Free Statistics

of Irreproducible Research!

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationMon, 15 Dec 2014 18:16:29 +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/2014/Dec/15/t14186674039wtqudocps7n3fl.htm/, Retrieved Thu, 16 May 2024 04:41:00 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=268840, Retrieved Thu, 16 May 2024 04:41:00 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact74
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Central Tendency] [] [2014-11-04 10:08:09] [32b17a345b130fdf5cc88718ed94a974]
- R  D  [Central Tendency] [] [2014-12-15 18:08:27] [6656361aa4da5489a6a45e803df0211c]
-    D      [Central Tendency] [] [2014-12-15 18:16:29] [457d039f1491608548baeb848eb0333c] [Current]
-   PD        [Central Tendency] [] [2014-12-17 16:14:22] [6656361aa4da5489a6a45e803df0211c]
Feedback Forum

Post a new message
Dataseries X:
16,1
12,7
12,3
11,6
12,1
12,6
4,3
5,6
9,6
12,6
18,9
11,6
14,6
13,85
15,9
10,95
15,1
15,95
14,6
17,6
15,35
12,9
12,6
10,35
15,4
9,6
14,85
13,6
12,65
16,6
11,2
15,85
11,15
15,6
13,1
12,4
14,9
11,2
14,6
14,75
7,85
7,85
10,95
9,95
14,9
13,4
16,85
10,95
12,2
15,2
8,1
7,4
6,7
12,6
13,3
11,1
8,2
11,4
6,4
11,9
13,8
11,7
10,9
9,9
9,0
10,8
13,0
10,8
10,9
13,3
10,1
14,3
9,3
14,5
7,7
4,35
12,7
18,1
17,85
17,1
16,1
14,7
10,6
12,6
16,2
13,6
14,1
14,5
14,75
14,8
12,45
12,65
17,35
8,6
16,1
17,75
15,25
17,65
13,6
18,25
16
18,25
18,95
16,1
15,4
15,4
13,35
19,1
19,25
12,75
9,85
15,25
12,4
18,15
12,35
15,6
18,4
12,85
9,5
4,5
13,6
11,7
14,05
13,35
11,85
13,2




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Sir Ronald Aylmer Fisher' @ fisher.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 & 1 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=268840&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]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=268840&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=268840&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 time1 seconds
R Server'Sir Ronald Aylmer Fisher' @ fisher.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean13.07341269841270.29087917445135844.9444781431023
Geometric Mean12.5881966505307
Harmonic Mean11.9772983788691
Quadratic Mean13.4718393825493
Winsorized Mean ( 1 / 42 )13.0726190476190.29058376228291644.9874381999754
Winsorized Mean ( 2 / 42 )13.0726190476190.28962515848300245.136338003545
Winsorized Mean ( 3 / 42 )13.0976190476190.28355669467140246.1904772264226
Winsorized Mean ( 4 / 42 )13.10714285714290.27587938144518247.5104112111666
Winsorized Mean ( 5 / 42 )13.11309523809520.27269622529935648.0868234376921
Winsorized Mean ( 6 / 42 )13.14642857142860.26668462949704749.2957865484112
Winsorized Mean ( 7 / 42 )13.15753968253970.26301733147089250.0253713660532
Winsorized Mean ( 8 / 42 )13.16388888888890.26096988750993650.4421755877397
Winsorized Mean ( 9 / 42 )13.14603174603170.25831788167282950.8909087551352
Winsorized Mean ( 10 / 42 )13.15793650793650.25395750969336451.8115669185126
Winsorized Mean ( 11 / 42 )13.15793650793650.25131742573026452.3558462756927
Winsorized Mean ( 12 / 42 )13.19126984126980.24476751481022653.8930578737024
Winsorized Mean ( 13 / 42 )13.2067460317460.2350355279963256.1904242491918
Winsorized Mean ( 14 / 42 )13.21230158730160.22647729239544958.3383060065545
Winsorized Mean ( 15 / 42 )13.20634920634920.2191976596785860.2485867126243
Winsorized Mean ( 16 / 42 )13.18730158730160.21334147046083861.8131184659774
Winsorized Mean ( 17 / 42 )13.13333333333330.2066812590854463.5439003586877
Winsorized Mean ( 18 / 42 )13.15476190476190.20019072538609865.7111456057264
Winsorized Mean ( 19 / 42 )13.16230158730160.19919894060719266.0761625899249
Winsorized Mean ( 20 / 42 )13.17023809523810.19816313511325466.4615953300852
Winsorized Mean ( 21 / 42 )13.19523809523810.19495007791693467.6852158061739
Winsorized Mean ( 22 / 42 )13.22142857142860.18742484510426670.5425610146475
Winsorized Mean ( 23 / 42 )13.25793650793650.18085898452996673.3053795607254
Winsorized Mean ( 24 / 42 )13.28650793650790.17532229976003375.783331354274
Winsorized Mean ( 25 / 42 )13.27658730158730.17414433578230276.2389844145397
Winsorized Mean ( 26 / 42 )13.24563492063490.16582072920875779.8792466046848
Winsorized Mean ( 27 / 42 )13.24563492063490.16582072920875779.8792466046848
Winsorized Mean ( 28 / 42 )13.21230158730160.15959938587216982.7841630786974
Winsorized Mean ( 29 / 42 )13.21230158730160.15959938587216982.7841630786974
Winsorized Mean ( 30 / 42 )13.21230158730160.15959938587216982.7841630786974
Winsorized Mean ( 31 / 42 )13.23690476190480.15411001900974485.8925645909356
