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

Wed, 02 Mar 2016 10:59:35 +0000

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/2016/Mar/02/t1456916438niphlc0x8tajbij.htm/, Retrieved Mon, 29 Apr 2024 00:32:31 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=293269, Retrieved Mon, 29 Apr 2024 00:32:31 +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

Estimated Impact

145

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

-       [Central Tendency] [] [2016-03-02 10:59:35] [55e0f811d0de406b35493d0ca672d497] [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	1 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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=293269&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=293269&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=293269&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	1 seconds
R Server	'Gwilym Jenkins' @ jenkins.wessa.net

Central Tendency - Ungrouped Data
Measure	Value	S.E.	Value/S.E.
Arithmetic Mean	99.0238888888889	0.799899068250447	123.795479729056
Geometric Mean	98.7819889269375
Harmonic Mean	98.5270497878464
Quadratic Mean	99.2530055240422
Winsorized Mean ( 1 / 24 )	99.0259722222222	0.79900350348461	123.936843568709
Winsorized Mean ( 2 / 24 )	99.02625	0.794410649492683	124.653729230895
Winsorized Mean ( 3 / 24 )	99.0258333333333	0.793472803803373	124.800538668333
Winsorized Mean ( 4 / 24 )	99.0119444444444	0.786669442754136	125.862197084716
Winsorized Mean ( 5 / 24 )	99.0202777777778	0.779824299365164	126.977676713059
Winsorized Mean ( 6 / 24 )	99.3361111111111	0.696118417481049	142.700018583857
Winsorized Mean ( 7 / 24 )	99.4313888888889	0.669011378667802	148.624361347763
Winsorized Mean ( 8 / 24 )	99.4213888888889	0.667183200878917	149.01662505578
Winsorized Mean ( 9 / 24 )	99.3113888888889	0.649254487166814	152.962191023522
Winsorized Mean ( 10 / 24 )	99.4044444444445	0.622418515035906	159.70676007077
Winsorized Mean ( 11 / 24 )	99.4991666666667	0.595259729150788	167.152524845943
Winsorized Mean ( 12 / 24 )	99.8708333333333	0.518772806689861	192.51362454902
Winsorized Mean ( 13 / 24 )	99.9231944444444	0.504651595305437	198.00431698619
Winsorized Mean ( 14 / 24 )	99.9309722222222	0.501916209195614	199.098914104357
Winsorized Mean ( 15 / 24 )	100.355972222222	0.419014496021864	239.504774118807
Winsorized Mean ( 16 / 24 )	100.495972222222	0.388409524237091	258.737147137715
Winsorized Mean ( 17 / 24 )	100.559722222222	0.346855479245856	289.918217353413
Winsorized Mean ( 18 / 24 )	100.557222222222	0.338300156923668	297.242611817385
Winsorized Mean ( 19 / 24 )	100.596805555556	0.327651386983737	307.023896592108
Winsorized Mean ( 20 / 24 )	100.519027777778	0.315674759807848	318.425926225346
Winsorized Mean ( 21 / 24 )	100.390694444444	0.294538001033438	340.841229628117
Winsorized Mean ( 22 / 24 )	100.607638888889	0.210965113398001	476.892303511271
Winsorized Mean ( 23 / 24 )	100.681111111111	0.191850754171558	524.78871686415
Winsorized Mean ( 24 / 24 )	100.754444444444	0.17734885659678	568.114429254651
Trimmed Mean ( 1 / 24 )	99.1338571428571	0.779142659176175	127.234539112101
Trimmed Mean ( 2 / 24 )	99.2480882352941	0.755281586354558	131.405412270574
Trimmed Mean ( 3 / 24 )	99.3690909090909	0.72944362765978	136.225867416087
Trimmed Mean ( 4 / 24 )	99.4978125	0.698428347211076	142.459585005833
Trimmed Mean ( 5 / 24 )	99.6388709677419	0.662940427815573	150.298377934285
Trimmed Mean ( 6 / 24 )	99.7873333333333	0.621189121500395	160.639215787152
Trimmed Mean ( 7 / 24 )	99.8806896551724	0.596890503834154	167.335028809445
Trimmed Mean ( 8 / 24 )	99.9632142857143	0.574570653208774	173.978976697566
Trimmed Mean ( 9 / 24 )	100.053518518519	0.547014842681371	182.908233400165
Trimmed Mean ( 10 / 24 )	100.167692307692	0.516332978561287	193.998246222428
Trimmed Mean ( 11 / 24 )	100.2776	0.484403741201279	207.01243915111
Trimmed Mean ( 12 / 24 )	100.38375	0.450556947011141	222.799250274389
Trimmed Mean ( 13 / 24 )	100.450652173913	0.428289531643436	234.539125410007
Trimmed Mean ( 14 / 24 )	100.517045454545	0.402838708817722	249.521814200898
Trimmed Mean ( 15 / 24 )	100.58880952381	0.369412095692305	272.294304103115
Trimmed Mean ( 16 / 24 )	100.61675	0.349480087745739	287.904099626995
Trimmed Mean ( 17 / 24 )	100.631052631579	0.331133616817846	303.898630403736
Trimmed Mean ( 18 / 24 )	100.639444444444	0.317522888674898	316.951779018004
Trimmed Mean ( 19 / 24 )	100.649117647059	0.300858062141644	334.540204542277
Trimmed Mean ( 20 / 24 )	100.6553125	0.280422702381759	358.941382580968
