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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, 20 Oct 2009 11:05:26 -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/20/t1256058582cuyzbio44xgl7j7.htm/, Retrieved Fri, 03 May 2024 02:20:11 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=48833, Retrieved Fri, 03 May 2024 02:20:11 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordscvm Mediaan berekend oef 2
Estimated Impact74
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]
- RMPD        [Central Tendency] [WS 3: Part 2 Yt-X...] [2009-10-20 17:05:26] [a5ada8bd39e806b5b90f09589c89554a] [Current]
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Dataseries X:
29,8
36,2
23,1
25
26,5
24,3
26,3
26
23
27,7
28,2
29,9
26,6
35,7
23,3
28,9
23,5
24,7
29,8
25,2
29,8
28,5
30
29,3
33,2
39,3
32,4
31,1
34,7
31,8
35,8
36
41,3
40
40,3
38
36,3
40,9
34,7
30,4
35,2
34,9
39,6
41,9
37,8
35,4
38,5
43,4
30,9
44,9
36,8
38,3
39,8
36,9
40,2
35,7
36,4
33,5
32,1
32,9
35,7




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=48833&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=48833&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=48833&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 Mean33.08688524590160.73340092364807445.114321756402
Geometric Mean32.5832080320558
Harmonic Mean32.0669800193009
Quadratic Mean33.5710379667346
Winsorized Mean ( 1 / 20 )33.06393442622950.72680915327445245.4919070257556
Winsorized Mean ( 2 / 20 )33.02131147540980.71438809749850446.2232105924455
Winsorized Mean ( 3 / 20 )33.00163934426230.70622328008172646.7297528629236
Winsorized Mean ( 4 / 20 )33.0278688524590.68974189814171547.8843882638445
Winsorized Mean ( 5 / 20 )33.01147540983610.67379967495598948.9930117760777
Winsorized Mean ( 6 / 20 )33.03114754098360.6660319696605249.5939369964774
Winsorized Mean ( 7 / 20 )33.03114754098360.65736076455307750.2481275459764
Winsorized Mean ( 8 / 20 )33.10983606557380.63247585719504452.349565108164
Winsorized Mean ( 9 / 20 )33.12459016393440.61908912349433953.5053660399791
Winsorized Mean ( 10 / 20 )33.10819672131150.60460570668593454.7599805215033
Winsorized Mean ( 11 / 20 )32.98196721311480.57748516502943957.1130986740299
Winsorized Mean ( 12 / 20 )33.15901639344260.53272357757547362.2443191727231
Winsorized Mean ( 13 / 20 )33.20163934426230.50460443742527965.7973590435949
Winsorized Mean ( 14 / 20 )33.22459016393440.48609999048805468.3492919441868
Winsorized Mean ( 15 / 20 )33.10163934426230.43677589133660975.7863242931418
Winsorized Mean ( 16 / 20 )33.18032786885250.41641076079471779.6817253366077
Winsorized Mean ( 17 / 20 )33.20819672131150.37923056327258187.5673005749862
Winsorized Mean ( 18 / 20 )33.17868852459020.37511466191717688.4494579737754
Winsorized Mean ( 19 / 20 )33.14754098360660.37081807771685589.3903047761253
Winsorized Mean ( 20 / 20 )33.11475409836070.35697450633418492.7650392696673
Trimmed Mean ( 1 / 20 )33.05762711864410.71046367993138146.5296510608915
Trimmed Mean ( 2 / 20 )33.05087719298250.69032938093297747.8769672939522
Trimmed Mean ( 3 / 20 )33.06727272727270.6736405666976349.0874130240961
Trimmed Mean ( 4 / 20 )33.09245283018870.65666643429218150.3946160516929
Trimmed Mean ( 5 / 20 )33.11176470588240.64172956895957951.597692092583
Trimmed Mean ( 6 / 20 )33.13673469387750.6280279974853352.7631488190964
Trimmed Mean ( 7 / 20 )33.15957446808510.61267569229293354.1225560034636
Trimmed Mean ( 8 / 20 )33.18444444444440.59517381855936955.755887456152
Trimmed Mean ( 9 / 20 )33.19767441860460.57926031012765057.3104592843397
Trimmed Mean ( 10 / 20 )33.2097560975610.56169174861663259.124521909663
Trimmed Mean ( 11 / 20 )33.2256410256410.54196022916464461.3064192493492
Trimmed Mean ( 12 / 20 )33.26216216216220.52241572378588463.6699100883015
Trimmed Mean ( 13 / 20 )33.27714285714290.50808729671231965.4949318207113
Trimmed Mean ( 14 / 20 )33.28787878787880.49535259816676167.200371838309
Trimmed Mean ( 15 / 20 )33.29677419354840.48174155099627469.1175052778578
Trimmed Mean ( 16 / 20 )33.32413793103450.4753700962245970.1014603057622
Trimmed Mean ( 17 / 20 )33.34444444444440.47020433617607670.9147957154483
Trimmed Mean ( 18 / 20 )33.3640.47134134835240970.7852177973036
Trimmed Mean ( 19 / 20 )33.39130434782610.47038429514357570.9872856993112
Trimmed Mean ( 20 / 20 )33.42857142857140.46583988957697571.7597873787227
Median33.5
Midrange33.95
Midmean - Weighted Average at Xnp33.1766666666667
Midmean - Weighted Average at X(n+1)p33.2967741935484
Midmean - Empirical Distribution Function33.2967741935484
Midmean - Empirical Distribution Function - Averaging33.2967741935484
Midmean - Empirical Distribution Function - Interpolation33.2967741935484
Midmean - Closest Observation33.146875
Midmean - True Basic - Statistics Graphics Toolkit33.2967741935484
Midmean - MS Excel (old versions)33.2967741935484
Number of observations61

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 33.0868852459016 & 0.733400923648074 & 45.114321756402 \tabularnewline
