winsorized Mean ( 7 / 20 )8.063333333333330.16486540764070248.9085821502719
Winsorized Mean ( 8 / 20 )8.023333333333330.15726056442226951.0193598936187
Winsorized Mean ( 9 / 20 )8.053333333333330.15153576644555353.1447692002596
Winsorized Mean ( 10 / 20 )8.070.14248203375690256.63871989481
Winsorized Mean ( 11 / 20 )8.051666666666670.13279889359237860.63052521643
Winsorized Mean ( 12 / 20 )8.031666666666670.12269321593064965.4613753967169
Winsorized Mean ( 13 / 20 )8.031666666666670.11560432387537169.4754867069273
Winsorized Mean ( 14 / 20 )8.0550.11180150388606872.047331386602
Winsorized Mean ( 15 / 20 )8.030.10791553508121374.410046653218
Winsorized Mean ( 16 / 20 )8.083333333333330.099580097694638981.1741856100681
Winsorized Mean ( 17 / 20 )8.083333333333330.091013336908894388.814822177379
Winsorized Mean ( 18 / 20 )8.083333333333330.091013336908894388.814822177379
Winsorized Mean ( 19 / 20 )8.051666666666670.086275464321436693.3251038402826
Winsorized Mean ( 20 / 20 )8.0850.081435739457666699.2807341573032
Trimmed Mean ( 1 / 20 )8.013793103448280.18993819282954742.1915833991321
Trimmed Mean ( 2 / 20 )8.023214285714290.18173033882166644.1490085680606
Trimmed Mean ( 3 / 20 )8.029629629629630.17496390023245845.8930649063115
Trimmed Mean ( 4 / 20 )8.038461538461540.1681716480677747.7991482560853
Trimmed Mean ( 5 / 20 )8.0460.16147812134611149.8271836018841
Trimmed Mean ( 6 / 20 )8.052083333333330.15364915776545352.4056457610065
Trimmed Mean ( 7 / 20 )8.052173913043480.14851077582317654.2194589477518
Trimmed Mean ( 8 / 20 )8.050.1425196103119456.4834550303678
Trimmed Mean ( 9 / 20 )8.05476190476190.13692331844142758.8268090230923
Trimmed Mean ( 10 / 20 )8.0550.13116587658185861.4107892228589
Trimmed Mean ( 11 / 20 )8.052631578947370.12603691358540463.8910565950253
Trimmed Mean ( 12 / 20 )8.052777777777780.12179126764583666.1195004652957
Trimmed Mean ( 13 / 20 )8.055882352941180.11868194561584367.8779094085374
Trimmed Mean ( 14 / 20 )8.0593750.11612522570206269.4024485315329
Trimmed Mean ( 15 / 20 )8.060.11331980987605371.1261341579717
Trimmed Mean ( 16 / 20 )8.064285714285710.11010027725052573.244917412297
Trimmed Mean ( 17 / 20 )8.061538461538460.10771428347208874.8418705642455
Trimmed Mean ( 18 / 20 )8.058333333333330.10647798075881075.6807489765119
Trimmed Mean ( 19 / 20 )8.054545454545450.10376615249578377.6220883285887
Trimmed Mean ( 20 / 20 )8.0550.10064920843153680.0304356638753
Median8.05
Midrange7.75
Midmean - Weighted Average at Xnp8.0258064516129
Midmean - Weighted Average at X(n+1)p8.0258064516129
Midmean - Empirical Distribution Function8.0258064516129
Midmean - Empirical Distribution Function - Averaging8.0258064516129
Midmean - Empirical Distribution Function - Interpolation8.0258064516129
Midmean - Closest Observation8.0258064516129
Midmean - True Basic - Statistics Graphics Toolkit8.0258064516129
Midmean - MS Excel (old versions)8.0909090909091
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 8.005 & 0.201132738585924 & 39.7995873584761 \tabularnewline
Geometric Mean & 7.84486129000795 &  &  \tabularnewline
Harmonic Mean & 7.6720468076057 &  &  \tabularnewline
Quadratic Mean & 8.15271938271724 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 8.005 & 0.19658705177746 & 40.7198741098260 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 8.01166666666667 & 0.191575266834014 & 41.8199426213416 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 8.00666666666667 & 0.188209924068554 & 42.5411502942337 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 8.01333333333333 & 0.183676617487573 & 43.627400389576 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 8.02166666666667 & 0.181769265590669 & 44.1310396485338 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 8.05166666666667 & 0.167137611469137 & 48.1738765792608 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 8.06333333333333 & 0.164865407640702 & 48.9085821502719 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 8.02333333333333 & 0.157260564422269 & 51.0193598936187 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 8.05333333333333 & 0.151535766445553 & 53.1447692002596 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 8.07 & 0.142482033756902 & 56.63871989481 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 8.05166666666667 & 0.132798893592378 & 60.63052521643 