Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationTue, 03 Aug 2010 17:22:02 +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/Aug/03/t1280856193zs9giiuyvsq82q6.htm/, Retrieved Thu, 02 May 2024 15:39:32 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=78279, Retrieved Thu, 02 May 2024 15:39:32 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsLisa Bruggeman
Estimated Impact108
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [TIJDREEKS B - STAP 9] [2010-08-03 17:22:02] [0e6aef37627b8cf9d1bd74110cef2cca] [Current]
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Dataseries X:
108
115
119
121
123
123
124
124
125
126
126
127
128
129
129
130
131
132
132
132
132
132
132
134
134
135
136
136
136
136
137
137
137
137
138
138
138
139
139
139
139
139
139
140
140
142
142
142
143
144
144
145
145
145
146
146
146
147
147
148
148
149
150
150
151
151
151
152
153
154
155
156
156
156
157
158
158
159
159
160
160
161
162
162




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 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 & 2 seconds \tabularnewline
R Server & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78279&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]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78279&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78279&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'RServer@AstonUniversity' @ vre.aston.ac.uk







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean140.751.30764939130466107.635885380233
Geometric Mean140.23748223639
Harmonic Mean139.716111865038
Quadratic Mean141.253276405321
Winsorized Mean ( 1 / 28 )140.8333333333331.28496238186768109.601133325501
Winsorized Mean ( 2 / 28 )140.9047619047621.25877517073947111.9379895474
Winsorized Mean ( 3 / 28 )140.9404761904761.23760071658812113.882025358735
Winsorized Mean ( 4 / 28 )141.0357142857141.21986879233072115.615478625571
Winsorized Mean ( 5 / 28 )140.976190476191.20894735112177116.610694705092
Winsorized Mean ( 6 / 28 )141.0476190476191.19641661879667117.891725032607
Winsorized Mean ( 7 / 28 )140.9642857142861.18164466573334119.294987572937
Winsorized Mean ( 8 / 28 )141.0595238095241.16550034199134121.029156944316
Winsorized Mean ( 9 / 28 )141.0595238095241.1295020443453124.886470560828
Winsorized Mean ( 10 / 28 )140.9404761904761.10964467268592127.014061041113
Winsorized Mean ( 11 / 28 )141.0714285714291.08882416883992129.5630943991
Winsorized Mean ( 12 / 28 )141.2142857142861.06704016184548132.342053058294
Winsorized Mean ( 13 / 28 )141.2142857142861.01876701891693138.612934156834
Winsorized Mean ( 14 / 28 )141.0476190476190.99206616943605142.17561629765
Winsorized Mean ( 15 / 28 )141.0476190476190.938576081512504150.278301169067
Winsorized Mean ( 16 / 28 )141.0476190476190.883147626898456159.71012631599
Winsorized Mean ( 17 / 28 )141.0476190476190.826085190399344170.742219672809
Winsorized Mean ( 18 / 28 )141.0476190476190.826085190399344170.742219672809
Winsorized Mean ( 19 / 28 )141.0476190476190.826085190399344170.742219672809
Winsorized Mean ( 20 / 28 )140.8095238095240.792151002094543177.755911988
Winsorized Mean ( 21 / 28 )140.8095238095240.792151002094543177.755911988
Winsorized Mean ( 22 / 28 )140.5476190476190.756195440255047185.861500302376
Winsorized Mean ( 23 / 28 )140.8214285714290.647197212942055217.586580651788
Winsorized Mean ( 24 / 28 )140.8214285714290.647197212942055217.586580651788
Winsorized Mean ( 25 / 28 )140.8214285714290.57064364478226246.776477507537
Winsorized Mean ( 26 / 28 )141.1309523809520.533657683009208264.459703053722
Winsorized Mean ( 27 / 28 )140.8095238095240.491895356193459286.259103763818
