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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationWed, 17 Oct 2012 05:20:49 -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/17/t1350465709a1x2mmwdqthsswk.htm/, Retrieved Sun, 05 May 2024 13:31:19 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=179360, Retrieved Sun, 05 May 2024 13:31:19 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact125
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2012-10-17 09:20:49] [f926d2a8812ea27da1e154fca8928f89] [Current]
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Dataseries X:
23,9
24,06
24,33
24,39
24,39
24,49
24,83
25,08
25,11
25,13
25,17
25,11
25,35
25,36
25,35
25,34
25,39
25,58
25,71
25,66
25,74
25,73
25,72
25,55
25,71
25,92
25,93
26
26,02
26,08
26,17
26,18
26,21
26,28
26,34
26,17
26,38
26,36
26,27
26,26
26,49
26,99
27,14
27,1
27,01
26,93
26,97
26,35
26,93
26,92
27,05
27,01
26,9
26,93
26,95
26,89
26,7
26,55
26,48
25,71
26,17
26,31
26,58
26,49
26,57
26,6
26,69
26,59
26,75
26,79
26,8
26,62




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=179360&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=179360&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=179360&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 Mean26.05152777777780.0954725623479139272.869263557029
Geometric Mean26.0388904404434
Harmonic Mean26.0260336563221
Quadratic Mean26.0639456966473
Winsorized Mean ( 1 / 24 )26.05319444444440.0947025708852334275.105461244736
Winsorized Mean ( 2 / 24 )26.05930555555560.0923877584019587282.064485666784
Winsorized Mean ( 3 / 24 )26.06013888888890.0914890496572205284.844350078263
Winsorized Mean ( 4 / 24 )26.06013888888890.0914890496572205284.844350078263
Winsorized Mean ( 5 / 24 )26.06569444444440.0895327434156927291.130299933106
Winsorized Mean ( 6 / 24 )26.09236111111110.0827118830450179315.460852183836
Winsorized Mean ( 7 / 24 )26.11472222222220.077511161350413336.915635983863
Winsorized Mean ( 8 / 24 )26.11583333333330.0765542526537489341.141509818585
Winsorized Mean ( 9 / 24 )26.11583333333330.0765542526537489341.141509818585
Winsorized Mean ( 10 / 24 )26.11861111111110.0760429069113741343.472023518927
Winsorized Mean ( 11 / 24 )26.12319444444440.0747046417904711349.686362431318
Winsorized Mean ( 12 / 24 )26.14819444444440.0693193846536967377.213308731384
Winsorized Mean ( 13 / 24 )26.14819444444440.0687484034211793380.346206503888
Winsorized Mean ( 14 / 24 )26.13069444444440.0661704911291952394.89950880711
Winsorized Mean ( 15 / 24 )26.13069444444440.0655288246043326398.766414661385
Winsorized Mean ( 16 / 24 )26.12847222222220.0631820096452301413.542911485956
Winsorized Mean ( 17 / 24 )26.15444444444440.0555280839746333471.012910447126
Winsorized Mean ( 18 / 24 )26.15944444444440.0540408936652717484.067576796112
Winsorized Mean ( 19 / 24 )26.16208333333330.0483907452044268540.642290644866
Winsorized Mean ( 20 / 24 )26.17041666666670.0456501621506633573.282008950902
Winsorized Mean ( 21 / 24 )26.16750.0452651508454811578.093732401918
Winsorized Mean ( 22 / 24 )26.16444444444440.044864989996893583.181773722816
Winsorized Mean ( 23 / 24 )26.16444444444440.0439940994447014594.726219531598
Winsorized Mean ( 24 / 24 )26.16111111111110.0426588697557753613.263109428006
Trimmed Mean ( 1 / 24 )26.06671428571430.091870311289454283.733819117978
Trimmed Mean ( 2 / 24 )26.08102941176470.0884673765919729294.8095718047
Trimmed Mean ( 3 / 24 )26.09287878787880.0858837956042348303.816087823116
Trimmed Mean ( 4 / 24 )26.105156250.0831733560231745313.864409207275
Trimmed Mean ( 5 / 24 )26.11822580645160.0798622307227263327.04102515157
Trimmed Mean ( 6 / 24 )26.13083333333330.0764702562710624341.712380833509
Trimmed Mean ( 7 / 24 )26.13879310344830.0744018607130794351.319077949528
Trimmed Mean ( 8 / 24 )26.14321428571430.0732382285842548356.961313662012
Trimmed Mean ( 9 / 24 )26.14777777777780.0719910831241114363.208561992316
Trimmed Mean ( 10 / 24 )26.15269230769230.070397554217923371.500013008036
Trimmed Mean ( 11 / 24 )26.15760.0684865903752296381.937542177027
Trimmed Mean ( 12 / 24 )26.16229166666670.0663573762403335394.26350390817
Trimmed Mean ( 13 / 24 )26.16413043478260.0648793574482235403.273575199365
Trimmed Mean ( 14 / 24 )26.16613636363640.0630590983497379414.946249604045
Trimmed Mean ( 15 / 24 )26.17047619047620.0612243948527185427.451773977219
Trimmed Mean ( 16 / 24 )26.175250.0589066922975301444.351040248401
Trimmed Mean ( 17 / 24 )26.18078947368420.0563536152729447464.580477168669
Trimmed Mean ( 18 / 24 )26.18388888888890.0548971300284592476.962800702239
