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R Software Module

rwasp_centraltendency.wasp

Title produced by software

Central Tendency

Date of computation

Mon, 08 Oct 2012 03:50:20 -0400

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/Oct/08/t1349682703r3jsjafje2locfi.htm/, Retrieved Thu, 02 May 2024 07:55:40 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=173256, Retrieved Thu, 02 May 2024 07:55:40 +0000

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Estimated Impact

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

-       [Central Tendency] [centrummaten gemi...] [2012-10-08 07:50:20] [d083c6d046cc71723436dadeef11a810] [Current]

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Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 seconds
R Server	'Gwilym Jenkins' @ jenkins.wessa.net

\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' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=173256&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' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=173256&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=173256&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 Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 seconds
R Server	'Gwilym Jenkins' @ jenkins.wessa.net

Central Tendency - Ungrouped Data
Measure	Value	S.E.	Value/S.E.
Arithmetic Mean	82.1815277777778	0.227850888468037	360.681182023594
Geometric Mean	82.1591673503643
Harmonic Mean	82.1368772121001
Quadratic Mean	82.2039509137689
Winsorized Mean ( 1 / 24 )	82.1816666666667	0.227220567353578	361.682340748598
Winsorized Mean ( 2 / 24 )	82.1822222222222	0.226912427371674	362.175942385081
Winsorized Mean ( 3 / 24 )	82.1755555555556	0.222975669115628	368.540459510593
Winsorized Mean ( 4 / 24 )	82.1527777777778	0.216796117181488	378.940263533431
Winsorized Mean ( 5 / 24 )	82.1548611111111	0.21601346037868	380.322878801583
Winsorized Mean ( 6 / 24 )	82.1548611111111	0.21601346037868	380.322878801583
Winsorized Mean ( 7 / 24 )	82.1548611111111	0.21601346037868	380.322878801583
Winsorized Mean ( 8 / 24 )	82.15375	0.214709054287326	382.628251392049
Winsorized Mean ( 9 / 24 )	82.1275	0.209702799419815	391.637594859117
Winsorized Mean ( 10 / 24 )	82.1066666666667	0.203142275357836	404.18306097062
Winsorized Mean ( 11 / 24 )	82.1097222222222	0.20220836456586	406.06491427054
Winsorized Mean ( 12 / 24 )	82.1097222222222	0.20220836456586	406.06491427054
Winsorized Mean ( 13 / 24 )	82.0952777777778	0.199325444226394	411.86552021193
Winsorized Mean ( 14 / 24 )	82.0894444444444	0.189524762802985	433.133081030567
Winsorized Mean ( 15 / 24 )	82.0311111111111	0.179566243542202	456.829243029924
Winsorized Mean ( 16 / 24 )	81.9955555555555	0.174541080457212	469.777976283679
Winsorized Mean ( 17 / 24 )	81.9908333333333	0.17186389030818	477.06841260436
Winsorized Mean ( 18 / 24 )	82.0033333333333	0.168599821599863	486.378529675741
Winsorized Mean ( 19 / 24 )	82.0376388888889	0.163639228389471	501.332349805724
Winsorized Mean ( 20 / 24 )	81.9876388888889	0.15002288467261	546.500882634058
Winsorized Mean ( 21 / 24 )	82.0226388888889	0.142739926927481	574.629962719263
Winsorized Mean ( 22 / 24 )	82.0348611111111	0.141055155342898	581.58002741331
Winsorized Mean ( 23 / 24 )	82.0316666666667	0.140639329386435	583.276861632839
Winsorized Mean ( 24 / 24 )	82.0116666666667	0.137168151264934	597.891463217762
Trimmed Mean ( 1 / 24 )	82.1685714285714	0.224600522825735	365.843188585652
Trimmed Mean ( 2 / 24 )	82.1547058823529	0.221411335287263	371.050135151228
Trimmed Mean ( 3 / 24 )	82.139696969697	0.217730610236345	377.253785678251
Trimmed Mean ( 4 / 24 )	82.12625	0.215014130672588	381.957454345442
Trimmed Mean ( 5 / 24 )	82.1185483870968	0.213827629762445	384.040867301984
Trimmed Mean ( 6 / 24 )	82.1098333333333	0.21244826444552	386.493311901777
Trimmed Mean ( 7 / 24 )	82.1005172413793	0.210593093053238	389.85379838941
Trimmed Mean ( 8 / 24 )	82.0905357142857	0.208155539316727	394.371132201184
Trimmed Mean ( 9 / 24 )	82.08	0.205305417525716	399.794613260601
Trimmed Mean ( 10 / 24 )	82.0726923076923	0.202770426358919	404.756718134119
Trimmed Mean ( 11 / 24 )	82.0678	0.200853340748407	408.595643439158
Trimmed Mean ( 12 / 24 )	82.0620833333333	0.198407212162415	413.604336450017
Trimmed Mean ( 13 / 24 )	82.0558695652174	0.195078722146954	420.629521570293
Trimmed Mean ( 14 / 24 )	82.0509090909091	0.191248766576138	429.027128173629
Trimmed Mean ( 15 / 24 )	82.0461904761905	0.18824421098954	435.849740318173
Trimmed Mean ( 16 / 24 )	82.048	0.186221951940729	440.59252491411
Trimmed Mean ( 17 / 24 )	82.0542105263158	0.184252992463389	445.334479669956