Winsorized Mean ( 32 / 42 )13.22420634920630.14993727167431788.1982591888897
Winsorized Mean ( 33 / 42 )13.23730158730160.14849395958848189.1437040535916
Winsorized Mean ( 34 / 42 )13.22380952380950.14703710177044589.9351889052779
Winsorized Mean ( 35 / 42 )13.25158730158730.13801303884564196.0169228387789
Winsorized Mean ( 36 / 42 )13.25158730158730.125887246738534105.265526452498
Winsorized Mean ( 37 / 42 )13.25158730158730.125887246738534105.265526452498
Winsorized Mean ( 38 / 42 )13.26666666666670.12116629003675109.491399486135
Winsorized Mean ( 39 / 42 )13.25119047619050.119555345868027110.837289457704
Winsorized Mean ( 40 / 42 )13.28293650793650.11302080535875117.526471925004
Winsorized Mean ( 41 / 42 )13.29920634920630.111378069322586119.405969506328
Winsorized Mean ( 42 / 42 )13.34920634920630.103048738856887129.542646492215
Trimmed Mean ( 1 / 42 )13.09435483870970.282527399503946.3472033569222
Trimmed Mean ( 2 / 42 )13.11680327868850.27357642932051947.9456629771311
Trimmed Mean ( 3 / 42 )13.140.26416561734895749.7415225034465
Trimmed Mean ( 4 / 42 )13.15508474576270.25623500463539951.339920415953
Trimmed Mean ( 5 / 42 )13.16810344827590.2499313223146752.6868874470118
Trimmed Mean ( 6 / 42 )13.18026315789470.24378839505569254.0643583747445
Trimmed Mean ( 7 / 42 )13.18660714285710.23838779584811355.3157811453523
Trimmed Mean ( 8 / 42 )13.19136363636360.23314835709956756.5792690991607
Trimmed Mean ( 9 / 42 )13.19537037037040.22769627594608357.951630150925
Trimmed Mean ( 10 / 42 )13.20188679245280.22207156326975759.4487947852022
Trimmed Mean ( 11 / 42 )13.20721153846150.21651542523318160.9989404876707
Trimmed Mean ( 12 / 42 )13.21274509803920.21070032142525162.7087087891635
Trimmed Mean ( 13 / 42 )13.2150.20519207557502864.4030719167222
Trimmed Mean ( 14 / 42 )13.21581632653060.20045261867763965.9298761658176
Trimmed Mean ( 15 / 42 )13.21614583333330.19633217744154967.3152307765137
Trimmed Mean ( 16 / 42 )13.21702127659570.19267285332833768.5982537149248
Trimmed Mean ( 17 / 42 )13.21956521739130.18929792793222469.834706390048
Trimmed Mean ( 18 / 42 )13.22666666666670.18630080518474570.9962936206875
Trimmed Mean ( 19 / 42 )13.23238636363640.18369758113398572.0335362172512
Trimmed Mean ( 20 / 42 )13.23779069767440.18082486188234373.2078020681017
Trimmed Mean ( 21 / 42 )13.24285714285710.17764302548805274.5475771225694
Trimmed Mean ( 22 / 42 )13.24634146341460.17438061009012175.9622383278099
Trimmed Mean ( 23 / 42 )13.2481250.1715538714657177.2242846332267
Trimmed Mean ( 24 / 42 )13.24743589743590.16907491890198578.3524604563946
Trimmed Mean ( 25 / 42 )13.24473684210530.16684002987253179.3858455445285
Trimmed Mean ( 26 / 42 )13.24256756756760.16434178236072780.5794325541656
Trimmed Mean ( 27 / 42 )13.24236111111110.16241845107448581.5323691582194
Trimmed Mean ( 28 / 42 )13.24214285714290.16010360166250582.709837378031
Trimmed Mean ( 29 / 42 )13.24411764705880.15811224984517483.7640199290548
Trimmed Mean ( 30 / 42 )13.24621212121210.15568972268795885.0808383014522
Trimmed Mean ( 31 / 42 )13.24843750.1527483371480386.7337592497707
Trimmed Mean ( 32 / 42 )13.24919354838710.14995368549700788.3552378487661
Trimmed Mean ( 33 / 42 )13.25083333333330.14713119009853690.0613481373936
Trimmed Mean ( 34 / 42 )13.2517241379310.14387034938024892.1087923607307
Trimmed Mean ( 35 / 42 )13.25357142857140.14006525116016694.6242648964793
Trimmed Mean ( 36 / 42 )13.25370370370370.13682439543051796.8665248766571
Trimmed Mean ( 37 / 42 )13.25384615384620.13472253869281498.3788331369467
Trimmed Mean ( 38 / 42 )13.2540.132000618427741100.408620488815
Trimmed Mean ( 39 / 42 )13.2531250.129317341624618102.485288001598
Trimmed Mean ( 40 / 42 )13.25326086956520.126112462021343105.090810671211
Trimmed Mean ( 41 / 42 )13.25113636363640.123189731418512107.566890608912
Trimmed Mean ( 42 / 42 )13.2476190476190.119619416579175110.74806604537
Median13.15
Midrange11.775
Midmean - Weighted Average at Xnp13.2150793650794
Midmean - Weighted Average at X(n+1)p13.2484375
Midmean - Empirical Distribution Function13.2484375
Midmean - Empirical Distribution Function - Averaging13.2484375
Midmean - Empirical Distribution Function - Interpolation13.2491935483871
Midmean - Closest Observation13.2484375
Midmean - True Basic - Statistics Graphics Toolkit13.2484375
Midmean - MS Excel (old versions)13.2484375
Number of observations126

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 13.0734126984127 & 0.290879174451358 & 44.9444781431023 \tabularnewline
Geometric Mean & 12.5881966505307 &  &  \tabularnewline