Winsorized Mean ( 28 / 28 )140.8095238095240.491895356193459286.259103763818
Trimmed Mean ( 1 / 28 )140.8902439024391.25107675365237112.615188069898
Trimmed Mean ( 2 / 28 )140.951.21174369600594116.319977949619
Trimmed Mean ( 3 / 28 )140.9743589743591.18233957028652119.233393279898
Trimmed Mean ( 4 / 28 )140.9868421052631.15735533688144121.818112046004
Trimmed Mean ( 5 / 28 )140.9729729729731.13426210676012124.286064158173
Trimmed Mean ( 6 / 28 )140.9722222222221.110303893008126.96724123006
Trimmed Mean ( 7 / 28 )140.9571428571431.0852742379449129.881589306001
Trimmed Mean ( 8 / 28 )140.9558823529411.05914509554612133.08458203289
Trimmed Mean ( 9 / 28 )140.9393939393941.03163906245753136.616961365978
Trimmed Mean ( 10 / 28 )140.9218751.00650283659285140.011403720471
Trimmed Mean ( 11 / 28 )140.919354838710.980318855923468143.748489572775
Trimmed Mean ( 12 / 28 )140.90.952753962465835147.887078459726
Trimmed Mean ( 13 / 28 )140.8620689655170.923396330914085152.547789339899
Trimmed Mean ( 14 / 28 )140.8214285714290.89700335998775156.990971107791
Trimmed Mean ( 15 / 28 )140.7962962962960.869701037667185161.890454533614
Trimmed Mean ( 16 / 28 )140.7692307692310.846256678243447166.343420841797
Trimmed Mean ( 17 / 28 )140.740.82749190759962170.080213120461
Trimmed Mean ( 18 / 28 )140.7083333333330.814299471227636172.796788288714
Trimmed Mean ( 19 / 28 )140.6739130434780.796765410062804176.556250141921
Trimmed Mean ( 20 / 28 )140.6363636363640.773566265087146181.802606943466
Trimmed Mean ( 21 / 28 )140.6190476190480.750495292091991187.368327424246
Trimmed Mean ( 22 / 28 )140.60.719508379167545195.411205860689
Trimmed Mean ( 23 / 28 )140.6052631578950.686736228984205204.744204868692
Trimmed Mean ( 24 / 28 )140.5833333333330.669488077350363209.986313557249
Trimmed Mean ( 25 / 28 )140.5588235294120.644725171133704218.013550304309
Trimmed Mean ( 26 / 28 )140.531250.630195142268416222.996403136577
Trimmed Mean ( 27 / 28 )140.4666666666670.617248870863589227.568932560607
Trimmed Mean ( 28 / 28 )140.4285714285710.609511408604009230.395312452315
Median139
Midrange135
Midmean - Weighted Average at Xnp140.085106382979
Midmean - Weighted Average at X(n+1)p140.085106382979
Midmean - Empirical Distribution Function140.085106382979
Midmean - Empirical Distribution Function - Averaging140.085106382979
Midmean - Empirical Distribution Function - Interpolation140.085106382979
Midmean - Closest Observation140.085106382979
Midmean - True Basic - Statistics Graphics Toolkit140.085106382979
Midmean - MS Excel (old versions)140.085106382979
Number of observations84

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 140.75 & 1.30764939130466 & 107.635885380233 \tabularnewline
Geometric Mean & 140.23748223639 &  &  \tabularnewline
Harmonic Mean & 139.716111865038 &  &  \tabularnewline
Quadratic Mean & 141.253276405321 &  &  \tabularnewline
Winsorized Mean ( 1 / 28 ) & 140.833333333333 & 1.28496238186768 & 109.601133325501 \tabularnewline
Winsorized Mean ( 2 / 28 ) & 140.904761904762 & 1.25877517073947 & 111.9379895474 \tabularnewline
Winsorized Mean ( 3 / 28 ) & 140.940476190476 & 1.23760071658812 & 113.882025358735 \tabularnewline
Winsorized Mean ( 4 / 28 ) & 141.035714285714 & 1.21986879233072 & 115.615478625571 \tabularnewline
Winsorized Mean ( 5 / 28 ) & 140.97619047619 & 1.20894735112177 & 116.610694705092 \tabularnewline
Winsorized Mean ( 6 / 28 ) & 141.047619047619 & 1.19641661879667 & 117.891725032607 \tabularnewline
Winsorized Mean ( 7 / 28 ) & 140.964285714286 & 1.18164466573334 & 119.294987572937 \tabularnewline
Winsorized Mean ( 8 / 28 ) & 141.059523809524 & 1.16550034199134 & 121.029156944316 \tabularnewline