Trimmed Mean ( 18 / 24 )	82.0616666666667	0.181788513091624	451.412827307226
Trimmed Mean ( 19 / 24 )	82.0685294117647	0.178786826904774	459.030068560232
Trimmed Mean ( 20 / 24 )	82.0721875	0.1754698384011	467.728176237299
Trimmed Mean ( 21 / 24 )	82.0823333333333	0.173830861996297	472.196550087188
Trimmed Mean ( 22 / 24 )	82.0896428571429	0.172774191364955	475.126766379957
Trimmed Mean ( 23 / 24 )	82.0965384615385	0.170784562721299	480.702337221841
Trimmed Mean ( 24 / 24 )	82.105	0.166876679278312	492.010030131699
Median	82.32
Midrange	82.635
Midmean - Weighted Average at Xnp	82.0108108108108
Midmean - Weighted Average at X(n+1)p	82.0616666666667
Midmean - Empirical Distribution Function	82.0108108108108
Midmean - Empirical Distribution Function - Averaging	82.0616666666667
Midmean - Empirical Distribution Function - Interpolation	82.0616666666667
Midmean - Closest Observation	82.0108108108108
Midmean - True Basic - Statistics Graphics Toolkit	82.0616666666667
Midmean - MS Excel (old versions)	82.0542105263158
Number of observations	72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 82.1815277777778 & 0.227850888468037 & 360.681182023594 \tabularnewline
Geometric Mean & 82.1591673503643 &  &  \tabularnewline
Harmonic Mean & 82.1368772121001 &  &  \tabularnewline
Quadratic Mean & 82.2039509137689 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 82.1816666666667 & 0.227220567353578 & 361.682340748598 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 82.1822222222222 & 0.226912427371674 & 362.175942385081 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 82.1755555555556 & 0.222975669115628 & 368.540459510593 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 82.1527777777778 & 0.216796117181488 & 378.940263533431 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 82.1548611111111 & 0.21601346037868 & 380.322878801583 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 82.1548611111111 & 0.21601346037868 & 380.322878801583 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 82.1548611111111 & 0.21601346037868 & 380.322878801583 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 82.15375 & 0.214709054287326 & 382.628251392049 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 82.1275 & 0.209702799419815 & 391.637594859117 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 82.1066666666667 & 0.203142275357836 & 404.18306097062 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 82.1097222222222 & 0.20220836456586 & 406.06491427054 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 82.1097222222222 & 0.20220836456586 & 406.06491427054 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 82.0952777777778 & 0.199325444226394 & 411.86552021193 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 82.0894444444444 & 0.189524762802985 & 433.133081030567 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 82.0311111111111 & 0.179566243542202 & 456.829243029924 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 81.9955555555555 & 0.174541080457212 & 469.777976283679 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 81.9908333333333 & 0.17186389030818 & 477.06841260436 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 82.0033333333333 & 0.168599821599863 & 486.378529675741 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 82.0376388888889 & 0.163639228389471 & 501.332349805724 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 81.9876388888889 & 0.15002288467261 & 546.500882634058 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 82.0226388888889 & 0.142739926927481 & 574.629962719263 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 82.0348611111111 & 0.141055155342898 & 581.58002741331 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 82.0316666666667 & 0.140639329386435 & 583.276861632839 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 82.0116666666667 & 0.137168151264934 & 597.891463217762 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 82.1685714285714 & 0.224600522825735 & 365.843188585652 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 82.1547058823529 & 0.221411335287263 & 371.050135151228 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 82.139696969697 & 0.217730610236345 & 377.253785678251 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 82.12625 & 0.215014130672588 & 381.957454345442 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 82.1185483870968 & 0.213827629762445 & 384.040867301984 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 82.1098333333333 & 0.21244826444552 & 386.493311901777 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 