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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationSat, 11 Dec 2010 10:52:21 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Dec/11/t1292064673vhtn3yv6q0mt9s3.htm/, Retrieved Sun, 28 Apr 2024 14:20:26 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=108055, Retrieved Sun, 28 Apr 2024 14:20:26 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact119
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Central Tendency] [Arabica Price in ...] [2008-01-06 21:28:17] [74be16979710d4c4e7c6647856088456]
-  M D  [Central Tendency] [Mini-tutorial Uni...] [2010-11-14 20:27:58] [6ca0fc48dd5333d51a15728999009c83]
-    D      [Central Tendency] [Univariate analys...] [2010-12-11 10:52:21] [b4ba846736d082ffaee409a197f454c7] [Current]
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Dataseries X:
15
15
14
10
10
12
18
12
14
18
9
11
11
17
8
16
21
24
21
14
7
18
18
13
11
13
13
18
14
12
9
12
8
5
10
11
11
12
12
15
12
16
14
17
13
10
17
12
13
13
11
13
12
12
12
9
7
17
12
12
9
9
13
10
11
12
10
13
6
7
13
11
18
9
9
11
11
15
8
11
14
14
12
12
8
11
10
17
16
13
15
11
12
16
20
16
11
15
15
12
9
24
15
18
17
12
15
11
11
15
12
14
11
20
11
12
17
12
11
10
11
12
9
8
6
12
15
13
17
14
16
15
16
11
11
16
15
14
9
13
11
14
11
12
8
7
11
13
9
12
10
12




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=108055&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=108055&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=108055&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 Mean12.71052631578950.27480332631729846.2531749019422
Geometric Mean12.2665415653407
Harmonic Mean11.8131067207993
Quadratic Mean13.1514457880413
Winsorized Mean ( 1 / 50 )12.71710526315790.2736572088658846.4709309718589
Winsorized Mean ( 2 / 50 )12.67763157894740.26412715801602447.9982129599041
Winsorized Mean ( 3 / 50 )12.69736842105260.26104721699710848.6401217646127
Winsorized Mean ( 4 / 50 )12.67105263157890.25577613004825949.5396213446041
Winsorized Mean ( 5 / 50 )12.67105263157890.25577613004825949.5396213446041
Winsorized Mean ( 6 / 50 )12.59210526315790.24240920424718951.945656528444
Winsorized Mean ( 7 / 50 )12.63815789473680.23588588872870353.5774223835502
Winsorized Mean ( 8 / 50 )12.63815789473680.23588588872870353.5774223835502
Winsorized Mean ( 9 / 50 )12.63815789473680.23588588872870353.5774223835502
Winsorized Mean ( 10 / 50 )12.63815789473680.23588588872870353.5774223835502
Winsorized Mean ( 11 / 50 )12.63815789473680.23588588872870353.5774223835502
Winsorized Mean ( 12 / 50 )12.63815789473680.23588588872870353.5774223835502
Winsorized Mean ( 13 / 50 )12.63815789473680.21318293210215259.2831601015832
Winsorized Mean ( 14 / 50 )12.63815789473680.21318293210215259.2831601015832
Winsorized Mean ( 15 / 50 )12.63815789473680.21318293210215259.2831601015832
Winsorized Mean ( 16 / 50 )12.63815789473680.21318293210215259.2831601015832
Winsorized Mean ( 17 / 50 )12.63815789473680.21318293210215259.2831601015832
Winsorized Mean ( 18 / 50 )12.63815789473680.21318293210215259.2831601015832
Winsorized Mean ( 19 / 50 )12.63815789473680.21318293210215259.2831601015832
Winsorized Mean ( 20 / 50 )12.63815789473680.21318293210215259.2831601015832
Winsorized Mean ( 21 / 50 )12.50.1955856511867863.9106188217394
Winsorized Mean ( 22 / 50 )12.50.1955856511867863.9106188217394
Winsorized Mean ( 23 / 50 )12.50.1955856511867863.9106188217394
Winsorized Mean ( 24 / 50 )12.65789473684210.17836669982356970.9655712045054
Winsorized Mean ( 25 / 50 )12.65789473684210.17836669982356970.9655712045054
Winsorized Mean ( 26 / 50 )12.65789473684210.17836669982356970.9655712045054
Winsorized Mean ( 27 / 50 )12.65789473684210.17836669982356970.9655712045054
Winsorized Mean ( 28 / 50 )12.65789473684210.17836669982356970.9655712045054
Winsorized Mean ( 29 / 50 )12.46710526315790.15617803694035379.8262387426428
Winsorized Mean ( 30 / 50 )12.46710526315790.15617803694035379.8262387426428
Winsorized Mean ( 31 / 50 )12.46710526315790.15617803694035379.8262387426428
Winsorized Mean ( 32 / 50 )12.46710526315790.15617803694035379.8262387426428
Winsorized Mean ( 33 / 50 )12.68421052631580.13573093650196393.4511383566
Winsorized Mean ( 34 / 50 )12.68421052631580.13573093650196393.4511383566
Winsorized Mean ( 35 / 50 )12.68421052631580.13573093650196393.4511383566
Winsorized Mean ( 36 / 50 )12.68421052631580.13573093650196393.4511383566
Winsorized Mean ( 37 / 50 )12.68421052631580.13573093650196393.4511383566
Winsorized Mean ( 38 / 50 )12.68421052631580.13573093650196393.4511383566
Winsorized Mean ( 39 / 50 )12.68421052631580.13573093650196393.4511383566
Winsorized Mean ( 40 / 50 )12.68421052631580.13573093650196393.4511383566
Winsorized Mean ( 41 / 50 )12.68421052631580.13573093650196393.4511383566
Winsorized Mean ( 42 / 50 )12.40789473684210.106168769066457116.869535607739
Winsorized Mean ( 43 / 50 )12.40789473684210.106168769066457116.869535607739
Winsorized Mean ( 44 / 50 )12.40789473684210.106168769066457116.869535607739
Winsorized Mean ( 45 / 50 )12.40789473684210.106168769066457116.869535607739
Winsorized Mean ( 46 / 50 )12.40789473684210.106168769066457116.869535607739
Winsorized Mean ( 47 / 50 )12.40789473684210.106168769066457116.869535607739
