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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationMon, 17 Dec 2007 12:33:09 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2007/Dec/17/t1197919019pr2gvr9iv9u4rmy.htm/, Retrieved Fri, 03 May 2024 16:32:30 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=4415, Retrieved Fri, 03 May 2024 16:32:30 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsPCTRMA
Estimated Impact203
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Paper - Central t...] [2007-12-17 19:33:09] [e51d7ab0e549b3dc96ac85a81d9bd259] [Current]
-    D    [Central Tendency] [Paper - Central t...] [2008-12-27 13:07:36] [1aad2bd7746abaf3ab17fe0d80878872]
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Dataseries X:
-0.385868851153837
4.81234262686034
-5.86804122114596
16.0725680225492
-8.57525163788969
5.08247518971098
0.092732021505415
3.83298655010795
5.81986266263392
37.1247698411582
-0.456916305824569
-3.62813490741323
-3.87648507892191
4.61958462101272
-12.967748044016
3.19886759717217
-5.74783565702396
-0.568909646003526
-7.15658094463292
-18.0497313555278
15.6314099338156
-18.6819481453537
-0.704909311621681
2.59171945848611
2.56763423323193
0.363060127151921
32.5587282582796
8.52568321864334
1.42269516052334
3.53469472344553
0.904411865388995
-1.1005444418027
13.3248076718110
-33.5907843348750
-0.845486516554237
42.0892768528428
-6.25360506437205
-11.0785340316643
-29.2902232669615
-11.1727173982373
13.9239510644368
13.5369579913798
-16.4941540115674
-9.38355957013267
-2.83541693438183
-2.88173330956316
6.18397479401454
3.71189006095175
3.17508248559435
-4.18249526402528
13.6042900329871
4.81933405297545
10.0482983006261
9.69015652302726
-13.6259654676286
2.81390485024080
2.39082408194279
9.1175078099302
14.2141474796521
3.49385172983141
5.51425675339953
-6.1504957612917
2.72297593670155
-11.1163190852539
-4.69675096946234
1.81576665288666
-10.4353591925503
6.036622781552




Summary of compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001

\begin{tabular}{lllllllll}
\hline
Summary of compuational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 3 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=4415&T=0

[TABLE]
[ROW][C]Summary of compuational 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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ 193.190.124.10:1001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=4415&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=4415&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 compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean1.017376445464831.51757459071150.670396336161532
Geometric MeanNaN
Harmonic Mean7.96341855770884
Quadratic Mean12.4634763048994
Winsorized Mean ( 1 / 22 )1.007612534527021.468896045563030.685965856855988
Winsorized Mean ( 2 / 22 )1.185325285666111.337447652298830.886259199475025
Winsorized Mean ( 3 / 22 )0.4858866042291471.123830738025660.432348562633862
Winsorized Mean ( 4 / 22 )0.5514406780660181.096596112960170.502865796758527
Winsorized Mean ( 5 / 22 )0.658126419961261.02925535203560.639419963821084
Winsorized Mean ( 6 / 22 )0.6905988618786691.012376858848190.682155914413516
Winsorized Mean ( 7 / 22 )0.8424751457066540.9702233606839640.868331128527711
Winsorized Mean ( 8 / 22 )0.8411888246920780.9674448148364060.869495408721915
Winsorized Mean ( 9 / 22 )0.8181110689007130.961044734611450.851272619719909
Winsorized Mean ( 10 / 22 )0.4308559906549930.8557824968578480.503464364177761
Winsorized Mean ( 11 / 22 )0.5430653479050910.8144540422198730.666784520370129
Winsorized Mean ( 12 / 22 )0.5846522689308420.7720322152962870.757289990426716
Winsorized Mean ( 13 / 22 )0.7427257884250890.7067003738462621.05097692871274
Winsorized Mean ( 14 / 22 )0.4465161469375740.6013536378103120.742518409905123
Winsorized Mean ( 15 / 22 )0.4367567257503260.5929716230060380.736555863392267