Geometric Mean & 32.5832080320558 &  &  \tabularnewline
Harmonic Mean & 32.0669800193009 &  &  \tabularnewline
Quadratic Mean & 33.5710379667346 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 33.0639344262295 & 0.726809153274452 & 45.4919070257556 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 33.0213114754098 & 0.714388097498504 & 46.2232105924455 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 33.0016393442623 & 0.706223280081726 & 46.7297528629236 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 33.027868852459 & 0.689741898141715 & 47.8843882638445 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 33.0114754098361 & 0.673799674955989 & 48.9930117760777 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 33.0311475409836 & 0.66603196966052 & 49.5939369964774 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 33.0311475409836 & 0.657360764553077 & 50.2481275459764 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 33.1098360655738 & 0.632475857195044 & 52.349565108164 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 33.1245901639344 & 0.619089123494339 & 53.5053660399791 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 33.1081967213115 & 0.604605706685934 & 54.7599805215033 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 32.9819672131148 & 0.577485165029439 & 57.1130986740299 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 33.1590163934426 & 0.532723577575473 & 62.2443191727231 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 33.2016393442623 & 0.504604437425279 & 65.7973590435949 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 33.2245901639344 & 0.486099990488054 & 68.3492919441868 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 33.1016393442623 & 0.436775891336609 & 75.7863242931418 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 33.1803278688525 & 0.416410760794717 & 79.6817253366077 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 33.2081967213115 & 0.379230563272581 & 87.5673005749862 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 33.1786885245902 & 0.375114661917176 & 88.4494579737754 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 33.1475409836066 & 0.370818077716855 & 89.3903047761253 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 33.1147540983607 & 0.356974506334184 & 92.7650392696673 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 33.0576271186441 & 0.710463679931381 & 46.5296510608915 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 33.0508771929825 & 0.690329380932977 & 47.8769672939522 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 33.0672727272727 & 0.67364056669763 & 49.0874130240961 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 33.0924528301887 & 0.656666434292181 & 50.3946160516929 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 33.1117647058824 & 0.641729568959579 & 51.597692092583 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 33.1367346938775 & 0.62802799748533 & 52.7631488190964 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 33.1595744680851 & 0.612675692292933 & 54.1225560034636 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 33.1844444444444 & 0.595173818559369 & 55.755887456152 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 33.1976744186046 & 0.579260310127650 & 57.3104592843397 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 33.209756097561 & 0.561691748616632 & 59.124521909663 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 33.225641025641 & 0.541960229164644 & 61.3064192493492 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 33.2621621621622 & 0.522415723785884 & 63.6699100883015 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 33.2771428571429 & 0.508087296712319 & 65.4949318207113 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 33.2878787878788 & 0.495352598166761 & 67.200371838309 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 33.2967741935484 & 0.481741550996274 & 69.1175052778578 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 33.3241379310345 & 0.47537009622459 & 70.1014603057622 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 33.3444444444444 & 0.470204336176076 & 70.9147957154483 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 33.364 & 0.471341348352409 & 70.7852177973036 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 33.3913043478261 & 0.470384295143575 & 70.9872856993112 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 33.4285714285714 & 0.465839889576975 & 71.7597873787227 \tabularnewline
Median & 33.5 &  &  \tabularnewline
Midrange & 33.95 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 33.1766666666667 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 33.2967741935484 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 33.2967741935484 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 33.2967741935484 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 33.2967741935484 &  &  \tabularnewline
