Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationSun, 21 Oct 2012 08:13:09 -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/21/t1350821621oucdpwg9lsi0jz2.htm/, Retrieved Sun, 28 Apr 2024 23:14:39 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=180840, Retrieved Sun, 28 Apr 2024 23:14:39 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact61
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [centrummaten gem ...] [2012-10-21 12:13:09] [b91e71fa3b5e2ab5567c9d258a8f1839] [Current]
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Dataseries X:
49.98
50.12
50.37
50.39
50.34
50.32
50.32
50.32
50.67
50.86
50.95
51.02
51.02
51.06
50.9
51.23
51.29
51.3
51.3
51.3
51.46
51.47
51.77
51.82
51.82
51.84
51.9
51.94
52.22
52.27
52.27
52.28
52.53
52.73
52.72
52.67
52.67
52.65
52.69
52.73
52.84
52.83
52.83
52.84
52.82
53.09
53.4
53.43
53.43
53.42
53.6
53.69
54.05
54.04
54.04
54.08
54.05
54.39
54.38
54.46
54.46
54.69
54.91
55.52
56.01
56.07
56.07
56.09
56.29
56.45
56.87
56.87




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=180840&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=180840&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=180840&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 Mean52.79888888888890.214812175077768245.79095141965
Geometric Mean52.7682024353795
Harmonic Mean52.7378564333716
Quadratic Mean52.8299054618794
Winsorized Mean ( 1 / 24 )52.80083333333330.214461306978493246.202142835157
Winsorized Mean ( 2 / 24 )52.79472222222220.21052545969377250.77595032457
Winsorized Mean ( 3 / 24 )52.78805555555560.20892326230938252.667199296291
Winsorized Mean ( 4 / 24 )52.77694444444450.206355080775469255.757911295967
Winsorized Mean ( 5 / 24 )52.77694444444440.205809276966518256.436178302257
Winsorized Mean ( 6 / 24 )52.77944444444440.205394281783581256.966474363959
Winsorized Mean ( 7 / 24 )52.77555555555560.203763100127927259.004478840486
Winsorized Mean ( 8 / 24 )52.75222222222220.186973383808567282.137602409938
Winsorized Mean ( 9 / 24 )52.69972222222220.168228942230519313.26192463369
Winsorized Mean ( 10 / 24 )52.67472222222220.161863049521985325.427714217554
Winsorized Mean ( 11 / 24 )52.64722222222220.154698229920263340.322072523768
Winsorized Mean ( 12 / 24 )52.65888888888890.152916170069367344.364424409801
Winsorized Mean ( 13 / 24 )52.646250.15083873975474349.023401319857
Winsorized Mean ( 14 / 24 )52.65208333333330.149347555689585352.547338925112
Winsorized Mean ( 15 / 24 )52.6250.134211748469462392.104272540449
Winsorized Mean ( 16 / 24 )52.63166666666670.131259547681645400.974006053402
Winsorized Mean ( 17 / 24 )52.63402777777780.130920160435808402.031494634358
Winsorized Mean ( 18 / 24 )52.63152777777780.130539787572093403.183801327325
Winsorized Mean ( 19 / 24 )52.63152777777780.130539787572093403.183801327325
Winsorized Mean ( 20 / 24 )52.578750.109802058621252478.850311735628
Winsorized Mean ( 21 / 24 )52.55541666666670.105682989493996497.293054618334
Winsorized Mean ( 22 / 24 )52.59513888888890.0855990108098556614.436293028205
Winsorized Mean ( 23 / 24 )52.61111111111110.0834481733484555630.464502697049
Winsorized Mean ( 24 / 24 )52.60777777777780.0829880693157562633.919769570897
Trimmed Mean ( 1 / 24 )52.7810.209182095477416252.320830229461
Trimmed Mean ( 2 / 24 )52.760.202874535762266260.062209393423
Trimmed Mean ( 3 / 24 )52.74106060606060.197845520108343266.576976709803
Trimmed Mean ( 4 / 24 )52.72343750.192522960230134273.855323214315
Trimmed Mean ( 5 / 24 )52.70790322580650.187048400218112281.78751149085
Trimmed Mean ( 6 / 24 )52.69133333333330.180546950975616291.8428311783
Trimmed Mean ( 7 / 24 )52.67310344827590.172672353010099305.046537734939
Trimmed Mean ( 8 / 24 )52.65428571428570.163369125733851322.302549381738
Trimmed Mean ( 9 / 24 )52.6379629629630.156435973518229336.482471257349
Trimmed Mean ( 10 / 24 )52.62846153846150.152544379373299345.004265346754
Trimmed Mean ( 11 / 24 )52.62180.14910855927471352.909318257528
Trimmed Mean ( 12 / 24 )52.61833333333330.146315969340878359.62126055254
Trimmed Mean ( 13 / 24 )52.61304347826090.143034021683508367.835867711795
Trimmed Mean ( 14 / 24 )52.60886363636360.139186406679473377.97414913882
Trimmed Mean ( 15 / 24 )52.60357142857140.134424320564337391.324807949427
Trimmed Mean ( 16 / 24 )52.6010.131679389193835399.462667028095
Trimmed Mean ( 17 / 24 )52.59736842105260.128540158837345409.190162022513
Trimmed Mean ( 18 / 24 )52.59305555555560.124201461691961423.449570070233
