Free Statistics

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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 computationSat, 18 Dec 2010 09:18:46 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Dec/18/t1292664296hkooe9q30vlguib.htm/, Retrieved Tue, 30 Apr 2024 08:01:34 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=111804, Retrieved Tue, 30 Apr 2024 08:01:34 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact197
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
F     [Univariate Data Series] [HPC Retail Sales] [2008-03-02 15:42:48] [74be16979710d4c4e7c6647856088456]
-  MPD  [Univariate Data Series] [WS8 1] [2010-11-30 15:47:30] [07a238a5afc23eb944f8545182f29d5a]
- RMP     [Classical Decomposition] [WS8 2] [2010-11-30 15:54:02] [07a238a5afc23eb944f8545182f29d5a]
- RMPD      [Univariate Data Series] [Statistiek: Werkl...] [2010-12-12 15:20:09] [07a238a5afc23eb944f8545182f29d5a]
-    D        [Univariate Data Series] [Statistiek: Werkl...] [2010-12-14 09:08:05] [07a238a5afc23eb944f8545182f29d5a]
-               [Univariate Data Series] [Statistiek: Werkl...] [2010-12-14 09:12:36] [07a238a5afc23eb944f8545182f29d5a]
- RMPD            [Univariate Explorative Data Analysis] [Statistiek: U EDA...] [2010-12-17 19:07:44] [07a238a5afc23eb944f8545182f29d5a]
- RMP                 [Central Tendency] [Statistiek: centr...] [2010-12-18 09:18:46] [67e3c2d70de1dbb070b545ca6c893d5e] [Current]
- RMP                   [Harrell-Davis Quantiles] [Statistiek: betro...] [2010-12-18 10:06:35] [07a238a5afc23eb944f8545182f29d5a]
- RMPD                    [Bivariate Explorative Data Analysis] [statistiek: Bivar...] [2010-12-18 13:22:48] [07a238a5afc23eb944f8545182f29d5a]
- RMPD                      [Pearson Correlation] [statistiek: pears...] [2010-12-18 14:12:28] [07a238a5afc23eb944f8545182f29d5a]
-                             [Pearson Correlation] [statistiek: pears...] [2010-12-18 14:15:15] [07a238a5afc23eb944f8545182f29d5a]
- RM D                          [Mean versus Median] [Statistiek: mean ...] [2010-12-18 14:31:13] [07a238a5afc23eb944f8545182f29d5a]
- RMPD                          [Bivariate Kernel Density Estimation] [statistiek: kerne...] [2010-12-18 15:29:35] [07a238a5afc23eb944f8545182f29d5a]
- RMPD                          [Trivariate Scatterplots] [Statistiek trivar...] [2010-12-18 16:57:07] [07a238a5afc23eb944f8545182f29d5a]
-   PD                            [Trivariate Scatterplots] [Statistiek: triva...] [2010-12-18 17:03:13] [07a238a5afc23eb944f8545182f29d5a]
- RMPD                            [Multiple Regression] [statistiek Multip...] [2010-12-18 19:03:25] [07a238a5afc23eb944f8545182f29d5a]
-    D                              [Multiple Regression] [statistiek Multip...] [2010-12-18 19:19:51] [07a238a5afc23eb944f8545182f29d5a]
-    D                                [Multiple Regression] [statistiek Multip...] [2010-12-18 19:32:07] [07a238a5afc23eb944f8545182f29d5a]
- RM                    [Percentiles] [statistiek: betro...] [2010-12-18 12:02:38] [07a238a5afc23eb944f8545182f29d5a]
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Dataseries X:
6.5
6.3
5.9
5.5
5.2
4.9
5.4
5.8
5.7
5.6
5.5
5.4
5.4
5.4
5.5
5.8
5.7
5.4
5.6
5.8
6.2
6.8
6.7
6.7
6.4
6.3
6.3
6.4
6.3
6
6.3
6.3
6.6
7.5
7.8
7.9
7.8
7.6
7.5
7.6
7.5
7.3
7.6
7.5
7.6
7.9
7.9
8.1
8.2
8
7.5
6.8
6.5
6.6
7.6
8
8.1
7.7
7.5
7.6
7.8
7.8
7.8
7.5
7.5
7.1
7.5
7.5
7.6
7.7
7.7
7.9
8.1
8.2
8.2
8.2
7.9
7.3
6.9
6.6
6.7
6.9
7
7.1
7.2
7.1
6.9
7
6.8
6.4
6.7
6.6
6.4
6.3
6.2
6.5
6.8
6.8
6.4
6.1
5.8
6.1
7.2
7.3
6.9
6.1
5.8
6.2
7.1
7.7
8
7.8
7.4
7.4
7.7
7.8
7.8
8
8.1
8.4




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'RServer@AstonUniversity' @ vre.aston.ac.uk

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 3 seconds \tabularnewline
R Server & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=111804&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]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=111804&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=111804&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'RServer@AstonUniversity' @ vre.aston.ac.uk







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean6.934166666666670.07888842449988987.8984047485499
Geometric Mean6.87859178665138
Harmonic Mean6.82099515832114
Quadratic Mean6.9873635943752
Winsorized Mean ( 1 / 40 )6.9350.078140593681852688.7502855204259
Winsorized Mean ( 2 / 40 )6.938333333333330.077551675491992589.4672267145246
Winsorized Mean ( 3 / 40 )6.938333333333330.077551675491992589.4672267145246
Winsorized Mean ( 4 / 40 )6.938333333333330.077551675491992589.4672267145246