Midmean - Closest Observation & 33.146875 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 33.2967741935484 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 33.2967741935484 &  &  \tabularnewline
Number of observations & 61 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=48833&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]33.0868852459016[/C][C]0.733400923648074[/C][C]45.114321756402[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]32.5832080320558[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]32.0669800193009[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]33.5710379667346[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]33.0639344262295[/C][C]0.726809153274452[/C][C]45.4919070257556[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]33.0213114754098[/C][C]0.714388097498504[/C][C]46.2232105924455[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]33.0016393442623[/C][C]0.706223280081726[/C][C]46.7297528629236[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]33.027868852459[/C][C]0.689741898141715[/C][C]47.8843882638445[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]33.0114754098361[/C][C]0.673799674955989[/C][C]48.9930117760777[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]33.0311475409836[/C][C]0.66603196966052[/C][C]49.5939369964774[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]33.0311475409836[/C][C]0.657360764553077[/C][C]50.2481275459764[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]33.1098360655738[/C][C]0.632475857195044[/C][C]52.349565108164[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]33.1245901639344[/C][C]0.619089123494339[/C][C]53.5053660399791[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]33.1081967213115[/C][C]0.604605706685934[/C][C]54.7599805215033[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]32.9819672131148[/C][C]0.577485165029439[/C][C]57.1130986740299[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]33.1590163934426[/C][C]0.532723577575473[/C][C]62.2443191727231[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]33.2016393442623[/C][C]0.504604437425279[/C][C]65.7973590435949[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]33.2245901639344[/C][C]0.486099990488054[/C][C]68.3492919441868[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]33.1016393442623[/C][C]0.436775891336609[/C][C]75.7863242931418[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]33.1803278688525[/C][C]0.416410760794717[/C][C]79.6817253366077[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]33.2081967213115[/C][C]0.379230563272581[/C][C]87.5673005749862[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]33.1786885245902[/C][C]0.375114661917176[/C][C]88.4494579737754[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]33.1475409836066[/C][C]0.370818077716855[/C][C]89.3903047761253[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]33.1147540983607[/C][C]0.356974506334184[/C][C]92.7650392696673[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]33.0576271186441[/C][C]0.710463679931381[/C][C]46.5296510608915[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]33.0508771929825[/C][C]0.690329380932977[/C][C]47.8769672939522[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]33.0672727272727[/C][C]0.67364056669763[/C][C]49.0874130240961[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]33.0924528301887[/C][C]0.656666434292181[/C][C]50.3946160516929[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]33.1117647058824[/C][C]0.641729568959579[/C][C]51.597692092583[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]33.1367346938775[/C][C]0.62802799748533[/C][C]52.7631488190964[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]33.1595744680851[/C][C]0.612675692292933[/C][C]54.1225560034636[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]33.1844444444444[/C][C]0.595173818559369[/C][C]55.755887456152[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]33.1976744186046[/C][C]0.579260310127650[/C][C]57.3104592843397[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]33.209756097561[/C][C]0.561691748616632[/C][C]59.124521909663[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]33.225641025641[/C][C]0.541960229164644[/C][C]61.3064192493492[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]33.2621621621622[/C][C]0.522415723785884[/C][C]63.6699100883015[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]33.2771428571429[/C][C]0.508087296712319[/C][C]65.4949318207113[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]33.2878787878788[/C][C]0.495352598166761[/C][C]67.200371838309[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]33.2967741935484[/C][C]0.481741550996274[/C][C]69.1175052778578[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]33.3241379310345[/C][C]0.47537009622459[/C][C]70.1014603057622[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]33.3444444444444[/C][C]0.470204336176076[/C][C]70.9147957154483[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]33.364[/C][C]0.471341348352409[/C][C]70.7852177973036[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]33.3913043478261[/C][C]0.470384295143575[/C][C]70.9872856993112[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]33.4285714285714[/C][C]0.465839889576975[/C][C]71.7597873787227[/C][/ROW]