Winsorized Mean ( 16 / 22 )0.4522142366274230.5748591940314020.786652177302952
Winsorized Mean ( 17 / 22 )0.4058641503493250.5593944288399110.725541995816831
Winsorized Mean ( 18 / 22 )0.5697973301980790.499084309221441.14168552220556
Winsorized Mean ( 19 / 22 )0.639961694982330.4668078998609991.37093158700376
Winsorized Mean ( 20 / 22 )0.7279083888024060.4527611239960561.60770956299850
Winsorized Mean ( 21 / 22 )0.7450765576094990.4331794160311541.72001838045765
Winsorized Mean ( 22 / 22 )0.7320718163270960.3638166025777522.01220013363915
Trimmed Mean ( 1 / 22 )0.919440996570311.331644432293920.690455330471706
Trimmed Mean ( 2 / 22 )0.8257587374913081.155489243128280.714639917595178
Trimmed Mean ( 3 / 22 )0.628577082040611.027568682509650.611712961614812
Trimmed Mean ( 4 / 22 )0.6824823736582730.980866898283550.695795091925898
Trimmed Mean ( 5 / 22 )0.720891146504280.9345231663460160.771399974302362
Trimmed Mean ( 6 / 22 )0.7361340086647270.9008162673995760.817185518629405
Trimmed Mean ( 7 / 22 )0.7456907678667390.8642296822312290.862838644862959
Trimmed Mean ( 8 / 22 )0.7276101698087330.8307346911990860.87586347063284
Trimmed Mean ( 9 / 22 )0.7083017984785640.7891669295903210.897531019002866
Trimmed Mean ( 10 / 22 )0.6910170059121150.7376951072447520.936724398909223
Trimmed Mean ( 11 / 22 )0.7294755907762110.7006824924514171.04109293244085
Trimmed Mean ( 12 / 22 )0.7556654596093430.6638034126175551.13838742803318
Trimmed Mean ( 13 / 22 )0.778738667875490.6268631154193051.24227865497334
Trimmed Mean ( 14 / 22 )0.7834480444190050.5957581083894741.31504386325000
Trimmed Mean ( 15 / 22 )0.8265145275557290.5811959538656861.42209270738787
Trimmed Mean ( 16 / 22 )0.8755951396349280.5627457789001531.55593373147324
Trimmed Mean ( 17 / 22 )0.9285177525108660.5415060390094141.71469510147923
Trimmed Mean ( 18 / 22 )0.9938494527810580.5151567862177081.92921743315840
Trimmed Mean ( 19 / 22 )1.047248608958170.4960511706459652.11117052217502
Trimmed Mean ( 20 / 22 )1.099307838564110.4775701151374282.30187736568852
Trimmed Mean ( 21 / 22 )1.147875458917560.4537313315325542.52985716247635
Trimmed Mean ( 22 / 22 )1.202221342427380.4232443615761562.84048991922852
Median1.619230906705
Midrange4.2492462589839
Midmean - Weighted Average at Xnp0.734330353263527
Midmean - Weighted Average at X(n+1)p0.928517752510866
Midmean - Empirical Distribution Function0.734330353263527
Midmean - Empirical Distribution Function - Averaging0.928517752510866
Midmean - Empirical Distribution Function - Interpolation0.928517752510866
Midmean - Closest Observation0.734330353263527
Midmean - True Basic - Statistics Graphics Toolkit0.928517752510866
Midmean - MS Excel (old versions)0.875595139634927
Number of observations68

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 1.01737644546483 & 1.5175745907115 & 0.670396336161532 \tabularnewline
Geometric Mean & NaN &  &  \tabularnewline
Harmonic Mean & 7.96341855770884 &  &  \tabularnewline
Quadratic Mean & 12.4634763048994 &  &  \tabularnewline
Winsorized Mean ( 1 / 22 ) & 1.00761253452702 & 1.46889604556303 & 0.685965856855988 \tabularnewline
Winsorized Mean ( 2 / 22 ) & 1.18532528566611 & 1.33744765229883 & 0.886259199475025 \tabularnewline
Winsorized Mean ( 3 / 22 ) & 0.485886604229147 & 1.12383073802566 & 0.432348562633862 \tabularnewline
Winsorized Mean ( 4 / 22 ) & 0.551440678066018 & 1.09659611296017 & 0.502865796758527 \tabularnewline
Winsorized Mean ( 5 / 22 ) & 0.65812641996126 & 1.0292553520356 & 0.639419963821084 \tabularnewline
Winsorized Mean ( 6 / 22 ) & 0.690598861878669 & 1.01237685884819 & 0.682155914413516 \tabularnewline
Winsorized Mean ( 7 / 22 ) & 0.842475145706654 & 0.970223360683964 & 0.868331128527711 \tabularnewline
Winsorized Mean ( 8 / 22 ) & 0.841188824692078 & 0.967444814836406 & 0.869495408721915 \tabularnewline
