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of Irreproducible Research!

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationWed, 28 Oct 2009 14:18:18 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Oct/28/t1256761183aabitoz4qz7b4ju.htm/, Retrieved Mon, 06 May 2024 02:42:53 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=51805, Retrieved Mon, 06 May 2024 02:42:53 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact80
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [controle derde as...] [2009-10-28 20:18:18] [99bf2a1e962091d45abf4c2600a412f9] [Current]
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Dataseries X:
-18860
-12410
-9669
-25109
-21596
-24788
-22339
-17975
-21825
-13041
-12975
-14092
-15622
-13517
-5490
-27201
-25015
-28774
-21434
-21696
-17589
-13253
-11959
-12627
-16376
-12651
-4356
-25825
-22405
-26026
-21123
-20881
-20662
-16213
-14567
-15321
-20476
-15236
-8929
-26040
-25864
-26189
-27540
-21000
-22426
-15636
-13683
-15726
-18604
-11779
-7104
-21425
-19990
-22998
-23032
-16931
-18856
-14850
-13108
-15849




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\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' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=51805&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' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=51805&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=51805&T=0

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean-18142.2166666667745.324943768288-24.3413518068260
Geometric MeanNaN
Harmonic Mean-15635.9154346946
Quadratic Mean19024.0656174401
Winsorized Mean ( 1 / 20 )-18140.55734.886321746316-24.6848382711662
Winsorized Mean ( 2 / 20 )-18183.05717.559982108624-25.3401115633110
Winsorized Mean ( 3 / 20 )-18223.7684.701966712773-26.6155216224824
Winsorized Mean ( 4 / 20 )-18263.1671.720577962859-27.1885373161961
Winsorized Mean ( 5 / 20 )-18437.7666666667636.747763950861-28.9561545568137
Winsorized Mean ( 6 / 20 )-18439.5666666667630.330851769951-29.2537904735091
Winsorized Mean ( 7 / 20 )-18487.6333333333620.466816681309-29.7963288870437
Winsorized Mean ( 8 / 20 )-18421.1597.04542157505-30.8537664544915
Winsorized Mean ( 9 / 20 )-18410.6593.785844805621-31.0054545103324
Winsorized Mean ( 10 / 20 )-18426.7666666667577.932745078763-31.8839290965515
Winsorized Mean ( 11 / 20 )-18116.9333333333519.921232553801-34.8455346675203
Winsorized Mean ( 12 / 20 )-18123.5333333333516.621566174443-35.0808687053798
Winsorized Mean ( 13 / 20 )-18031.0166666667492.150214478376-36.6372220029967
Winsorized Mean ( 14 / 20 )-18087.7166666667481.380889804257-37.574646293129
Winsorized Mean ( 15 / 20 )-18112.7166666667472.236641155183-38.3551700316168
Winsorized Mean ( 16 / 20 )-18084.7166666667434.661017405275-41.6064840013122
Winsorized Mean ( 17 / 20 )-18182.75408.755704965457-44.4831711927704
Winsorized Mean ( 18 / 20 )-18237.65391.802780165223-46.5480362143148
Winsorized Mean ( 19 / 20 )-18308.5833333333366.72583879889-49.9244432661142
Winsorized Mean ( 20 / 20 )-18333.9166666667362.283497234104-50.6065465488743
Trimmed Mean ( 1 / 20 )-18196.6034482759709.292882516055-25.6545693560713
Trimmed Mean ( 2 / 20 )-18256.6607142857677.629045685288-26.9419689585807
Trimmed Mean ( 3 / 20 )-18297.5555555556650.163798458866-28.1429935024492
Trimmed Mean ( 4 / 20 )-18325.9615384615632.132847886206-28.9906806769208
Trimmed Mean ( 5 / 20 )-18344.82614.535053509429-29.8515436918336
Trimmed Mean ( 6 / 20 )-18321.5833333333604.032778390359-30.3321011521215
Trimmed Mean ( 7 / 20 )-18295.9347826087592.103207319503-30.8999082532179
Trimmed Mean ( 8 / 20 )-18258.5909090909579.020569216021-31.5335790813314
Trimmed Mean ( 9 / 20 )-18229.5714285714568.04305154816-32.0918834917319
Trimmed Mean ( 10 / 20 )-18199.4553.800294700406-32.8627488539808
Trimmed Mean ( 11 / 20 )-18163.5538.484026305386-33.7308055814066
Trimmed Mean ( 12 / 20 )-18170.5555555556532.847073633768-34.1008827009987
Trimmed Mean ( 13 / 20 )-18177.4705882353524.626554617466-34.6483997583566
Trimmed Mean ( 14 / 20 )-18198.59375518.310647330186-35.1113638968075
