Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationMon, 08 Oct 2012 03:32:22 -0400
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/Oct/08/t1349681764y1aok9lucs1gaoc.htm/, Retrieved Thu, 02 May 2024 13:37:02 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=173208, Retrieved Thu, 02 May 2024 13:37:02 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact91
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Centrummaten gemi...] [2012-10-08 07:32:22] [0c7e7d09d2015d04a0f0c5141ec0f270] [Current]
Feedback Forum

Post a new message
Dataseries X:
23,15
23,18
23,32
23,37
23,43
23,65
23,76
23,81
23,85
23,83
23,85
23,71
23,74
23,87
24,13
24,23
24,27
24,41
24,39
24,34
24,31
24,34
24,41
24,39
24,54
24,9
25,63
26,7
27,12
27,68
27,84
27,84
27,77
27,8
27,82
27,72
27,87
27,83
28,07
28,05
28,15
28,3
28,41
28,43
28,43
28,29
28,19
27,53
27,92
27,98
27,92
27,89
27,95
28,02
27,97
27,81
27,78
27,56
27,52
27,18
27,18
27,26
27,38
27,31
27,43
27,4
27,32
27,31
27,34
27,3
27,3
26,94




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=173208&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=173208&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=173208&T=0

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean26.32805555555560.21823983222518120.638177215927
Geometric Mean26.2621257685532
Harmonic Mean26.1946537061896
Quadratic Mean26.3921985000618
Winsorized Mean ( 1 / 24 )26.32847222222220.218154754381475120.687134675887
Winsorized Mean ( 2 / 24 )26.33180555555560.217304795786623121.174525671359
Winsorized Mean ( 3 / 24 )26.32930555555560.216297928046448121.727035452238
Winsorized Mean ( 4 / 24 )26.33208333333330.215589588788999122.139865293333
Winsorized Mean ( 5 / 24 )26.34041666666670.211903442066855124.303864107863
Winsorized Mean ( 6 / 24 )26.34208333333330.210609902903675125.075236112621
Winsorized Mean ( 7 / 24 )26.33722222222220.209174192504587125.910476368372
Winsorized Mean ( 8 / 24 )26.33722222222220.208528286457319126.300477837633
Winsorized Mean ( 9 / 24 )26.33972222222220.207015169983683127.23571042788
Winsorized Mean ( 10 / 24 )26.33694444444440.205908198440498127.906244840733
Winsorized Mean ( 11 / 24 )26.33847222222220.205213890832705128.346439489781
Winsorized Mean ( 12 / 24 )26.33513888888890.204842203578281128.563052090117
Winsorized Mean ( 13 / 24 )26.33333333333330.203628086216238129.320732825477
Winsorized Mean ( 14 / 24 )26.38388888888890.195206298678205135.159003923241
Winsorized Mean ( 15 / 24 )26.39847222222220.191157893806976138.097735314443
Winsorized Mean ( 16 / 24 )26.40291666666670.189255443119587139.509417702629
Winsorized Mean ( 17 / 24 )26.40527777777780.186991142809312141.211382427376
Winsorized Mean ( 18 / 24 )26.41277777777780.185810117944225142.149297734724
Winsorized Mean ( 19 / 24 )26.41013888888890.185525149522807142.353416541202
Winsorized Mean ( 20 / 24 )26.421250.183049175591324144.33962848862
Winsorized Mean ( 21 / 24 )26.41833333333330.18273579532215144.571200660274
Winsorized Mean ( 22 / 24 )26.42138888888890.181453691928217145.609541520606
Winsorized Mean ( 23 / 24 )26.4150.180772122437037146.123194461028
Winsorized Mean ( 24 / 24 )26.4550.173667067664645152.33170200746
Trimmed Mean ( 1 / 24 )26.34342857142860.217715780087577120.999169471463
Trimmed Mean ( 2 / 24 )26.35926470588240.217013745167425121.463572206204
Trimmed Mean ( 3 / 24 )26.37424242424240.216513597779891121.813330408257
Trimmed Mean ( 4 / 24 )26.391093750.216136613221307122.103762785334
Trimmed Mean ( 5 / 24 )26.40822580645160.215699828175307122.43044433484
Trimmed Mean ( 6 / 24 )26.42450.216001468006102122.334816721031
Trimmed Mean ( 7 / 24 )26.44155172413790.21638966914465122.194150158169
Trimmed Mean ( 8 / 24 )26.46071428571430.216847971333868122.024264847626
Trimmed Mean ( 9 / 24 )26.48129629629630.217176797670198121.934279261777
Trimmed Mean ( 10 / 24 )26.50307692307690.217503582339309121.851220278899
Trimmed Mean ( 11 / 24 )26.5270.217692021733757121.855637100211
Trimmed Mean ( 12 / 24 )26.55270833333330.217603757672363122.023206847892
Trimmed Mean ( 13 / 24 )26.58108695652170.217062788009019122.45805557154
Trimmed Mean ( 14 / 24 )26.61227272727270.21608809759796123.154736531513
Trimmed Mean ( 15 / 24 )26.64023809523810.216132860184377123.258620056719
Trimmed Mean ( 16 / 24 )26.669250.216374078824566123.255290767168
Trimmed Mean ( 17 / 24 )26.70078947368420.216331229353488123.425496880318
Trimmed Mean ( 18 / 24 )26.73555555555560.215919019374602123.822142361491