Winsorized Mean ( 5 / 40 )6.934166666666670.077001726428800890.0520934823235
Winsorized Mean ( 6 / 40 )6.934166666666670.077001726428800890.0520934823235
Winsorized Mean ( 7 / 40 )6.940.076049151141585791.2567713882742
Winsorized Mean ( 8 / 40 )6.940.076049151141585791.2567713882742
Winsorized Mean ( 9 / 40 )6.93250.075120468142135392.2851011375892
Winsorized Mean ( 10 / 40 )6.940833333333330.073816486750272394.0282264694442
Winsorized Mean ( 11 / 40 )6.940833333333330.073816486750272394.0282264694442
Winsorized Mean ( 12 / 40 )6.950833333333330.072326251121616996.10387965008
Winsorized Mean ( 13 / 40 )6.940.071050540263313297.6769490320605
Winsorized Mean ( 14 / 40 )6.951666666666670.0693808485644683100.195757337952
Winsorized Mean ( 15 / 40 )6.951666666666670.0693808485644683100.195757337952
Winsorized Mean ( 16 / 40 )6.951666666666670.0693808485644683100.195757337952
Winsorized Mean ( 17 / 40 )6.951666666666670.0693808485644683100.195757337952
Winsorized Mean ( 18 / 40 )6.936666666666670.0677151445615223102.438925761495
Winsorized Mean ( 19 / 40 )6.95250.0655291166280335106.097874620603
Winsorized Mean ( 20 / 40 )6.969166666666670.0633318129701045110.042115326091
Winsorized Mean ( 21 / 40 )6.986666666666670.0611392007423521114.27474651017
Winsorized Mean ( 22 / 40 )6.986666666666670.0611392007423521114.27474651017
Winsorized Mean ( 23 / 40 )6.986666666666670.0611392007423521114.27474651017
Winsorized Mean ( 24 / 40 )7.006666666666670.0587657045382646119.230539678195
Winsorized Mean ( 25 / 40 )7.006666666666670.0587657045382646119.230539678195
Winsorized Mean ( 26 / 40 )6.9850.056380683860743123.889948147003
Winsorized Mean ( 27 / 40 )7.00750.0538199417916239130.202667760793
Winsorized Mean ( 28 / 40 )7.00750.0538199417916239130.202667760793
Winsorized Mean ( 29 / 40 )7.00750.0538199417916239130.202667760793
Winsorized Mean ( 30 / 40 )7.00750.0538199417916239130.202667760793
Winsorized Mean ( 31 / 40 )6.981666666666670.0511079394542254136.606303075861
Winsorized Mean ( 32 / 40 )6.981666666666670.0511079394542254136.606303075861
Winsorized Mean ( 33 / 40 )6.981666666666670.0511079394542254136.606303075861
Winsorized Mean ( 34 / 40 )7.010.0480050184117982146.026399570699
Winsorized Mean ( 35 / 40 )7.010.0480050184117982146.026399570699
Winsorized Mean ( 36 / 40 )7.010.0480050184117982146.026399570699
Winsorized Mean ( 37 / 40 )7.010.0480050184117982146.026399570699
Winsorized Mean ( 38 / 40 )6.978333333333330.0448180781685131155.703537913769
Winsorized Mean ( 39 / 40 )7.010833333333330.0413666368723047169.480379924894
Winsorized Mean ( 40 / 40 )7.010833333333330.0413666368723047169.480379924894
Trimmed Mean ( 1 / 40 )6.938983050847460.077340199405077989.7202632553837
Trimmed Mean ( 2 / 40 )6.943103448275860.07644876715746790.8203455259737
Trimmed Mean ( 3 / 40 )6.945614035087720.07579358496557191.6385474871356
Trimmed Mean ( 4 / 40 )6.948214285714290.075058773012492292.5703153255366
Trimmed Mean ( 5 / 40 )6.950909090909090.074234997046976293.6338569059352
Trimmed Mean ( 6 / 40 )6.954629629629630.073452469299598694.6820399088698
Trimmed Mean ( 7 / 40 )6.958490566037740.072571406413283695.8847418005122
Trimmed Mean ( 8 / 40 )6.961538461538460.071776087552980896.9896618619658
Trimmed Mean ( 9 / 40 )6.964705882352940.070877231484937398.264361296802
Trimmed Mean ( 10 / 40 )6.9690.070017241743831599.532626913484
Trimmed Mean ( 11 / 40 )6.972448979591840.0692568318441585100.675251725075
Trimmed Mean ( 12 / 40 )6.976041666666670.0683891212953472102.005136702075
Trimmed Mean ( 13 / 40 )6.978723404255320.0676241977532428103.198612865181
Trimmed Mean ( 14 / 40 )6.982608695652170.0669199644556308104.342683868007
Trimmed Mean ( 15 / 40 )6.985555555555560.0663392919069414105.300423847675
Trimmed Mean ( 16 / 40 )6.988636363636360.0656618068534734106.433811351426
Trimmed Mean ( 17 / 40 )6.991860465116280.0648731291827087107.777450435979
Trimmed Mean ( 18 / 40 )6.99523809523810.0639560404173495109.375721973878
Trimmed Mean ( 19 / 40 )70.0630930162234764110.947303188136
Trimmed Mean ( 20 / 40 )7.003750.0623750332944281112.28450920323
Trimmed Mean ( 21 / 40 )7.006410256410260.061811367617931113.351484143149
Trimmed Mean ( 22 / 40 )7.00789473684210.0614092729124084114.11785882627
Trimmed Mean ( 23 / 40 )7.009459459459460.0609127452048657115.073773737906
Trimmed Mean ( 24 / 40 )7.011111111111110.0603055455538896116.259807397745
Trimmed Mean ( 25 / 40 )7.011428571428570.0598667553318725117.117230298529
Trimmed Mean ( 26 / 40 )7.011764705882350.0593175044810625118.207344817092
Trimmed Mean ( 27 / 40 )7.013636363636360.0589293110424382119.017789951514