Winsorized Mean ( 48 / 50 )12.40789473684210.106168769066457116.869535607739
Winsorized Mean ( 49 / 50 )12.40789473684210.106168769066457116.869535607739
Winsorized Mean ( 50 / 50 )12.40789473684210.106168769066457116.869535607739
Trimmed Mean ( 1 / 50 )12.68666666666670.26302944547554748.232876147116
Trimmed Mean ( 2 / 50 )12.65540540540540.25125404134597750.3689625751289
Trimmed Mean ( 3 / 50 )12.64383561643840.24391309347468251.8374615988
Trimmed Mean ( 4 / 50 )12.6250.23711450946386853.2443165479245
Trimmed Mean ( 5 / 50 )12.6126760563380.23135682522090354.516118313325
Trimmed Mean ( 6 / 50 )12.60.22504995448652855.98756964314
Trimmed Mean ( 7 / 50 )12.60144927536230.22120235740864656.9679700659003
Trimmed Mean ( 8 / 50 )12.59558823529410.21827674177285857.7046740435648
Trimmed Mean ( 9 / 50 )12.5895522388060.21507872588592658.5346234823952
Trimmed Mean ( 10 / 50 )12.58333333333330.21157835927317959.4736313135239
Trimmed Mean ( 11 / 50 )12.57692307692310.20774088965581460.5413941268883
Trimmed Mean ( 12 / 50 )12.57031250.20352564024939761.7627955111529
Trimmed Mean ( 13 / 50 )12.56349206349210.198884518377663.169783983081
Trimmed Mean ( 14 / 50 )12.55645161290320.19678187849632463.8089833721033
Trimmed Mean ( 15 / 50 )12.54918032786890.19445728987416364.5343784025255
Trimmed Mean ( 16 / 50 )12.54166666666670.19188575956687565.3600699446158
Trimmed Mean ( 17 / 50 )12.53389830508470.18903837386275466.303460239161
Trimmed Mean ( 18 / 50 )12.52586206896550.18588142747983767.3863023261119
Trimmed Mean ( 19 / 50 )12.51754385964910.18237528513114268.6361852739424
Trimmed Mean ( 20 / 50 )12.50892857142860.178472865334270.0886857394538
Trimmed Mean ( 21 / 50 )12.50.1741175774459571.7905692426733
Trimmed Mean ( 22 / 50 )12.50.17127583068410972.98169245522
Trimmed Mean ( 23 / 50 )12.50.16809807602296874.3613508003034
Trimmed Mean ( 24 / 50 )12.50.16453705394526175.9707293905878
Trimmed Mean ( 25 / 50 )12.49019607843140.16233654655245276.9401366709232
Trimmed Mean ( 26 / 50 )12.480.1598484130403478.0739687221699
Trimmed Mean ( 27 / 50 )12.4693877551020.15703174652172979.4067953219678
Trimmed Mean ( 28 / 50 )12.45833333333330.15383736760785680.9837916954653
Trimmed Mean ( 29 / 50 )12.44680851063830.15020539683783782.8652549953049
Trimmed Mean ( 30 / 50 )12.4456521739130.14854295560385183.784869658204
Trimmed Mean ( 31 / 50 )12.44444444444440.14663185755733484.8686271302166
Trimmed Mean ( 32 / 50 )12.44318181818180.14443522640010486.1506027879418
Trimmed Mean ( 33 / 50 )12.44186046511630.14190867293286987.675123781913
Trimmed Mean ( 34 / 50 )12.42857142857140.14098021154593788.1582691094326
Trimmed Mean ( 35 / 50 )12.41463414634150.1398489522757888.77173510646
Trimmed Mean ( 36 / 50 )12.40.13848182259731289.5424378985657
Trimmed Mean ( 37 / 50 )12.38461538461540.13683882811070590.5051260348125
Trimmed Mean ( 38 / 50 )12.36842105263160.13487109539496591.7054986200793
Trimmed Mean ( 39 / 50 )12.35135135135140.13251816279282793.2049697267607
Trimmed Mean ( 40 / 50 )12.33333333333330.12970412942292395.0882087425169
Trimmed Mean ( 41 / 50 )12.31428571428570.12633200391996397.4755828466661
Trimmed Mean ( 42 / 50 )12.29411764705880.122275081595546100.54475111883
Trimmed Mean ( 43 / 50 )12.28787878787880.121691940757357100.975288185926
Trimmed Mean ( 44 / 50 )12.281250.120902586886605101.57971236396
Trimmed Mean ( 45 / 50 )12.27419354838710.119865416418821102.399790657715
Trimmed Mean ( 46 / 50 )12.26666666666670.118528326650028103.491435451424
Trimmed Mean ( 47 / 50 )12.25862068965520.116825174910173104.931327507798
Trimmed Mean ( 48 / 50 )12.250.114670618073466106.827714071898
Trimmed Mean ( 49 / 50 )12.24074074074070.111952324587579109.338870682984
Trimmed Mean ( 50 / 50 )12.23076923076920.10851869957016112.706559138794
Median12
Midrange14.5
Midmean - Weighted Average at Xnp12.5555555555556
Midmean - Weighted Average at X(n+1)p12.5555555555556
Midmean - Empirical Distribution Function12.5555555555556
Midmean - Empirical Distribution Function - Averaging12.5555555555556
Midmean - Empirical Distribution Function - Interpolation12.5555555555556
Midmean - Closest Observation12.5555555555556
Midmean - True Basic - Statistics Graphics Toolkit12.5555555555556
Midmean - MS Excel (old versions)12.5555555555556
Number of observations152

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 12.7105263157895 & 0.274803326317298 & 46.2531749019422 \tabularnewline
Geometric Mean & 12.2665415653407 &  &  \tabularnewline
Harmonic Mean & 11.8131067207993 &  &  \tabularnewline
Quadratic Mean & 13.1514457880413 &  &  \tabularnewline
Winsorized Mean ( 1 / 50 ) & 12.7171052631579 & 0.27365720886588 & 46.4709309718589 \tabularnewline
Winsorized Mean ( 2 / 50 ) & 12.6776315789474 & 0.264127158016024 & 47.9982129599041 \tabularnewline
Winsorized Mean ( 3 / 50 ) & 12.6973684210526 & 0.261047216997108 & 48.6401217646127 \tabularnewline
Winsorized Mean ( 4 / 50 ) & 12.6710526315789 & 0.255776130048259 & 49.5396213446041 \tabularnewline
Winsorized Mean ( 5 / 50 ) & 12.6710526315789 & 0.255776130048259 & 49.5396213446041 \tabularnewline
Winsorized Mean ( 6 / 50 ) & 12.5921052631579 & 0.242409204247189 & 51.945656528444 \tabularnewline