Trimmed Mean ( 19 / 24 )26.77352941176470.214731471138941124.683770244563
Trimmed Mean ( 20 / 24 )26.81656250.212126146172793126.417996950531
Trimmed Mean ( 21 / 24 )26.8640.20809734680463129.09342868855
Trimmed Mean ( 22 / 24 )26.91857142857140.20110785379655133.85141813409
Trimmed Mean ( 23 / 24 )26.98115384615380.189753951553525142.190208031284
Trimmed Mean ( 24 / 24 )27.0550.170381073317806158.791111437215
Median27.31
Midrange25.79
Midmean - Weighted Average at Xnp26.7007894736842
Midmean - Weighted Average at X(n+1)p26.7654054054054
Midmean - Empirical Distribution Function26.7007894736842
Midmean - Empirical Distribution Function - Averaging26.7654054054054
Midmean - Empirical Distribution Function - Interpolation26.7654054054054
Midmean - Closest Observation26.7007894736842
Midmean - True Basic - Statistics Graphics Toolkit26.7654054054054
Midmean - MS Excel (old versions)26.7007894736842
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 26.3280555555556 & 0.21823983222518 & 120.638177215927 \tabularnewline
Geometric Mean & 26.2621257685532 &  &  \tabularnewline
Harmonic Mean & 26.1946537061896 &  &  \tabularnewline
Quadratic Mean & 26.3921985000618 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 26.3284722222222 & 0.218154754381475 & 120.687134675887 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 26.3318055555556 & 0.217304795786623 & 121.174525671359 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 26.3293055555556 & 0.216297928046448 & 121.727035452238 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 26.3320833333333 & 0.215589588788999 & 122.139865293333 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 26.3404166666667 & 0.211903442066855 & 124.303864107863 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 26.3420833333333 & 0.210609902903675 & 125.075236112621 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 26.3372222222222 & 0.209174192504587 & 125.910476368372 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 26.3372222222222 & 0.208528286457319 & 126.300477837633 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 26.3397222222222 & 0.207015169983683 & 127.23571042788 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 26.3369444444444 & 0.205908198440498 & 127.906244840733 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 26.3384722222222 & 0.205213890832705 & 128.346439489781 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 26.3351388888889 & 0.204842203578281 & 128.563052090117 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 26.3333333333333 & 0.203628086216238 & 129.320732825477 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 26.3838888888889 & 0.195206298678205 & 135.159003923241 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 26.3984722222222 & 0.191157893806976 & 138.097735314443 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 26.4029166666667 & 0.189255443119587 & 139.509417702629 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 26.4052777777778 & 0.186991142809312 & 141.211382427376 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 26.4127777777778 & 0.185810117944225 & 142.149297734724 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 26.4101388888889 & 0.185525149522807 & 142.353416541202 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 26.42125 & 0.183049175591324 & 144.33962848862 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 26.4183333333333 & 0.18273579532215 & 144.571200660274 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 26.4213888888889 & 0.181453691928217 & 145.609541520606 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 26.415 & 0.180772122437037 & 146.123194461028 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 26.455 & 0.173667067664645 & 152.33170200746 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 26.3434285714286 & 0.217715780087577 & 120.999169471463 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 26.3592647058824 & 0.217013745167425 & 121.463572206204 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 26.3742424242424 & 0.216513597779891 & 121.813330408257 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 26.39109375 & 0.216136613221307 & 122.103762785334 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 26.4082258064516 & 0.215699828175307 & 122.43044433484 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 26.4245 & 0.216001468006102 & 122.334816721031 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 26.4415517241379 & 0.21638966914465 & 122.194150158169 