Harmonic Mean & 11.9772983788691 &  &  \tabularnewline
Quadratic Mean & 13.4718393825493 &  &  \tabularnewline
Winsorized Mean ( 1 / 42 ) & 13.072619047619 & 0.290583762282916 & 44.9874381999754 \tabularnewline
Winsorized Mean ( 2 / 42 ) & 13.072619047619 & 0.289625158483002 & 45.136338003545 \tabularnewline
Winsorized Mean ( 3 / 42 ) & 13.097619047619 & 0.283556694671402 & 46.1904772264226 \tabularnewline
Winsorized Mean ( 4 / 42 ) & 13.1071428571429 & 0.275879381445182 & 47.5104112111666 \tabularnewline
Winsorized Mean ( 5 / 42 ) & 13.1130952380952 & 0.272696225299356 & 48.0868234376921 \tabularnewline
Winsorized Mean ( 6 / 42 ) & 13.1464285714286 & 0.266684629497047 & 49.2957865484112 \tabularnewline
Winsorized Mean ( 7 / 42 ) & 13.1575396825397 & 0.263017331470892 & 50.0253713660532 \tabularnewline
Winsorized Mean ( 8 / 42 ) & 13.1638888888889 & 0.260969887509936 & 50.4421755877397 \tabularnewline
Winsorized Mean ( 9 / 42 ) & 13.1460317460317 & 0.258317881672829 & 50.8909087551352 \tabularnewline
Winsorized Mean ( 10 / 42 ) & 13.1579365079365 & 0.253957509693364 & 51.8115669185126 \tabularnewline
Winsorized Mean ( 11 / 42 ) & 13.1579365079365 & 0.251317425730264 & 52.3558462756927 \tabularnewline
Winsorized Mean ( 12 / 42 ) & 13.1912698412698 & 0.244767514810226 & 53.8930578737024 \tabularnewline
Winsorized Mean ( 13 / 42 ) & 13.206746031746 & 0.23503552799632 & 56.1904242491918 \tabularnewline
Winsorized Mean ( 14 / 42 ) & 13.2123015873016 & 0.226477292395449 & 58.3383060065545 \tabularnewline
Winsorized Mean ( 15 / 42 ) & 13.2063492063492 & 0.21919765967858 & 60.2485867126243 \tabularnewline
Winsorized Mean ( 16 / 42 ) & 13.1873015873016 & 0.213341470460838 & 61.8131184659774 \tabularnewline
Winsorized Mean ( 17 / 42 ) & 13.1333333333333 & 0.20668125908544 & 63.5439003586877 \tabularnewline
Winsorized Mean ( 18 / 42 ) & 13.1547619047619 & 0.200190725386098 & 65.7111456057264 \tabularnewline
Winsorized Mean ( 19 / 42 ) & 13.1623015873016 & 0.199198940607192 & 66.0761625899249 \tabularnewline
Winsorized Mean ( 20 / 42 ) & 13.1702380952381 & 0.198163135113254 & 66.4615953300852 \tabularnewline
Winsorized Mean ( 21 / 42 ) & 13.1952380952381 & 0.194950077916934 & 67.6852158061739 \tabularnewline
Winsorized Mean ( 22 / 42 ) & 13.2214285714286 & 0.187424845104266 & 70.5425610146475 \tabularnewline
Winsorized Mean ( 23 / 42 ) & 13.2579365079365 & 0.180858984529966 & 73.3053795607254 \tabularnewline
Winsorized Mean ( 24 / 42 ) & 13.2865079365079 & 0.175322299760033 & 75.783331354274 \tabularnewline
Winsorized Mean ( 25 / 42 ) & 13.2765873015873 & 0.174144335782302 & 76.2389844145397 \tabularnewline
Winsorized Mean ( 26 / 42 ) & 13.2456349206349 & 0.165820729208757 & 79.8792466046848 \tabularnewline
Winsorized Mean ( 27 / 42 ) & 13.2456349206349 & 0.165820729208757 & 79.8792466046848 \tabularnewline
Winsorized Mean ( 28 / 42 ) & 13.2123015873016 & 0.159599385872169 & 82.7841630786974 \tabularnewline
Winsorized Mean ( 29 / 42 ) & 13.2123015873016 & 0.159599385872169 & 82.7841630786974 \tabularnewline
Winsorized Mean ( 30 / 42 ) & 13.2123015873016 & 0.159599385872169 & 82.7841630786974 \tabularnewline
Winsorized Mean ( 31 / 42 ) & 13.2369047619048 & 0.154110019009744 & 85.8925645909356 \tabularnewline
Winsorized Mean ( 32 / 42 ) & 13.2242063492063 & 0.149937271674317 & 88.1982591888897 \tabularnewline
Winsorized Mean ( 33 / 42 ) & 13.2373015873016 & 0.148493959588481 & 89.1437040535916 \tabularnewline
Winsorized Mean ( 34 / 42 ) & 13.2238095238095 & 0.147037101770445 & 89.9351889052779 \tabularnewline
Winsorized Mean ( 35 / 42 ) & 13.2515873015873 & 0.138013038845641 & 96.0169228387789 \tabularnewline
Winsorized Mean ( 36 / 42 ) & 13.2515873015873 & 0.125887246738534 & 105.265526452498 \tabularnewline
Winsorized Mean ( 37 / 42 ) & 13.2515873015873 & 0.125887246738534 & 105.265526452498 \tabularnewline
Winsorized Mean ( 38 / 42 ) & 13.2666666666667 & 0.12116629003675 & 109.491399486135 \tabularnewline
Winsorized Mean ( 39 / 42 ) & 13.2511904761905 & 0.119555345868027 & 110.837289457704 \tabularnewline
Winsorized Mean ( 40 / 42 ) & 13.2829365079365 & 0.11302080535875 & 117.526471925004 \tabularnewline
Winsorized Mean ( 41 / 42 ) & 13.2992063492063 & 0.111378069322586 & 119.405969506328 \tabularnewline
Winsorized Mean ( 42 / 42 ) & 13.3492063492063 & 0.103048738856887 & 129.542646492215 \tabularnewline
Trimmed Mean ( 1 / 42 ) & 13.0943548387097 & 0.2825273995039 & 46.3472033569222 \tabularnewline
Trimmed Mean ( 2 / 42 ) & 13.1168032786885 & 0.273576429320519 & 47.9456629771311 \tabularnewline