Winsorized Mean ( 7 / 50 ) & 12.6381578947368 & 0.235885888728703 & 53.5774223835502 \tabularnewline
Winsorized Mean ( 8 / 50 ) & 12.6381578947368 & 0.235885888728703 & 53.5774223835502 \tabularnewline
Winsorized Mean ( 9 / 50 ) & 12.6381578947368 & 0.235885888728703 & 53.5774223835502 \tabularnewline
Winsorized Mean ( 10 / 50 ) & 12.6381578947368 & 0.235885888728703 & 53.5774223835502 \tabularnewline
Winsorized Mean ( 11 / 50 ) & 12.6381578947368 & 0.235885888728703 & 53.5774223835502 \tabularnewline
Winsorized Mean ( 12 / 50 ) & 12.6381578947368 & 0.235885888728703 & 53.5774223835502 \tabularnewline
Winsorized Mean ( 13 / 50 ) & 12.6381578947368 & 0.213182932102152 & 59.2831601015832 \tabularnewline
Winsorized Mean ( 14 / 50 ) & 12.6381578947368 & 0.213182932102152 & 59.2831601015832 \tabularnewline
Winsorized Mean ( 15 / 50 ) & 12.6381578947368 & 0.213182932102152 & 59.2831601015832 \tabularnewline
Winsorized Mean ( 16 / 50 ) & 12.6381578947368 & 0.213182932102152 & 59.2831601015832 \tabularnewline
Winsorized Mean ( 17 / 50 ) & 12.6381578947368 & 0.213182932102152 & 59.2831601015832 \tabularnewline
Winsorized Mean ( 18 / 50 ) & 12.6381578947368 & 0.213182932102152 & 59.2831601015832 \tabularnewline
Winsorized Mean ( 19 / 50 ) & 12.6381578947368 & 0.213182932102152 & 59.2831601015832 \tabularnewline
Winsorized Mean ( 20 / 50 ) & 12.6381578947368 & 0.213182932102152 & 59.2831601015832 \tabularnewline
Winsorized Mean ( 21 / 50 ) & 12.5 & 0.19558565118678 & 63.9106188217394 \tabularnewline
Winsorized Mean ( 22 / 50 ) & 12.5 & 0.19558565118678 & 63.9106188217394 \tabularnewline
Winsorized Mean ( 23 / 50 ) & 12.5 & 0.19558565118678 & 63.9106188217394 \tabularnewline
Winsorized Mean ( 24 / 50 ) & 12.6578947368421 & 0.178366699823569 & 70.9655712045054 \tabularnewline
Winsorized Mean ( 25 / 50 ) & 12.6578947368421 & 0.178366699823569 & 70.9655712045054 \tabularnewline
Winsorized Mean ( 26 / 50 ) & 12.6578947368421 & 0.178366699823569 & 70.9655712045054 \tabularnewline
Winsorized Mean ( 27 / 50 ) & 12.6578947368421 & 0.178366699823569 & 70.9655712045054 \tabularnewline
Winsorized Mean ( 28 / 50 ) & 12.6578947368421 & 0.178366699823569 & 70.9655712045054 \tabularnewline
Winsorized Mean ( 29 / 50 ) & 12.4671052631579 & 0.156178036940353 & 79.8262387426428 \tabularnewline
Winsorized Mean ( 30 / 50 ) & 12.4671052631579 & 0.156178036940353 & 79.8262387426428 \tabularnewline
Winsorized Mean ( 31 / 50 ) & 12.4671052631579 & 0.156178036940353 & 79.8262387426428 \tabularnewline
Winsorized Mean ( 32 / 50 ) & 12.4671052631579 & 0.156178036940353 & 79.8262387426428 \tabularnewline
Winsorized Mean ( 33 / 50 ) & 12.6842105263158 & 0.135730936501963 & 93.4511383566 \tabularnewline
Winsorized Mean ( 34 / 50 ) & 12.6842105263158 & 0.135730936501963 & 93.4511383566 \tabularnewline
Winsorized Mean ( 35 / 50 ) & 12.6842105263158 & 0.135730936501963 & 93.4511383566 \tabularnewline
Winsorized Mean ( 36 / 50 ) & 12.6842105263158 & 0.135730936501963 & 93.4511383566 \tabularnewline
Winsorized Mean ( 37 / 50 ) & 12.6842105263158 & 0.135730936501963 & 93.4511383566 \tabularnewline
Winsorized Mean ( 38 / 50 ) & 12.6842105263158 & 0.135730936501963 & 93.4511383566 \tabularnewline
Winsorized Mean ( 39 / 50 ) & 12.6842105263158 & 0.135730936501963 & 93.4511383566 \tabularnewline
Winsorized Mean ( 40 / 50 ) & 12.6842105263158 & 0.135730936501963 & 93.4511383566 \tabularnewline
Winsorized Mean ( 41 / 50 ) & 12.6842105263158 & 0.135730936501963 & 93.4511383566 \tabularnewline
Winsorized Mean ( 42 / 50 ) & 12.4078947368421 & 0.106168769066457 & 116.869535607739 \tabularnewline
Winsorized Mean ( 43 / 50 ) & 12.4078947368421 & 0.106168769066457 & 116.869535607739 \tabularnewline
Winsorized Mean ( 44 / 50 ) & 12.4078947368421 & 0.106168769066457 & 116.869535607739 \tabularnewline
Winsorized Mean ( 45 / 50 ) & 12.4078947368421 & 0.106168769066457 & 116.869535607739 \tabularnewline
Winsorized Mean ( 46 / 50 ) & 12.4078947368421 & 0.106168769066457 & 116.869535607739 \tabularnewline
Winsorized Mean ( 47 / 50 ) & 12.4078947368421 & 0.106168769066457 & 116.869535607739 \tabularnewline
Winsorized Mean ( 48 / 50 ) & 12.4078947368421 & 0.106168769066457 & 116.869535607739 \tabularnewline
Winsorized Mean ( 49 / 50 ) & 12.4078947368421 & 0.106168769066457 & 116.869535607739 \tabularnewline
Winsorized Mean ( 50 / 50 ) & 12.4078947368421 & 0.106168769066457 & 116.869535607739 \tabularnewline
Trimmed Mean ( 1 / 50 ) & 12.6866666666667 & 0.263029445475547 & 48.232876147116 \tabularnewline
Trimmed Mean ( 2 / 50 ) & 12.6554054054054 & 0.251254041345977 & 50.3689625751289 \tabularnewline
Trimmed Mean ( 3 / 50 ) & 12.6438356164384 & 0.243913093474682 & 51.8374615988 \tabularnewline
Trimmed Mean ( 4 / 50 ) & 12.625 & 0.237114509463868 & 53.2443165479245 \tabularnewline
Trimmed Mean ( 5 / 50 ) & 12.612676056338 & 0.231356825220903 & 54.516118313325 \tabularnewline
Trimmed Mean ( 6 / 50 ) & 12.6 & 0.225049954486528 & 55.98756964314 \tabularnewline
Trimmed Mean ( 7 / 50 ) & 12.6014492753623 & 0.221202357408646 & 56.9679700659003 \tabularnewline
Trimmed Mean ( 8 / 50 ) & 12.5955882352941 & 0.218276741772858 & 57.7046740435648 \tabularnewline