Winsorized Mean ( 9 / 28 ) & 141.059523809524 & 1.1295020443453 & 124.886470560828 \tabularnewline
Winsorized Mean ( 10 / 28 ) & 140.940476190476 & 1.10964467268592 & 127.014061041113 \tabularnewline
Winsorized Mean ( 11 / 28 ) & 141.071428571429 & 1.08882416883992 & 129.5630943991 \tabularnewline
Winsorized Mean ( 12 / 28 ) & 141.214285714286 & 1.06704016184548 & 132.342053058294 \tabularnewline
Winsorized Mean ( 13 / 28 ) & 141.214285714286 & 1.01876701891693 & 138.612934156834 \tabularnewline
Winsorized Mean ( 14 / 28 ) & 141.047619047619 & 0.99206616943605 & 142.17561629765 \tabularnewline
Winsorized Mean ( 15 / 28 ) & 141.047619047619 & 0.938576081512504 & 150.278301169067 \tabularnewline
Winsorized Mean ( 16 / 28 ) & 141.047619047619 & 0.883147626898456 & 159.71012631599 \tabularnewline
Winsorized Mean ( 17 / 28 ) & 141.047619047619 & 0.826085190399344 & 170.742219672809 \tabularnewline
Winsorized Mean ( 18 / 28 ) & 141.047619047619 & 0.826085190399344 & 170.742219672809 \tabularnewline
Winsorized Mean ( 19 / 28 ) & 141.047619047619 & 0.826085190399344 & 170.742219672809 \tabularnewline
Winsorized Mean ( 20 / 28 ) & 140.809523809524 & 0.792151002094543 & 177.755911988 \tabularnewline
Winsorized Mean ( 21 / 28 ) & 140.809523809524 & 0.792151002094543 & 177.755911988 \tabularnewline
Winsorized Mean ( 22 / 28 ) & 140.547619047619 & 0.756195440255047 & 185.861500302376 \tabularnewline
Winsorized Mean ( 23 / 28 ) & 140.821428571429 & 0.647197212942055 & 217.586580651788 \tabularnewline
Winsorized Mean ( 24 / 28 ) & 140.821428571429 & 0.647197212942055 & 217.586580651788 \tabularnewline
Winsorized Mean ( 25 / 28 ) & 140.821428571429 & 0.57064364478226 & 246.776477507537 \tabularnewline
Winsorized Mean ( 26 / 28 ) & 141.130952380952 & 0.533657683009208 & 264.459703053722 \tabularnewline
Winsorized Mean ( 27 / 28 ) & 140.809523809524 & 0.491895356193459 & 286.259103763818 \tabularnewline
Winsorized Mean ( 28 / 28 ) & 140.809523809524 & 0.491895356193459 & 286.259103763818 \tabularnewline
Trimmed Mean ( 1 / 28 ) & 140.890243902439 & 1.25107675365237 & 112.615188069898 \tabularnewline
Trimmed Mean ( 2 / 28 ) & 140.95 & 1.21174369600594 & 116.319977949619 \tabularnewline
Trimmed Mean ( 3 / 28 ) & 140.974358974359 & 1.18233957028652 & 119.233393279898 \tabularnewline
Trimmed Mean ( 4 / 28 ) & 140.986842105263 & 1.15735533688144 & 121.818112046004 \tabularnewline
Trimmed Mean ( 5 / 28 ) & 140.972972972973 & 1.13426210676012 & 124.286064158173 \tabularnewline
Trimmed Mean ( 6 / 28 ) & 140.972222222222 & 1.110303893008 & 126.96724123006 \tabularnewline
Trimmed Mean ( 7 / 28 ) & 140.957142857143 & 1.0852742379449 & 129.881589306001 \tabularnewline
Trimmed Mean ( 8 / 28 ) & 140.955882352941 & 1.05914509554612 & 133.08458203289 \tabularnewline
Trimmed Mean ( 9 / 28 ) & 140.939393939394 & 1.03163906245753 & 136.616961365978 \tabularnewline
Trimmed Mean ( 10 / 28 ) & 140.921875 & 1.00650283659285 & 140.011403720471 \tabularnewline
Trimmed Mean ( 11 / 28 ) & 140.91935483871 & 0.980318855923468 & 143.748489572775 \tabularnewline
Trimmed Mean ( 12 / 28 ) & 140.9 & 0.952753962465835 & 147.887078459726 \tabularnewline
Trimmed Mean ( 13 / 28 ) & 140.862068965517 & 0.923396330914085 & 152.547789339899 \tabularnewline
Trimmed Mean ( 14 / 28 ) & 140.821428571429 & 0.89700335998775 & 156.990971107791 \tabularnewline
Trimmed Mean ( 15 / 28 ) & 140.796296296296 & 0.869701037667185 & 161.890454533614 \tabularnewline
Trimmed Mean ( 16 / 28 ) & 140.769230769231 & 0.846256678243447 & 166.343420841797 \tabularnewline
Trimmed Mean ( 17 / 28 ) & 140.74 & 0.82749190759962 & 170.080213120461 \tabularnewline
Trimmed Mean ( 18 / 28 ) & 140.708333333333 & 0.814299471227636 & 172.796788288714 \tabularnewline