Winsorized Mean ( 9 / 22 ) & 0.818111068900713 & 0.96104473461145 & 0.851272619719909 \tabularnewline
Winsorized Mean ( 10 / 22 ) & 0.430855990654993 & 0.855782496857848 & 0.503464364177761 \tabularnewline
Winsorized Mean ( 11 / 22 ) & 0.543065347905091 & 0.814454042219873 & 0.666784520370129 \tabularnewline
Winsorized Mean ( 12 / 22 ) & 0.584652268930842 & 0.772032215296287 & 0.757289990426716 \tabularnewline
Winsorized Mean ( 13 / 22 ) & 0.742725788425089 & 0.706700373846262 & 1.05097692871274 \tabularnewline
Winsorized Mean ( 14 / 22 ) & 0.446516146937574 & 0.601353637810312 & 0.742518409905123 \tabularnewline
Winsorized Mean ( 15 / 22 ) & 0.436756725750326 & 0.592971623006038 & 0.736555863392267 \tabularnewline
Winsorized Mean ( 16 / 22 ) & 0.452214236627423 & 0.574859194031402 & 0.786652177302952 \tabularnewline
Winsorized Mean ( 17 / 22 ) & 0.405864150349325 & 0.559394428839911 & 0.725541995816831 \tabularnewline
Winsorized Mean ( 18 / 22 ) & 0.569797330198079 & 0.49908430922144 & 1.14168552220556 \tabularnewline
Winsorized Mean ( 19 / 22 ) & 0.63996169498233 & 0.466807899860999 & 1.37093158700376 \tabularnewline
Winsorized Mean ( 20 / 22 ) & 0.727908388802406 & 0.452761123996056 & 1.60770956299850 \tabularnewline
Winsorized Mean ( 21 / 22 ) & 0.745076557609499 & 0.433179416031154 & 1.72001838045765 \tabularnewline
Winsorized Mean ( 22 / 22 ) & 0.732071816327096 & 0.363816602577752 & 2.01220013363915 \tabularnewline
Trimmed Mean ( 1 / 22 ) & 0.91944099657031 & 1.33164443229392 & 0.690455330471706 \tabularnewline
Trimmed Mean ( 2 / 22 ) & 0.825758737491308 & 1.15548924312828 & 0.714639917595178 \tabularnewline
Trimmed Mean ( 3 / 22 ) & 0.62857708204061 & 1.02756868250965 & 0.611712961614812 \tabularnewline
Trimmed Mean ( 4 / 22 ) & 0.682482373658273 & 0.98086689828355 & 0.695795091925898 \tabularnewline
Trimmed Mean ( 5 / 22 ) & 0.72089114650428 & 0.934523166346016 & 0.771399974302362 \tabularnewline
Trimmed Mean ( 6 / 22 ) & 0.736134008664727 & 0.900816267399576 & 0.817185518629405 \tabularnewline
Trimmed Mean ( 7 / 22 ) & 0.745690767866739 & 0.864229682231229 & 0.862838644862959 \tabularnewline
Trimmed Mean ( 8 / 22 ) & 0.727610169808733 & 0.830734691199086 & 0.87586347063284 \tabularnewline
Trimmed Mean ( 9 / 22 ) & 0.708301798478564 & 0.789166929590321 & 0.897531019002866 \tabularnewline
Trimmed Mean ( 10 / 22 ) & 0.691017005912115 & 0.737695107244752 & 0.936724398909223 \tabularnewline
Trimmed Mean ( 11 / 22 ) & 0.729475590776211 & 0.700682492451417 & 1.04109293244085 \tabularnewline
Trimmed Mean ( 12 / 22 ) & 0.755665459609343 & 0.663803412617555 & 1.13838742803318 \tabularnewline
Trimmed Mean ( 13 / 22 ) & 0.77873866787549 & 0.626863115419305 & 1.24227865497334 \tabularnewline
Trimmed Mean ( 14 / 22 ) & 0.783448044419005 & 0.595758108389474 & 1.31504386325000 \tabularnewline
Trimmed Mean ( 15 / 22 ) & 0.826514527555729 & 0.581195953865686 & 1.42209270738787 \tabularnewline
Trimmed Mean ( 16 / 22 ) & 0.875595139634928 & 0.562745778900153 & 1.55593373147324 \tabularnewline
Trimmed Mean ( 17 / 22 ) & 0.928517752510866 & 0.541506039009414 & 1.71469510147923 \tabularnewline
Trimmed Mean ( 18 / 22 ) & 0.993849452781058 & 0.515156786217708 & 1.92921743315840 \tabularnewline
Trimmed Mean ( 19 / 22 ) & 1.04724860895817 & 0.496051170645965 & 2.11117052217502 \tabularnewline
Trimmed Mean ( 20 / 22 ) & 1.09930783856411 & 0.477570115137428 & 2.30187736568852 \tabularnewline
Trimmed Mean ( 21 / 22 ) & 1.14787545891756 & 0.453731331532554 & 2.52985716247635 \tabularnewline
Trimmed Mean ( 22 / 22 ) & 1.20222134242738 & 0.423244361576156 & 2.84048991922852 \tabularnewline
Median & 1.619230906705 &  &  \tabularnewline
