Repository of Reproducible Computations

Free Statistics

of Irreproducible Research!

Author's title

Author

*Unverified author*

R Software Module

rwasp_centraltendency.wasp

Title produced by software

Central Tendency

Date of computation

Sun, 16 Oct 2011 11:27:52 -0400

Cite this page as follows

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Oct/16/t1318778909sqt1oa1dr5lq1ht.htm/, Retrieved Thu, 16 May 2024 15:41:50 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=130125, Retrieved Thu, 16 May 2024 15:41:50 +0000

QR Codes:

Paste this QR Code to cite your computation.

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

KDG2011W52a

Estimated Impact

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

-       [Central Tendency] [] [2011-10-16 15:27:52] [c442720b665eade0c8a11d0ab9dda6bb] [Current]

Feedback Forum

Post a new message

Dataseries X:

Download CSV

Histogram

Boxplots

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 seconds
R Server	'George Udny Yule' @ yule.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 & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=130125&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]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=130125&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=130125&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 Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 seconds
R Server	'George Udny Yule' @ yule.wessa.net

Central Tendency - Ungrouped Data
Measure	Value	S.E.	Value/S.E.
Arithmetic Mean	78.5386111111111	0.196611684201266	399.460547984083
Geometric Mean	78.5209058983669
Harmonic Mean	78.5029674116377
Quadratic Mean	78.5560820192951
Winsorized Mean ( 1 / 24 )	78.5383333333333	0.196460562807537	399.766407114865
Winsorized Mean ( 2 / 24 )	78.5438888888889	0.194970058649474	402.85102970656
Winsorized Mean ( 3 / 24 )	78.5451388888889	0.194668269763115	403.48197980322
Winsorized Mean ( 4 / 24 )	78.5490277777778	0.192899501078979	407.201819281106
Winsorized Mean ( 5 / 24 )	78.5413888888889	0.191848179570516	409.393454056832
Winsorized Mean ( 6 / 24 )	78.5380555555556	0.190184166456955	412.957908214359
Winsorized Mean ( 7 / 24 )	78.5429166666667	0.188344492325937	417.017326584445
Winsorized Mean ( 8 / 24 )	78.54625	0.184789716539667	425.057473277411
Winsorized Mean ( 9 / 24 )	78.55125	0.183647185207357	427.72912588509
Winsorized Mean ( 10 / 24 )	78.5526388888889	0.183330878457268	428.474676769731
Winsorized Mean ( 11 / 24 )	78.5511111111111	0.182058473507934	431.46089054563
Winsorized Mean ( 12 / 24 )	78.8361111111111	0.117637568978596	670.161002098365
Winsorized Mean ( 13 / 24 )	78.8379166666667	0.116201611246065	678.458033595781
Winsorized Mean ( 14 / 24 )	78.8301388888889	0.114474456263215	688.62645398928
Winsorized Mean ( 15 / 24 )	78.8072222222222	0.111282399270553	708.173284713457
Winsorized Mean ( 16 / 24 )	78.8338888888889	0.105499511520047	747.244112821403
Winsorized Mean ( 17 / 24 )	78.8693055555556	0.099831298698746	790.025839426912
Winsorized Mean ( 18 / 24 )	78.8893055555555	0.093810885578841	840.939780802463
Winsorized Mean ( 19 / 24 )	78.9051388888889	0.0906706436091757	870.23909556658
Winsorized Mean ( 20 / 24 )	78.9245833333333	0.0822785208196091	959.23677950374
Winsorized Mean ( 21 / 24 )	78.9479166666667	0.0701451483904836	1125.49361542697
Winsorized Mean ( 22 / 24 )	78.9234722222222	0.066040533778948	1195.07623130964
Winsorized Mean ( 23 / 24 )	78.9138888888889	0.0631008072547048	1250.60030643277
Winsorized Mean ( 24 / 24 )	78.8805555555555	0.0589242002969022	1338.67842343382
Trimmed Mean ( 1 / 24 )	78.5607142857143	0.193391365756099	406.226586065861
Trimmed Mean ( 2 / 24 )	78.5844117647059	0.189672605312447	414.316087635607
Trimmed Mean ( 3 / 24 )	78.6065151515152	0.186117552199037	422.348747996922
Trimmed Mean ( 4 / 24 )	78.62953125	0.181921434192417	432.216971018566
Trimmed Mean ( 5 / 24 )	78.6529032258065	0.177454590030332	443.22833921829
Trimmed Mean ( 6 / 24 )	78.6796666666667	0.172275066918381	456.709540585713
Trimmed Mean ( 7 / 24 )	78.7089655172414	0.166332761042307	473.201821601589
Trimmed Mean ( 8 / 24 )	78.7394642857143	0.159433538578187	493.87014167725
Trimmed Mean ( 9 / 24 )	78.7716666666667	0.151702370990308	519.251387782853
Trimmed Mean ( 10 / 24 )	78.805576923077	0.142137160368364	554.433314404506
Trimmed Mean ( 11 / 24 )	78.842	0.129721208122399	607.780340170811
Trimmed Mean ( 12 / 24 )	78.8816666666667	0.113266041766692	696.428209517101
Trimmed Mean ( 13 / 24 )	78.8876086956522	0.110871028691677	711.525902001255
Trimmed Mean ( 14 / 24 )	78.8938636363636	0.108022399950308	730.34725827843
Trimmed Mean ( 15 / 24 )	78.9016666666667	0.10461472741642	754.211845838853