Trimmed Mean ( 19 / 24 )26.18676470588240.0532051499729364492.184773827395
Trimmed Mean ( 20 / 24 )26.18968750.052273868554655501.009170052477
Trimmed Mean ( 21 / 24 )26.1920.0515515588357016508.073869957565
Trimmed Mean ( 22 / 24 )26.1950.0504096971438786519.642082459544
Trimmed Mean ( 23 / 24 )26.19884615384620.0486315090105073538.721637204094
Trimmed Mean ( 24 / 24 )26.20333333333330.0460334891747721569.223272080223
Median26.235
Midrange25.52
Midmean - Weighted Average at Xnp26.1667567567568
Midmean - Weighted Average at X(n+1)p26.1838888888889
Midmean - Empirical Distribution Function26.1667567567568
Midmean - Empirical Distribution Function - Averaging26.1838888888889
Midmean - Empirical Distribution Function - Interpolation26.1838888888889
Midmean - Closest Observation26.1667567567568
Midmean - True Basic - Statistics Graphics Toolkit26.1838888888889
Midmean - MS Excel (old versions)26.1807894736842
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 26.0515277777778 & 0.0954725623479139 & 272.869263557029 \tabularnewline
Geometric Mean & 26.0388904404434 &  &  \tabularnewline
Harmonic Mean & 26.0260336563221 &  &  \tabularnewline
Quadratic Mean & 26.0639456966473 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 26.0531944444444 & 0.0947025708852334 & 275.105461244736 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 26.0593055555556 & 0.0923877584019587 & 282.064485666784 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 26.0601388888889 & 0.0914890496572205 & 284.844350078263 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 26.0601388888889 & 0.0914890496572205 & 284.844350078263 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 26.0656944444444 & 0.0895327434156927 & 291.130299933106 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 26.0923611111111 & 0.0827118830450179 & 315.460852183836 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 26.1147222222222 & 0.077511161350413 & 336.915635983863 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 26.1158333333333 & 0.0765542526537489 & 341.141509818585 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 26.1158333333333 & 0.0765542526537489 & 341.141509818585 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 26.1186111111111 & 0.0760429069113741 & 343.472023518927 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 26.1231944444444 & 0.0747046417904711 & 349.686362431318 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 26.1481944444444 & 0.0693193846536967 & 377.213308731384 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 26.1481944444444 & 0.0687484034211793 & 380.346206503888 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 26.1306944444444 & 0.0661704911291952 & 394.89950880711 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 26.1306944444444 & 0.0655288246043326 & 398.766414661385 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 26.1284722222222 & 0.0631820096452301 & 413.542911485956 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 26.1544444444444 & 0.0555280839746333 & 471.012910447126 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 26.1594444444444 & 0.0540408936652717 & 484.067576796112 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 26.1620833333333 & 0.0483907452044268 & 540.642290644866 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 26.1704166666667 & 0.0456501621506633 & 573.282008950902 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 26.1675 & 0.0452651508454811 & 578.093732401918 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 26.1644444444444 & 0.044864989996893 & 583.181773722816 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 26.1644444444444 & 0.0439940994447014 & 594.726219531598 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 26.1611111111111 & 0.0426588697557753 & 613.263109428006 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 26.0667142857143 & 0.091870311289454 & 283.733819117978 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 26.0810294117647 & 0.0884673765919729 & 294.8095718047 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 26.0928787878788 & 0.0858837956042348 & 303.816087823116 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 26.10515625 & 0.0831733560231745 & 313.864409207275 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 26.1182258064516 & 0.0798622307227263 & 327.04102515157 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 26.1308333333333 & 0.0764702562710624 & 341.712380833509 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 