Trimmed Mean ( 9 / 50 ) & 12.589552238806 & 0.215078725885926 & 58.5346234823952 \tabularnewline
Trimmed Mean ( 10 / 50 ) & 12.5833333333333 & 0.211578359273179 & 59.4736313135239 \tabularnewline
Trimmed Mean ( 11 / 50 ) & 12.5769230769231 & 0.207740889655814 & 60.5413941268883 \tabularnewline
Trimmed Mean ( 12 / 50 ) & 12.5703125 & 0.203525640249397 & 61.7627955111529 \tabularnewline
Trimmed Mean ( 13 / 50 ) & 12.5634920634921 & 0.1988845183776 & 63.169783983081 \tabularnewline
Trimmed Mean ( 14 / 50 ) & 12.5564516129032 & 0.196781878496324 & 63.8089833721033 \tabularnewline
Trimmed Mean ( 15 / 50 ) & 12.5491803278689 & 0.194457289874163 & 64.5343784025255 \tabularnewline
Trimmed Mean ( 16 / 50 ) & 12.5416666666667 & 0.191885759566875 & 65.3600699446158 \tabularnewline
Trimmed Mean ( 17 / 50 ) & 12.5338983050847 & 0.189038373862754 & 66.303460239161 \tabularnewline
Trimmed Mean ( 18 / 50 ) & 12.5258620689655 & 0.185881427479837 & 67.3863023261119 \tabularnewline
Trimmed Mean ( 19 / 50 ) & 12.5175438596491 & 0.182375285131142 & 68.6361852739424 \tabularnewline
Trimmed Mean ( 20 / 50 ) & 12.5089285714286 & 0.1784728653342 & 70.0886857394538 \tabularnewline
Trimmed Mean ( 21 / 50 ) & 12.5 & 0.17411757744595 & 71.7905692426733 \tabularnewline
Trimmed Mean ( 22 / 50 ) & 12.5 & 0.171275830684109 & 72.98169245522 \tabularnewline
Trimmed Mean ( 23 / 50 ) & 12.5 & 0.168098076022968 & 74.3613508003034 \tabularnewline
Trimmed Mean ( 24 / 50 ) & 12.5 & 0.164537053945261 & 75.9707293905878 \tabularnewline
Trimmed Mean ( 25 / 50 ) & 12.4901960784314 & 0.162336546552452 & 76.9401366709232 \tabularnewline
Trimmed Mean ( 26 / 50 ) & 12.48 & 0.15984841304034 & 78.0739687221699 \tabularnewline
Trimmed Mean ( 27 / 50 ) & 12.469387755102 & 0.157031746521729 & 79.4067953219678 \tabularnewline
Trimmed Mean ( 28 / 50 ) & 12.4583333333333 & 0.153837367607856 & 80.9837916954653 \tabularnewline
Trimmed Mean ( 29 / 50 ) & 12.4468085106383 & 0.150205396837837 & 82.8652549953049 \tabularnewline
Trimmed Mean ( 30 / 50 ) & 12.445652173913 & 0.148542955603851 & 83.784869658204 \tabularnewline
Trimmed Mean ( 31 / 50 ) & 12.4444444444444 & 0.146631857557334 & 84.8686271302166 \tabularnewline
Trimmed Mean ( 32 / 50 ) & 12.4431818181818 & 0.144435226400104 & 86.1506027879418 \tabularnewline
Trimmed Mean ( 33 / 50 ) & 12.4418604651163 & 0.141908672932869 & 87.675123781913 \tabularnewline
Trimmed Mean ( 34 / 50 ) & 12.4285714285714 & 0.140980211545937 & 88.1582691094326 \tabularnewline
Trimmed Mean ( 35 / 50 ) & 12.4146341463415 & 0.13984895227578 & 88.77173510646 \tabularnewline
Trimmed Mean ( 36 / 50 ) & 12.4 & 0.138481822597312 & 89.5424378985657 \tabularnewline
Trimmed Mean ( 37 / 50 ) & 12.3846153846154 & 0.136838828110705 & 90.5051260348125 \tabularnewline
Trimmed Mean ( 38 / 50 ) & 12.3684210526316 & 0.134871095394965 & 91.7054986200793 \tabularnewline
Trimmed Mean ( 39 / 50 ) & 12.3513513513514 & 0.132518162792827 & 93.2049697267607 \tabularnewline
Trimmed Mean ( 40 / 50 ) & 12.3333333333333 & 0.129704129422923 & 95.0882087425169 \tabularnewline
Trimmed Mean ( 41 / 50 ) & 12.3142857142857 & 0.126332003919963 & 97.4755828466661 \tabularnewline
Trimmed Mean ( 42 / 50 ) & 12.2941176470588 & 0.122275081595546 & 100.54475111883 \tabularnewline
Trimmed Mean ( 43 / 50 ) & 12.2878787878788 & 0.121691940757357 & 100.975288185926 \tabularnewline
Trimmed Mean ( 44 / 50 ) & 12.28125 & 0.120902586886605 & 101.57971236396 \tabularnewline
Trimmed Mean ( 45 / 50 ) & 12.2741935483871 & 0.119865416418821 & 102.399790657715 \tabularnewline
Trimmed Mean ( 46 / 50 ) & 12.2666666666667 & 0.118528326650028 & 103.491435451424 \tabularnewline
Trimmed Mean ( 47 / 50 ) & 12.2586206896552 & 0.116825174910173 & 104.931327507798 \tabularnewline
Trimmed Mean ( 48 / 50 ) & 12.25 & 0.114670618073466 & 106.827714071898 \tabularnewline
Trimmed Mean ( 49 / 50 ) & 12.2407407407407 & 0.111952324587579 & 109.338870682984 \tabularnewline
Trimmed Mean ( 50 / 50 ) & 12.2307692307692 & 0.10851869957016 & 112.706559138794 \tabularnewline
Median & 12 &  &  \tabularnewline
Midrange & 14.5 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 12.5555555555556 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 12.5555555555556 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 12.5555555555556 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 12.5555555555556 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 12.5555555555556 &  &  \tabularnewline
Midmean - Closest Observation & 12.5555555555556 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 12.5555555555556 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 12.5555555555556 &  &  \tabularnewline