Trimmed Mean ( 28 / 40 )7.01406250.0587513587946547119.385536673548
Trimmed Mean ( 29 / 40 )7.014516129032260.058486407239639119.934125895122
Trimmed Mean ( 30 / 40 )7.0150.0581166273357406120.705559176279
Trimmed Mean ( 31 / 40 )7.015517241379310.0576197416584248121.755444218545
Trimmed Mean ( 32 / 40 )7.017857142857140.0573272188279954122.417540678426
Trimmed Mean ( 33 / 40 )7.020370370370370.0569047673580666123.370513514193
Trimmed Mean ( 34 / 40 )7.023076923076920.0563210593303954124.697173784988
Trimmed Mean ( 35 / 40 )7.0240.0560291469337384125.363322206329
Trimmed Mean ( 36 / 40 )7.0250.055583621752205126.386150785889
Trimmed Mean ( 37 / 40 )7.026086956521740.0549426387405523127.880406139574
Trimmed Mean ( 38 / 40 )7.027272727272730.0540498982876103130.014541190794
Trimmed Mean ( 39 / 40 )7.030952380952380.0533966046628895131.67414717361
Trimmed Mean ( 40 / 40 )7.03250.0531552515677498132.301132862416
Median7
Midrange6.65
Midmean - Weighted Average at Xnp7.02388059701493
Midmean - Weighted Average at X(n+1)p7.02388059701493
Midmean - Empirical Distribution Function7.02388059701493
Midmean - Empirical Distribution Function - Averaging7.02388059701493
Midmean - Empirical Distribution Function - Interpolation7.02388059701493
Midmean - Closest Observation7.02388059701493
Midmean - True Basic - Statistics Graphics Toolkit7.02388059701493
Midmean - MS Excel (old versions)7.02388059701493
Number of observations120

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 6.93416666666667 & 0.078888424499889 & 87.8984047485499 \tabularnewline
Geometric Mean & 6.87859178665138 &  &  \tabularnewline
Harmonic Mean & 6.82099515832114 &  &  \tabularnewline
Quadratic Mean & 6.9873635943752 &  &  \tabularnewline
Winsorized Mean ( 1 / 40 ) & 6.935 & 0.0781405936818526 & 88.7502855204259 \tabularnewline
Winsorized Mean ( 2 / 40 ) & 6.93833333333333 & 0.0775516754919925 & 89.4672267145246 \tabularnewline
Winsorized Mean ( 3 / 40 ) & 6.93833333333333 & 0.0775516754919925 & 89.4672267145246 \tabularnewline
Winsorized Mean ( 4 / 40 ) & 6.93833333333333 & 0.0775516754919925 & 89.4672267145246 \tabularnewline
Winsorized Mean ( 5 / 40 ) & 6.93416666666667 & 0.0770017264288008 & 90.0520934823235 \tabularnewline
Winsorized Mean ( 6 / 40 ) & 6.93416666666667 & 0.0770017264288008 & 90.0520934823235 \tabularnewline
Winsorized Mean ( 7 / 40 ) & 6.94 & 0.0760491511415857 & 91.2567713882742 \tabularnewline
Winsorized Mean ( 8 / 40 ) & 6.94 & 0.0760491511415857 & 91.2567713882742 \tabularnewline
Winsorized Mean ( 9 / 40 ) & 6.9325 & 0.0751204681421353 & 92.2851011375892 \tabularnewline
Winsorized Mean ( 10 / 40 ) & 6.94083333333333 & 0.0738164867502723 & 94.0282264694442 \tabularnewline
Winsorized Mean ( 11 / 40 ) & 6.94083333333333 & 0.0738164867502723 & 94.0282264694442 \tabularnewline
Winsorized Mean ( 12 / 40 ) & 6.95083333333333 & 0.0723262511216169 & 96.10387965008 \tabularnewline
Winsorized Mean ( 13 / 40 ) & 6.94 & 0.0710505402633132 & 97.6769490320605 \tabularnewline
Winsorized Mean ( 14 / 40 ) & 6.95166666666667 & 0.0693808485644683 & 100.195757337952 \tabularnewline
Winsorized Mean ( 15 / 40 ) & 6.95166666666667 & 0.0693808485644683 & 100.195757337952 \tabularnewline
Winsorized Mean ( 16 / 40 ) & 6.95166666666667 & 0.0693808485644683 & 100.195757337952 \tabularnewline
Winsorized Mean ( 17 / 40 ) & 6.95166666666667 & 0.0693808485644683 & 100.195757337952 \tabularnewline
Winsorized Mean ( 18 / 40 ) & 6.93666666666667 & 0.0677151445615223 & 102.438925761495 \tabularnewline
Winsorized Mean ( 19 / 40 ) & 6.9525 & 0.0655291166280335 & 106.097874620603 \tabularnewline
Winsorized Mean ( 20 / 40 ) & 6.96916666666667 & 0.0633318129701045 & 110.042115326091 \tabularnewline
Winsorized Mean ( 21 / 40 ) & 6.98666666666667 & 0.0611392007423521 & 114.27474651017 \tabularnewline
Winsorized Mean ( 22 / 40 ) & 6.98666666666667 & 0.0611392007423521 & 114.27474651017 \tabularnewline
Winsorized Mean ( 23 / 40 ) & 6.98666666666667 & 0.0611392007423521 & 114.27474651017 \tabularnewline
Winsorized Mean ( 24 / 40 ) & 7.00666666666667 & 0.0587657045382646 & 119.230539678195 \tabularnewline
Winsorized Mean ( 25 / 40 ) & 7.00666666666667 & 0.0587657045382646 & 119.230539678195 \tabularnewline
Winsorized Mean ( 26 / 40 ) & 6.985 & 0.056380683860743 & 123.889948147003 \tabularnewline
Winsorized Mean ( 27 / 40 ) & 7.0075 & 0.0538199417916239 & 130.202667760793 \tabularnewline
Winsorized Mean ( 28 / 40 ) & 7.0075 & 0.0538199417916239 & 130.202667760793 \tabularnewline
Winsorized Mean ( 29 / 40 ) & 7.0075 & 0.0538199417916239 & 130.202667760793 \tabularnewline