[ROW][C]Median[/C][C]33.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]33.95[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]33.1766666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]33.2967741935484[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]33.2967741935484[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]33.2967741935484[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]33.2967741935484[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]33.146875[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]33.2967741935484[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]33.2967741935484[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]61[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=48833&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=48833&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 Mean33.08688524590160.73340092364807445.114321756402
Geometric Mean32.5832080320558
Harmonic Mean32.0669800193009
Quadratic Mean33.5710379667346
Winsorized Mean ( 1 / 20 )33.06393442622950.72680915327445245.4919070257556
Winsorized Mean ( 2 / 20 )33.02131147540980.71438809749850446.2232105924455
Winsorized Mean ( 3 / 20 )33.00163934426230.70622328008172646.7297528629236
Winsorized Mean ( 4 / 20 )33.0278688524590.68974189814171547.8843882638445
Winsorized Mean ( 5 / 20 )33.01147540983610.67379967495598948.9930117760777
Winsorized Mean ( 6 / 20 )33.03114754098360.6660319696605249.5939369964774
Winsorized Mean ( 7 / 20 )33.03114754098360.65736076455307750.2481275459764
Winsorized Mean ( 8 / 20 )33.10983606557380.63247585719504452.349565108164
Winsorized Mean ( 9 / 20 )33.12459016393440.61908912349433953.5053660399791
Winsorized Mean ( 10 / 20 )33.10819672131150.60460570668593454.7599805215033
Winsorized Mean ( 11 / 20 )32.98196721311480.57748516502943957.1130986740299
Winsorized Mean ( 12 / 20 )33.15901639344260.53272357757547362.2443191727231
Winsorized Mean ( 13 / 20 )33.20163934426230.50460443742527965.7973590435949
Winsorized Mean ( 14 / 20 )33.22459016393440.48609999048805468.3492919441868
Winsorized Mean ( 15 / 20 )33.10163934426230.43677589133660975.7863242931418
Winsorized Mean ( 16 / 20 )33.18032786885250.41641076079471779.6817253366077
Winsorized Mean ( 17 / 20 )33.20819672131150.37923056327258187.5673005749862
Winsorized Mean ( 18 / 20 )33.17868852459020.37511466191717688.4494579737754
Winsorized Mean ( 19 / 20 )33.14754098360660.37081807771685589.3903047761253
Winsorized Mean ( 20 / 20 )33.11475409836070.35697450633418492.7650392696673
Trimmed Mean ( 1 / 20 )33.05762711864410.71046367993138146.5296510608915
Trimmed Mean ( 2 / 20 )33.05087719298250.69032938093297747.8769672939522
Trimmed Mean ( 3 / 20 )33.06727272727270.6736405666976349.0874130240961
Trimmed Mean ( 4 / 20 )33.09245283018870.65666643429218150.3946160516929
Trimmed Mean ( 5 / 20 )33.11176470588240.64172956895957951.597692092583
Trimmed Mean ( 6 / 20 )33.13673469387750.6280279974853352.7631488190964
Trimmed Mean ( 7 / 20 )33.15957446808510.61267569229293354.1225560034636
Trimmed Mean ( 8 / 20 )33.18444444444440.59517381855936955.755887456152
Trimmed Mean ( 9 / 20 )33.19767441860460.57926031012765057.3104592843397
Trimmed Mean ( 10 / 20 )33.2097560975610.56169174861663259.124521909663
Trimmed Mean ( 11 / 20 )33.2256410256410.54196022916464461.3064192493492
Trimmed Mean ( 12 / 20 )33.26216216216220.52241572378588463.6699100883015
Trimmed Mean ( 13 / 20 )33.27714285714290.50808729671231965.4949318207113
Trimmed Mean ( 14 / 20 )33.28787878787880.49535259816676167.200371838309
Trimmed Mean ( 15 / 20 )33.29677419354840.48174155099627469.1175052778578
Trimmed Mean ( 16 / 20 )33.32413793103450.4753700962245970.1014603057622
Trimmed Mean ( 17 / 20 )33.34444444444440.47020433617607670.9147957154483
Trimmed Mean ( 18 / 20 )33.3640.47134134835240970.7852177973036
Trimmed Mean ( 19 / 20 )33.39130434782610.47038429514357570.9872856993112
Trimmed Mean ( 20 / 20 )33.42857142857140.46583988957697571.7597873787227
Median33.5
Midrange33.95
Midmean - Weighted Average at Xnp33.1766666666667
Midmean - Weighted Average at X(n+1)p33.2967741935484
Midmean - Empirical Distribution Function33.2967741935484
Midmean - Empirical Distribution Function - Averaging33.2967741935484
Midmean - Empirical Distribution Function - Interpolation33.2967741935484
Midmean - Closest Observation33.146875
Midmean - True Basic - Statistics Graphics Toolkit33.2967741935484
Midmean - MS Excel (old versions)33.2967741935484
Number of observations61



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')