Number of observations & 152 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=108055&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]12.7105263157895[/C][C]0.274803326317298[/C][C]46.2531749019422[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]12.2665415653407[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]11.8131067207993[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]13.1514457880413[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 50 )[/C][C]12.7171052631579[/C][C]0.27365720886588[/C][C]46.4709309718589[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 50 )[/C][C]12.6776315789474[/C][C]0.264127158016024[/C][C]47.9982129599041[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 50 )[/C][C]12.6973684210526[/C][C]0.261047216997108[/C][C]48.6401217646127[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 50 )[/C][C]12.6710526315789[/C][C]0.255776130048259[/C][C]49.5396213446041[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 50 )[/C][C]12.6710526315789[/C][C]0.255776130048259[/C][C]49.5396213446041[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 50 )[/C][C]12.5921052631579[/C][C]0.242409204247189[/C][C]51.945656528444[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 50 )[/C][C]12.6381578947368[/C][C]0.235885888728703[/C][C]53.5774223835502[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 50 )[/C][C]12.6381578947368[/C][C]0.235885888728703[/C][C]53.5774223835502[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 50 )[/C][C]12.6381578947368[/C][C]0.235885888728703[/C][C]53.5774223835502[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 50 )[/C][C]12.6381578947368[/C][C]0.235885888728703[/C][C]53.5774223835502[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 50 )[/C][C]12.6381578947368[/C][C]0.235885888728703[/C][C]53.5774223835502[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 50 )[/C][C]12.6381578947368[/C][C]0.235885888728703[/C][C]53.5774223835502[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 50 )[/C][C]12.6381578947368[/C][C]0.213182932102152[/C][C]59.2831601015832[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 50 )[/C][C]12.6381578947368[/C][C]0.213182932102152[/C][C]59.2831601015832[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 50 )[/C][C]12.6381578947368[/C][C]0.213182932102152[/C][C]59.2831601015832[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 50 )[/C][C]12.6381578947368[/C][C]0.213182932102152[/C][C]59.2831601015832[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 50 )[/C][C]12.6381578947368[/C][C]0.213182932102152[/C][C]59.2831601015832[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 50 )[/C][C]12.6381578947368[/C][C]0.213182932102152[/C][C]59.2831601015832[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 50 )[/C][C]12.6381578947368[/C][C]0.213182932102152[/C][C]59.2831601015832[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 50 )[/C][C]12.6381578947368[/C][C]0.213182932102152[/C][C]59.2831601015832[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 50 )[/C][C]12.5[/C][C]0.19558565118678[/C][C]63.9106188217394[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 50 )[/C][C]12.5[/C][C]0.19558565118678[/C][C]63.9106188217394[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 50 )[/C][C]12.5[/C][C]0.19558565118678[/C][C]63.9106188217394[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 50 )[/C][C]12.6578947368421[/C][C]0.178366699823569[/C][C]70.9655712045054[/C][/ROW]
[ROW][C]Winsorized Mean ( 25 / 50 )[/C][C]12.6578947368421[/C][C]0.178366699823569[/C][C]70.9655712045054[/C][/ROW]
[ROW][C]Winsorized Mean ( 26 / 50 )[/C][C]12.6578947368421[/C][C]0.178366699823569[/C][C]70.9655712045054[/C][/ROW]
[ROW][C]Winsorized Mean ( 27 / 50 )[/C][C]12.6578947368421[/C][C]0.178366699823569[/C][C]70.9655712045054[/C][/ROW]
[ROW][C]Winsorized Mean ( 28 / 50 )[/C][C]12.6578947368421[/C][C]0.178366699823569[/C][C]70.9655712045054[/C][/ROW]
[ROW][C]Winsorized Mean ( 29 / 50 )[/C][C]12.4671052631579[/C][C]0.156178036940353[/C][C]79.8262387426428[/C][/ROW]
[ROW][C]Winsorized Mean ( 30 / 50 )[/C][C]12.4671052631579[/C][C]0.156178036940353[/C][C]79.8262387426428[/C][/ROW]
[ROW][C]Winsorized Mean ( 31 / 50 )[/C][C]12.4671052631579[/C][C]0.156178036940353[/C][C]79.8262387426428[/C][/ROW]
[ROW][C]Winsorized Mean ( 32 / 50 )[/C][C]12.4671052631579[/C][C]0.156178036940353[/C][C]79.8262387426428[/C][/ROW]
[ROW][C]Winsorized Mean ( 33 / 50 )[/C][C]12.6842105263158[/C][C]0.135730936501963[/C][C]93.4511383566[/C][/ROW]
[ROW][C]Winsorized Mean ( 34 / 50 )[/C][C]12.6842105263158[/C][C]0.135730936501963[/C][C]93.4511383566[/C][/ROW]
[ROW][C]Winsorized Mean ( 35 / 50 )[/C][C]12.6842105263158[/C][C]0.135730936501963[/C][C]93.4511383566[/C][/ROW]
[ROW][C]Winsorized Mean ( 36 / 50 )[/C][C]12.6842105263158[/C][C]0.135730936501963[/C][C]93.4511383566[/C][/ROW]
[ROW][C]Winsorized Mean ( 37 / 50 )[/C][C]12.6842105263158[/C][C]0.135730936501963[/C][C]93.4511383566[/C][/ROW]
[ROW][C]Winsorized Mean ( 38 / 50 )[/C][C]12.6842105263158[/C][C]0.135730936501963[/C][C]93.4511383566[/C][/ROW]
[ROW][C]Winsorized Mean ( 39 / 50 )[/C][C]12.6842105263158[/C][C]0.135730936501963[/C][C]93.4511383566[/C][/ROW]
[ROW][C]Winsorized Mean ( 40 / 50 )[/C][C]12.6842105263158[/C][C]0.135730936501963[/C][C]93.4511383566[/C][/ROW]
[ROW][C]Winsorized Mean ( 41 / 50 )[/C][C]12.6842105263158[/C][C]0.135730936501963[/C][C]93.4511383566[/C][/ROW]
[ROW][C]Winsorized Mean ( 42 / 50 )[/C][C]12.4078947368421[/C][C]0.106168769066457[/C][C]116.869535607739[/C][/ROW]
[ROW][C]Winsorized Mean ( 43 / 50 )[/C][C]12.4078947368421[/C][C]0.106168769066457[/C][C]116.869535607739[/C][/ROW]