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 8.03166666666667 & 0.122693215930649 & 65.4613753967169 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 8.03166666666667 & 0.115604323875371 & 69.4754867069273 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 8.055 & 0.111801503886068 & 72.047331386602 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 8.03 & 0.107915535081213 & 74.410046653218 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 8.08333333333333 & 0.0995800976946389 & 81.1741856100681 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 8.08333333333333 & 0.0910133369088943 & 88.814822177379 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 8.08333333333333 & 0.0910133369088943 & 88.814822177379 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 8.05166666666667 & 0.0862754643214366 & 93.3251038402826 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 8.085 & 0.0814357394576666 & 99.2807341573032 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 8.01379310344828 & 0.189938192829547 & 42.1915833991321 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 8.02321428571429 & 0.181730338821666 & 44.1490085680606 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 8.02962962962963 & 0.174963900232458 & 45.8930649063115 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 8.03846153846154 & 0.16817164806777 & 47.7991482560853 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 8.046 & 0.161478121346111 & 49.8271836018841 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 8.05208333333333 & 0.153649157765453 & 52.4056457610065 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 8.05217391304348 & 0.148510775823176 & 54.2194589477518 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 8.05 & 0.14251961031194 & 56.4834550303678 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 8.0547619047619 & 0.136923318441427 & 58.8268090230923 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 8.055 & 0.131165876581858 & 61.4107892228589 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 8.05263157894737 & 0.126036913585404 & 63.8910565950253 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 8.05277777777778 & 0.121791267645836 & 66.1195004652957 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 8.05588235294118 & 0.118681945615843 & 67.8779094085374 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 8.059375 & 0.116125225702062 & 69.4024485315329 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 8.06 & 0.113319809876053 & 71.1261341579717 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 8.06428571428571 & 0.110100277250525 & 73.244917412297 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 8.06153846153846 & 0.107714283472088 & 74.8418705642455 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 8.05833333333333 & 0.106477980758810 & 75.6807489765119 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 8.05454545454545 & 0.103766152495783 & 77.6220883285887 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 8.055 & 0.100649208431536 & 80.0304356638753 \tabularnewline
Median & 8.05 &  &  \tabularnewline
Midrange & 7.75 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 8.0258064516129 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 8.0258064516129 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 8.0258064516129 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 8.0258064516129 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 8.0258064516129 &  &  \tabularnewline
Midmean - Closest Observation & 8.0258064516129 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 8.0258064516129 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 8.0909090909091 