Midrange & 4.2492462589839 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 0.734330353263527 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 0.928517752510866 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 0.734330353263527 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 0.928517752510866 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 0.928517752510866 &  &  \tabularnewline
Midmean - Closest Observation & 0.734330353263527 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 0.928517752510866 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 0.875595139634927 &  &  \tabularnewline
Number of observations & 68 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=4415&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]1.01737644546483[/C][C]1.5175745907115[/C][C]0.670396336161532[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]NaN[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]7.96341855770884[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]12.4634763048994[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 22 )[/C][C]1.00761253452702[/C][C]1.46889604556303[/C][C]0.685965856855988[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 22 )[/C][C]1.18532528566611[/C][C]1.33744765229883[/C][C]0.886259199475025[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 22 )[/C][C]0.485886604229147[/C][C]1.12383073802566[/C][C]0.432348562633862[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 22 )[/C][C]0.551440678066018[/C][C]1.09659611296017[/C][C]0.502865796758527[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 22 )[/C][C]0.65812641996126[/C][C]1.0292553520356[/C][C]0.639419963821084[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 22 )[/C][C]0.690598861878669[/C][C]1.01237685884819[/C][C]0.682155914413516[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 22 )[/C][C]0.842475145706654[/C][C]0.970223360683964[/C][C]0.868331128527711[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 22 )[/C][C]0.841188824692078[/C][C]0.967444814836406[/C][C]0.869495408721915[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 22 )[/C][C]0.818111068900713[/C][C]0.96104473461145[/C][C]0.851272619719909[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 22 )[/C][C]0.430855990654993[/C][C]0.855782496857848[/C][C]0.503464364177761[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 22 )[/C][C]0.543065347905091[/C][C]0.814454042219873[/C][C]0.666784520370129[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 22 )[/C][C]0.584652268930842[/C][C]0.772032215296287[/C][C]0.757289990426716[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 22 )[/C][C]0.742725788425089[/C][C]0.706700373846262[/C][C]1.05097692871274[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 22 )[/C][C]0.446516146937574[/C][C]0.601353637810312[/C][C]0.742518409905123[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 22 )[/C][C]0.436756725750326[/C][C]0.592971623006038[/C][C]0.736555863392267[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 22 )[/C][C]0.452214236627423[/C][C]0.574859194031402[/C][C]0.786652177302952[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 22 )[/C][C]0.405864150349325[/C][C]0.559394428839911[/C][C]0.725541995816831[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 22 )[/C][C]0.569797330198079[/C][C]0.49908430922144[/C][C]1.14168552220556[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 22 )[/C][C]0.63996169498233[/C][C]0.466807899860999[/C][C]1.37093158700376[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 22 )[/C][C]0.727908388802406[/C][C]0.452761123996056[/C][C]1.60770956299850[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 22 )[/C][C]0.745076557609499[/C][C]0.433179416031154[/C][C]1.72001838045765[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 22 )[/C][C]0.732071816327096[/C][C]0.363816602577752[/C][C]2.01220013363915[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 22 )[/C][C]0.91944099657031[/C][C]1.33164443229392[/C][C]0.690455330471706[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 