[ROW][C]Winsorized Mean ( 44 / 50 )[/C][C]12.4078947368421[/C][C]0.106168769066457[/C][C]116.869535607739[/C][/ROW]
[ROW][C]Winsorized Mean ( 45 / 50 )[/C][C]12.4078947368421[/C][C]0.106168769066457[/C][C]116.869535607739[/C][/ROW]
[ROW][C]Winsorized Mean ( 46 / 50 )[/C][C]12.4078947368421[/C][C]0.106168769066457[/C][C]116.869535607739[/C][/ROW]
[ROW][C]Winsorized Mean ( 47 / 50 )[/C][C]12.4078947368421[/C][C]0.106168769066457[/C][C]116.869535607739[/C][/ROW]
[ROW][C]Winsorized Mean ( 48 / 50 )[/C][C]12.4078947368421[/C][C]0.106168769066457[/C][C]116.869535607739[/C][/ROW]
[ROW][C]Winsorized Mean ( 49 / 50 )[/C][C]12.4078947368421[/C][C]0.106168769066457[/C][C]116.869535607739[/C][/ROW]
[ROW][C]Winsorized Mean ( 50 / 50 )[/C][C]12.4078947368421[/C][C]0.106168769066457[/C][C]116.869535607739[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 50 )[/C][C]12.6866666666667[/C][C]0.263029445475547[/C][C]48.232876147116[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 50 )[/C][C]12.6554054054054[/C][C]0.251254041345977[/C][C]50.3689625751289[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 50 )[/C][C]12.6438356164384[/C][C]0.243913093474682[/C][C]51.8374615988[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 50 )[/C][C]12.625[/C][C]0.237114509463868[/C][C]53.2443165479245[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 50 )[/C][C]12.612676056338[/C][C]0.231356825220903[/C][C]54.516118313325[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 50 )[/C][C]12.6[/C][C]0.225049954486528[/C][C]55.98756964314[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 50 )[/C][C]12.6014492753623[/C][C]0.221202357408646[/C][C]56.9679700659003[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 50 )[/C][C]12.5955882352941[/C][C]0.218276741772858[/C][C]57.7046740435648[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 50 )[/C][C]12.589552238806[/C][C]0.215078725885926[/C][C]58.5346234823952[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 50 )[/C][C]12.5833333333333[/C][C]0.211578359273179[/C][C]59.4736313135239[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 50 )[/C][C]12.5769230769231[/C][C]0.207740889655814[/C][C]60.5413941268883[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 50 )[/C][C]12.5703125[/C][C]0.203525640249397[/C][C]61.7627955111529[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 50 )[/C][C]12.5634920634921[/C][C]0.1988845183776[/C][C]63.169783983081[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 50 )[/C][C]12.5564516129032[/C][C]0.196781878496324[/C][C]63.8089833721033[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 50 )[/C][C]12.5491803278689[/C][C]0.194457289874163[/C][C]64.5343784025255[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 50 )[/C][C]12.5416666666667[/C][C]0.191885759566875[/C][C]65.3600699446158[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 50 )[/C][C]12.5338983050847[/C][C]0.189038373862754[/C][C]66.303460239161[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 50 )[/C][C]12.5258620689655[/C][C]0.185881427479837[/C][C]67.3863023261119[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 50 )[/C][C]12.5175438596491[/C][C]0.182375285131142[/C][C]68.6361852739424[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 50 )[/C][C]12.5089285714286[/C][C]0.1784728653342[/C][C]70.0886857394538[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 50 )[/C][C]12.5[/C][C]0.17411757744595[/C][C]71.7905692426733[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 50 )[/C][C]12.5[/C][C]0.171275830684109[/C][C]72.98169245522[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 50 )[/C][C]12.5[/C][C]0.168098076022968[/C][C]74.3613508003034[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 50 )[/C][C]12.5[/C][C]0.164537053945261[/C][C]75.9707293905878[/C][/ROW]
[ROW][C]Trimmed Mean ( 25 / 50 )[/C][C]12.4901960784314[/C][C]0.162336546552452[/C][C]76.9401366709232[/C][/ROW]
[ROW][C]Trimmed Mean ( 26 / 50 )[/C][C]12.48[/C][C]0.15984841304034[/C][C]78.0739687221699[/C][/ROW]
[ROW][C]Trimmed Mean ( 27 / 50 )[/C][C]12.469387755102[/C][C]0.157031746521729[/C][C]79.4067953219678[/C][/ROW]
[ROW][C]Trimmed Mean ( 28 / 50 )[/C][C]12.4583333333333[/C][C]0.153837367607856[/C][C]80.9837916954653[/C][/ROW]
[ROW][C]Trimmed Mean ( 29 / 50 )[/C][C]12.4468085106383[/C][C]0.150205396837837[/C][C]82.8652549953049[/C][/ROW]
[ROW][C]Trimmed Mean ( 30 / 50 )[/C][C]12.445652173913[/C][C]0.148542955603851[/C][C]83.784869658204[/C][/ROW]
[ROW][C]Trimmed Mean ( 31 / 50 )[/C][C]12.4444444444444[/C][C]0.146631857557334[/C][C]84.8686271302166[/C][/ROW]
[ROW][C]Trimmed Mean ( 32 / 50 )[/C][C]12.4431818181818[/C][C]0.144435226400104[/C][C]86.1506027879418[/C][/ROW]
[ROW][C]Trimmed Mean ( 33 / 50 )[/C][C]12.4418604651163[/C][C]0.141908672932869[/C][C]87.675123781913[/C][/ROW]
[ROW][C]Trimmed Mean ( 34 / 50 )[/C][C]12.4285714285714[/C][C]0.140980211545937[/C][C]88.1582691094326[/C][/ROW]
[ROW][C]Trimmed Mean ( 35 / 50 )[/C][C]12.4146341463415[/C][C]0.13984895227578[/C][C]88.77173510646[/C][/ROW]
[ROW][C]Trimmed Mean ( 36 / 50 )[/C][C]12.4[/C][C]0.138481822597312[/C][C]89.5424378985657[/C][/ROW]
[ROW][C]Trimmed Mean ( 37 / 50 )[/C][C]12.3846153846154[/C][C]0.136838828110705[/C][C]90.5051260348125[/C][/ROW]