82.1005172413793 & 0.210593093053238 & 389.85379838941 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 82.0905357142857 & 0.208155539316727 & 394.371132201184 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 82.08 & 0.205305417525716 & 399.794613260601 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 82.0726923076923 & 0.202770426358919 & 404.756718134119 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 82.0678 & 0.200853340748407 & 408.595643439158 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 82.0620833333333 & 0.198407212162415 & 413.604336450017 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 82.0558695652174 & 0.195078722146954 & 420.629521570293 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 82.0509090909091 & 0.191248766576138 & 429.027128173629 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 82.0461904761905 & 0.18824421098954 & 435.849740318173 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 82.048 & 0.186221951940729 & 440.59252491411 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 82.0542105263158 & 0.184252992463389 & 445.334479669956 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 82.0616666666667 & 0.181788513091624 & 451.412827307226 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 82.0685294117647 & 0.178786826904774 & 459.030068560232 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 82.0721875 & 0.1754698384011 & 467.728176237299 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 82.0823333333333 & 0.173830861996297 & 472.196550087188 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 82.0896428571429 & 0.172774191364955 & 475.126766379957 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 82.0965384615385 & 0.170784562721299 & 480.702337221841 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 82.105 & 0.166876679278312 & 492.010030131699 \tabularnewline
Median & 82.32 &  &  \tabularnewline
Midrange & 82.635 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 82.0108108108108 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 82.0616666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 82.0108108108108 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 82.0616666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 82.0616666666667 &  &  \tabularnewline
Midmean - Closest Observation & 82.0108108108108 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 82.0616666666667 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 82.0542105263158 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=173256&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]82.1815277777778[/C][C]0.227850888468037[/C][C]360.681182023594[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]82.1591673503643[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]82.1368772121001[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]82.2039509137689[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]82.1816666666667[/C][C]0.227220567353578[/C][C]361.682340748598[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]82.1822222222222[/C][C]0.226912427371674[/C][C]362.175942385081[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]82.1755555555556[/C][C]0.222975669115628[/C][C]368.540459510593[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]82.1527777777778[/C][C]0.216796117181488[/C][C]378.940263533431[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]82.1548611111111[/C][C]0.21601346037868[/C][C]380.322878801583[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]82.1548611111111[/C][C]0.21601346037868[/C][C]380.322878801583[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]82.1548611111111[/C][C]0.21601346037868[/C][C]380.322878801583[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]82.15375[/C][C]0.214709054287326[/C][C]382.628251392049[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]82.1275[/C][C]0.209702799419815[/C][C]391.637594859117[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]82.1066666666667[/C][C]0.203142275357836[/C][C]404.18306097062[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]82.1097222222222[/C][C]0.20220836456586[/C][C]406.06491427054[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]82.1097222222222[/C][C]0.20220836456586[/C][C]406.06491427054[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]82.0952777777778[/C][C]0.199325444226394[/C][C]411.86552021193[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]82.0894444444444[/C][C]0.189524762802985[/C][C]433.133081030567[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]82.0311111111111[/C][C]0.179566243542202[/