Trimmed Mean ( 19 / 28 ) & 140.673913043478 & 0.796765410062804 & 176.556250141921 \tabularnewline
Trimmed Mean ( 20 / 28 ) & 140.636363636364 & 0.773566265087146 & 181.802606943466 \tabularnewline
Trimmed Mean ( 21 / 28 ) & 140.619047619048 & 0.750495292091991 & 187.368327424246 \tabularnewline
Trimmed Mean ( 22 / 28 ) & 140.6 & 0.719508379167545 & 195.411205860689 \tabularnewline
Trimmed Mean ( 23 / 28 ) & 140.605263157895 & 0.686736228984205 & 204.744204868692 \tabularnewline
Trimmed Mean ( 24 / 28 ) & 140.583333333333 & 0.669488077350363 & 209.986313557249 \tabularnewline
Trimmed Mean ( 25 / 28 ) & 140.558823529412 & 0.644725171133704 & 218.013550304309 \tabularnewline
Trimmed Mean ( 26 / 28 ) & 140.53125 & 0.630195142268416 & 222.996403136577 \tabularnewline
Trimmed Mean ( 27 / 28 ) & 140.466666666667 & 0.617248870863589 & 227.568932560607 \tabularnewline
Trimmed Mean ( 28 / 28 ) & 140.428571428571 & 0.609511408604009 & 230.395312452315 \tabularnewline
Median & 139 &  &  \tabularnewline
Midrange & 135 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 140.085106382979 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 140.085106382979 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 140.085106382979 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 140.085106382979 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 140.085106382979 &  &  \tabularnewline
Midmean - Closest Observation & 140.085106382979 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 140.085106382979 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 140.085106382979 &  &  \tabularnewline
Number of observations & 84 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78279&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]140.75[/C][C]1.30764939130466[/C][C]107.635885380233[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]140.23748223639[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]139.716111865038[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]141.253276405321[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 28 )[/C][C]140.833333333333[/C][C]1.28496238186768[/C][C]109.601133325501[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 28 )[/C][C]140.904761904762[/C][C]1.25877517073947[/C][C]111.9379895474[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 28 )[/C][C]140.940476190476[/C][C]1.23760071658812[/C][C]113.882025358735[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 28 )[/C][C]141.035714285714[/C][C]1.21986879233072[/C][C]115.615478625571[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 28 )[/C][C]140.97619047619[/C][C]1.20894735112177[/C][C]116.610694705092[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 28 )[/C][C]141.047619047619[/C][C]1.19641661879667[/C][C]117.891725032607[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 28 )[/C][C]140.964285714286[/C][C]1.18164466573334[/C][C]119.294987572937[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 28 )[/C][C]141.059523809524[/C][C]1.16550034199134[/C][C]121.029156944316[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 28 )[/C][C]141.059523809524[/C][C]1.1295020443453[/C][C]124.886470560828[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 28 )[/C][C]140.940476190476[/C][C]1.10964467268592[/C][C]127.014061041113[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 28 )[/C][C]141.071428571429[/C][C]1.08882416883992[/C][C]129.5630943991[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 28 )[/C][C]141.214285714286[/C][C]1.06704016184548[/C][C]132.342053058294[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 28 )[/C][C]141.214285714286[/C][C]1.01876701891693[/C][C]138.612934156834[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 