Winsorized Mean ( 30 / 40 ) & 7.0075 & 0.0538199417916239 & 130.202667760793 \tabularnewline
Winsorized Mean ( 31 / 40 ) & 6.98166666666667 & 0.0511079394542254 & 136.606303075861 \tabularnewline
Winsorized Mean ( 32 / 40 ) & 6.98166666666667 & 0.0511079394542254 & 136.606303075861 \tabularnewline
Winsorized Mean ( 33 / 40 ) & 6.98166666666667 & 0.0511079394542254 & 136.606303075861 \tabularnewline
Winsorized Mean ( 34 / 40 ) & 7.01 & 0.0480050184117982 & 146.026399570699 \tabularnewline
Winsorized Mean ( 35 / 40 ) & 7.01 & 0.0480050184117982 & 146.026399570699 \tabularnewline
Winsorized Mean ( 36 / 40 ) & 7.01 & 0.0480050184117982 & 146.026399570699 \tabularnewline
Winsorized Mean ( 37 / 40 ) & 7.01 & 0.0480050184117982 & 146.026399570699 \tabularnewline
Winsorized Mean ( 38 / 40 ) & 6.97833333333333 & 0.0448180781685131 & 155.703537913769 \tabularnewline
Winsorized Mean ( 39 / 40 ) & 7.01083333333333 & 0.0413666368723047 & 169.480379924894 \tabularnewline
Winsorized Mean ( 40 / 40 ) & 7.01083333333333 & 0.0413666368723047 & 169.480379924894 \tabularnewline
Trimmed Mean ( 1 / 40 ) & 6.93898305084746 & 0.0773401994050779 & 89.7202632553837 \tabularnewline
Trimmed Mean ( 2 / 40 ) & 6.94310344827586 & 0.076448767157467 & 90.8203455259737 \tabularnewline
Trimmed Mean ( 3 / 40 ) & 6.94561403508772 & 0.075793584965571 & 91.6385474871356 \tabularnewline
Trimmed Mean ( 4 / 40 ) & 6.94821428571429 & 0.0750587730124922 & 92.5703153255366 \tabularnewline
Trimmed Mean ( 5 / 40 ) & 6.95090909090909 & 0.0742349970469762 & 93.6338569059352 \tabularnewline
Trimmed Mean ( 6 / 40 ) & 6.95462962962963 & 0.0734524692995986 & 94.6820399088698 \tabularnewline
Trimmed Mean ( 7 / 40 ) & 6.95849056603774 & 0.0725714064132836 & 95.8847418005122 \tabularnewline
Trimmed Mean ( 8 / 40 ) & 6.96153846153846 & 0.0717760875529808 & 96.9896618619658 \tabularnewline
Trimmed Mean ( 9 / 40 ) & 6.96470588235294 & 0.0708772314849373 & 98.264361296802 \tabularnewline
Trimmed Mean ( 10 / 40 ) & 6.969 & 0.0700172417438315 & 99.532626913484 \tabularnewline
Trimmed Mean ( 11 / 40 ) & 6.97244897959184 & 0.0692568318441585 & 100.675251725075 \tabularnewline
Trimmed Mean ( 12 / 40 ) & 6.97604166666667 & 0.0683891212953472 & 102.005136702075 \tabularnewline
Trimmed Mean ( 13 / 40 ) & 6.97872340425532 & 0.0676241977532428 & 103.198612865181 \tabularnewline
Trimmed Mean ( 14 / 40 ) & 6.98260869565217 & 0.0669199644556308 & 104.342683868007 \tabularnewline
Trimmed Mean ( 15 / 40 ) & 6.98555555555556 & 0.0663392919069414 & 105.300423847675 \tabularnewline
Trimmed Mean ( 16 / 40 ) & 6.98863636363636 & 0.0656618068534734 & 106.433811351426 \tabularnewline
Trimmed Mean ( 17 / 40 ) & 6.99186046511628 & 0.0648731291827087 & 107.777450435979 \tabularnewline
Trimmed Mean ( 18 / 40 ) & 6.9952380952381 & 0.0639560404173495 & 109.375721973878 \tabularnewline
Trimmed Mean ( 19 / 40 ) & 7 & 0.0630930162234764 & 110.947303188136 \tabularnewline
Trimmed Mean ( 20 / 40 ) & 7.00375 & 0.0623750332944281 & 112.28450920323 \tabularnewline
Trimmed Mean ( 21 / 40 ) & 7.00641025641026 & 0.061811367617931 & 113.351484143149 \tabularnewline
Trimmed Mean ( 22 / 40 ) & 7.0078947368421 & 0.0614092729124084 & 114.11785882627 \tabularnewline
Trimmed Mean ( 23 / 40 ) & 7.00945945945946 & 0.0609127452048657 & 115.073773737906 \tabularnewline
Trimmed Mean ( 24 / 40 ) & 7.01111111111111 & 0.0603055455538896 & 116.259807397745 \tabularnewline
Trimmed Mean ( 25 / 40 ) & 7.01142857142857 & 0.0598667553318725 & 117.117230298529 \tabularnewline
Trimmed Mean ( 26 / 40 ) & 7.01176470588235 & 0.0593175044810625 & 118.207344817092 \tabularnewline
Trimmed Mean ( 27 / 40 ) & 7.01363636363636 & 0.0589293110424382 & 119.017789951514 \tabularnewline
Trimmed Mean ( 28 / 40 ) & 7.0140625 & 0.0587513587946547 & 119.385536673548 \tabularnewline
Trimmed Mean ( 29 / 40 ) & 7.01451612903226 & 0.058486407239639 & 119.934125895122 \tabularnewline
Trimmed Mean ( 30 / 40 ) & 7.015 & 0.0581166273357406 & 120.705559176279 \tabularnewline
Trimmed Mean ( 31 / 40 ) & 7.01551724137931 & 0.0576197416584248 & 121.755444218545 \tabularnewline
Trimmed Mean ( 32 / 40 ) & 7.01785714285714 & 0.0573272188279954 & 122.417540678426 \tabularnewline
Trimmed Mean ( 33 / 40 ) & 7.02037037037037 & 0.0569047673580666 & 123.370513514193 \tabularnewline
Trimmed Mean ( 34 / 40 ) & 7.02307692307692 & 0.0563210593303954 & 124.697173784988 \tabularnewline
Trimmed Mean ( 35 / 40 ) & 7.024 & 0.0560291469337384 & 125.363322206329 \tabularnewline
Trimmed Mean ( 36 / 40 ) & 7.025 & 0.055583621752205 & 126.386150785889 \tabularnewline
Trimmed Mean ( 37 / 40 ) & 7.02608695652174 & 0.0549426387405523 & 127.880406139574 \tabularnewline