Trimmed Mean ( 3 / 42 ) & 13.14 & 0.264165617348957 & 49.7415225034465 \tabularnewline
Trimmed Mean ( 4 / 42 ) & 13.1550847457627 & 0.256235004635399 & 51.339920415953 \tabularnewline
Trimmed Mean ( 5 / 42 ) & 13.1681034482759 & 0.24993132231467 & 52.6868874470118 \tabularnewline
Trimmed Mean ( 6 / 42 ) & 13.1802631578947 & 0.243788395055692 & 54.0643583747445 \tabularnewline
Trimmed Mean ( 7 / 42 ) & 13.1866071428571 & 0.238387795848113 & 55.3157811453523 \tabularnewline
Trimmed Mean ( 8 / 42 ) & 13.1913636363636 & 0.233148357099567 & 56.5792690991607 \tabularnewline
Trimmed Mean ( 9 / 42 ) & 13.1953703703704 & 0.227696275946083 & 57.951630150925 \tabularnewline
Trimmed Mean ( 10 / 42 ) & 13.2018867924528 & 0.222071563269757 & 59.4487947852022 \tabularnewline
Trimmed Mean ( 11 / 42 ) & 13.2072115384615 & 0.216515425233181 & 60.9989404876707 \tabularnewline
Trimmed Mean ( 12 / 42 ) & 13.2127450980392 & 0.210700321425251 & 62.7087087891635 \tabularnewline
Trimmed Mean ( 13 / 42 ) & 13.215 & 0.205192075575028 & 64.4030719167222 \tabularnewline
Trimmed Mean ( 14 / 42 ) & 13.2158163265306 & 0.200452618677639 & 65.9298761658176 \tabularnewline
Trimmed Mean ( 15 / 42 ) & 13.2161458333333 & 0.196332177441549 & 67.3152307765137 \tabularnewline
Trimmed Mean ( 16 / 42 ) & 13.2170212765957 & 0.192672853328337 & 68.5982537149248 \tabularnewline
Trimmed Mean ( 17 / 42 ) & 13.2195652173913 & 0.189297927932224 & 69.834706390048 \tabularnewline
Trimmed Mean ( 18 / 42 ) & 13.2266666666667 & 0.186300805184745 & 70.9962936206875 \tabularnewline
Trimmed Mean ( 19 / 42 ) & 13.2323863636364 & 0.183697581133985 & 72.0335362172512 \tabularnewline
Trimmed Mean ( 20 / 42 ) & 13.2377906976744 & 0.180824861882343 & 73.2078020681017 \tabularnewline
Trimmed Mean ( 21 / 42 ) & 13.2428571428571 & 0.177643025488052 & 74.5475771225694 \tabularnewline
Trimmed Mean ( 22 / 42 ) & 13.2463414634146 & 0.174380610090121 & 75.9622383278099 \tabularnewline
Trimmed Mean ( 23 / 42 ) & 13.248125 & 0.17155387146571 & 77.2242846332267 \tabularnewline
Trimmed Mean ( 24 / 42 ) & 13.2474358974359 & 0.169074918901985 & 78.3524604563946 \tabularnewline
Trimmed Mean ( 25 / 42 ) & 13.2447368421053 & 0.166840029872531 & 79.3858455445285 \tabularnewline
Trimmed Mean ( 26 / 42 ) & 13.2425675675676 & 0.164341782360727 & 80.5794325541656 \tabularnewline
Trimmed Mean ( 27 / 42 ) & 13.2423611111111 & 0.162418451074485 & 81.5323691582194 \tabularnewline
Trimmed Mean ( 28 / 42 ) & 13.2421428571429 & 0.160103601662505 & 82.709837378031 \tabularnewline
Trimmed Mean ( 29 / 42 ) & 13.2441176470588 & 0.158112249845174 & 83.7640199290548 \tabularnewline
Trimmed Mean ( 30 / 42 ) & 13.2462121212121 & 0.155689722687958 & 85.0808383014522 \tabularnewline
Trimmed Mean ( 31 / 42 ) & 13.2484375 & 0.15274833714803 & 86.7337592497707 \tabularnewline
Trimmed Mean ( 32 / 42 ) & 13.2491935483871 & 0.149953685497007 & 88.3552378487661 \tabularnewline
Trimmed Mean ( 33 / 42 ) & 13.2508333333333 & 0.147131190098536 & 90.0613481373936 \tabularnewline
Trimmed Mean ( 34 / 42 ) & 13.251724137931 & 0.143870349380248 & 92.1087923607307 \tabularnewline
Trimmed Mean ( 35 / 42 ) & 13.2535714285714 & 0.140065251160166 & 94.6242648964793 \tabularnewline
Trimmed Mean ( 36 / 42 ) & 13.2537037037037 & 0.136824395430517 & 96.8665248766571 \tabularnewline
Trimmed Mean ( 37 / 42 ) & 13.2538461538462 & 0.134722538692814 & 98.3788331369467 \tabularnewline
Trimmed Mean ( 38 / 42 ) & 13.254 & 0.132000618427741 & 100.408620488815 \tabularnewline
Trimmed Mean ( 39 / 42 ) & 13.253125 & 0.129317341624618 & 102.485288001598 \tabularnewline
Trimmed Mean ( 40 / 42 ) & 13.2532608695652 & 0.126112462021343 & 105.090810671211 \tabularnewline
Trimmed Mean ( 41 / 42 ) & 13.2511363636364 & 0.123189731418512 & 107.566890608912 \tabularnewline
Trimmed Mean ( 42 / 42 ) & 13.247619047619 & 0.119619416579175 & 110.74806604537 \tabularnewline
Median & 13.15 &  &  \tabularnewline
Midrange & 11.775 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 13.2150793650794 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 13.2484375 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 13.2484375 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 13.2484375 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 13.2491935483871 &  &  \tabularnewline
Midmean - Closest Observation & 13.2484375 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 13.2484375 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 13.2484375 &  &  \tabularnewline