C][C]456.829243029924[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]81.9955555555555[/C][C]0.174541080457212[/C][C]469.777976283679[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]81.9908333333333[/C][C]0.17186389030818[/C][C]477.06841260436[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]82.0033333333333[/C][C]0.168599821599863[/C][C]486.378529675741[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]82.0376388888889[/C][C]0.163639228389471[/C][C]501.332349805724[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]81.9876388888889[/C][C]0.15002288467261[/C][C]546.500882634058[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]82.0226388888889[/C][C]0.142739926927481[/C][C]574.629962719263[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]82.0348611111111[/C][C]0.141055155342898[/C][C]581.58002741331[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]82.0316666666667[/C][C]0.140639329386435[/C][C]583.276861632839[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]82.0116666666667[/C][C]0.137168151264934[/C][C]597.891463217762[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]82.1685714285714[/C][C]0.224600522825735[/C][C]365.843188585652[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]82.1547058823529[/C][C]0.221411335287263[/C][C]371.050135151228[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]82.139696969697[/C][C]0.217730610236345[/C][C]377.253785678251[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]82.12625[/C][C]0.215014130672588[/C][C]381.957454345442[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]82.1185483870968[/C][C]0.213827629762445[/C][C]384.040867301984[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]82.1098333333333[/C][C]0.21244826444552[/C][C]386.493311901777[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]82.1005172413793[/C][C]0.210593093053238[/C][C]389.85379838941[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]82.0905357142857[/C][C]0.208155539316727[/C][C]394.371132201184[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]82.08[/C][C]0.205305417525716[/C][C]399.794613260601[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]82.0726923076923[/C][C]0.202770426358919[/C][C]404.756718134119[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]82.0678[/C][C]0.200853340748407[/C][C]408.595643439158[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]82.0620833333333[/C][C]0.198407212162415[/C][C]413.604336450017[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]82.0558695652174[/C][C]0.195078722146954[/C][C]420.629521570293[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]82.0509090909091[/C][C]0.191248766576138[/C][C]429.027128173629[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]82.0461904761905[/C][C]0.18824421098954[/C][C]435.849740318173[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]82.048[/C][C]0.186221951940729[/C][C]440.59252491411[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]82.0542105263158[/C][C]0.184252992463389[/C][C]445.334479669956[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]82.0616666666667[/C][C]0.181788513091624[/C][C]451.412827307226[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]82.0685294117647[/C][C]0.178786826904774[/C][C]459.030068560232[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]82.0721875[/C][C]0.1754698384011[/C][C]467.728176237299[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]82.0823333333333[/C][C]0.173830861996297[/C][C]472.196550087188[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]82.0896428571429[/C][C]0.172774191364955[/C][C]475.126766379957[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]82.0965384615385[/C][C]0.170784562721299[/C][C]480.702337221841[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]82.105[/C][C]0.166876679278312[/C][C]492.010030131699[/C][/ROW]
[ROW][C]Median[/C][C]82.32[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]82.635[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]82.0108108108108[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]82.0616666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]82.0108108108108[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]82.0616666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]82.0616666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]82.0108108108108[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]82.0616666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]82.0542105263158[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]72[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=173256&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=173256&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