[ROW][C]Trimmed Mean ( 38 / 50 )[/C][C]12.3684210526316[/C][C]0.134871095394965[/C][C]91.7054986200793[/C][/ROW]
[ROW][C]Trimmed Mean ( 39 / 50 )[/C][C]12.3513513513514[/C][C]0.132518162792827[/C][C]93.2049697267607[/C][/ROW]
[ROW][C]Trimmed Mean ( 40 / 50 )[/C][C]12.3333333333333[/C][C]0.129704129422923[/C][C]95.0882087425169[/C][/ROW]
[ROW][C]Trimmed Mean ( 41 / 50 )[/C][C]12.3142857142857[/C][C]0.126332003919963[/C][C]97.4755828466661[/C][/ROW]
[ROW][C]Trimmed Mean ( 42 / 50 )[/C][C]12.2941176470588[/C][C]0.122275081595546[/C][C]100.54475111883[/C][/ROW]
[ROW][C]Trimmed Mean ( 43 / 50 )[/C][C]12.2878787878788[/C][C]0.121691940757357[/C][C]100.975288185926[/C][/ROW]
[ROW][C]Trimmed Mean ( 44 / 50 )[/C][C]12.28125[/C][C]0.120902586886605[/C][C]101.57971236396[/C][/ROW]
[ROW][C]Trimmed Mean ( 45 / 50 )[/C][C]12.2741935483871[/C][C]0.119865416418821[/C][C]102.399790657715[/C][/ROW]
[ROW][C]Trimmed Mean ( 46 / 50 )[/C][C]12.2666666666667[/C][C]0.118528326650028[/C][C]103.491435451424[/C][/ROW]
[ROW][C]Trimmed Mean ( 47 / 50 )[/C][C]12.2586206896552[/C][C]0.116825174910173[/C][C]104.931327507798[/C][/ROW]
[ROW][C]Trimmed Mean ( 48 / 50 )[/C][C]12.25[/C][C]0.114670618073466[/C][C]106.827714071898[/C][/ROW]
[ROW][C]Trimmed Mean ( 49 / 50 )[/C][C]12.2407407407407[/C][C]0.111952324587579[/C][C]109.338870682984[/C][/ROW]
[ROW][C]Trimmed Mean ( 50 / 50 )[/C][C]12.2307692307692[/C][C]0.10851869957016[/C][C]112.706559138794[/C][/ROW]
[ROW][C]Median[/C][C]12[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]14.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]12.5555555555556[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]12.5555555555556[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]12.5555555555556[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]12.5555555555556[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]12.5555555555556[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]12.5555555555556[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]12.5555555555556[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]12.5555555555556[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]152[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=108055&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=108055&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 Mean12.71052631578950.27480332631729846.2531749019422
Geometric Mean12.2665415653407
Harmonic Mean11.8131067207993
Quadratic Mean13.1514457880413
Winsorized Mean ( 1 / 50 )12.71710526315790.2736572088658846.4709309718589
Winsorized Mean ( 2 / 50 )12.67763157894740.26412715801602447.9982129599041
Winsorized Mean ( 3 / 50 )12.69736842105260.26104721699710848.6401217646127
Winsorized Mean ( 4 / 50 )12.67105263157890.25577613004825949.5396213446041
Winsorized Mean ( 5 / 50 )12.67105263157890.25577613004825949.5396213446041
Winsorized Mean ( 6 / 50 )12.59210526315790.24240920424718951.945656528444
Winsorized Mean ( 7 / 50 )12.63815789473680.23588588872870353.5774223835502
Winsorized Mean ( 8 / 50 )12.63815789473680.23588588872870353.5774223835502
Winsorized Mean ( 9 / 50 )12.63815789473680.23588588872870353.5774223835502
Winsorized Mean ( 10 / 50 )12.63815789473680.23588588872870353.5774223835502
Winsorized Mean ( 11 / 50 )12.63815789473680.23588588872870353.5774223835502
Winsorized Mean ( 12 / 50 )12.63815789473680.23588588872870353.5774223835502
Winsorized Mean ( 13 / 50 )12.63815789473680.21318293210215259.2831601015832
Winsorized Mean ( 14 / 50 )12.63815789473680.21318293210215259.2831601015832
Winsorized Mean ( 15 / 50 )12.63815789473680.21318293210215259.2831601015832
Winsorized Mean ( 16 / 50 )12.63815789473680.21318293210215259.2831601015832
Winsorized Mean ( 17 / 50 )12.63815789473680.21318293210215259.2831601015832
Winsorized Mean ( 18 / 50 )12.63815789473680.21318293210215259.2831601015832
Winsorized Mean ( 19 / 50 )12.63815789473680.21318293210215259.2831601015832
Winsorized Mean ( 20 / 50 )12.63815789473680.21318293210215259.2831601015832
Winsorized Mean ( 21 / 50 )12.50.1955856511867863.9106188217394
Winsorized Mean ( 22 / 50 )12.50.1955856511867863.9106188217394
Winsorized Mean ( 23 / 50 )12.50.1955856511867863.9106188217394
Winsorized Mean ( 24 / 50 )12.65789473684210.17836669982356970.9655712045054
Winsorized Mean ( 25 / 50 )12.65789473684210.17836669982356970.9655712045054
Winsorized Mean ( 26 / 50 )12.65789473684210.17836669982356970.9655712045054
Winsorized Mean ( 27 / 50 )12.65789473684210.17836669982356970.9655712045054
Winsorized Mean ( 28 / 50 )12.65789473684210.17836669982356970.9655712045054
Winsorized Mean ( 29 / 50 )12.46710526315790.15617803694035379.8262387426428
Winsorized Mean ( 30 / 50 )12.46710526315790.15617803694035379.8262387426428
Winsorized Mean ( 31 / 50 )12.46710526315790.15617803694035379.8262387426428
Winsorized Mean ( 32 / 50 )12.46710526315790.15617803694035379.8262387426428
Winsorized Mean ( 33 / 50 )12.68421052631580.13573093650196393.4511383566
Winsorized Mean ( 34 / 50 )12.68421052631580.13573093650196393.4511383566
Winsorized Mean ( 35 / 50 )12.68421052631580.13573093650196393.4511383566
Winsorized Mean ( 36 / 50 )12.68421052631580.13573093650196393.4511383566