Trimmed Mean ( 38 / 40 ) & 7.02727272727273 & 0.0540498982876103 & 130.014541190794 \tabularnewline
Trimmed Mean ( 39 / 40 ) & 7.03095238095238 & 0.0533966046628895 & 131.67414717361 \tabularnewline
Trimmed Mean ( 40 / 40 ) & 7.0325 & 0.0531552515677498 & 132.301132862416 \tabularnewline
Median & 7 &  &  \tabularnewline
Midrange & 6.65 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 7.02388059701493 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 7.02388059701493 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 7.02388059701493 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 7.02388059701493 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 7.02388059701493 &  &  \tabularnewline
Midmean - Closest Observation & 7.02388059701493 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 7.02388059701493 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 7.02388059701493 &  &  \tabularnewline
Number of observations & 120 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=111804&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]6.93416666666667[/C][C]0.078888424499889[/C][C]87.8984047485499[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]6.87859178665138[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]6.82099515832114[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]6.9873635943752[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 40 )[/C][C]6.935[/C][C]0.0781405936818526[/C][C]88.7502855204259[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 40 )[/C][C]6.93833333333333[/C][C]0.0775516754919925[/C][C]89.4672267145246[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 40 )[/C][C]6.93833333333333[/C][C]0.0775516754919925[/C][C]89.4672267145246[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 40 )[/C][C]6.93833333333333[/C][C]0.0775516754919925[/C][C]89.4672267145246[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 40 )[/C][C]6.93416666666667[/C][C]0.0770017264288008[/C][C]90.0520934823235[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 40 )[/C][C]6.93416666666667[/C][C]0.0770017264288008[/C][C]90.0520934823235[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 40 )[/C][C]6.94[/C][C]0.0760491511415857[/C][C]91.2567713882742[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 40 )[/C][C]6.94[/C][C]0.0760491511415857[/C][C]91.2567713882742[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 40 )[/C][C]6.9325[/C][C]0.0751204681421353[/C][C]92.2851011375892[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 40 )[/C][C]6.94083333333333[/C][C]0.0738164867502723[/C][C]94.0282264694442[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 40 )[/C][C]6.94083333333333[/C][C]0.0738164867502723[/C][C]94.0282264694442[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 40 )[/C][C]6.95083333333333[/C][C]0.0723262511216169[/C][C]96.10387965008[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 40 )[/C][C]6.94[/C][C]0.0710505402633132[/C][C]97.6769490320605[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 40 )[/C][C]6.95166666666667[/C][C]0.0693808485644683[/C][C]100.195757337952[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 40 )[/C][C]6.95166666666667[/C][C]0.0693808485644683[/C][C]100.195757337952[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 40 )[/C][C]6.95166666666667[/C][C]0.0693808485644683[/C][C]100.195757337952[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 40 )[/C][C]6.95166666666667[/C][C]0.0693808485644683[/C][C]100.195757337952[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 40 )[/C][C]6.93666666666667[/C][C]0.0677151445615223[/C][C]102.438925761495[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 40 )[/C][C]6.9525[/C][C]0.0655291166280335[/C][C]106.097874620603[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 40 )[/C][C]6.96916666666667[/C][C]0.0633318129701045[/C][C]110.042115326091[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 40 )[/C][C]6.98666666666667[/C][C]0.0611392007423521[/C][C]114.27474651017[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 40 )[/C][C]6.98666666666667[/C][C]0.0611392007423521[/C][C]114.27474651017[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 40 )[/C][C]6.98666666666667[/C][C]0.0611392007423521[/C][C]114.27474651017[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 40 )[/C][C]7.00666666666667[/C][C]0.0587657045382646[/C][C]119.230539678195[/C][/ROW]
[ROW][C]Winsorized Mean ( 25 / 40 )[/C][C]7.00666666666667[/C][C]0.0587657045382646[/C][C]119.230539678195[/C][/ROW]
[ROW][C]Winsorized Mean ( 26 / 40 )[/C][C]6.985[/C][C]0.056380683860743[/C][C]123.889948147003[/C][/ROW]