Trimmed Mean ( 15 / 20 )-18214.4333333333510.665623066969-35.6680232829079
Trimmed Mean ( 16 / 20 )-18228.9642857143500.431307313004-36.4265065341179
Trimmed Mean ( 17 / 20 )-18249.7692307692495.004286874032-36.8679013792327
Trimmed Mean ( 18 / 20 )-18259.625492.38288835107-37.0841989678993
Trimmed Mean ( 19 / 20 )-18262.9545454545490.317939422774-37.2471677600754
Trimmed Mean ( 20 / 20 )-18255.75491.643794219694-37.132066375361
Median-18289.5
Midrange-16565
Midmean - Weighted Average at Xnp-18349.6129032258
Midmean - Weighted Average at X(n+1)p-18214.4333333333
Midmean - Empirical Distribution Function-18349.6129032258
Midmean - Empirical Distribution Function - Averaging-18214.4333333333
Midmean - Empirical Distribution Function - Interpolation-18214.4333333333
Midmean - Closest Observation-18349.6129032258
Midmean - True Basic - Statistics Graphics Toolkit-18214.4333333333
Midmean - MS Excel (old versions)-18198.59375
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & -18142.2166666667 & 745.324943768288 & -24.3413518068260 \tabularnewline
Geometric Mean & NaN &  &  \tabularnewline
Harmonic Mean & -15635.9154346946 &  &  \tabularnewline
Quadratic Mean & 19024.0656174401 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & -18140.55 & 734.886321746316 & -24.6848382711662 \tabularnewline
Winsorized Mean ( 2 / 20 ) & -18183.05 & 717.559982108624 & -25.3401115633110 \tabularnewline
Winsorized Mean ( 3 / 20 ) & -18223.7 & 684.701966712773 & -26.6155216224824 \tabularnewline
Winsorized Mean ( 4 / 20 ) & -18263.1 & 671.720577962859 & -27.1885373161961 \tabularnewline
Winsorized Mean ( 5 / 20 ) & -18437.7666666667 & 636.747763950861 & -28.9561545568137 \tabularnewline
Winsorized Mean ( 6 / 20 ) & -18439.5666666667 & 630.330851769951 & -29.2537904735091 \tabularnewline
Winsorized Mean ( 7 / 20 ) & -18487.6333333333 & 620.466816681309 & -29.7963288870437 \tabularnewline
Winsorized Mean ( 8 / 20 ) & -18421.1 & 597.04542157505 & -30.8537664544915 \tabularnewline
Winsorized Mean ( 9 / 20 ) & -18410.6 & 593.785844805621 & -31.0054545103324 \tabularnewline
Winsorized Mean ( 10 / 20 ) & -18426.7666666667 & 577.932745078763 & -31.8839290965515 \tabularnewline
Winsorized Mean ( 11 / 20 ) & -18116.9333333333 & 519.921232553801 & -34.8455346675203 \tabularnewline
Winsorized Mean ( 12 / 20 ) & -18123.5333333333 & 516.621566174443 & -35.0808687053798 \tabularnewline
Winsorized Mean ( 13 / 20 ) & -18031.0166666667 & 492.150214478376 & -36.6372220029967 \tabularnewline
Winsorized Mean ( 14 / 20 ) & -18087.7166666667 & 481.380889804257 & -37.574646293129 \tabularnewline
Winsorized Mean ( 15 / 20 ) & -18112.7166666667 & 472.236641155183 & -38.3551700316168 \tabularnewline
Winsorized Mean ( 16 / 20 ) & -18084.7166666667 & 434.661017405275 & -41.6064840013122 \tabularnewline
Winsorized Mean ( 17 / 20 ) & -18182.75 & 408.755704965457 & -44.4831711927704 \tabularnewline
Winsorized Mean ( 18 / 20 ) & -18237.65 & 391.802780165223 & -46.5480362143148 \tabularnewline
Winsorized Mean ( 19 / 20 ) & -18308.5833333333 & 366.72583879889 & -49.9244432661142 \tabularnewline
Winsorized Mean ( 20 / 20 ) & -18333.9166666667 & 362.283497234104 & -50.6065465488743 \tabularnewline
Trimmed Mean ( 1 / 20 ) & -18196.6034482759 & 709.292882516055 & -25.6545693560713 \tabularnewline
Trimmed Mean ( 2 / 20 ) & -18256.6607142857 & 677.629045685288 & -26.9419689585807 \tabularnewline
Trimmed Mean ( 3 / 20 ) & -18297.5555555556 & 650.163798458866 & -28.1429935024492 \tabularnewline
Trimmed Mean ( 4 / 20 ) & -18325.9615384615 & 632.132847886206 & -28.9906806769208 \tabularnewline
Trimmed Mean ( 5 / 20 ) & -18344.82 & 614.535053509429 & -29.8515436918336 \tabularnewline
Trimmed Mean ( 6 / 20 ) & -18321.5833333333 & 604.032778390359 & -30.3321011521215 \tabularnewline
Trimmed Mean ( 7 / 20 ) & -18295.9347826087 & 592.103207319503 & -30.8999082532179 \tabularnewline
Trimmed Mean ( 8 / 20 ) & -18258.5909090909 & 579.020569216021 & -31.5335790813314 \tabularnewline
Trimmed Mean ( 9 / 20 ) & -18229.5714285714 & 568.04305154816 & -32.0918834917319 \tabularnewline