Trimmed Mean ( 21 / 24 )	100.671666666667	0.254528224089663	395.522606684291
Trimmed Mean ( 22 / 24 )	100.706071428571	0.223087604263695	451.419395357953
Trimmed Mean ( 23 / 24 )	100.718461538462	0.211068849363419	477.182975328795
Trimmed Mean ( 24 / 24 )	100.723333333333	0.199777654183623	504.177175094643
Median	100.7
Midrange	95.175
Midmean - Weighted Average at Xnp	100.535675675676
Midmean - Weighted Average at X(n+1)p	100.639444444444
Midmean - Empirical Distribution Function	100.535675675676
Midmean - Empirical Distribution Function - Averaging	100.639444444444
Midmean - Empirical Distribution Function - Interpolation	100.639444444444
Midmean - Closest Observation	100.535675675676
Midmean - True Basic - Statistics Graphics Toolkit	100.639444444444
Midmean - MS Excel (old versions)	100.631052631579
Number of observations	72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 99.0238888888889 & 0.799899068250447 & 123.795479729056 \tabularnewline
Geometric Mean & 98.7819889269375 &  &  \tabularnewline
Harmonic Mean & 98.5270497878464 &  &  \tabularnewline
Quadratic Mean & 99.2530055240422 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 99.0259722222222 & 0.79900350348461 & 123.936843568709 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 99.02625 & 0.794410649492683 & 124.653729230895 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 99.0258333333333 & 0.793472803803373 & 124.800538668333 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 99.0119444444444 & 0.786669442754136 & 125.862197084716 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 99.0202777777778 & 0.779824299365164 & 126.977676713059 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 99.3361111111111 & 0.696118417481049 & 142.700018583857 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 99.4313888888889 & 0.669011378667802 & 148.624361347763 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 99.4213888888889 & 0.667183200878917 & 149.01662505578 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 99.3113888888889 & 0.649254487166814 & 152.962191023522 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 99.4044444444445 & 0.622418515035906 & 159.70676007077 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 99.4991666666667 & 0.595259729150788 & 167.152524845943 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 99.8708333333333 & 0.518772806689861 & 192.51362454902 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 99.9231944444444 & 0.504651595305437 & 198.00431698619 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 99.9309722222222 & 0.501916209195614 & 199.098914104357 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 100.355972222222 & 0.419014496021864 & 239.504774118807 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 100.495972222222 & 0.388409524237091 & 258.737147137715 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 100.559722222222 & 0.346855479245856 & 289.918217353413 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 100.557222222222 & 0.338300156923668 & 297.242611817385 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 100.596805555556 & 0.327651386983737 & 307.023896592108 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 100.519027777778 & 0.315674759807848 & 318.425926225346 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 100.390694444444 & 0.294538001033438 & 340.841229628117 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 100.607638888889 & 0.210965113398001 & 476.892303511271 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 100.681111111111 & 0.191850754171558 & 524.78871686415 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 100.754444444444 & 0.17734885659678 & 568.114429254651 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 99.1338571428571 & 0.779142659176175 & 127.234539112101 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 99.2480882352941 & 0.755281586354558 & 131.405412270574 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 99.3690909090909 & 0.72944362765978 & 136.225867416087 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 99.4978125 & 0.698428347211076 & 142.459585005833 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 99.6388709677419 & 0.662940427815573 & 150.298377934285 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 99.7873333333333 & 0.621189121500395 & 160.639215787152 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 99.8806896551724 & 0.596890503834154 & 167.335028809445 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 