Number of observations & 126 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=268840&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]13.0734126984127[/C][C]0.290879174451358[/C][C]44.9444781431023[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]12.5881966505307[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]11.9772983788691[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]13.4718393825493[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 42 )[/C][C]13.072619047619[/C][C]0.290583762282916[/C][C]44.9874381999754[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 42 )[/C][C]13.072619047619[/C][C]0.289625158483002[/C][C]45.136338003545[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 42 )[/C][C]13.097619047619[/C][C]0.283556694671402[/C][C]46.1904772264226[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 42 )[/C][C]13.1071428571429[/C][C]0.275879381445182[/C][C]47.5104112111666[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 42 )[/C][C]13.1130952380952[/C][C]0.272696225299356[/C][C]48.0868234376921[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 42 )[/C][C]13.1464285714286[/C][C]0.266684629497047[/C][C]49.2957865484112[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 42 )[/C][C]13.1575396825397[/C][C]0.263017331470892[/C][C]50.0253713660532[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 42 )[/C][C]13.1638888888889[/C][C]0.260969887509936[/C][C]50.4421755877397[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 42 )[/C][C]13.1460317460317[/C][C]0.258317881672829[/C][C]50.8909087551352[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 42 )[/C][C]13.1579365079365[/C][C]0.253957509693364[/C][C]51.8115669185126[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 42 )[/C][C]13.1579365079365[/C][C]0.251317425730264[/C][C]52.3558462756927[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 42 )[/C][C]13.1912698412698[/C][C]0.244767514810226[/C][C]53.8930578737024[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 42 )[/C][C]13.206746031746[/C][C]0.23503552799632[/C][C]56.1904242491918[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 42 )[/C][C]13.2123015873016[/C][C]0.226477292395449[/C][C]58.3383060065545[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 42 )[/C][C]13.2063492063492[/C][C]0.21919765967858[/C][C]60.2485867126243[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 42 )[/C][C]13.1873015873016[/C][C]0.213341470460838[/C][C]61.8131184659774[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 42 )[/C][C]13.1333333333333[/C][C]0.20668125908544[/C][C]63.5439003586877[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 42 )[/C][C]13.1547619047619[/C][C]0.200190725386098[/C][C]65.7111456057264[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 42 )[/C][C]13.1623015873016[/C][C]0.199198940607192[/C][C]66.0761625899249[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 42 )[/C][C]13.1702380952381[/C][C]0.198163135113254[/C][C]66.4615953300852[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 42 )[/C][C]13.1952380952381[/C][C]0.194950077916934[/C][C]67.6852158061739[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 42 )[/C][C]13.2214285714286[/C][C]0.187424845104266[/C][C]70.5425610146475[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 42 )[/C][C]13.2579365079365[/C][C]0.180858984529966[/C][C]73.3053795607254[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 42 )[/C][C]13.2865079365079[/C][C]0.175322299760033[/C][C]75.783331354274[/C][/ROW]
[ROW][C]Winsorized Mean ( 25 / 42 )[/C][C]13.2765873015873[/C][C]0.174144335782302[/C][C]76.2389844145397[/C][/ROW]
[ROW][C]Winsorized Mean ( 26 / 42 )[/C][C]13.2456349206349[/C][C]0.165820729208757[/C][C]79.8792466046848[/C][/ROW]
[ROW][C]Winsorized Mean ( 27 / 42 )[/C][C]13.2456349206349[/C][C]0.165820729208757[/C][C]79.8792466046848[/C][/ROW]
[ROW][C]Winsorized Mean ( 28 / 42 )[/C][C]13.2123015873016[/C][C]0.159599385872169[/C][C]82.7841630786974[/C][/ROW]
[ROW][C]Winsorized Mean ( 29 / 42 )[/C][C]13.2123015873016[/C][C]0.159599385872169[/C][C]82.7841630786974[/C][/ROW]
[ROW][C]Winsorized Mean ( 30 / 42 )[/C][C]13.2123015873016[/C][C]0.159599385872169[/C][C]82.7841630786974[/C][/ROW]
[ROW][C]Winsorized Mean ( 31 / 42 )[/C][C]13.2369047619048[/C][C]0.154110019009744[/C][C]85.8925645909356[/C][/ROW]
[ROW][C]Winsorized Mean ( 32 / 42 )[/C][C]13.2242063492063[/C][C]0.149937271674317[/C][C]88.1982591888897[/C][/ROW]
[ROW][C]Winsorized Mean ( 33 / 42 )[/C][C]13.2373015873016[/C][C]0.148493959588481[/C][C]89.1437040535916[/C][/ROW]
[ROW][C]Winsorized Mean ( 34 / 42 )[/C][C]13.2238095238095[/C][C]0.147037101770445[/C][C]89.9351889052779[/C][/ROW]