22 )[/C][C]0.825758737491308[/C][C]1.15548924312828[/C][C]0.714639917595178[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 22 )[/C][C]0.62857708204061[/C][C]1.02756868250965[/C][C]0.611712961614812[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 22 )[/C][C]0.682482373658273[/C][C]0.98086689828355[/C][C]0.695795091925898[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 22 )[/C][C]0.72089114650428[/C][C]0.934523166346016[/C][C]0.771399974302362[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 22 )[/C][C]0.736134008664727[/C][C]0.900816267399576[/C][C]0.817185518629405[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 22 )[/C][C]0.745690767866739[/C][C]0.864229682231229[/C][C]0.862838644862959[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 22 )[/C][C]0.727610169808733[/C][C]0.830734691199086[/C][C]0.87586347063284[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 22 )[/C][C]0.708301798478564[/C][C]0.789166929590321[/C][C]0.897531019002866[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 22 )[/C][C]0.691017005912115[/C][C]0.737695107244752[/C][C]0.936724398909223[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 22 )[/C][C]0.729475590776211[/C][C]0.700682492451417[/C][C]1.04109293244085[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 22 )[/C][C]0.755665459609343[/C][C]0.663803412617555[/C][C]1.13838742803318[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 22 )[/C][C]0.77873866787549[/C][C]0.626863115419305[/C][C]1.24227865497334[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 22 )[/C][C]0.783448044419005[/C][C]0.595758108389474[/C][C]1.31504386325000[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 22 )[/C][C]0.826514527555729[/C][C]0.581195953865686[/C][C]1.42209270738787[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 22 )[/C][C]0.875595139634928[/C][C]0.562745778900153[/C][C]1.55593373147324[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 22 )[/C][C]0.928517752510866[/C][C]0.541506039009414[/C][C]1.71469510147923[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 22 )[/C][C]0.993849452781058[/C][C]0.515156786217708[/C][C]1.92921743315840[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 22 )[/C][C]1.04724860895817[/C][C]0.496051170645965[/C][C]2.11117052217502[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 22 )[/C][C]1.09930783856411[/C][C]0.477570115137428[/C][C]2.30187736568852[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 22 )[/C][C]1.14787545891756[/C][C]0.453731331532554[/C][C]2.52985716247635[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 22 )[/C][C]1.20222134242738[/C][C]0.423244361576156[/C][C]2.84048991922852[/C][/ROW]
[ROW][C]Median[/C][C]1.619230906705[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]4.2492462589839[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]0.734330353263527[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]0.928517752510866[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]0.734330353263527[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]0.928517752510866[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]0.928517752510866[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]0.734330353263527[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]0.928517752510866[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]0.875595139634927[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]68[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=4415&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=4415&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 Mean1.017376445464831.51757459071150.670396336161532
Geometric MeanNaN
Harmonic Mean7.96341855770884
Quadratic Mean12.4634763048994
Winsorized Mean ( 1 / 22 )1.007612534527021.468896045563030.685965856855988