99.9632142857143 & 0.574570653208774 & 173.978976697566 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 100.053518518519 & 0.547014842681371 & 182.908233400165 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 100.167692307692 & 0.516332978561287 & 193.998246222428 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 100.2776 & 0.484403741201279 & 207.01243915111 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 100.38375 & 0.450556947011141 & 222.799250274389 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 100.450652173913 & 0.428289531643436 & 234.539125410007 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 100.517045454545 & 0.402838708817722 & 249.521814200898 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 100.58880952381 & 0.369412095692305 & 272.294304103115 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 100.61675 & 0.349480087745739 & 287.904099626995 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 100.631052631579 & 0.331133616817846 & 303.898630403736 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 100.639444444444 & 0.317522888674898 & 316.951779018004 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 100.649117647059 & 0.300858062141644 & 334.540204542277 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 100.6553125 & 0.280422702381759 & 358.941382580968 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 100.671666666667 & 0.254528224089663 & 395.522606684291 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 100.706071428571 & 0.223087604263695 & 451.419395357953 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 100.718461538462 & 0.211068849363419 & 477.182975328795 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 100.723333333333 & 0.199777654183623 & 504.177175094643 \tabularnewline
Median & 100.7 &  &  \tabularnewline
Midrange & 95.175 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 100.535675675676 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 100.639444444444 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 100.535675675676 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 100.639444444444 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 100.639444444444 &  &  \tabularnewline
Midmean - Closest Observation & 100.535675675676 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 100.639444444444 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 100.631052631579 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=293269&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]99.0238888888889[/C][C]0.799899068250447[/C][C]123.795479729056[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]98.7819889269375[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]98.5270497878464[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]99.2530055240422[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]99.0259722222222[/C][C]0.79900350348461[/C][C]123.936843568709[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]99.02625[/C][C]0.794410649492683[/C][C]124.653729230895[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]99.0258333333333[/C][C]0.793472803803373[/C][C]124.800538668333[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]99.0119444444444[/C][C]0.786669442754136[/C][C]125.862197084716[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]99.0202777777778[/C][C]0.779824299365164[/C][C]126.977676713059[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]99.3361111111111[/C][C]0.696118417481049[/C][C]142.700018583857[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]99.4313888888889[/C][C]0.669011378667802[/C][C]148.624361347763[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]99.4213888888889[/C][C]0.667183200878917[/C][C]149.01662505578[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]99.3113888888889[/C][C]0.649254487166814[/C][C]152.962191023522[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]99.4044444444445[/C][C]0.622418515035906[/C][C]159.70676007077[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]99.4991666666667[/C][C]0.595259729150788[/C][C]167.152524845943[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]99.8708333333333[/C][C]0.518772806689861[/C][C]192.51362454902[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]99.9231944444444[/C][C]0.504651595305437[/C][C]198.00431698619[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]99.9309722222222[/C][C]0.501916209195614[/C][C]199.098914104357[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]100.355972222222[/C][C]0.419014496021864[/C][C]239