28 )[/C][C]141.047619047619[/C][C]0.99206616943605[/C][C]142.17561629765[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 28 )[/C][C]141.047619047619[/C][C]0.938576081512504[/C][C]150.278301169067[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 28 )[/C][C]141.047619047619[/C][C]0.883147626898456[/C][C]159.71012631599[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 28 )[/C][C]141.047619047619[/C][C]0.826085190399344[/C][C]170.742219672809[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 28 )[/C][C]141.047619047619[/C][C]0.826085190399344[/C][C]170.742219672809[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 28 )[/C][C]141.047619047619[/C][C]0.826085190399344[/C][C]170.742219672809[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 28 )[/C][C]140.809523809524[/C][C]0.792151002094543[/C][C]177.755911988[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 28 )[/C][C]140.809523809524[/C][C]0.792151002094543[/C][C]177.755911988[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 28 )[/C][C]140.547619047619[/C][C]0.756195440255047[/C][C]185.861500302376[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 28 )[/C][C]140.821428571429[/C][C]0.647197212942055[/C][C]217.586580651788[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 28 )[/C][C]140.821428571429[/C][C]0.647197212942055[/C][C]217.586580651788[/C][/ROW]
[ROW][C]Winsorized Mean ( 25 / 28 )[/C][C]140.821428571429[/C][C]0.57064364478226[/C][C]246.776477507537[/C][/ROW]
[ROW][C]Winsorized Mean ( 26 / 28 )[/C][C]141.130952380952[/C][C]0.533657683009208[/C][C]264.459703053722[/C][/ROW]
[ROW][C]Winsorized Mean ( 27 / 28 )[/C][C]140.809523809524[/C][C]0.491895356193459[/C][C]286.259103763818[/C][/ROW]
[ROW][C]Winsorized Mean ( 28 / 28 )[/C][C]140.809523809524[/C][C]0.491895356193459[/C][C]286.259103763818[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 28 )[/C][C]140.890243902439[/C][C]1.25107675365237[/C][C]112.615188069898[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 28 )[/C][C]140.95[/C][C]1.21174369600594[/C][C]116.319977949619[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 28 )[/C][C]140.974358974359[/C][C]1.18233957028652[/C][C]119.233393279898[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 28 )[/C][C]140.986842105263[/C][C]1.15735533688144[/C][C]121.818112046004[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 28 )[/C][C]140.972972972973[/C][C]1.13426210676012[/C][C]124.286064158173[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 28 )[/C][C]140.972222222222[/C][C]1.110303893008[/C][C]126.96724123006[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 28 )[/C][C]140.957142857143[/C][C]1.0852742379449[/C][C]129.881589306001[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 28 )[/C][C]140.955882352941[/C][C]1.05914509554612[/C][C]133.08458203289[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 28 )[/C][C]140.939393939394[/C][C]1.03163906245753[/C][C]136.616961365978[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 28 )[/C][C]140.921875[/C][C]1.00650283659285[/C][C]140.011403720471[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 28 )[/C][C]140.91935483871[/C][C]0.980318855923468[/C][C]143.748489572775[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 28 )[/C][C]140.9[/C][C]0.952753962465835[/C][C]147.887078459726[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 28 )[/C][C]140.862068965517[/C][C]0.923396330914085[/C][C]152.547789339899[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 28 )[/C][C]140.821428571429[/C][C]0.89700335998775[/C][C]156.990971107791[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 