[ROW][C]Winsorized Mean ( 35 / 42 )[/C][C]13.2515873015873[/C][C]0.138013038845641[/C][C]96.0169228387789[/C][/ROW]
[ROW][C]Winsorized Mean ( 36 / 42 )[/C][C]13.2515873015873[/C][C]0.125887246738534[/C][C]105.265526452498[/C][/ROW]
[ROW][C]Winsorized Mean ( 37 / 42 )[/C][C]13.2515873015873[/C][C]0.125887246738534[/C][C]105.265526452498[/C][/ROW]
[ROW][C]Winsorized Mean ( 38 / 42 )[/C][C]13.2666666666667[/C][C]0.12116629003675[/C][C]109.491399486135[/C][/ROW]
[ROW][C]Winsorized Mean ( 39 / 42 )[/C][C]13.2511904761905[/C][C]0.119555345868027[/C][C]110.837289457704[/C][/ROW]
[ROW][C]Winsorized Mean ( 40 / 42 )[/C][C]13.2829365079365[/C][C]0.11302080535875[/C][C]117.526471925004[/C][/ROW]
[ROW][C]Winsorized Mean ( 41 / 42 )[/C][C]13.2992063492063[/C][C]0.111378069322586[/C][C]119.405969506328[/C][/ROW]
[ROW][C]Winsorized Mean ( 42 / 42 )[/C][C]13.3492063492063[/C][C]0.103048738856887[/C][C]129.542646492215[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 42 )[/C][C]13.0943548387097[/C][C]0.2825273995039[/C][C]46.3472033569222[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 42 )[/C][C]13.1168032786885[/C][C]0.273576429320519[/C][C]47.9456629771311[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 42 )[/C][C]13.14[/C][C]0.264165617348957[/C][C]49.7415225034465[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 42 )[/C][C]13.1550847457627[/C][C]0.256235004635399[/C][C]51.339920415953[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 42 )[/C][C]13.1681034482759[/C][C]0.24993132231467[/C][C]52.6868874470118[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 42 )[/C][C]13.1802631578947[/C][C]0.243788395055692[/C][C]54.0643583747445[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 42 )[/C][C]13.1866071428571[/C][C]0.238387795848113[/C][C]55.3157811453523[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 42 )[/C][C]13.1913636363636[/C][C]0.233148357099567[/C][C]56.5792690991607[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 42 )[/C][C]13.1953703703704[/C][C]0.227696275946083[/C][C]57.951630150925[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 42 )[/C][C]13.2018867924528[/C][C]0.222071563269757[/C][C]59.4487947852022[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 42 )[/C][C]13.2072115384615[/C][C]0.216515425233181[/C][C]60.9989404876707[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 42 )[/C][C]13.2127450980392[/C][C]0.210700321425251[/C][C]62.7087087891635[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 42 )[/C][C]13.215[/C][C]0.205192075575028[/C][C]64.4030719167222[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 42 )[/C][C]13.2158163265306[/C][C]0.200452618677639[/C][C]65.9298761658176[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 42 )[/C][C]13.2161458333333[/C][C]0.196332177441549[/C][C]67.3152307765137[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 42 )[/C][C]13.2170212765957[/C][C]0.192672853328337[/C][C]68.5982537149248[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 42 )[/C][C]13.2195652173913[/C][C]0.189297927932224[/C][C]69.834706390048[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 42 )[/C][C]13.2266666666667[/C][C]0.186300805184745[/C][C]70.9962936206875[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 42 )[/C][C]13.2323863636364[/C][C]0.183697581133985[/C][C]72.0335362172512[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 42 )[/C][C]13.2377906976744[/C][C]0.180824861882343[/C][C]73.2078020681017[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 42 )[/C][C]13.2428571428571[/C][C]0.177643025488052[/C][C]74.5475771225694[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 42 )[/C][C]13.2463414634146[/C][C]0.174380610090121[/C][C]75.9622383278099[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 42 )[/C][C]13.248125[/C][C]0.17155387146571[/C][C]77.2242846332267[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 42 )[/C][C]13.2474358974359[/C][C]0.169074918901985[/C][C]78.3524604563946[/C][/ROW]
[ROW][C]Trimmed Mean ( 25 / 42 )[/C][C]13.2447368421053[/C][C]0.166840029872531[/C][C]79.3858455445285[/C][/ROW]
[ROW][C]Trimmed Mean ( 26 / 42 )[/C][C]13.2425675675676[/C][C]0.164341782360727[/C][C]80.5794325541656[/C][/ROW]
[ROW][C]Trimmed Mean ( 27 / 42 )[/C][C]13.2423611111111[/C][C]0.162418451074485[/C][C]81.5323691582194[/C][/ROW]
[ROW][C]Trimmed Mean ( 28 / 42 )[/C][C]13.2421428571429[/C][C]0.160103601662505[/C][C]82.709837378031[/C][/ROW]
[ROW][C]Trimmed Mean ( 29 / 42 )[/C][C]13.2441176470588[/C][C]0.158112249845174[/C][C]83.7640199290548[/C][/ROW]
[ROW][C]Trimmed Mean ( 30 / 42 )[/C][C]13.2462121212121[/C][C]0.155689722687958[/C][C]85.0808383014522[/C][/ROW]