Trimmed Mean ( 19 / 24 )52.58852941176470.118179998332509444.986716481435
Trimmed Mean ( 20 / 24 )52.58343750.109537710194422480.048719355811
Trimmed Mean ( 21 / 24 )52.5840.104033151215005505.454265163272
Trimmed Mean ( 22 / 24 )52.58750.0971983530789994541.032829612439
Trimmed Mean ( 23 / 24 )52.58653846153850.0941699646836544558.421558701787
Trimmed Mean ( 24 / 24 )52.58333333333330.089936907568557584.669128113507
Median52.68
Midrange53.425
Midmean - Weighted Average at Xnp52.5581081081081
Midmean - Weighted Average at X(n+1)p52.5581081081081
Midmean - Empirical Distribution Function52.5581081081081
Midmean - Empirical Distribution Function - Averaging52.5581081081081
Midmean - Empirical Distribution Function - Interpolation52.5581081081081
Midmean - Closest Observation52.5581081081081
Midmean - True Basic - Statistics Graphics Toolkit52.5581081081081
Midmean - MS Excel (old versions)52.6346153846154
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 52.7988888888889 & 0.214812175077768 & 245.79095141965 \tabularnewline
Geometric Mean & 52.7682024353795 &  &  \tabularnewline
Harmonic Mean & 52.7378564333716 &  &  \tabularnewline
Quadratic Mean & 52.8299054618794 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 52.8008333333333 & 0.214461306978493 & 246.202142835157 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 52.7947222222222 & 0.21052545969377 & 250.77595032457 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 52.7880555555556 & 0.20892326230938 & 252.667199296291 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 52.7769444444445 & 0.206355080775469 & 255.757911295967 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 52.7769444444444 & 0.205809276966518 & 256.436178302257 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 52.7794444444444 & 0.205394281783581 & 256.966474363959 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 52.7755555555556 & 0.203763100127927 & 259.004478840486 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 52.7522222222222 & 0.186973383808567 & 282.137602409938 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 52.6997222222222 & 0.168228942230519 & 313.26192463369 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 52.6747222222222 & 0.161863049521985 & 325.427714217554 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 52.6472222222222 & 0.154698229920263 & 340.322072523768 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 52.6588888888889 & 0.152916170069367 & 344.364424409801 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 52.64625 & 0.15083873975474 & 349.023401319857 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 52.6520833333333 & 0.149347555689585 & 352.547338925112 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 52.625 & 0.134211748469462 & 392.104272540449 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 52.6316666666667 & 0.131259547681645 & 400.974006053402 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 52.6340277777778 & 0.130920160435808 & 402.031494634358 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 52.6315277777778 & 0.130539787572093 & 403.183801327325 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 52.6315277777778 & 0.130539787572093 & 403.183801327325 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 52.57875 & 0.109802058621252 & 478.850311735628 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 52.5554166666667 & 0.105682989493996 & 497.293054618334 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 52.5951388888889 & 0.0855990108098556 & 614.436293028205 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 52.6111111111111 & 0.0834481733484555 & 630.464502697049 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 52.6077777777778 & 0.0829880693157562 & 633.919769570897 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 52.781 & 0.209182095477416 & 252.320830229461 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 52.76 & 0.202874535762266 & 260.062209393423 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 52.7410606060606 & 0.197845520108343 & 266.576976709803 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 52.7234375 & 0.192522960230134 & 273.855323214315 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 52.7079032258065 & 0.187048400218112 & 281.78751149085 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 52.6913333333333 & 0.180546950975616 & 291.8428311783 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 52.6731034482759 & 0.172672353010099 & 305.046537734939 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 52.6542857142857 & 0.163369125733851 & 322.302549381738 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 52.637962962963 & 0.156435973518229 & 336.482471257349 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 52.6284615384615 & 0.152544379373299 & 345.004265346754 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 52.6218 & 0.14910855927471 & 352.909318257528 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 52.6183333333333 & 0.146315969340878 & 359.62126055254 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 52.6130434782609 & 0.143034021683508 & 367.835867711795 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 52.6088636363636 & 0.139186406679473 & 377.97414913882 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 52.6035714285714 & 0.134424320564337 & 391.324807949427 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 52.601 & 0.131679389193835 & 399.462667028095 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 52.5973684210526 & 0.128540158837345 & 409.190162022513 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 52.5930555555556 & 0.124201461691961 & 423.449570070233 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 52.5885294117647 & 0.118179998332509 & 444.986716481435 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 52.5834375 & 0.109537710194422 & 480.048719355811 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 52.584 & 0.104033151215005 & 505.454265163272 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 52.5875 & 0.0971983530789994 & 541.032829612439 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 52.5865384615385 & 0.0941699646836544 & 558.421558701787 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 52.5833333333333 & 0.089936907568557 & 584.669128113507 \tabularnewline
Median & 52.68 &  &  \tabularnewline
Midrange & 53.425 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 52.5581081081081 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 52.5581081081081 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 52.5581081081081 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 52.5581081081081 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 52.5581081081081 &  &  \tabularnewline
Midmean - Closest Observation & 52.5581081081081 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 52.5581081081081 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 52.6346153846154 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=180840&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]52.7988888888889[/C][C]0.214812175077768[/C][C]245.79095141965[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]52.7682024353795[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]52.7378564333716[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]52.8299054618794[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]52.8008333333333[/C][C]0.214461306978493[/C][C]246.202142835157[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]52.7947222222222[/C][C]0.21052545969377[/C][C]250.77595032457[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]52.7880555555556[/C][C]0.20892326230938[/C][C]252.667199296291[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]52.7769444444445[/C][C]0.206355080775469[/C][C]255.757911295967[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]52.7769444444444[/C][C]0.205809276966518[/C][C]256.436178302257[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]52.7794444444444[/C][C]0.205394281783581[/C][C]256.966474363959[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]52.7755555555556[/C][C]0.203763100127927[/C][C]259.004478840486[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]52.7522222222222[/C][C]0.186973383808567[/C][C]282.137602409938[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]52.6997222222222[/C][C]0.168228942230519[/C][C]313.26192463369[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]52.6747222222222[/C][C]0.161863049521985[/C][C]325.427714217554[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]52.6472222222222[/C][C]0.154698229920263[/C][C]340.322072523768[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]52.6588888888889[/C][C]0.152916170069367[/C][C]344.364424409801[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]52.64625[/C][C]0.15083873975474[/C][C]349.023401319857[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]52.6520833333333[/C][C]0.149347555689585