Trimmed Mean ( 16 / 24 )	78.913	0.100747335652242	783.276296977125
Trimmed Mean ( 17 / 24 )	78.9223684210526	0.0970257801896586	813.416478247133
Trimmed Mean ( 18 / 24 )	78.9286111111111	0.0934541333708235	844.570574507651
Trimmed Mean ( 19 / 24 )	78.9332352941177	0.0901056228975765	876.007875599966
Trimmed Mean ( 20 / 24 )	78.9365625	0.0862159345712375	915.568135896935
Trimmed Mean ( 21 / 24 )	78.938	0.0831248887303722	949.631346347386
Trimmed Mean ( 22 / 24 )	78.9367857142857	0.082131095316197	961.107183709003
Trimmed Mean ( 23 / 24 )	78.9384615384615	0.0814988292651963	968.583993784704
Trimmed Mean ( 24 / 24 )	78.9416666666667	0.0809581808907543	975.09190298126
Median	79.155
Midrange	77.765
Midmean - Weighted Average at Xnp	78.897027027027
Midmean - Weighted Average at X(n+1)p	78.9286111111111
Midmean - Empirical Distribution Function	78.897027027027
Midmean - Empirical Distribution Function - Averaging	78.9286111111111
Midmean - Empirical Distribution Function - Interpolation	78.9286111111111
Midmean - Closest Observation	78.897027027027
Midmean - True Basic - Statistics Graphics Toolkit	78.9286111111111
Midmean - MS Excel (old versions)	78.9464102564102
Number of observations	72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 78.5386111111111 & 0.196611684201266 & 399.460547984083 \tabularnewline
Geometric Mean & 78.5209058983669 &  &  \tabularnewline
Harmonic Mean & 78.5029674116377 &  &  \tabularnewline
Quadratic Mean & 78.5560820192951 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 78.5383333333333 & 0.196460562807537 & 399.766407114865 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 78.5438888888889 & 0.194970058649474 & 402.85102970656 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 78.5451388888889 & 0.194668269763115 & 403.48197980322 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 78.5490277777778 & 0.192899501078979 & 407.201819281106 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 78.5413888888889 & 0.191848179570516 & 409.393454056832 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 78.5380555555556 & 0.190184166456955 & 412.957908214359 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 78.5429166666667 & 0.188344492325937 & 417.017326584445 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 78.54625 & 0.184789716539667 & 425.057473277411 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 78.55125 & 0.183647185207357 & 427.72912588509 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 78.5526388888889 & 0.183330878457268 & 428.474676769731 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 78.5511111111111 & 0.182058473507934 & 431.46089054563 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 78.8361111111111 & 0.117637568978596 & 670.161002098365 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 78.8379166666667 & 0.116201611246065 & 678.458033595781 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 78.8301388888889 & 0.114474456263215 & 688.62645398928 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 78.8072222222222 & 0.111282399270553 & 708.173284713457 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 78.8338888888889 & 0.105499511520047 & 747.244112821403 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 78.8693055555556 & 0.099831298698746 & 790.025839426912 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 78.8893055555555 & 0.093810885578841 & 840.939780802463 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 78.9051388888889 & 0.0906706436091757 & 870.23909556658 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 78.9245833333333 & 0.0822785208196091 & 959.23677950374 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 78.9479166666667 & 0.0701451483904836 & 1125.49361542697 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 78.9234722222222 & 0.066040533778948 & 1195.07623130964 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 78.9138888888889 & 0.0631008072547048 & 1250.60030643277 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 78.8805555555555 & 0.0589242002969022 & 1338.67842343382 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 78.5607142857143 & 0.193391365756099 & 406.226586065861 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 78.5844117647059 & 0.189672605312447 & 414.316087635607 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 78.6065151515152 & 0.186117552199037 & 422.348747996922 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 78.62953125 & 0.181921434192417 & 432.216971018566 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 78.6529032258065 & 0.177454590030332 & 443.22833921829 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 