28 )[/C][C]140.796296296296[/C][C]0.869701037667185[/C][C]161.890454533614[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 28 )[/C][C]140.769230769231[/C][C]0.846256678243447[/C][C]166.343420841797[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 28 )[/C][C]140.74[/C][C]0.82749190759962[/C][C]170.080213120461[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 28 )[/C][C]140.708333333333[/C][C]0.814299471227636[/C][C]172.796788288714[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 28 )[/C][C]140.673913043478[/C][C]0.796765410062804[/C][C]176.556250141921[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 28 )[/C][C]140.636363636364[/C][C]0.773566265087146[/C][C]181.802606943466[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 28 )[/C][C]140.619047619048[/C][C]0.750495292091991[/C][C]187.368327424246[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 28 )[/C][C]140.6[/C][C]0.719508379167545[/C][C]195.411205860689[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 28 )[/C][C]140.605263157895[/C][C]0.686736228984205[/C][C]204.744204868692[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 28 )[/C][C]140.583333333333[/C][C]0.669488077350363[/C][C]209.986313557249[/C][/ROW]
[ROW][C]Trimmed Mean ( 25 / 28 )[/C][C]140.558823529412[/C][C]0.644725171133704[/C][C]218.013550304309[/C][/ROW]
[ROW][C]Trimmed Mean ( 26 / 28 )[/C][C]140.53125[/C][C]0.630195142268416[/C][C]222.996403136577[/C][/ROW]
[ROW][C]Trimmed Mean ( 27 / 28 )[/C][C]140.466666666667[/C][C]0.617248870863589[/C][C]227.568932560607[/C][/ROW]
[ROW][C]Trimmed Mean ( 28 / 28 )[/C][C]140.428571428571[/C][C]0.609511408604009[/C][C]230.395312452315[/C][/ROW]
[ROW][C]Median[/C][C]139[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]135[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]140.085106382979[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]140.085106382979[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]140.085106382979[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]140.085106382979[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]140.085106382979[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]140.085106382979[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]140.085106382979[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]140.085106382979[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]84[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78279&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78279&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 Mean140.751.30764939130466107.635885380233
Geometric Mean140.23748223639
Harmonic Mean139.716111865038
Quadratic Mean141.253276405321
Winsorized Mean ( 1 / 28 )140.8333333333331.28496238186768109.601133325501
Winsorized Mean ( 2 / 28 )140.9047619047621.25877517073947111.9379895474
Winsorized Mean ( 3 / 28 )140.9404761904761.23760071658812113.882025358735
Winsorized Mean ( 4 / 28 )141.0357142857141.21986879233072115.615478625571
Winsorized Mean ( 5 / 28 )140.976190476191.20894735112177116.610694705092
Winsorized Mean ( 6 / 28 )141.0476190476191.19641661879667117.891725032607
Winsorized Mean ( 7 / 28 )140.9642857142861.18164466573334119.294987572937
Winsorized Mean ( 8 / 28 )141.0595238095241.16550034199134121.029156944316
Winsorized Mean ( 9 / 28 )141.0595238095241.1295020443453124.886470560828
Winsorized Mean ( 10 / 28 )140.9404761904761.10964467268592127.014061041113
Winsorized Mean ( 11 / 28 )141.0714285714291.08882416883992129.5630943991
Winsorized Mean ( 12 / 28 )141.2142857142861.06704016184548132.342053058294
Winsorized Mean ( 13 / 28 )141.2142857142861.01876701891693138.612934156834