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 26.4607142857143 & 0.216847971333868 & 122.024264847626 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 26.4812962962963 & 0.217176797670198 & 121.934279261777 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 26.5030769230769 & 0.217503582339309 & 121.851220278899 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 26.527 & 0.217692021733757 & 121.855637100211 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 26.5527083333333 & 0.217603757672363 & 122.023206847892 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 26.5810869565217 & 0.217062788009019 & 122.45805557154 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 26.6122727272727 & 0.21608809759796 & 123.154736531513 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 26.6402380952381 & 0.216132860184377 & 123.258620056719 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 26.66925 & 0.216374078824566 & 123.255290767168 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 26.7007894736842 & 0.216331229353488 & 123.425496880318 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 26.7355555555556 & 0.215919019374602 & 123.822142361491 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 26.7735294117647 & 0.214731471138941 & 124.683770244563 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 26.8165625 & 0.212126146172793 & 126.417996950531 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 26.864 & 0.20809734680463 & 129.09342868855 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 26.9185714285714 & 0.20110785379655 & 133.85141813409 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 26.9811538461538 & 0.189753951553525 & 142.190208031284 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 27.055 & 0.170381073317806 & 158.791111437215 \tabularnewline
Median & 27.31 &  &  \tabularnewline
Midrange & 25.79 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 26.7007894736842 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 26.7654054054054 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 26.7007894736842 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 26.7654054054054 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 26.7654054054054 &  &  \tabularnewline
Midmean - Closest Observation & 26.7007894736842 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 26.7654054054054 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 26.7007894736842 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=173208&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]26.3280555555556[/C][C]0.21823983222518[/C][C]120.638177215927[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]26.2621257685532[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]26.1946537061896[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]26.3921985000618[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]26.3284722222222[/C][C]0.218154754381475[/C][C]120.687134675887[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]26.3318055555556[/C][C]0.217304795786623[/C][C]121.174525671359[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]26.3293055555556[/C][C]0.216297928046448[/C][C]121.727035452238[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]26.3320833333333[/C][C]0.215589588788999[/C][C]122.139865293333[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]26.3404166666667[/C][C]0.211903442066855[/C][C]124.303864107863[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]26.3420833333333[/C][C]0.210609902903675[/C][C]125.075236112621[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]26.3372222222222[/C][C]0.209174192504587[/C][C]125.910476368372[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]26.3372222222222[/C][C]0.208528286457319[/C][C]126.300477837633[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]26.3397222222222[/C][C]0.207015169983683[/C][C]127.23571042788[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]26.3369444444444[/C][C]0.205908198440498[/C][C]127.906244840733[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]26.3384722222222[/C][C]0.205213890832705[/C][C]128.346439489781[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]26.3351388888889[/C][C]0.204842203578281[/C][C]128.563052090117[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]26.3333333333333[/C][C]0.203628086216238[/C][C]129.320732825477[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]26.3838888888889[/C][C]0.195206298678205[/C][C]135.159003923241[