26.1387931034483 & 0.0744018607130794 & 351.319077949528 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 26.1432142857143 & 0.0732382285842548 & 356.961313662012 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 26.1477777777778 & 0.0719910831241114 & 363.208561992316 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 26.1526923076923 & 0.070397554217923 & 371.500013008036 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 26.1576 & 0.0684865903752296 & 381.937542177027 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 26.1622916666667 & 0.0663573762403335 & 394.26350390817 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 26.1641304347826 & 0.0648793574482235 & 403.273575199365 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 26.1661363636364 & 0.0630590983497379 & 414.946249604045 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 26.1704761904762 & 0.0612243948527185 & 427.451773977219 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 26.17525 & 0.0589066922975301 & 444.351040248401 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 26.1807894736842 & 0.0563536152729447 & 464.580477168669 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 26.1838888888889 & 0.0548971300284592 & 476.962800702239 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 26.1867647058824 & 0.0532051499729364 & 492.184773827395 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 26.1896875 & 0.052273868554655 & 501.009170052477 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 26.192 & 0.0515515588357016 & 508.073869957565 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 26.195 & 0.0504096971438786 & 519.642082459544 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 26.1988461538462 & 0.0486315090105073 & 538.721637204094 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 26.2033333333333 & 0.0460334891747721 & 569.223272080223 \tabularnewline
Median & 26.235 &  &  \tabularnewline
Midrange & 25.52 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 26.1667567567568 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 26.1838888888889 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 26.1667567567568 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 26.1838888888889 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 26.1838888888889 &  &  \tabularnewline
Midmean - Closest Observation & 26.1667567567568 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 26.1838888888889 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 26.1807894736842 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=179360&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]26.0515277777778[/C][C]0.0954725623479139[/C][C]272.869263557029[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]26.0388904404434[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]26.0260336563221[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]26.0639456966473[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]26.0531944444444[/C][C]0.0947025708852334[/C][C]275.105461244736[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]26.0593055555556[/C][C]0.0923877584019587[/C][C]282.064485666784[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]26.0601388888889[/C][C]0.0914890496572205[/C][C]284.844350078263[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]26.0601388888889[/C][C]0.0914890496572205[/C][C]284.844350078263[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]26.0656944444444[/C][C]0.0895327434156927[/C][C]291.130299933106[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]26.0923611111111[/C][C]0.0827118830450179[/C][C]315.460852183836[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]26.1147222222222[/C][C]0.077511161350413[/C][C]336.915635983863[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]26.1158333333333[/C][C]0.0765542526537489[/C][C]341.141509818585[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]26.1158333333333[/C][C]0.0765542526537489[/C][C]341.141509818585[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]26.1186111111111[/C][C]0.0760429069113741[/C][C]343.472023518927[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]26.1231944444444[/C][C]0.0747046417904711[/C][C]349.686362431318[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]26.1481944444444[/C][C]0.0693193846536967[/C][C]377.213308731384[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]26.1481944444444[/C][C]0.0687484034211793[/C][C]380.346206503888[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]26.1306944444444[/C][C]0.0661704911291