Winsorized Mean ( 14 / 28 )141.0476190476190.99206616943605142.17561629765
Winsorized Mean ( 15 / 28 )141.0476190476190.938576081512504150.278301169067
Winsorized Mean ( 16 / 28 )141.0476190476190.883147626898456159.71012631599
Winsorized Mean ( 17 / 28 )141.0476190476190.826085190399344170.742219672809
Winsorized Mean ( 18 / 28 )141.0476190476190.826085190399344170.742219672809
Winsorized Mean ( 19 / 28 )141.0476190476190.826085190399344170.742219672809
Winsorized Mean ( 20 / 28 )140.8095238095240.792151002094543177.755911988
Winsorized Mean ( 21 / 28 )140.8095238095240.792151002094543177.755911988
Winsorized Mean ( 22 / 28 )140.5476190476190.756195440255047185.861500302376
Winsorized Mean ( 23 / 28 )140.8214285714290.647197212942055217.586580651788
Winsorized Mean ( 24 / 28 )140.8214285714290.647197212942055217.586580651788
Winsorized Mean ( 25 / 28 )140.8214285714290.57064364478226246.776477507537
Winsorized Mean ( 26 / 28 )141.1309523809520.533657683009208264.459703053722
Winsorized Mean ( 27 / 28 )140.8095238095240.491895356193459286.259103763818
Winsorized Mean ( 28 / 28 )140.8095238095240.491895356193459286.259103763818
Trimmed Mean ( 1 / 28 )140.8902439024391.25107675365237112.615188069898
Trimmed Mean ( 2 / 28 )140.951.21174369600594116.319977949619
Trimmed Mean ( 3 / 28 )140.9743589743591.18233957028652119.233393279898
Trimmed Mean ( 4 / 28 )140.9868421052631.15735533688144121.818112046004
Trimmed Mean ( 5 / 28 )140.9729729729731.13426210676012124.286064158173
Trimmed Mean ( 6 / 28 )140.9722222222221.110303893008126.96724123006
Trimmed Mean ( 7 / 28 )140.9571428571431.0852742379449129.881589306001
Trimmed Mean ( 8 / 28 )140.9558823529411.05914509554612133.08458203289
Trimmed Mean ( 9 / 28 )140.9393939393941.03163906245753136.616961365978
Trimmed Mean ( 10 / 28 )140.9218751.00650283659285140.011403720471
Trimmed Mean ( 11 / 28 )140.919354838710.980318855923468143.748489572775
Trimmed Mean ( 12 / 28 )140.90.952753962465835147.887078459726
Trimmed Mean ( 13 / 28 )140.8620689655170.923396330914085152.547789339899
Trimmed Mean ( 14 / 28 )140.8214285714290.89700335998775156.990971107791
Trimmed Mean ( 15 / 28 )140.7962962962960.869701037667185161.890454533614
Trimmed Mean ( 16 / 28 )140.7692307692310.846256678243447166.343420841797
Trimmed Mean ( 17 / 28 )140.740.82749190759962170.080213120461
Trimmed Mean ( 18 / 28 )140.7083333333330.814299471227636172.796788288714
Trimmed Mean ( 19 / 28 )140.6739130434780.796765410062804176.556250141921
Trimmed Mean ( 20 / 28 )140.6363636363640.773566265087146181.802606943466
Trimmed Mean ( 21 / 28 )140.6190476190480.750495292091991187.368327424246
Trimmed Mean ( 22 / 28 )140.60.719508379167545195.411205860689
Trimmed Mean ( 23 / 28 )140.6052631578950.686736228984205204.744204868692
Trimmed Mean ( 24 / 28 )140.5833333333330.669488077350363209.986313557249
Trimmed Mean ( 25 / 28 )140.5588235294120.644725171133704218.013550304309
Trimmed Mean ( 26 / 28 )140.531250.630195142268416222.996403136577
Trimmed Mean ( 27 / 28 )140.4666666666670.617248870863589227.568932560607
Trimmed Mean ( 28 / 28 )140.4285714285710.609511408604009230.395312452315
Median139
Midrange135
Midmean - Weighted Average at Xnp140.085106382979
Midmean - Weighted Average at X(n+1)p140.085106382979
Midmean - Empirical Distribution Function140.085106382979
Midmean - Empirical Distribution Function - Averaging140.085106382979
Midmean - Empirical Distribution Function - Interpolation140.085106382979
Midmean - Closest Observation140.085106382979
Midmean - True Basic - Statistics Graphics Toolkit140.085106382979
Midmean - MS Excel (old versions)140.085106382979
Number of observations84



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')