[ROW][C]Winsorized Mean ( 27 / 40 )[/C][C]7.0075[/C][C]0.0538199417916239[/C][C]130.202667760793[/C][/ROW]
[ROW][C]Winsorized Mean ( 28 / 40 )[/C][C]7.0075[/C][C]0.0538199417916239[/C][C]130.202667760793[/C][/ROW]
[ROW][C]Winsorized Mean ( 29 / 40 )[/C][C]7.0075[/C][C]0.0538199417916239[/C][C]130.202667760793[/C][/ROW]
[ROW][C]Winsorized Mean ( 30 / 40 )[/C][C]7.0075[/C][C]0.0538199417916239[/C][C]130.202667760793[/C][/ROW]
[ROW][C]Winsorized Mean ( 31 / 40 )[/C][C]6.98166666666667[/C][C]0.0511079394542254[/C][C]136.606303075861[/C][/ROW]
[ROW][C]Winsorized Mean ( 32 / 40 )[/C][C]6.98166666666667[/C][C]0.0511079394542254[/C][C]136.606303075861[/C][/ROW]
[ROW][C]Winsorized Mean ( 33 / 40 )[/C][C]6.98166666666667[/C][C]0.0511079394542254[/C][C]136.606303075861[/C][/ROW]
[ROW][C]Winsorized Mean ( 34 / 40 )[/C][C]7.01[/C][C]0.0480050184117982[/C][C]146.026399570699[/C][/ROW]
[ROW][C]Winsorized Mean ( 35 / 40 )[/C][C]7.01[/C][C]0.0480050184117982[/C][C]146.026399570699[/C][/ROW]
[ROW][C]Winsorized Mean ( 36 / 40 )[/C][C]7.01[/C][C]0.0480050184117982[/C][C]146.026399570699[/C][/ROW]
[ROW][C]Winsorized Mean ( 37 / 40 )[/C][C]7.01[/C][C]0.0480050184117982[/C][C]146.026399570699[/C][/ROW]
[ROW][C]Winsorized Mean ( 38 / 40 )[/C][C]6.97833333333333[/C][C]0.0448180781685131[/C][C]155.703537913769[/C][/ROW]
[ROW][C]Winsorized Mean ( 39 / 40 )[/C][C]7.01083333333333[/C][C]0.0413666368723047[/C][C]169.480379924894[/C][/ROW]
[ROW][C]Winsorized Mean ( 40 / 40 )[/C][C]7.01083333333333[/C][C]0.0413666368723047[/C][C]169.480379924894[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 40 )[/C][C]6.93898305084746[/C][C]0.0773401994050779[/C][C]89.7202632553837[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 40 )[/C][C]6.94310344827586[/C][C]0.076448767157467[/C][C]90.8203455259737[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 40 )[/C][C]6.94561403508772[/C][C]0.075793584965571[/C][C]91.6385474871356[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 40 )[/C][C]6.94821428571429[/C][C]0.0750587730124922[/C][C]92.5703153255366[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 40 )[/C][C]6.95090909090909[/C][C]0.0742349970469762[/C][C]93.6338569059352[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 40 )[/C][C]6.95462962962963[/C][C]0.0734524692995986[/C][C]94.6820399088698[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 40 )[/C][C]6.95849056603774[/C][C]0.0725714064132836[/C][C]95.8847418005122[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 40 )[/C][C]6.96153846153846[/C][C]0.0717760875529808[/C][C]96.9896618619658[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 40 )[/C][C]6.96470588235294[/C][C]0.0708772314849373[/C][C]98.264361296802[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 40 )[/C][C]6.969[/C][C]0.0700172417438315[/C][C]99.532626913484[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 40 )[/C][C]6.97244897959184[/C][C]0.0692568318441585[/C][C]100.675251725075[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 40 )[/C][C]6.97604166666667[/C][C]0.0683891212953472[/C][C]102.005136702075[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 40 )[/C][C]6.97872340425532[/C][C]0.0676241977532428[/C][C]103.198612865181[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 40 )[/C][C]6.98260869565217[/C][C]0.0669199644556308[/C][C]104.342683868007[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 40 )[/C][C]6.98555555555556[/C][C]0.0663392919069414[/C][C]105.300423847675[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 40 )[/C][C]6.98863636363636[/C][C]0.0656618068534734[/C][C]106.433811351426[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 40 )[/C][C]6.99186046511628[/C][C]0.0648731291827087[/C][C]107.777450435979[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 40 )[/C][C]6.9952380952381[/C][C]0.0639560404173495[/C][C]109.375721973878[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 40 )[/C][C]7[/C][C]0.0630930162234764[/C][C]110.947303188136[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 40 )[/C][C]7.00375[/C][C]0.0623750332944281[/C][C]112.28450920323[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 40 )[/C][C]7.00641025641026[/C][C]0.061811367617931[/C][C]113.351484143149[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 40 )[/C][C]7.0078947368421[/C][C]0.0614092729124084[/C][C]114.11785882627[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 40 )[/C][C]7.00945945945946[/C][C]0.0609127452048657[/C][C]115.073773737906[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 40 )[/C][C]7.01111111111111[/C][C]0.0603055455538896[/C][C]116.259807397745[/C][/ROW]