[/C][C]352.547338925112[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]52.625[/C][C]0.134211748469462[/C][C]392.104272540449[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]52.6316666666667[/C][C]0.131259547681645[/C][C]400.974006053402[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]52.6340277777778[/C][C]0.130920160435808[/C][C]402.031494634358[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]52.6315277777778[/C][C]0.130539787572093[/C][C]403.183801327325[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]52.6315277777778[/C][C]0.130539787572093[/C][C]403.183801327325[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]52.57875[/C][C]0.109802058621252[/C][C]478.850311735628[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]52.5554166666667[/C][C]0.105682989493996[/C][C]497.293054618334[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]52.5951388888889[/C][C]0.0855990108098556[/C][C]614.436293028205[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]52.6111111111111[/C][C]0.0834481733484555[/C][C]630.464502697049[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]52.6077777777778[/C][C]0.0829880693157562[/C][C]633.919769570897[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]52.781[/C][C]0.209182095477416[/C][C]252.320830229461[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]52.76[/C][C]0.202874535762266[/C][C]260.062209393423[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]52.7410606060606[/C][C]0.197845520108343[/C][C]266.576976709803[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]52.7234375[/C][C]0.192522960230134[/C][C]273.855323214315[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]52.7079032258065[/C][C]0.187048400218112[/C][C]281.78751149085[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]52.6913333333333[/C][C]0.180546950975616[/C][C]291.8428311783[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]52.6731034482759[/C][C]0.172672353010099[/C][C]305.046537734939[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]52.6542857142857[/C][C]0.163369125733851[/C][C]322.302549381738[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]52.637962962963[/C][C]0.156435973518229[/C][C]336.482471257349[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]52.6284615384615[/C][C]0.152544379373299[/C][C]345.004265346754[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]52.6218[/C][C]0.14910855927471[/C][C]352.909318257528[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]52.6183333333333[/C][C]0.146315969340878[/C][C]359.62126055254[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]52.6130434782609[/C][C]0.143034021683508[/C][C]367.835867711795[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]52.6088636363636[/C][C]0.139186406679473[/C][C]377.97414913882[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]52.6035714285714[/C][C]0.134424320564337[/C][C]391.324807949427[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]52.601[/C][C]0.131679389193835[/C][C]399.462667028095[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]52.5973684210526[/C][C]0.128540158837345[/C][C]409.190162022513[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]52.5930555555556[/C][C]0.124201461691961[/C][C]423.449570070233[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]52.5885294117647[/C][C]0.118179998332509[/C][C]444.986716481435[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]52.5834375[/C][C]0.109537710194422[/C][C]480.048719355811[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]52.584[/C][C]0.104033151215005[/C][C]505.454265163272[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]52.5875[/C][C]0.0971983530789994[/C][C]541.032829612439[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]52.5865384615385[/C][C]0.0941699646836544[/C][C]558.421558701787[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]52.5833333333333[/C][C]0.089936907568557[/C][C]584.669128113507[/C][/ROW]
[ROW][C]Median[/C][C]52.68[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]53.425[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]52.5581081081081[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]52.5581081081081[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]52.5581081081081[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]52.5581081081081[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]52.5581081081081[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]52.5581081081081[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]52.5581081081081[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]52.6346153846154[/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=180840&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=180840&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 Mean52.79888888888890.214812175077768245.79095141965