Measure	Value	S.E.	Value/S.E.
Arithmetic Mean	82.1815277777778	0.227850888468037	360.681182023594
Geometric Mean	82.1591673503643
Harmonic Mean	82.1368772121001
Quadratic Mean	82.2039509137689
Winsorized Mean ( 1 / 24 )	82.1816666666667	0.227220567353578	361.682340748598
Winsorized Mean ( 2 / 24 )	82.1822222222222	0.226912427371674	362.175942385081
Winsorized Mean ( 3 / 24 )	82.1755555555556	0.222975669115628	368.540459510593
Winsorized Mean ( 4 / 24 )	82.1527777777778	0.216796117181488	378.940263533431
Winsorized Mean ( 5 / 24 )	82.1548611111111	0.21601346037868	380.322878801583
Winsorized Mean ( 6 / 24 )	82.1548611111111	0.21601346037868	380.322878801583
Winsorized Mean ( 7 / 24 )	82.1548611111111	0.21601346037868	380.322878801583
Winsorized Mean ( 8 / 24 )	82.15375	0.214709054287326	382.628251392049
Winsorized Mean ( 9 / 24 )	82.1275	0.209702799419815	391.637594859117
Winsorized Mean ( 10 / 24 )	82.1066666666667	0.203142275357836	404.18306097062
Winsorized Mean ( 11 / 24 )	82.1097222222222	0.20220836456586	406.06491427054
Winsorized Mean ( 12 / 24 )	82.1097222222222	0.20220836456586	406.06491427054
Winsorized Mean ( 13 / 24 )	82.0952777777778	0.199325444226394	411.86552021193
Winsorized Mean ( 14 / 24 )	82.0894444444444	0.189524762802985	433.133081030567
Winsorized Mean ( 15 / 24 )	82.0311111111111	0.179566243542202	456.829243029924
Winsorized Mean ( 16 / 24 )	81.9955555555555	0.174541080457212	469.777976283679
Winsorized Mean ( 17 / 24 )	81.9908333333333	0.17186389030818	477.06841260436
Winsorized Mean ( 18 / 24 )	82.0033333333333	0.168599821599863	486.378529675741
Winsorized Mean ( 19 / 24 )	82.0376388888889	0.163639228389471	501.332349805724
Winsorized Mean ( 20 / 24 )	81.9876388888889	0.15002288467261	546.500882634058
Winsorized Mean ( 21 / 24 )	82.0226388888889	0.142739926927481	574.629962719263
Winsorized Mean ( 22 / 24 )	82.0348611111111	0.141055155342898	581.58002741331
Winsorized Mean ( 23 / 24 )	82.0316666666667	0.140639329386435	583.276861632839
Winsorized Mean ( 24 / 24 )	82.0116666666667	0.137168151264934	597.891463217762
Trimmed Mean ( 1 / 24 )	82.1685714285714	0.224600522825735	365.843188585652
Trimmed Mean ( 2 / 24 )	82.1547058823529	0.221411335287263	371.050135151228
Trimmed Mean ( 3 / 24 )	82.139696969697	0.217730610236345	377.253785678251
Trimmed Mean ( 4 / 24 )	82.12625	0.215014130672588	381.957454345442
Trimmed Mean ( 5 / 24 )	82.1185483870968	0.213827629762445	384.040867301984
Trimmed Mean ( 6 / 24 )	82.1098333333333	0.21244826444552	386.493311901777
Trimmed Mean ( 7 / 24 )	82.1005172413793	0.210593093053238	389.85379838941
Trimmed Mean ( 8 / 24 )	82.0905357142857	0.208155539316727	394.371132201184
Trimmed Mean ( 9 / 24 )	82.08	0.205305417525716	399.794613260601
Trimmed Mean ( 10 / 24 )	82.0726923076923	0.202770426358919	404.756718134119
Trimmed Mean ( 11 / 24 )	82.0678	0.200853340748407	408.595643439158
Trimmed Mean ( 12 / 24 )	82.0620833333333	0.198407212162415	413.604336450017
Trimmed Mean ( 13 / 24 )	82.0558695652174	0.195078722146954	420.629521570293
Trimmed Mean ( 14 / 24 )	82.0509090909091	0.191248766576138	429.027128173629
Trimmed Mean ( 15 / 24 )	82.0461904761905	0.18824421098954	435.849740318173
Trimmed Mean ( 16 / 24 )	82.048	0.186221951940729	440.59252491411
Trimmed Mean ( 17 / 24 )	82.0542105263158	0.184252992463389	445.334479669956
Trimmed Mean ( 18 / 24 )	82.0616666666667	0.181788513091624	451.412827307226
Trimmed Mean ( 19 / 24 )	82.0685294117647	0.178786826904774	459.030068560232
Trimmed Mean ( 20 / 24 )	82.0721875	0.1754698384011	467.728176237299
Trimmed Mean ( 21 / 24 )	82.0823333333333	0.173830861996297	472.196550087188
Trimmed Mean ( 22 / 24 )	82.0896428571429	0.172774191364955	475.126766379957
Trimmed Mean ( 23 / 24 )	82.0965384615385	0.170784562721299	480.702337221841
Trimmed Mean ( 24 / 24 )	82.105	0.166876679278312	492.010030131699
Median	82.32
Midrange	82.635
Midmean - Weighted Average at Xnp	82.0108108108108
Midmean - Weighted Average at X(n+1)p	82.0616666666667
Midmean - Empirical Distribution Function	82.0108108108108
Midmean - Empirical Distribution Function - Averaging	82.0616666666667
Midmean - Empirical Distribution Function - Interpolation	82.0616666666667
Midmean - Closest Observation	82.0108108108108
Midmean - True Basic - Statistics Graphics Toolkit	82.0616666666667
Midmean - MS Excel (old versions)	82.0542105263158
Number of observations	72

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

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')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code