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=18345&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]8.005[/C][C]0.201132738585924[/C][C]39.7995873584761[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]7.84486129000795[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]7.6720468076057[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]8.15271938271724[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]8.005[/C][C]0.19658705177746[/C][C]40.7198741098260[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]8.01166666666667[/C][C]0.191575266834014[/C][C]41.8199426213416[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]8.00666666666667[/C][C]0.188209924068554[/C][C]42.5411502942337[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]8.01333333333333[/C][C]0.183676617487573[/C][C]43.627400389576[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]8.02166666666667[/C][C]0.181769265590669[/C][C]44.1310396485338[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]8.05166666666667[/C][C]0.167137611469137[/C][C]48.1738765792608[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]8.06333333333333[/C][C]0.164865407640702[/C][C]48.9085821502719[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]8.02333333333333[/C][C]0.157260564422269[/C][C]51.0193598936187[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]8.05333333333333[/C][C]0.151535766445553[/C][C]53.1447692002596[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]8.07[/C][C]0.142482033756902[/C][C]56.63871989481[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]8.05166666666667[/C][C]0.132798893592378[/C][C]60.63052521643[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]8.03166666666667[/C][C]0.122693215930649[/C][C]65.4613753967169[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]8.03166666666667[/C][C]0.115604323875371[/C][C]69.4754867069273[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]8.055[/C][C]0.111801503886068[/C][C]72.047331386602[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]8.03[/C][C]0.107915535081213[/C][C]74.410046653218[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]8.08333333333333[/C][C]0.0995800976946389[/C][C]81.1741856100681[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]8.08333333333333[/C][C]0.0910133369088943[/C][C]88.814822177379[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]8.08333333333333[/C][C]0.0910133369088943[/C][C]88.814822177379[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]8.05166666666667[/C][C]0.0862754643214366[/C][C]93.3251038402826[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]8.085[/C][C]0.0814357394576666[/C][C]99.2807341573032[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]8.01379310344828[/C][C]0.189938192829547[/C][C]42.1915833991321[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]8.02321428571429[/C][C]0.181730338821666[/C][C]44.1490085680606[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]8.02962962962963[/C][C]0.174963900232458[/C][C]45.8930649063115[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]8.03846153846154[/C][C]0.16817164806777[/C][C]47.7991482560853[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]8.046[/C][C]0.161478121346111[/C][C]49.8271836018841[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]8.05208333333333[/C][C]0.153649157765453[/C][C]52.4056457610065[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]8.05217391304348[/C][C]0.148510775823176[/C][C]54.2194589477518[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]8.05[/C][C]0.14251961031194[/C][C]56.4834550303678[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]8.0547619047619[/C][C]0.136923318441427[/C][C]58.8268090230923[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]8.055[/C][C]0.131165876581858[/C][C]61.4107892228589[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]8.05263157894737[/C][C]0.126036913585404[/C][C]63.8910565950253[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]8.05277777777778[/C][C]0.121791267645836[/C][C]66.1195004652957[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]8.05588235294118[/C][C]0.118681945615843[/C][C]67.8779094085374[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]8.059375[/C][C]0.116125225702062[/C][C]69.4024485315329[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]8.06[/C][C]0.113319809876053[/C][C]71.1261341579717[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]8.06428571428571[/C][C]0.110100277250525[/C][C]73.244917412297[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]8.06153846153846[/C][C]0.107714283472088[/C][C]74.8418705642455[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]8.05833333333333[/C][C]0.106477980758810[/C][C]75.6807489765119[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]8.05454545454545[/C][C]0.103766152495783[/C][C]77.6220883285887[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]8.055[/C][C]0.100649208431536[/C][C]80.0304356638753[/C][/ROW]