Trimmed Mean ( 10 / 20 ) & -18199.4 & 553.800294700406 & -32.8627488539808 \tabularnewline
Trimmed Mean ( 11 / 20 ) & -18163.5 & 538.484026305386 & -33.7308055814066 \tabularnewline
Trimmed Mean ( 12 / 20 ) & -18170.5555555556 & 532.847073633768 & -34.1008827009987 \tabularnewline
Trimmed Mean ( 13 / 20 ) & -18177.4705882353 & 524.626554617466 & -34.6483997583566 \tabularnewline
Trimmed Mean ( 14 / 20 ) & -18198.59375 & 518.310647330186 & -35.1113638968075 \tabularnewline
Trimmed Mean ( 15 / 20 ) & -18214.4333333333 & 510.665623066969 & -35.6680232829079 \tabularnewline
Trimmed Mean ( 16 / 20 ) & -18228.9642857143 & 500.431307313004 & -36.4265065341179 \tabularnewline
Trimmed Mean ( 17 / 20 ) & -18249.7692307692 & 495.004286874032 & -36.8679013792327 \tabularnewline
Trimmed Mean ( 18 / 20 ) & -18259.625 & 492.38288835107 & -37.0841989678993 \tabularnewline
Trimmed Mean ( 19 / 20 ) & -18262.9545454545 & 490.317939422774 & -37.2471677600754 \tabularnewline
Trimmed Mean ( 20 / 20 ) & -18255.75 & 491.643794219694 & -37.132066375361 \tabularnewline
Median & -18289.5 &  &  \tabularnewline
Midrange & -16565 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & -18349.6129032258 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & -18214.4333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function & -18349.6129032258 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & -18214.4333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & -18214.4333333333 &  &  \tabularnewline
Midmean - Closest Observation & -18349.6129032258 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & -18214.4333333333 &  &  \tabularnewline
Midmean - MS Excel (old versions) & -18198.59375 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=51805&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]-18142.2166666667[/C][C]745.324943768288[/C][C]-24.3413518068260[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]NaN[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]-15635.9154346946[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]19024.0656174401[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]-18140.55[/C][C]734.886321746316[/C][C]-24.6848382711662[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]-18183.05[/C][C]717.559982108624[/C][C]-25.3401115633110[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]-18223.7[/C][C]684.701966712773[/C][C]-26.6155216224824[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]-18263.1[/C][C]671.720577962859[/C][C]-27.1885373161961[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]-18437.7666666667[/C][C]636.747763950861[/C][C]-28.9561545568137[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]-18439.5666666667[/C][C]630.330851769951[/C][C]-29.2537904735091[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]-18487.6333333333[/C][C]620.466816681309[/C][C]-29.7963288870437[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]-18421.1[/C][C]597.04542157505[/C][C]-30.8537664544915[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]-18410.6[/C][C]593.785844805621[/C][C]-31.0054545103324[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]-18426.7666666667[/C][C]577.932745078763[/C][C]-31.8839290965515[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]-18116.9333333333[/C][C]519.921232553801[/C][C]-34.8455346675203[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]-18123.5333333333[/C][C]516.621566174443[/C][C]-35.0808687053798[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]-18031.0166666667[/C][C]492.150214478376[/C][C]-36.6372220029967[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]-18087.7166666667[/C][C]481.380889804257[/C][C]-37.574646293129[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]-18112.7166666667[/C][C]472.236641155183[/C][C]-38.3551700316168[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]-18084.7166666667[/C][C]434.661017405275[/C][C]-41.6064840013122[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]-18182.75[/C][C]408.755704965457[/C][C]-44.4831