.504774118807[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]100.495972222222[/C][C]0.388409524237091[/C][C]258.737147137715[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]100.559722222222[/C][C]0.346855479245856[/C][C]289.918217353413[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]100.557222222222[/C][C]0.338300156923668[/C][C]297.242611817385[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]100.596805555556[/C][C]0.327651386983737[/C][C]307.023896592108[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]100.519027777778[/C][C]0.315674759807848[/C][C]318.425926225346[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]100.390694444444[/C][C]0.294538001033438[/C][C]340.841229628117[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]100.607638888889[/C][C]0.210965113398001[/C][C]476.892303511271[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]100.681111111111[/C][C]0.191850754171558[/C][C]524.78871686415[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]100.754444444444[/C][C]0.17734885659678[/C][C]568.114429254651[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]99.1338571428571[/C][C]0.779142659176175[/C][C]127.234539112101[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]99.2480882352941[/C][C]0.755281586354558[/C][C]131.405412270574[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]99.3690909090909[/C][C]0.72944362765978[/C][C]136.225867416087[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]99.4978125[/C][C]0.698428347211076[/C][C]142.459585005833[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]99.6388709677419[/C][C]0.662940427815573[/C][C]150.298377934285[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]99.7873333333333[/C][C]0.621189121500395[/C][C]160.639215787152[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]99.8806896551724[/C][C]0.596890503834154[/C][C]167.335028809445[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]99.9632142857143[/C][C]0.574570653208774[/C][C]173.978976697566[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]100.053518518519[/C][C]0.547014842681371[/C][C]182.908233400165[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]100.167692307692[/C][C]0.516332978561287[/C][C]193.998246222428[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]100.2776[/C][C]0.484403741201279[/C][C]207.01243915111[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]100.38375[/C][C]0.450556947011141[/C][C]222.799250274389[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]100.450652173913[/C][C]0.428289531643436[/C][C]234.539125410007[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]100.517045454545[/C][C]0.402838708817722[/C][C]249.521814200898[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]100.58880952381[/C][C]0.369412095692305[/C][C]272.294304103115[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]100.61675[/C][C]0.349480087745739[/C][C]287.904099626995[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]100.631052631579[/C][C]0.331133616817846[/C][C]303.898630403736[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]100.639444444444[/C][C]0.317522888674898[/C][C]316.951779018004[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]100.649117647059[/C][C]0.300858062141644[/C][C]334.540204542277[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]100.6553125[/C][C]0.280422702381759[/C][C]358.941382580968[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]100.671666666667[/C][C]0.254528224089663[/C][C]395.522606684291[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]100.706071428571[/C][C]0.223087604263695[/C][C]451.419395357953[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]100.718461538462[/C][C]0.211068849363419[/C][C]477.182975328795[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]100.723333333333[/C][C]0.199777654183623[/C][C]504.177175094643[/C][/ROW]
[ROW][C]Median[/C][C]100.7[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]95.175[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]100.535675675676[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]100.639444444444[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]100.535675675676[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]100.639444444444[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]100.639444444444[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]100.535675675676[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]100.639444444444[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]100.631052631579[/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=293269&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=293269&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	99.0238888888889	0.799899068250447	123.795479729056