[ROW][C]Trimmed Mean ( 25 / 40 )[/C][C]7.01142857142857[/C][C]0.0598667553318725[/C][C]117.117230298529[/C][/ROW]
[ROW][C]Trimmed Mean ( 26 / 40 )[/C][C]7.01176470588235[/C][C]0.0593175044810625[/C][C]118.207344817092[/C][/ROW]
[ROW][C]Trimmed Mean ( 27 / 40 )[/C][C]7.01363636363636[/C][C]0.0589293110424382[/C][C]119.017789951514[/C][/ROW]
[ROW][C]Trimmed Mean ( 28 / 40 )[/C][C]7.0140625[/C][C]0.0587513587946547[/C][C]119.385536673548[/C][/ROW]
[ROW][C]Trimmed Mean ( 29 / 40 )[/C][C]7.01451612903226[/C][C]0.058486407239639[/C][C]119.934125895122[/C][/ROW]
[ROW][C]Trimmed Mean ( 30 / 40 )[/C][C]7.015[/C][C]0.0581166273357406[/C][C]120.705559176279[/C][/ROW]
[ROW][C]Trimmed Mean ( 31 / 40 )[/C][C]7.01551724137931[/C][C]0.0576197416584248[/C][C]121.755444218545[/C][/ROW]
[ROW][C]Trimmed Mean ( 32 / 40 )[/C][C]7.01785714285714[/C][C]0.0573272188279954[/C][C]122.417540678426[/C][/ROW]
[ROW][C]Trimmed Mean ( 33 / 40 )[/C][C]7.02037037037037[/C][C]0.0569047673580666[/C][C]123.370513514193[/C][/ROW]
[ROW][C]Trimmed Mean ( 34 / 40 )[/C][C]7.02307692307692[/C][C]0.0563210593303954[/C][C]124.697173784988[/C][/ROW]
[ROW][C]Trimmed Mean ( 35 / 40 )[/C][C]7.024[/C][C]0.0560291469337384[/C][C]125.363322206329[/C][/ROW]
[ROW][C]Trimmed Mean ( 36 / 40 )[/C][C]7.025[/C][C]0.055583621752205[/C][C]126.386150785889[/C][/ROW]
[ROW][C]Trimmed Mean ( 37 / 40 )[/C][C]7.02608695652174[/C][C]0.0549426387405523[/C][C]127.880406139574[/C][/ROW]
[ROW][C]Trimmed Mean ( 38 / 40 )[/C][C]7.02727272727273[/C][C]0.0540498982876103[/C][C]130.014541190794[/C][/ROW]
[ROW][C]Trimmed Mean ( 39 / 40 )[/C][C]7.03095238095238[/C][C]0.0533966046628895[/C][C]131.67414717361[/C][/ROW]
[ROW][C]Trimmed Mean ( 40 / 40 )[/C][C]7.0325[/C][C]0.0531552515677498[/C][C]132.301132862416[/C][/ROW]
[ROW][C]Median[/C][C]7[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]6.65[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]7.02388059701493[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]7.02388059701493[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]7.02388059701493[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]7.02388059701493[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]7.02388059701493[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]7.02388059701493[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]7.02388059701493[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]7.02388059701493[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]120[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=111804&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=111804&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 Mean6.934166666666670.07888842449988987.8984047485499
Geometric Mean6.87859178665138
Harmonic Mean6.82099515832114
Quadratic Mean6.9873635943752
Winsorized Mean ( 1 / 40 )6.9350.078140593681852688.7502855204259
Winsorized Mean ( 2 / 40 )6.938333333333330.077551675491992589.4672267145246
Winsorized Mean ( 3 / 40 )6.938333333333330.077551675491992589.4672267145246
Winsorized Mean ( 4 / 40 )6.938333333333330.077551675491992589.4672267145246
Winsorized Mean ( 5 / 40 )6.934166666666670.077001726428800890.0520934823235
Winsorized Mean ( 6 / 40 )6.934166666666670.077001726428800890.0520934823235
Winsorized Mean ( 7 / 40 )6.940.076049151141585791.2567713882742
Winsorized Mean ( 8 / 40 )6.940.076049151141585791.2567713882742
Winsorized Mean ( 9 / 40 )6.93250.075120468142135392.2851011375892
Winsorized Mean ( 10 / 40 )6.940833333333330.073816486750272394.0282264694442
Winsorized Mean ( 11 / 40 )6.940833333333330.073816486750272394.0282264694442
Winsorized Mean ( 12 / 40 )6.950833333333330.072326251121616996.10387965008
Winsorized Mean ( 13 / 40 )6.940.071050540263313297.6769490320605
Winsorized Mean ( 14 / 40 )6.951666666666670.0693808485644683100.195757337952
Winsorized Mean ( 15 / 40 )6.951666666666670.0693808485644683100.195757337952
Winsorized Mean ( 16 / 40 )6.951666666666670.0693808485644683100.195757337952
Winsorized Mean ( 17 / 40 )6.951666666666670.0693808485644683100.195757337952
Winsorized Mean ( 18 / 40 )6.936666666666670.0677151445615223102.438925761495
Winsorized Mean ( 19 / 40 )6.95250.0655291166280335106.097874620603
Winsorized Mean ( 20 / 40 )6.969166666666670.0633318129701045110.042115326091
Winsorized Mean ( 21 / 40 )6.986666666666670.0611392007423521114.27474651017
Winsorized Mean ( 22 / 40 )6.986666666666670.0611392007423521114.27474651017
Winsorized Mean ( 23 / 40 )6.986666666666670.0611392007423521114.27474651017
Winsorized Mean ( 24 / 40 )7.006666666666670.0587657045382646119.230539678195