78.6796666666667 & 0.172275066918381 & 456.709540585713 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 78.7089655172414 & 0.166332761042307 & 473.201821601589 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 78.7394642857143 & 0.159433538578187 & 493.87014167725 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 78.7716666666667 & 0.151702370990308 & 519.251387782853 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 78.805576923077 & 0.142137160368364 & 554.433314404506 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 78.842 & 0.129721208122399 & 607.780340170811 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 78.8816666666667 & 0.113266041766692 & 696.428209517101 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 78.8876086956522 & 0.110871028691677 & 711.525902001255 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 78.8938636363636 & 0.108022399950308 & 730.34725827843 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 78.9016666666667 & 0.10461472741642 & 754.211845838853 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 78.913 & 0.100747335652242 & 783.276296977125 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 78.9223684210526 & 0.0970257801896586 & 813.416478247133 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 78.9286111111111 & 0.0934541333708235 & 844.570574507651 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 78.9332352941177 & 0.0901056228975765 & 876.007875599966 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 78.9365625 & 0.0862159345712375 & 915.568135896935 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 78.938 & 0.0831248887303722 & 949.631346347386 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 78.9367857142857 & 0.082131095316197 & 961.107183709003 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 78.9384615384615 & 0.0814988292651963 & 968.583993784704 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 78.9416666666667 & 0.0809581808907543 & 975.09190298126 \tabularnewline
Median & 79.155 &  &  \tabularnewline
Midrange & 77.765 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 78.897027027027 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 78.9286111111111 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 78.897027027027 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 78.9286111111111 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 78.9286111111111 &  &  \tabularnewline
Midmean - Closest Observation & 78.897027027027 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 78.9286111111111 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 78.9464102564102 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=130125&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]78.5386111111111[/C][C]0.196611684201266[/C][C]399.460547984083[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]78.5209058983669[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]78.5029674116377[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]78.5560820192951[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]78.5383333333333[/C][C]0.196460562807537[/C][C]399.766407114865[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]78.5438888888889[/C][C]0.194970058649474[/C][C]402.85102970656[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]78.5451388888889[/C][C]0.194668269763115[/C][C]403.48197980322[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]78.5490277777778[/C][C]0.192899501078979[/C][C]407.201819281106[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]78.5413888888889[/C][C]0.191848179570516[/C][C]409.393454056832[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]78.5380555555556[/C][C]0.190184166456955[/C][C]412.957908214359[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]78.5429166666667[/C][C]0.188344492325937[/C][C]417.017326584445[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]78.54625[/C][C]0.184789716539667[/C][C]425.057473277411[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]78.55125[/C][C]0.183647185207357[/C][C]427.72912588509[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]78.5526388888889[/C][C]0.183330878457268[/C][C]428.474676769731[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]78.5511111111111[/C][C]0.182058473507934[/C][C]431.46089054563[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]78.8361111111111[/C][C]0.117637568978596[/C][C]670.161002098365[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]78.8379166666667[/C][C]0.116201611246065[/C][C]678.458033595781[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]78.8301388888889[/C][C]0.114474456263215[/C][C]688.62645398928[