Geometric Mean	98.7819889269375
Harmonic Mean	98.5270497878464
Quadratic Mean	99.2530055240422
Winsorized Mean ( 1 / 24 )	99.0259722222222	0.79900350348461	123.936843568709
Winsorized Mean ( 2 / 24 )	99.02625	0.794410649492683	124.653729230895
Winsorized Mean ( 3 / 24 )	99.0258333333333	0.793472803803373	124.800538668333
Winsorized Mean ( 4 / 24 )	99.0119444444444	0.786669442754136	125.862197084716
Winsorized Mean ( 5 / 24 )	99.0202777777778	0.779824299365164	126.977676713059
Winsorized Mean ( 6 / 24 )	99.3361111111111	0.696118417481049	142.700018583857
Winsorized Mean ( 7 / 24 )	99.4313888888889	0.669011378667802	148.624361347763
Winsorized Mean ( 8 / 24 )	99.4213888888889	0.667183200878917	149.01662505578
Winsorized Mean ( 9 / 24 )	99.3113888888889	0.649254487166814	152.962191023522
Winsorized Mean ( 10 / 24 )	99.4044444444445	0.622418515035906	159.70676007077
Winsorized Mean ( 11 / 24 )	99.4991666666667	0.595259729150788	167.152524845943
Winsorized Mean ( 12 / 24 )	99.8708333333333	0.518772806689861	192.51362454902
Winsorized Mean ( 13 / 24 )	99.9231944444444	0.504651595305437	198.00431698619
Winsorized Mean ( 14 / 24 )	99.9309722222222	0.501916209195614	199.098914104357
Winsorized Mean ( 15 / 24 )	100.355972222222	0.419014496021864	239.504774118807
Winsorized Mean ( 16 / 24 )	100.495972222222	0.388409524237091	258.737147137715
Winsorized Mean ( 17 / 24 )	100.559722222222	0.346855479245856	289.918217353413
Winsorized Mean ( 18 / 24 )	100.557222222222	0.338300156923668	297.242611817385
Winsorized Mean ( 19 / 24 )	100.596805555556	0.327651386983737	307.023896592108
Winsorized Mean ( 20 / 24 )	100.519027777778	0.315674759807848	318.425926225346
Winsorized Mean ( 21 / 24 )	100.390694444444	0.294538001033438	340.841229628117
Winsorized Mean ( 22 / 24 )	100.607638888889	0.210965113398001	476.892303511271
Winsorized Mean ( 23 / 24 )	100.681111111111	0.191850754171558	524.78871686415
Winsorized Mean ( 24 / 24 )	100.754444444444	0.17734885659678	568.114429254651
Trimmed Mean ( 1 / 24 )	99.1338571428571	0.779142659176175	127.234539112101
Trimmed Mean ( 2 / 24 )	99.2480882352941	0.755281586354558	131.405412270574
Trimmed Mean ( 3 / 24 )	99.3690909090909	0.72944362765978	136.225867416087
Trimmed Mean ( 4 / 24 )	99.4978125	0.698428347211076	142.459585005833
Trimmed Mean ( 5 / 24 )	99.6388709677419	0.662940427815573	150.298377934285
Trimmed Mean ( 6 / 24 )	99.7873333333333	0.621189121500395	160.639215787152
Trimmed Mean ( 7 / 24 )	99.8806896551724	0.596890503834154	167.335028809445
Trimmed Mean ( 8 / 24 )	99.9632142857143	0.574570653208774	173.978976697566
Trimmed Mean ( 9 / 24 )	100.053518518519	0.547014842681371	182.908233400165
Trimmed Mean ( 10 / 24 )	100.167692307692	0.516332978561287	193.998246222428
Trimmed Mean ( 11 / 24 )	100.2776	0.484403741201279	207.01243915111
Trimmed Mean ( 12 / 24 )	100.38375	0.450556947011141	222.799250274389
Trimmed Mean ( 13 / 24 )	100.450652173913	0.428289531643436	234.539125410007
Trimmed Mean ( 14 / 24 )	100.517045454545	0.402838708817722	249.521814200898
Trimmed Mean ( 15 / 24 )	100.58880952381	0.369412095692305	272.294304103115
Trimmed Mean ( 16 / 24 )	100.61675	0.349480087745739	287.904099626995
Trimmed Mean ( 17 / 24 )	100.631052631579	0.331133616817846	303.898630403736
Trimmed Mean ( 18 / 24 )	100.639444444444	0.317522888674898	316.951779018004
Trimmed Mean ( 19 / 24 )	100.649117647059	0.300858062141644	334.540204542277
Trimmed Mean ( 20 / 24 )	100.6553125	0.280422702381759	358.941382580968
Trimmed Mean ( 21 / 24 )	100.671666666667	0.254528224089663	395.522606684291
Trimmed Mean ( 22 / 24 )	100.706071428571	0.223087604263695	451.419395357953
Trimmed Mean ( 23 / 24 )	100.718461538462	0.211068849363419	477.182975328795
Trimmed Mean ( 24 / 24 )	100.723333333333	0.199777654183623	504.177175094643
Median	100.7
Midrange	95.175
Midmean - Weighted Average at Xnp	100.535675675676
Midmean - Weighted Average at X(n+1)p	100.639444444444
Midmean - Empirical Distribution Function	100.535675675676
Midmean - Empirical Distribution Function - Averaging	100.639444444444
Midmean - Empirical Distribution Function - Interpolation	100.639444444444
Midmean - Closest Observation	100.535675675676
Midmean - True Basic - Statistics Graphics Toolkit	100.639444444444
Midmean - MS Excel (old versions)	100.631052631579
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