[ROW][C]Trimmed Mean ( 31 / 42 )[/C][C]13.2484375[/C][C]0.15274833714803[/C][C]86.7337592497707[/C][/ROW]
[ROW][C]Trimmed Mean ( 32 / 42 )[/C][C]13.2491935483871[/C][C]0.149953685497007[/C][C]88.3552378487661[/C][/ROW]
[ROW][C]Trimmed Mean ( 33 / 42 )[/C][C]13.2508333333333[/C][C]0.147131190098536[/C][C]90.0613481373936[/C][/ROW]
[ROW][C]Trimmed Mean ( 34 / 42 )[/C][C]13.251724137931[/C][C]0.143870349380248[/C][C]92.1087923607307[/C][/ROW]
[ROW][C]Trimmed Mean ( 35 / 42 )[/C][C]13.2535714285714[/C][C]0.140065251160166[/C][C]94.6242648964793[/C][/ROW]
[ROW][C]Trimmed Mean ( 36 / 42 )[/C][C]13.2537037037037[/C][C]0.136824395430517[/C][C]96.8665248766571[/C][/ROW]
[ROW][C]Trimmed Mean ( 37 / 42 )[/C][C]13.2538461538462[/C][C]0.134722538692814[/C][C]98.3788331369467[/C][/ROW]
[ROW][C]Trimmed Mean ( 38 / 42 )[/C][C]13.254[/C][C]0.132000618427741[/C][C]100.408620488815[/C][/ROW]
[ROW][C]Trimmed Mean ( 39 / 42 )[/C][C]13.253125[/C][C]0.129317341624618[/C][C]102.485288001598[/C][/ROW]
[ROW][C]Trimmed Mean ( 40 / 42 )[/C][C]13.2532608695652[/C][C]0.126112462021343[/C][C]105.090810671211[/C][/ROW]
[ROW][C]Trimmed Mean ( 41 / 42 )[/C][C]13.2511363636364[/C][C]0.123189731418512[/C][C]107.566890608912[/C][/ROW]
[ROW][C]Trimmed Mean ( 42 / 42 )[/C][C]13.247619047619[/C][C]0.119619416579175[/C][C]110.74806604537[/C][/ROW]
[ROW][C]Median[/C][C]13.15[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]11.775[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]13.2150793650794[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]13.2484375[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]13.2484375[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]13.2484375[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]13.2491935483871[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]13.2484375[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]13.2484375[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]13.2484375[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]126[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=268840&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=268840&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 Mean13.07341269841270.29087917445135844.9444781431023
Geometric Mean12.5881966505307
Harmonic Mean11.9772983788691
Quadratic Mean13.4718393825493
Winsorized Mean ( 1 / 42 )13.0726190476190.29058376228291644.9874381999754
Winsorized Mean ( 2 / 42 )13.0726190476190.28962515848300245.136338003545
Winsorized Mean ( 3 / 42 )13.0976190476190.28355669467140246.1904772264226
Winsorized Mean ( 4 / 42 )13.10714285714290.27587938144518247.5104112111666
Winsorized Mean ( 5 / 42 )13.11309523809520.27269622529935648.0868234376921
Winsorized Mean ( 6 / 42 )13.14642857142860.26668462949704749.2957865484112
Winsorized Mean ( 7 / 42 )13.15753968253970.26301733147089250.0253713660532
Winsorized Mean ( 8 / 42 )13.16388888888890.26096988750993650.4421755877397
Winsorized Mean ( 9 / 42 )13.14603174603170.25831788167282950.8909087551352
Winsorized Mean ( 10 / 42 )13.15793650793650.25395750969336451.8115669185126
Winsorized Mean ( 11 / 42 )13.15793650793650.25131742573026452.3558462756927
Winsorized Mean ( 12 / 42 )13.19126984126980.24476751481022653.8930578737024
Winsorized Mean ( 13 / 42 )13.2067460317460.2350355279963256.1904242491918
Winsorized Mean ( 14 / 42 )13.21230158730160.22647729239544958.3383060065545
Winsorized Mean ( 15 / 42 )13.20634920634920.2191976596785860.2485867126243
Winsorized Mean ( 16 / 42 )13.18730158730160.21334147046083861.8131184659774
Winsorized Mean ( 17 / 42 )13.13333333333330.2066812590854463.5439003586877
Winsorized Mean ( 18 / 42 )13.15476190476190.20019072538609865.7111456057264
Winsorized Mean ( 19 / 42 )13.16230158730160.19919894060719266.0761625899249
Winsorized Mean ( 20 / 42 )13.17023809523810.19816313511325466.4615953300852
Winsorized Mean ( 21 / 42 )13.19523809523810.19495007791693467.6852158061739
Winsorized Mean ( 22 / 42 )13.22142857142860.18742484510426670.5425610146475
Winsorized Mean ( 23 / 42 )13.25793650793650.18085898452996673.3053795607254
Winsorized Mean ( 24 / 42 )13.28650793650790.17532229976003375.783331354274
Winsorized Mean ( 25 / 42 )13.27658730158730.17414433578230276.2389844145397
Winsorized Mean ( 26 / 42 )13.24563492063490.16582072920875779.8792466046848
Winsorized Mean ( 27 / 42 )13.24563492063490.16582072920875779.8792466046848
Winsorized Mean ( 28 / 42 )13.21230158730160.15959938587216982.7841630786974
Winsorized Mean ( 29 / 42 )13.21230158730160.15959938587216982.7841630786974