952[/C][C]394.89950880711[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]26.1306944444444[/C][C]0.0655288246043326[/C][C]398.766414661385[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]26.1284722222222[/C][C]0.0631820096452301[/C][C]413.542911485956[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]26.1544444444444[/C][C]0.0555280839746333[/C][C]471.012910447126[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]26.1594444444444[/C][C]0.0540408936652717[/C][C]484.067576796112[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]26.1620833333333[/C][C]0.0483907452044268[/C][C]540.642290644866[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]26.1704166666667[/C][C]0.0456501621506633[/C][C]573.282008950902[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]26.1675[/C][C]0.0452651508454811[/C][C]578.093732401918[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]26.1644444444444[/C][C]0.044864989996893[/C][C]583.181773722816[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]26.1644444444444[/C][C]0.0439940994447014[/C][C]594.726219531598[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]26.1611111111111[/C][C]0.0426588697557753[/C][C]613.263109428006[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]26.0667142857143[/C][C]0.091870311289454[/C][C]283.733819117978[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]26.0810294117647[/C][C]0.0884673765919729[/C][C]294.8095718047[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]26.0928787878788[/C][C]0.0858837956042348[/C][C]303.816087823116[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]26.10515625[/C][C]0.0831733560231745[/C][C]313.864409207275[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]26.1182258064516[/C][C]0.0798622307227263[/C][C]327.04102515157[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]26.1308333333333[/C][C]0.0764702562710624[/C][C]341.712380833509[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]26.1387931034483[/C][C]0.0744018607130794[/C][C]351.319077949528[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]26.1432142857143[/C][C]0.0732382285842548[/C][C]356.961313662012[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]26.1477777777778[/C][C]0.0719910831241114[/C][C]363.208561992316[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]26.1526923076923[/C][C]0.070397554217923[/C][C]371.500013008036[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]26.1576[/C][C]0.0684865903752296[/C][C]381.937542177027[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]26.1622916666667[/C][C]0.0663573762403335[/C][C]394.26350390817[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]26.1641304347826[/C][C]0.0648793574482235[/C][C]403.273575199365[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]26.1661363636364[/C][C]0.0630590983497379[/C][C]414.946249604045[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]26.1704761904762[/C][C]0.0612243948527185[/C][C]427.451773977219[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]26.17525[/C][C]0.0589066922975301[/C][C]444.351040248401[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]26.1807894736842[/C][C]0.0563536152729447[/C][C]464.580477168669[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]26.1838888888889[/C][C]0.0548971300284592[/C][C]476.962800702239[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]26.1867647058824[/C][C]0.0532051499729364[/C][C]492.184773827395[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]26.1896875[/C][C]0.052273868554655[/C][C]501.009170052477[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]26.192[/C][C]0.0515515588357016[/C][C]508.073869957565[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]26.195[/C][C]0.0504096971438786[/C][C]519.642082459544[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]26.1988461538462[/C][C]0.0486315090105073[/C][C]538.721637204094[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]26.2033333333333[/C][C]0.0460334891747721[/C][C]569.223272080223[/C][/ROW]
[ROW][C]Median[/C][C]26.235[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]25.52[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]26.1667567567568[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]26.1838888888889[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]26.1667567567568[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]26.1838888888889[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]26.1838888888889[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]26.1667567567568[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]26.1838888888889[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]26.1807894736842[/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=179360&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=179360&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 Mean26.05152777777780.0954725623479139272.869263557029