Winsorized Mean ( 2 / 22 )1.185325285666111.337447652298830.886259199475025
Winsorized Mean ( 3 / 22 )0.4858866042291471.123830738025660.432348562633862
Winsorized Mean ( 4 / 22 )0.5514406780660181.096596112960170.502865796758527
Winsorized Mean ( 5 / 22 )0.658126419961261.02925535203560.639419963821084
Winsorized Mean ( 6 / 22 )0.6905988618786691.012376858848190.682155914413516
Winsorized Mean ( 7 / 22 )0.8424751457066540.9702233606839640.868331128527711
Winsorized Mean ( 8 / 22 )0.8411888246920780.9674448148364060.869495408721915
Winsorized Mean ( 9 / 22 )0.8181110689007130.961044734611450.851272619719909
Winsorized Mean ( 10 / 22 )0.4308559906549930.8557824968578480.503464364177761
Winsorized Mean ( 11 / 22 )0.5430653479050910.8144540422198730.666784520370129
Winsorized Mean ( 12 / 22 )0.5846522689308420.7720322152962870.757289990426716
Winsorized Mean ( 13 / 22 )0.7427257884250890.7067003738462621.05097692871274
Winsorized Mean ( 14 / 22 )0.4465161469375740.6013536378103120.742518409905123
Winsorized Mean ( 15 / 22 )0.4367567257503260.5929716230060380.736555863392267
Winsorized Mean ( 16 / 22 )0.4522142366274230.5748591940314020.786652177302952
Winsorized Mean ( 17 / 22 )0.4058641503493250.5593944288399110.725541995816831
Winsorized Mean ( 18 / 22 )0.5697973301980790.499084309221441.14168552220556
Winsorized Mean ( 19 / 22 )0.639961694982330.4668078998609991.37093158700376
Winsorized Mean ( 20 / 22 )0.7279083888024060.4527611239960561.60770956299850
Winsorized Mean ( 21 / 22 )0.7450765576094990.4331794160311541.72001838045765
Winsorized Mean ( 22 / 22 )0.7320718163270960.3638166025777522.01220013363915
Trimmed Mean ( 1 / 22 )0.919440996570311.331644432293920.690455330471706
Trimmed Mean ( 2 / 22 )0.8257587374913081.155489243128280.714639917595178
Trimmed Mean ( 3 / 22 )0.628577082040611.027568682509650.611712961614812
Trimmed Mean ( 4 / 22 )0.6824823736582730.980866898283550.695795091925898
Trimmed Mean ( 5 / 22 )0.720891146504280.9345231663460160.771399974302362
Trimmed Mean ( 6 / 22 )0.7361340086647270.9008162673995760.817185518629405
Trimmed Mean ( 7 / 22 )0.7456907678667390.8642296822312290.862838644862959
Trimmed Mean ( 8 / 22 )0.7276101698087330.8307346911990860.87586347063284
Trimmed Mean ( 9 / 22 )0.7083017984785640.7891669295903210.897531019002866
Trimmed Mean ( 10 / 22 )0.6910170059121150.7376951072447520.936724398909223
Trimmed Mean ( 11 / 22 )0.7294755907762110.7006824924514171.04109293244085
Trimmed Mean ( 12 / 22 )0.7556654596093430.6638034126175551.13838742803318
Trimmed Mean ( 13 / 22 )0.778738667875490.6268631154193051.24227865497334
Trimmed Mean ( 14 / 22 )0.7834480444190050.5957581083894741.31504386325000
Trimmed Mean ( 15 / 22 )0.8265145275557290.5811959538656861.42209270738787
Trimmed Mean ( 16 / 22 )0.8755951396349280.5627457789001531.55593373147324
Trimmed Mean ( 17 / 22 )0.9285177525108660.5415060390094141.71469510147923
Trimmed Mean ( 18 / 22 )0.9938494527810580.5151567862177081.92921743315840
Trimmed Mean ( 19 / 22 )1.047248608958170.4960511706459652.11117052217502
Trimmed Mean ( 20 / 22 )1.099307838564110.4775701151374282.30187736568852
Trimmed Mean ( 21 / 22 )1.147875458917560.4537313315325542.52985716247635
Trimmed Mean ( 22 / 22 )1.202221342427380.4232443615761562.84048991922852
Median1.619230906705
Midrange4.2492462589839
Midmean - Weighted Average at Xnp0.734330353263527
Midmean - Weighted Average at X(n+1)p0.928517752510866
Midmean - Empirical Distribution Function0.734330353263527
Midmean - Empirical Distribution Function - Averaging0.928517752510866
Midmean - Empirical Distribution Function - Interpolation0.928517752510866
Midmean - Closest Observation0.734330353263527
Midmean - True Basic - Statistics Graphics Toolkit0.928517752510866
Midmean - MS Excel (old versions)0.875595139634927
Number of observations68



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')