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]78.8072222222222[/C][C]0.111282399270553[/C][C]708.173284713457[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]78.8338888888889[/C][C]0.105499511520047[/C][C]747.244112821403[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]78.8693055555556[/C][C]0.099831298698746[/C][C]790.025839426912[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]78.8893055555555[/C][C]0.093810885578841[/C][C]840.939780802463[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]78.9051388888889[/C][C]0.0906706436091757[/C][C]870.23909556658[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]78.9245833333333[/C][C]0.0822785208196091[/C][C]959.23677950374[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]78.9479166666667[/C][C]0.0701451483904836[/C][C]1125.49361542697[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]78.9234722222222[/C][C]0.066040533778948[/C][C]1195.07623130964[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]78.9138888888889[/C][C]0.0631008072547048[/C][C]1250.60030643277[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]78.8805555555555[/C][C]0.0589242002969022[/C][C]1338.67842343382[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]78.5607142857143[/C][C]0.193391365756099[/C][C]406.226586065861[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]78.5844117647059[/C][C]0.189672605312447[/C][C]414.316087635607[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]78.6065151515152[/C][C]0.186117552199037[/C][C]422.348747996922[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]78.62953125[/C][C]0.181921434192417[/C][C]432.216971018566[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]78.6529032258065[/C][C]0.177454590030332[/C][C]443.22833921829[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]78.6796666666667[/C][C]0.172275066918381[/C][C]456.709540585713[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]78.7089655172414[/C][C]0.166332761042307[/C][C]473.201821601589[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]78.7394642857143[/C][C]0.159433538578187[/C][C]493.87014167725[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]78.7716666666667[/C][C]0.151702370990308[/C][C]519.251387782853[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]78.805576923077[/C][C]0.142137160368364[/C][C]554.433314404506[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]78.842[/C][C]0.129721208122399[/C][C]607.780340170811[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]78.8816666666667[/C][C]0.113266041766692[/C][C]696.428209517101[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]78.8876086956522[/C][C]0.110871028691677[/C][C]711.525902001255[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]78.8938636363636[/C][C]0.108022399950308[/C][C]730.34725827843[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]78.9016666666667[/C][C]0.10461472741642[/C][C]754.211845838853[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]78.913[/C][C]0.100747335652242[/C][C]783.276296977125[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]78.9223684210526[/C][C]0.0970257801896586[/C][C]813.416478247133[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]78.9286111111111[/C][C]0.0934541333708235[/C][C]844.570574507651[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]78.9332352941177[/C][C]0.0901056228975765[/C][C]876.007875599966[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]78.9365625[/C][C]0.0862159345712375[/C][C]915.568135896935[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]78.938[/C][C]0.0831248887303722[/C][C]949.631346347386[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]78.9367857142857[/C][C]0.082131095316197[/C][C]961.107183709003[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]78.9384615384615[/C][C]0.0814988292651963[/C][C]968.583993784704[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]78.9416666666667[/C][C]0.0809581808907543[/C][C]975.09190298126[/C][/ROW]
[ROW][C]Median[/C][C]79.155[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]77.765[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]78.897027027027[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]78.9286111111111[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]78.897027027027[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]78.9286111111111[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]78.9286111111111[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]78.897027027027[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]78.9286111111111[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]78.9464102564102[/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=130125&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=130125&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