[ROW][C]Median[/C][C]8.05[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]7.75[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]8.0258064516129[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]8.0258064516129[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]8.0258064516129[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]8.0258064516129[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]8.0258064516129[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]8.0258064516129[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]8.0258064516129[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]8.0909090909091[/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=18345&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=18345&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 Mean8.0050.20113273858592439.7995873584761
Geometric Mean7.84486129000795
Harmonic Mean7.6720468076057
Quadratic Mean8.15271938271724
Winsorized Mean ( 1 / 20 )8.0050.1965870517774640.7198741098260
Winsorized Mean ( 2 / 20 )8.011666666666670.19157526683401441.8199426213416
Winsorized Mean ( 3 / 20 )8.006666666666670.18820992406855442.5411502942337
Winsorized Mean ( 4 / 20 )8.013333333333330.18367661748757343.627400389576
Winsorized Mean ( 5 / 20 )8.021666666666670.18176926559066944.1310396485338
Winsorized Mean ( 6 / 20 )8.051666666666670.16713761146913748.1738765792608
Winsorized Mean ( 7 / 20 )8.063333333333330.16486540764070248.9085821502719
Winsorized Mean ( 8 / 20 )8.023333333333330.15726056442226951.0193598936187
Winsorized Mean ( 9 / 20 )8.053333333333330.15153576644555353.1447692002596
Winsorized Mean ( 10 / 20 )8.070.14248203375690256.63871989481
Winsorized Mean ( 11 / 20 )8.051666666666670.13279889359237860.63052521643
Winsorized Mean ( 12 / 20 )8.031666666666670.12269321593064965.4613753967169
Winsorized Mean ( 13 / 20 )8.031666666666670.11560432387537169.4754867069273
Winsorized Mean ( 14 / 20 )8.0550.11180150388606872.047331386602
Winsorized Mean ( 15 / 20 )8.030.10791553508121374.410046653218
Winsorized Mean ( 16 / 20 )8.083333333333330.099580097694638981.1741856100681
Winsorized Mean ( 17 / 20 )8.083333333333330.091013336908894388.814822177379
Winsorized Mean ( 18 / 20 )8.083333333333330.091013336908894388.814822177379
Winsorized Mean ( 19 / 20 )8.051666666666670.086275464321436693.3251038402826
Winsorized Mean ( 20 / 20 )8.0850.081435739457666699.2807341573032
Trimmed Mean ( 1 / 20 )8.013793103448280.18993819282954742.1915833991321
Trimmed Mean ( 2 / 20 )8.023214285714290.18173033882166644.1490085680606
Trimmed Mean ( 3 / 20 )8.029629629629630.17496390023245845.8930649063115
Trimmed Mean ( 4 / 20 )8.038461538461540.1681716480677747.7991482560853
Trimmed Mean ( 5 / 20 )8.0460.16147812134611149.8271836018841
Trimmed Mean ( 6 / 20 )8.052083333333330.15364915776545352.4056457610065
Trimmed Mean ( 7 / 20 )8.052173913043480.14851077582317654.2194589477518
Trimmed Mean ( 8 / 20 )8.050.1425196103119456.4834550303678
Trimmed Mean ( 9 / 20 )8.05476190476190.13692331844142758.8268090230923
Trimmed Mean ( 10 / 20 )8.0550.13116587658185861.4107892228589
Trimmed Mean ( 11 / 20 )8.052631578947370.12603691358540463.8910565950253
Trimmed Mean ( 12 / 20 )8.052777777777780.12179126764583666.1195004652957
Trimmed Mean ( 13 / 20 )8.055882352941180.11868194561584367.8779094085374
Trimmed Mean ( 14 / 20 )8.0593750.11612522570206269.4024485315329
Trimmed Mean ( 15 / 20 )8.060.11331980987605371.1261341579717
Trimmed Mean ( 16 / 20 )8.064285714285710.11010027725052573.244917412297
Trimmed Mean ( 17 / 20 )8.061538461538460.10771428347208874.8418705642455
Trimmed Mean ( 18 / 20 )8.058333333333330.10647798075881075.6807489765119
Trimmed Mean ( 19 / 20 )8.054545454545450.10376615249578377.6220883285887
Trimmed Mean ( 20 / 20 )8.0550.10064920843153680.0304356638753
Median8.05
Midrange7.75
Midmean - Weighted Average at Xnp8.0258064516129
Midmean - Weighted Average at X(n+1)p8.0258064516129
Midmean - Empirical Distribution Function8.0258064516129
Midmean - Empirical Distribution Function - Averaging8.0258064516129
Midmean - Empirical Distribution Function - Interpolation8.0258064516129
Midmean - Closest Observation8.0258064516129
Midmean - True Basic - Statistics Graphics Toolkit8.0258064516129
Midmean - MS Excel (old versions)8.0909090909091
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')