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]26.3984722222222[/C][C]0.191157893806976[/C][C]138.097735314443[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]26.4029166666667[/C][C]0.189255443119587[/C][C]139.509417702629[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]26.4052777777778[/C][C]0.186991142809312[/C][C]141.211382427376[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]26.4127777777778[/C][C]0.185810117944225[/C][C]142.149297734724[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]26.4101388888889[/C][C]0.185525149522807[/C][C]142.353416541202[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]26.42125[/C][C]0.183049175591324[/C][C]144.33962848862[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]26.4183333333333[/C][C]0.18273579532215[/C][C]144.571200660274[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]26.4213888888889[/C][C]0.181453691928217[/C][C]145.609541520606[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]26.415[/C][C]0.180772122437037[/C][C]146.123194461028[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]26.455[/C][C]0.173667067664645[/C][C]152.33170200746[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]26.3434285714286[/C][C]0.217715780087577[/C][C]120.999169471463[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]26.3592647058824[/C][C]0.217013745167425[/C][C]121.463572206204[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]26.3742424242424[/C][C]0.216513597779891[/C][C]121.813330408257[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]26.39109375[/C][C]0.216136613221307[/C][C]122.103762785334[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]26.4082258064516[/C][C]0.215699828175307[/C][C]122.43044433484[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]26.4245[/C][C]0.216001468006102[/C][C]122.334816721031[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]26.4415517241379[/C][C]0.21638966914465[/C][C]122.194150158169[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]26.4607142857143[/C][C]0.216847971333868[/C][C]122.024264847626[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]26.4812962962963[/C][C]0.217176797670198[/C][C]121.934279261777[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]26.5030769230769[/C][C]0.217503582339309[/C][C]121.851220278899[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]26.527[/C][C]0.217692021733757[/C][C]121.855637100211[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]26.5527083333333[/C][C]0.217603757672363[/C][C]122.023206847892[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]26.5810869565217[/C][C]0.217062788009019[/C][C]122.45805557154[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]26.6122727272727[/C][C]0.21608809759796[/C][C]123.154736531513[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]26.6402380952381[/C][C]0.216132860184377[/C][C]123.258620056719[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]26.66925[/C][C]0.216374078824566[/C][C]123.255290767168[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]26.7007894736842[/C][C]0.216331229353488[/C][C]123.425496880318[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]26.7355555555556[/C][C]0.215919019374602[/C][C]123.822142361491[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]26.7735294117647[/C][C]0.214731471138941[/C][C]124.683770244563[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]26.8165625[/C][C]0.212126146172793[/C][C]126.417996950531[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]26.864[/C][C]0.20809734680463[/C][C]129.09342868855[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]26.9185714285714[/C][C]0.20110785379655[/C][C]133.85141813409[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]26.9811538461538[/C][C]0.189753951553525[/C][C]142.190208031284[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]27.055[/C][C]0.170381073317806[/C][C]158.791111437215[/C][/ROW]
[ROW][C]Median[/C][C]27.31[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]25.79[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]26.7007894736842[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]26.7654054054054[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]26.7007894736842[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]26.7654054054054[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]26.7654054054054[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]26.7007894736842[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]26.7654054054054[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]26.7007894736842[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]72[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=173208&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=173208&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 Mean26.32805555555560.21823983222518120.638177215927