Winsorized Mean ( 37 / 50 )12.68421052631580.13573093650196393.4511383566
Winsorized Mean ( 38 / 50 )12.68421052631580.13573093650196393.4511383566
Winsorized Mean ( 39 / 50 )12.68421052631580.13573093650196393.4511383566
Winsorized Mean ( 40 / 50 )12.68421052631580.13573093650196393.4511383566
Winsorized Mean ( 41 / 50 )12.68421052631580.13573093650196393.4511383566
Winsorized Mean ( 42 / 50 )12.40789473684210.106168769066457116.869535607739
Winsorized Mean ( 43 / 50 )12.40789473684210.106168769066457116.869535607739
Winsorized Mean ( 44 / 50 )12.40789473684210.106168769066457116.869535607739
Winsorized Mean ( 45 / 50 )12.40789473684210.106168769066457116.869535607739
Winsorized Mean ( 46 / 50 )12.40789473684210.106168769066457116.869535607739
Winsorized Mean ( 47 / 50 )12.40789473684210.106168769066457116.869535607739
Winsorized Mean ( 48 / 50 )12.40789473684210.106168769066457116.869535607739
Winsorized Mean ( 49 / 50 )12.40789473684210.106168769066457116.869535607739
Winsorized Mean ( 50 / 50 )12.40789473684210.106168769066457116.869535607739
Trimmed Mean ( 1 / 50 )12.68666666666670.26302944547554748.232876147116
Trimmed Mean ( 2 / 50 )12.65540540540540.25125404134597750.3689625751289
Trimmed Mean ( 3 / 50 )12.64383561643840.24391309347468251.8374615988
Trimmed Mean ( 4 / 50 )12.6250.23711450946386853.2443165479245
Trimmed Mean ( 5 / 50 )12.6126760563380.23135682522090354.516118313325
Trimmed Mean ( 6 / 50 )12.60.22504995448652855.98756964314
Trimmed Mean ( 7 / 50 )12.60144927536230.22120235740864656.9679700659003
Trimmed Mean ( 8 / 50 )12.59558823529410.21827674177285857.7046740435648
Trimmed Mean ( 9 / 50 )12.5895522388060.21507872588592658.5346234823952
Trimmed Mean ( 10 / 50 )12.58333333333330.21157835927317959.4736313135239
Trimmed Mean ( 11 / 50 )12.57692307692310.20774088965581460.5413941268883
Trimmed Mean ( 12 / 50 )12.57031250.20352564024939761.7627955111529
Trimmed Mean ( 13 / 50 )12.56349206349210.198884518377663.169783983081
Trimmed Mean ( 14 / 50 )12.55645161290320.19678187849632463.8089833721033
Trimmed Mean ( 15 / 50 )12.54918032786890.19445728987416364.5343784025255
Trimmed Mean ( 16 / 50 )12.54166666666670.19188575956687565.3600699446158
Trimmed Mean ( 17 / 50 )12.53389830508470.18903837386275466.303460239161
Trimmed Mean ( 18 / 50 )12.52586206896550.18588142747983767.3863023261119
Trimmed Mean ( 19 / 50 )12.51754385964910.18237528513114268.6361852739424
Trimmed Mean ( 20 / 50 )12.50892857142860.178472865334270.0886857394538
Trimmed Mean ( 21 / 50 )12.50.1741175774459571.7905692426733
Trimmed Mean ( 22 / 50 )12.50.17127583068410972.98169245522
Trimmed Mean ( 23 / 50 )12.50.16809807602296874.3613508003034
Trimmed Mean ( 24 / 50 )12.50.16453705394526175.9707293905878
Trimmed Mean ( 25 / 50 )12.49019607843140.16233654655245276.9401366709232
Trimmed Mean ( 26 / 50 )12.480.1598484130403478.0739687221699
Trimmed Mean ( 27 / 50 )12.4693877551020.15703174652172979.4067953219678
Trimmed Mean ( 28 / 50 )12.45833333333330.15383736760785680.9837916954653
Trimmed Mean ( 29 / 50 )12.44680851063830.15020539683783782.8652549953049
Trimmed Mean ( 30 / 50 )12.4456521739130.14854295560385183.784869658204
Trimmed Mean ( 31 / 50 )12.44444444444440.14663185755733484.8686271302166
Trimmed Mean ( 32 / 50 )12.44318181818180.14443522640010486.1506027879418
Trimmed Mean ( 33 / 50 )12.44186046511630.14190867293286987.675123781913
Trimmed Mean ( 34 / 50 )12.42857142857140.14098021154593788.1582691094326
Trimmed Mean ( 35 / 50 )12.41463414634150.1398489522757888.77173510646
Trimmed Mean ( 36 / 50 )12.40.13848182259731289.5424378985657
Trimmed Mean ( 37 / 50 )12.38461538461540.13683882811070590.5051260348125
Trimmed Mean ( 38 / 50 )12.36842105263160.13487109539496591.7054986200793
Trimmed Mean ( 39 / 50 )12.35135135135140.13251816279282793.2049697267607
Trimmed Mean ( 40 / 50 )12.33333333333330.12970412942292395.0882087425169
Trimmed Mean ( 41 / 50 )12.31428571428570.12633200391996397.4755828466661
Trimmed Mean ( 42 / 50 )12.29411764705880.122275081595546100.54475111883
Trimmed Mean ( 43 / 50 )12.28787878787880.121691940757357100.975288185926
Trimmed Mean ( 44 / 50 )12.281250.120902586886605101.57971236396
Trimmed Mean ( 45 / 50 )12.27419354838710.119865416418821102.399790657715
Trimmed Mean ( 46 / 50 )12.26666666666670.118528326650028103.491435451424
Trimmed Mean ( 47 / 50 )12.25862068965520.116825174910173104.931327507798
Trimmed Mean ( 48 / 50 )12.250.114670618073466106.827714071898
Trimmed Mean ( 49 / 50 )12.24074074074070.111952324587579109.338870682984
Trimmed Mean ( 50 / 50 )12.23076923076920.10851869957016112.706559138794
Median12
Midrange14.5
Midmean - Weighted Average at Xnp12.5555555555556
Midmean - Weighted Average at X(n+1)p12.5555555555556
Midmean - Empirical Distribution Function12.5555555555556
Midmean - Empirical Distribution Function - Averaging12.5555555555556
Midmean - Empirical Distribution Function - Interpolation12.5555555555556
Midmean - Closest Observation12.5555555555556
Midmean - True Basic - Statistics Graphics Toolkit12.5555555555556
Midmean - MS Excel (old versions)12.5555555555556
Number of observations152



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')