Winsorized Mean ( 30 / 42 )13.21230158730160.15959938587216982.7841630786974
Winsorized Mean ( 31 / 42 )13.23690476190480.15411001900974485.8925645909356
Winsorized Mean ( 32 / 42 )13.22420634920630.14993727167431788.1982591888897
Winsorized Mean ( 33 / 42 )13.23730158730160.14849395958848189.1437040535916
Winsorized Mean ( 34 / 42 )13.22380952380950.14703710177044589.9351889052779
Winsorized Mean ( 35 / 42 )13.25158730158730.13801303884564196.0169228387789
Winsorized Mean ( 36 / 42 )13.25158730158730.125887246738534105.265526452498
Winsorized Mean ( 37 / 42 )13.25158730158730.125887246738534105.265526452498
Winsorized Mean ( 38 / 42 )13.26666666666670.12116629003675109.491399486135
Winsorized Mean ( 39 / 42 )13.25119047619050.119555345868027110.837289457704
Winsorized Mean ( 40 / 42 )13.28293650793650.11302080535875117.526471925004
Winsorized Mean ( 41 / 42 )13.29920634920630.111378069322586119.405969506328
Winsorized Mean ( 42 / 42 )13.34920634920630.103048738856887129.542646492215
Trimmed Mean ( 1 / 42 )13.09435483870970.282527399503946.3472033569222
Trimmed Mean ( 2 / 42 )13.11680327868850.27357642932051947.9456629771311
Trimmed Mean ( 3 / 42 )13.140.26416561734895749.7415225034465
Trimmed Mean ( 4 / 42 )13.15508474576270.25623500463539951.339920415953
Trimmed Mean ( 5 / 42 )13.16810344827590.2499313223146752.6868874470118
Trimmed Mean ( 6 / 42 )13.18026315789470.24378839505569254.0643583747445
Trimmed Mean ( 7 / 42 )13.18660714285710.23838779584811355.3157811453523
Trimmed Mean ( 8 / 42 )13.19136363636360.23314835709956756.5792690991607
Trimmed Mean ( 9 / 42 )13.19537037037040.22769627594608357.951630150925
Trimmed Mean ( 10 / 42 )13.20188679245280.22207156326975759.4487947852022
Trimmed Mean ( 11 / 42 )13.20721153846150.21651542523318160.9989404876707
Trimmed Mean ( 12 / 42 )13.21274509803920.21070032142525162.7087087891635
Trimmed Mean ( 13 / 42 )13.2150.20519207557502864.4030719167222
Trimmed Mean ( 14 / 42 )13.21581632653060.20045261867763965.9298761658176
Trimmed Mean ( 15 / 42 )13.21614583333330.19633217744154967.3152307765137
Trimmed Mean ( 16 / 42 )13.21702127659570.19267285332833768.5982537149248
Trimmed Mean ( 17 / 42 )13.21956521739130.18929792793222469.834706390048
Trimmed Mean ( 18 / 42 )13.22666666666670.18630080518474570.9962936206875
Trimmed Mean ( 19 / 42 )13.23238636363640.18369758113398572.0335362172512
Trimmed Mean ( 20 / 42 )13.23779069767440.18082486188234373.2078020681017
Trimmed Mean ( 21 / 42 )13.24285714285710.17764302548805274.5475771225694
Trimmed Mean ( 22 / 42 )13.24634146341460.17438061009012175.9622383278099
Trimmed Mean ( 23 / 42 )13.2481250.1715538714657177.2242846332267
Trimmed Mean ( 24 / 42 )13.24743589743590.16907491890198578.3524604563946
Trimmed Mean ( 25 / 42 )13.24473684210530.16684002987253179.3858455445285
Trimmed Mean ( 26 / 42 )13.24256756756760.16434178236072780.5794325541656
Trimmed Mean ( 27 / 42 )13.24236111111110.16241845107448581.5323691582194
Trimmed Mean ( 28 / 42 )13.24214285714290.16010360166250582.709837378031
Trimmed Mean ( 29 / 42 )13.24411764705880.15811224984517483.7640199290548
Trimmed Mean ( 30 / 42 )13.24621212121210.15568972268795885.0808383014522
Trimmed Mean ( 31 / 42 )13.24843750.1527483371480386.7337592497707
Trimmed Mean ( 32 / 42 )13.24919354838710.14995368549700788.3552378487661
Trimmed Mean ( 33 / 42 )13.25083333333330.14713119009853690.0613481373936
Trimmed Mean ( 34 / 42 )13.2517241379310.14387034938024892.1087923607307
Trimmed Mean ( 35 / 42 )13.25357142857140.14006525116016694.6242648964793
Trimmed Mean ( 36 / 42 )13.25370370370370.13682439543051796.8665248766571
Trimmed Mean ( 37 / 42 )13.25384615384620.13472253869281498.3788331369467
Trimmed Mean ( 38 / 42 )13.2540.132000618427741100.408620488815
Trimmed Mean ( 39 / 42 )13.2531250.129317341624618102.485288001598
Trimmed Mean ( 40 / 42 )13.25326086956520.126112462021343105.090810671211
Trimmed Mean ( 41 / 42 )13.25113636363640.123189731418512107.566890608912
Trimmed Mean ( 42 / 42 )13.2476190476190.119619416579175110.74806604537
Median13.15
Midrange11.775
Midmean - Weighted Average at Xnp13.2150793650794
Midmean - Weighted Average at X(n+1)p13.2484375
Midmean - Empirical Distribution Function13.2484375
Midmean - Empirical Distribution Function - Averaging13.2484375
Midmean - Empirical Distribution Function - Interpolation13.2491935483871
Midmean - Closest Observation13.2484375
Midmean - True Basic - Statistics Graphics Toolkit13.2484375
Midmean - MS Excel (old versions)13.2484375
Number of observations126



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')