Geometric Mean26.2621257685532
Harmonic Mean26.1946537061896
Quadratic Mean26.3921985000618
Winsorized Mean ( 1 / 24 )26.32847222222220.218154754381475120.687134675887
Winsorized Mean ( 2 / 24 )26.33180555555560.217304795786623121.174525671359
Winsorized Mean ( 3 / 24 )26.32930555555560.216297928046448121.727035452238
Winsorized Mean ( 4 / 24 )26.33208333333330.215589588788999122.139865293333
Winsorized Mean ( 5 / 24 )26.34041666666670.211903442066855124.303864107863
Winsorized Mean ( 6 / 24 )26.34208333333330.210609902903675125.075236112621
Winsorized Mean ( 7 / 24 )26.33722222222220.209174192504587125.910476368372
Winsorized Mean ( 8 / 24 )26.33722222222220.208528286457319126.300477837633
Winsorized Mean ( 9 / 24 )26.33972222222220.207015169983683127.23571042788
Winsorized Mean ( 10 / 24 )26.33694444444440.205908198440498127.906244840733
Winsorized Mean ( 11 / 24 )26.33847222222220.205213890832705128.346439489781
Winsorized Mean ( 12 / 24 )26.33513888888890.204842203578281128.563052090117
Winsorized Mean ( 13 / 24 )26.33333333333330.203628086216238129.320732825477
Winsorized Mean ( 14 / 24 )26.38388888888890.195206298678205135.159003923241
Winsorized Mean ( 15 / 24 )26.39847222222220.191157893806976138.097735314443
Winsorized Mean ( 16 / 24 )26.40291666666670.189255443119587139.509417702629
Winsorized Mean ( 17 / 24 )26.40527777777780.186991142809312141.211382427376
Winsorized Mean ( 18 / 24 )26.41277777777780.185810117944225142.149297734724
Winsorized Mean ( 19 / 24 )26.41013888888890.185525149522807142.353416541202
Winsorized Mean ( 20 / 24 )26.421250.183049175591324144.33962848862
Winsorized Mean ( 21 / 24 )26.41833333333330.18273579532215144.571200660274
Winsorized Mean ( 22 / 24 )26.42138888888890.181453691928217145.609541520606
Winsorized Mean ( 23 / 24 )26.4150.180772122437037146.123194461028
Winsorized Mean ( 24 / 24 )26.4550.173667067664645152.33170200746
Trimmed Mean ( 1 / 24 )26.34342857142860.217715780087577120.999169471463
Trimmed Mean ( 2 / 24 )26.35926470588240.217013745167425121.463572206204
Trimmed Mean ( 3 / 24 )26.37424242424240.216513597779891121.813330408257
Trimmed Mean ( 4 / 24 )26.391093750.216136613221307122.103762785334
Trimmed Mean ( 5 / 24 )26.40822580645160.215699828175307122.43044433484
Trimmed Mean ( 6 / 24 )26.42450.216001468006102122.334816721031
Trimmed Mean ( 7 / 24 )26.44155172413790.21638966914465122.194150158169
Trimmed Mean ( 8 / 24 )26.46071428571430.216847971333868122.024264847626
Trimmed Mean ( 9 / 24 )26.48129629629630.217176797670198121.934279261777
Trimmed Mean ( 10 / 24 )26.50307692307690.217503582339309121.851220278899
Trimmed Mean ( 11 / 24 )26.5270.217692021733757121.855637100211
Trimmed Mean ( 12 / 24 )26.55270833333330.217603757672363122.023206847892
Trimmed Mean ( 13 / 24 )26.58108695652170.217062788009019122.45805557154
Trimmed Mean ( 14 / 24 )26.61227272727270.21608809759796123.154736531513
Trimmed Mean ( 15 / 24 )26.64023809523810.216132860184377123.258620056719
Trimmed Mean ( 16 / 24 )26.669250.216374078824566123.255290767168
Trimmed Mean ( 17 / 24 )26.70078947368420.216331229353488123.425496880318
Trimmed Mean ( 18 / 24 )26.73555555555560.215919019374602123.822142361491
Trimmed Mean ( 19 / 24 )26.77352941176470.214731471138941124.683770244563
Trimmed Mean ( 20 / 24 )26.81656250.212126146172793126.417996950531
Trimmed Mean ( 21 / 24 )26.8640.20809734680463129.09342868855
Trimmed Mean ( 22 / 24 )26.91857142857140.20110785379655133.85141813409
Trimmed Mean ( 23 / 24 )26.98115384615380.189753951553525142.190208031284
Trimmed Mean ( 24 / 24 )27.0550.170381073317806158.791111437215
Median27.31
Midrange25.79
Midmean - Weighted Average at Xnp26.7007894736842
Midmean - Weighted Average at X(n+1)p26.7654054054054
Midmean - Empirical Distribution Function26.7007894736842
Midmean - Empirical Distribution Function - Averaging26.7654054054054
Midmean - Empirical Distribution Function - Interpolation26.7654054054054
Midmean - Closest Observation26.7007894736842
Midmean - True Basic - Statistics Graphics Toolkit26.7654054054054
Midmean - MS Excel (old versions)26.7007894736842
Number of observations72



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')