Geometric Mean26.0388904404434
Harmonic Mean26.0260336563221
Quadratic Mean26.0639456966473
Winsorized Mean ( 1 / 24 )26.05319444444440.0947025708852334275.105461244736
Winsorized Mean ( 2 / 24 )26.05930555555560.0923877584019587282.064485666784
Winsorized Mean ( 3 / 24 )26.06013888888890.0914890496572205284.844350078263
Winsorized Mean ( 4 / 24 )26.06013888888890.0914890496572205284.844350078263
Winsorized Mean ( 5 / 24 )26.06569444444440.0895327434156927291.130299933106
Winsorized Mean ( 6 / 24 )26.09236111111110.0827118830450179315.460852183836
Winsorized Mean ( 7 / 24 )26.11472222222220.077511161350413336.915635983863
Winsorized Mean ( 8 / 24 )26.11583333333330.0765542526537489341.141509818585
Winsorized Mean ( 9 / 24 )26.11583333333330.0765542526537489341.141509818585
Winsorized Mean ( 10 / 24 )26.11861111111110.0760429069113741343.472023518927
Winsorized Mean ( 11 / 24 )26.12319444444440.0747046417904711349.686362431318
Winsorized Mean ( 12 / 24 )26.14819444444440.0693193846536967377.213308731384
Winsorized Mean ( 13 / 24 )26.14819444444440.0687484034211793380.346206503888
Winsorized Mean ( 14 / 24 )26.13069444444440.0661704911291952394.89950880711
Winsorized Mean ( 15 / 24 )26.13069444444440.0655288246043326398.766414661385
Winsorized Mean ( 16 / 24 )26.12847222222220.0631820096452301413.542911485956
Winsorized Mean ( 17 / 24 )26.15444444444440.0555280839746333471.012910447126
Winsorized Mean ( 18 / 24 )26.15944444444440.0540408936652717484.067576796112
Winsorized Mean ( 19 / 24 )26.16208333333330.0483907452044268540.642290644866
Winsorized Mean ( 20 / 24 )26.17041666666670.0456501621506633573.282008950902
Winsorized Mean ( 21 / 24 )26.16750.0452651508454811578.093732401918
Winsorized Mean ( 22 / 24 )26.16444444444440.044864989996893583.181773722816
Winsorized Mean ( 23 / 24 )26.16444444444440.0439940994447014594.726219531598
Winsorized Mean ( 24 / 24 )26.16111111111110.0426588697557753613.263109428006
Trimmed Mean ( 1 / 24 )26.06671428571430.091870311289454283.733819117978
Trimmed Mean ( 2 / 24 )26.08102941176470.0884673765919729294.8095718047
Trimmed Mean ( 3 / 24 )26.09287878787880.0858837956042348303.816087823116
Trimmed Mean ( 4 / 24 )26.105156250.0831733560231745313.864409207275
Trimmed Mean ( 5 / 24 )26.11822580645160.0798622307227263327.04102515157
Trimmed Mean ( 6 / 24 )26.13083333333330.0764702562710624341.712380833509
Trimmed Mean ( 7 / 24 )26.13879310344830.0744018607130794351.319077949528
Trimmed Mean ( 8 / 24 )26.14321428571430.0732382285842548356.961313662012
Trimmed Mean ( 9 / 24 )26.14777777777780.0719910831241114363.208561992316
Trimmed Mean ( 10 / 24 )26.15269230769230.070397554217923371.500013008036
Trimmed Mean ( 11 / 24 )26.15760.0684865903752296381.937542177027
Trimmed Mean ( 12 / 24 )26.16229166666670.0663573762403335394.26350390817
Trimmed Mean ( 13 / 24 )26.16413043478260.0648793574482235403.273575199365
Trimmed Mean ( 14 / 24 )26.16613636363640.0630590983497379414.946249604045
Trimmed Mean ( 15 / 24 )26.17047619047620.0612243948527185427.451773977219
Trimmed Mean ( 16 / 24 )26.175250.0589066922975301444.351040248401
Trimmed Mean ( 17 / 24 )26.18078947368420.0563536152729447464.580477168669
Trimmed Mean ( 18 / 24 )26.18388888888890.0548971300284592476.962800702239
Trimmed Mean ( 19 / 24 )26.18676470588240.0532051499729364492.184773827395
Trimmed Mean ( 20 / 24 )26.18968750.052273868554655501.009170052477
Trimmed Mean ( 21 / 24 )26.1920.0515515588357016508.073869957565
Trimmed Mean ( 22 / 24 )26.1950.0504096971438786519.642082459544
Trimmed Mean ( 23 / 24 )26.19884615384620.0486315090105073538.721637204094
Trimmed Mean ( 24 / 24 )26.20333333333330.0460334891747721569.223272080223
Median26.235
Midrange25.52
Midmean - Weighted Average at Xnp26.1667567567568
Midmean - Weighted Average at X(n+1)p26.1838888888889
Midmean - Empirical Distribution Function26.1667567567568
Midmean - Empirical Distribution Function - Averaging26.1838888888889
Midmean - Empirical Distribution Function - Interpolation26.1838888888889
Midmean - Closest Observation26.1667567567568
Midmean - True Basic - Statistics Graphics Toolkit26.1838888888889
Midmean - MS Excel (old versions)26.1807894736842
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')