Geometric Mean52.7682024353795
Harmonic Mean52.7378564333716
Quadratic Mean52.8299054618794
Winsorized Mean ( 1 / 24 )52.80083333333330.214461306978493246.202142835157
Winsorized Mean ( 2 / 24 )52.79472222222220.21052545969377250.77595032457
Winsorized Mean ( 3 / 24 )52.78805555555560.20892326230938252.667199296291
Winsorized Mean ( 4 / 24 )52.77694444444450.206355080775469255.757911295967
Winsorized Mean ( 5 / 24 )52.77694444444440.205809276966518256.436178302257
Winsorized Mean ( 6 / 24 )52.77944444444440.205394281783581256.966474363959
Winsorized Mean ( 7 / 24 )52.77555555555560.203763100127927259.004478840486
Winsorized Mean ( 8 / 24 )52.75222222222220.186973383808567282.137602409938
Winsorized Mean ( 9 / 24 )52.69972222222220.168228942230519313.26192463369
Winsorized Mean ( 10 / 24 )52.67472222222220.161863049521985325.427714217554
Winsorized Mean ( 11 / 24 )52.64722222222220.154698229920263340.322072523768
Winsorized Mean ( 12 / 24 )52.65888888888890.152916170069367344.364424409801
Winsorized Mean ( 13 / 24 )52.646250.15083873975474349.023401319857
Winsorized Mean ( 14 / 24 )52.65208333333330.149347555689585352.547338925112
Winsorized Mean ( 15 / 24 )52.6250.134211748469462392.104272540449
Winsorized Mean ( 16 / 24 )52.63166666666670.131259547681645400.974006053402
Winsorized Mean ( 17 / 24 )52.63402777777780.130920160435808402.031494634358
Winsorized Mean ( 18 / 24 )52.63152777777780.130539787572093403.183801327325
Winsorized Mean ( 19 / 24 )52.63152777777780.130539787572093403.183801327325
Winsorized Mean ( 20 / 24 )52.578750.109802058621252478.850311735628
Winsorized Mean ( 21 / 24 )52.55541666666670.105682989493996497.293054618334
Winsorized Mean ( 22 / 24 )52.59513888888890.0855990108098556614.436293028205
Winsorized Mean ( 23 / 24 )52.61111111111110.0834481733484555630.464502697049
Winsorized Mean ( 24 / 24 )52.60777777777780.0829880693157562633.919769570897
Trimmed Mean ( 1 / 24 )52.7810.209182095477416252.320830229461
Trimmed Mean ( 2 / 24 )52.760.202874535762266260.062209393423
Trimmed Mean ( 3 / 24 )52.74106060606060.197845520108343266.576976709803
Trimmed Mean ( 4 / 24 )52.72343750.192522960230134273.855323214315
Trimmed Mean ( 5 / 24 )52.70790322580650.187048400218112281.78751149085
Trimmed Mean ( 6 / 24 )52.69133333333330.180546950975616291.8428311783
Trimmed Mean ( 7 / 24 )52.67310344827590.172672353010099305.046537734939
Trimmed Mean ( 8 / 24 )52.65428571428570.163369125733851322.302549381738
Trimmed Mean ( 9 / 24 )52.6379629629630.156435973518229336.482471257349
Trimmed Mean ( 10 / 24 )52.62846153846150.152544379373299345.004265346754
Trimmed Mean ( 11 / 24 )52.62180.14910855927471352.909318257528
Trimmed Mean ( 12 / 24 )52.61833333333330.146315969340878359.62126055254
Trimmed Mean ( 13 / 24 )52.61304347826090.143034021683508367.835867711795
Trimmed Mean ( 14 / 24 )52.60886363636360.139186406679473377.97414913882
Trimmed Mean ( 15 / 24 )52.60357142857140.134424320564337391.324807949427
Trimmed Mean ( 16 / 24 )52.6010.131679389193835399.462667028095
Trimmed Mean ( 17 / 24 )52.59736842105260.128540158837345409.190162022513
Trimmed Mean ( 18 / 24 )52.59305555555560.124201461691961423.449570070233
Trimmed Mean ( 19 / 24 )52.58852941176470.118179998332509444.986716481435
Trimmed Mean ( 20 / 24 )52.58343750.109537710194422480.048719355811
Trimmed Mean ( 21 / 24 )52.5840.104033151215005505.454265163272
Trimmed Mean ( 22 / 24 )52.58750.0971983530789994541.032829612439
Trimmed Mean ( 23 / 24 )52.58653846153850.0941699646836544558.421558701787
Trimmed Mean ( 24 / 24 )52.58333333333330.089936907568557584.669128113507
Median52.68
Midrange53.425
Midmean - Weighted Average at Xnp52.5581081081081
Midmean - Weighted Average at X(n+1)p52.5581081081081
Midmean - Empirical Distribution Function52.5581081081081
Midmean - Empirical Distribution Function - Averaging52.5581081081081
Midmean - Empirical Distribution Function - Interpolation52.5581081081081
Midmean - Closest Observation52.5581081081081
Midmean - True Basic - Statistics Graphics Toolkit52.5581081081081
Midmean - MS Excel (old versions)52.6346153846154
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')