Measure	Value	S.E.	Value/S.E.
Arithmetic Mean	78.5386111111111	0.196611684201266	399.460547984083
Geometric Mean	78.5209058983669
Harmonic Mean	78.5029674116377
Quadratic Mean	78.5560820192951
Winsorized Mean ( 1 / 24 )	78.5383333333333	0.196460562807537	399.766407114865
Winsorized Mean ( 2 / 24 )	78.5438888888889	0.194970058649474	402.85102970656
Winsorized Mean ( 3 / 24 )	78.5451388888889	0.194668269763115	403.48197980322
Winsorized Mean ( 4 / 24 )	78.5490277777778	0.192899501078979	407.201819281106
Winsorized Mean ( 5 / 24 )	78.5413888888889	0.191848179570516	409.393454056832
Winsorized Mean ( 6 / 24 )	78.5380555555556	0.190184166456955	412.957908214359
Winsorized Mean ( 7 / 24 )	78.5429166666667	0.188344492325937	417.017326584445
Winsorized Mean ( 8 / 24 )	78.54625	0.184789716539667	425.057473277411
Winsorized Mean ( 9 / 24 )	78.55125	0.183647185207357	427.72912588509
Winsorized Mean ( 10 / 24 )	78.5526388888889	0.183330878457268	428.474676769731
Winsorized Mean ( 11 / 24 )	78.5511111111111	0.182058473507934	431.46089054563
Winsorized Mean ( 12 / 24 )	78.8361111111111	0.117637568978596	670.161002098365
Winsorized Mean ( 13 / 24 )	78.8379166666667	0.116201611246065	678.458033595781
Winsorized Mean ( 14 / 24 )	78.8301388888889	0.114474456263215	688.62645398928
Winsorized Mean ( 15 / 24 )	78.8072222222222	0.111282399270553	708.173284713457
Winsorized Mean ( 16 / 24 )	78.8338888888889	0.105499511520047	747.244112821403
Winsorized Mean ( 17 / 24 )	78.8693055555556	0.099831298698746	790.025839426912
Winsorized Mean ( 18 / 24 )	78.8893055555555	0.093810885578841	840.939780802463
Winsorized Mean ( 19 / 24 )	78.9051388888889	0.0906706436091757	870.23909556658
Winsorized Mean ( 20 / 24 )	78.9245833333333	0.0822785208196091	959.23677950374
Winsorized Mean ( 21 / 24 )	78.9479166666667	0.0701451483904836	1125.49361542697
Winsorized Mean ( 22 / 24 )	78.9234722222222	0.066040533778948	1195.07623130964
Winsorized Mean ( 23 / 24 )	78.9138888888889	0.0631008072547048	1250.60030643277
Winsorized Mean ( 24 / 24 )	78.8805555555555	0.0589242002969022	1338.67842343382
Trimmed Mean ( 1 / 24 )	78.5607142857143	0.193391365756099	406.226586065861
Trimmed Mean ( 2 / 24 )	78.5844117647059	0.189672605312447	414.316087635607
Trimmed Mean ( 3 / 24 )	78.6065151515152	0.186117552199037	422.348747996922
Trimmed Mean ( 4 / 24 )	78.62953125	0.181921434192417	432.216971018566
Trimmed Mean ( 5 / 24 )	78.6529032258065	0.177454590030332	443.22833921829
Trimmed Mean ( 6 / 24 )	78.6796666666667	0.172275066918381	456.709540585713
Trimmed Mean ( 7 / 24 )	78.7089655172414	0.166332761042307	473.201821601589
Trimmed Mean ( 8 / 24 )	78.7394642857143	0.159433538578187	493.87014167725
Trimmed Mean ( 9 / 24 )	78.7716666666667	0.151702370990308	519.251387782853
Trimmed Mean ( 10 / 24 )	78.805576923077	0.142137160368364	554.433314404506
Trimmed Mean ( 11 / 24 )	78.842	0.129721208122399	607.780340170811
Trimmed Mean ( 12 / 24 )	78.8816666666667	0.113266041766692	696.428209517101
Trimmed Mean ( 13 / 24 )	78.8876086956522	0.110871028691677	711.525902001255
Trimmed Mean ( 14 / 24 )	78.8938636363636	0.108022399950308	730.34725827843
Trimmed Mean ( 15 / 24 )	78.9016666666667	0.10461472741642	754.211845838853
Trimmed Mean ( 16 / 24 )	78.913	0.100747335652242	783.276296977125
Trimmed Mean ( 17 / 24 )	78.9223684210526	0.0970257801896586	813.416478247133
Trimmed Mean ( 18 / 24 )	78.9286111111111	0.0934541333708235	844.570574507651
Trimmed Mean ( 19 / 24 )	78.9332352941177	0.0901056228975765	876.007875599966
Trimmed Mean ( 20 / 24 )	78.9365625	0.0862159345712375	915.568135896935
Trimmed Mean ( 21 / 24 )	78.938	0.0831248887303722	949.631346347386
Trimmed Mean ( 22 / 24 )	78.9367857142857	0.082131095316197	961.107183709003
Trimmed Mean ( 23 / 24 )	78.9384615384615	0.0814988292651963	968.583993784704
Trimmed Mean ( 24 / 24 )	78.9416666666667	0.0809581808907543	975.09190298126
Median	79.155
Midrange	77.765
Midmean - Weighted Average at Xnp	78.897027027027
Midmean - Weighted Average at X(n+1)p	78.9286111111111
Midmean - Empirical Distribution Function	78.897027027027
Midmean - Empirical Distribution Function - Averaging	78.9286111111111
Midmean - Empirical Distribution Function - Interpolation	78.9286111111111
Midmean - Closest Observation	78.897027027027
Midmean - True Basic - Statistics Graphics Toolkit	78.9286111111111
Midmean - MS Excel (old versions)	78.9464102564102
Number of observations	72

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

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')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code