Winsorized Mean ( 25 / 40 )7.006666666666670.0587657045382646119.230539678195
Winsorized Mean ( 26 / 40 )6.9850.056380683860743123.889948147003
Winsorized Mean ( 27 / 40 )7.00750.0538199417916239130.202667760793
Winsorized Mean ( 28 / 40 )7.00750.0538199417916239130.202667760793
Winsorized Mean ( 29 / 40 )7.00750.0538199417916239130.202667760793
Winsorized Mean ( 30 / 40 )7.00750.0538199417916239130.202667760793
Winsorized Mean ( 31 / 40 )6.981666666666670.0511079394542254136.606303075861
Winsorized Mean ( 32 / 40 )6.981666666666670.0511079394542254136.606303075861
Winsorized Mean ( 33 / 40 )6.981666666666670.0511079394542254136.606303075861
Winsorized Mean ( 34 / 40 )7.010.0480050184117982146.026399570699
Winsorized Mean ( 35 / 40 )7.010.0480050184117982146.026399570699
Winsorized Mean ( 36 / 40 )7.010.0480050184117982146.026399570699
Winsorized Mean ( 37 / 40 )7.010.0480050184117982146.026399570699
Winsorized Mean ( 38 / 40 )6.978333333333330.0448180781685131155.703537913769
Winsorized Mean ( 39 / 40 )7.010833333333330.0413666368723047169.480379924894
Winsorized Mean ( 40 / 40 )7.010833333333330.0413666368723047169.480379924894
Trimmed Mean ( 1 / 40 )6.938983050847460.077340199405077989.7202632553837
Trimmed Mean ( 2 / 40 )6.943103448275860.07644876715746790.8203455259737
Trimmed Mean ( 3 / 40 )6.945614035087720.07579358496557191.6385474871356
Trimmed Mean ( 4 / 40 )6.948214285714290.075058773012492292.5703153255366
Trimmed Mean ( 5 / 40 )6.950909090909090.074234997046976293.6338569059352
Trimmed Mean ( 6 / 40 )6.954629629629630.073452469299598694.6820399088698
Trimmed Mean ( 7 / 40 )6.958490566037740.072571406413283695.8847418005122
Trimmed Mean ( 8 / 40 )6.961538461538460.071776087552980896.9896618619658
Trimmed Mean ( 9 / 40 )6.964705882352940.070877231484937398.264361296802
Trimmed Mean ( 10 / 40 )6.9690.070017241743831599.532626913484
Trimmed Mean ( 11 / 40 )6.972448979591840.0692568318441585100.675251725075
Trimmed Mean ( 12 / 40 )6.976041666666670.0683891212953472102.005136702075
Trimmed Mean ( 13 / 40 )6.978723404255320.0676241977532428103.198612865181
Trimmed Mean ( 14 / 40 )6.982608695652170.0669199644556308104.342683868007
Trimmed Mean ( 15 / 40 )6.985555555555560.0663392919069414105.300423847675
Trimmed Mean ( 16 / 40 )6.988636363636360.0656618068534734106.433811351426
Trimmed Mean ( 17 / 40 )6.991860465116280.0648731291827087107.777450435979
Trimmed Mean ( 18 / 40 )6.99523809523810.0639560404173495109.375721973878
Trimmed Mean ( 19 / 40 )70.0630930162234764110.947303188136
Trimmed Mean ( 20 / 40 )7.003750.0623750332944281112.28450920323
Trimmed Mean ( 21 / 40 )7.006410256410260.061811367617931113.351484143149
Trimmed Mean ( 22 / 40 )7.00789473684210.0614092729124084114.11785882627
Trimmed Mean ( 23 / 40 )7.009459459459460.0609127452048657115.073773737906
Trimmed Mean ( 24 / 40 )7.011111111111110.0603055455538896116.259807397745
Trimmed Mean ( 25 / 40 )7.011428571428570.0598667553318725117.117230298529
Trimmed Mean ( 26 / 40 )7.011764705882350.0593175044810625118.207344817092
Trimmed Mean ( 27 / 40 )7.013636363636360.0589293110424382119.017789951514
Trimmed Mean ( 28 / 40 )7.01406250.0587513587946547119.385536673548
Trimmed Mean ( 29 / 40 )7.014516129032260.058486407239639119.934125895122
Trimmed Mean ( 30 / 40 )7.0150.0581166273357406120.705559176279
Trimmed Mean ( 31 / 40 )7.015517241379310.0576197416584248121.755444218545
Trimmed Mean ( 32 / 40 )7.017857142857140.0573272188279954122.417540678426
Trimmed Mean ( 33 / 40 )7.020370370370370.0569047673580666123.370513514193
Trimmed Mean ( 34 / 40 )7.023076923076920.0563210593303954124.697173784988
Trimmed Mean ( 35 / 40 )7.0240.0560291469337384125.363322206329
Trimmed Mean ( 36 / 40 )7.0250.055583621752205126.386150785889
Trimmed Mean ( 37 / 40 )7.026086956521740.0549426387405523127.880406139574
Trimmed Mean ( 38 / 40 )7.027272727272730.0540498982876103130.014541190794
Trimmed Mean ( 39 / 40 )7.030952380952380.0533966046628895131.67414717361
Trimmed Mean ( 40 / 40 )7.03250.0531552515677498132.301132862416
Median7
Midrange6.65
Midmean - Weighted Average at Xnp7.02388059701493
Midmean - Weighted Average at X(n+1)p7.02388059701493
Midmean - Empirical Distribution Function7.02388059701493
Midmean - Empirical Distribution Function - Averaging7.02388059701493
Midmean - Empirical Distribution Function - Interpolation7.02388059701493
Midmean - Closest Observation7.02388059701493
Midmean - True Basic - Statistics Graphics Toolkit7.02388059701493
Midmean - MS Excel (old versions)7.02388059701493
Number of observations120



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')