711927704[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]-18237.65[/C][C]391.802780165223[/C][C]-46.5480362143148[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]-18308.5833333333[/C][C]366.72583879889[/C][C]-49.9244432661142[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]-18333.9166666667[/C][C]362.283497234104[/C][C]-50.6065465488743[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]-18196.6034482759[/C][C]709.292882516055[/C][C]-25.6545693560713[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]-18256.6607142857[/C][C]677.629045685288[/C][C]-26.9419689585807[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]-18297.5555555556[/C][C]650.163798458866[/C][C]-28.1429935024492[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]-18325.9615384615[/C][C]632.132847886206[/C][C]-28.9906806769208[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]-18344.82[/C][C]614.535053509429[/C][C]-29.8515436918336[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]-18321.5833333333[/C][C]604.032778390359[/C][C]-30.3321011521215[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]-18295.9347826087[/C][C]592.103207319503[/C][C]-30.8999082532179[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]-18258.5909090909[/C][C]579.020569216021[/C][C]-31.5335790813314[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]-18229.5714285714[/C][C]568.04305154816[/C][C]-32.0918834917319[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]-18199.4[/C][C]553.800294700406[/C][C]-32.8627488539808[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]-18163.5[/C][C]538.484026305386[/C][C]-33.7308055814066[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]-18170.5555555556[/C][C]532.847073633768[/C][C]-34.1008827009987[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]-18177.4705882353[/C][C]524.626554617466[/C][C]-34.6483997583566[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]-18198.59375[/C][C]518.310647330186[/C][C]-35.1113638968075[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]-18214.4333333333[/C][C]510.665623066969[/C][C]-35.6680232829079[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]-18228.9642857143[/C][C]500.431307313004[/C][C]-36.4265065341179[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]-18249.7692307692[/C][C]495.004286874032[/C][C]-36.8679013792327[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]-18259.625[/C][C]492.38288835107[/C][C]-37.0841989678993[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]-18262.9545454545[/C][C]490.317939422774[/C][C]-37.2471677600754[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]-18255.75[/C][C]491.643794219694[/C][C]-37.132066375361[/C][/ROW]
[ROW][C]Median[/C][C]-18289.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]-16565[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]-18349.6129032258[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]-18214.4333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]-18349.6129032258[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]-18214.4333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]-18214.4333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]-18349.6129032258[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]-18214.4333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]-18198.59375[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]60[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=51805&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=51805&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 Mean-18142.2166666667745.324943768288-24.3413518068260
Geometric MeanNaN
Harmonic Mean-15635.9154346946
Quadratic Mean19024.0656174401
Winsorized Mean ( 1 / 20 )-18140.55734.886321746316-24.6848382711662
Winsorized Mean ( 2 / 20 )-18183.05717.559982108624-25.3401115633110
Winsorized Mean ( 3 / 20 )-18223.7684.701966712773-26.6155216224824
Winsorized Mean ( 4 / 20 )-18263.1671.720577962859-27.1885373161961
Winsorized Mean ( 5 / 20 )-18437.7666666667636.747763950861-28.9561545568137
Winsorized Mean ( 6 / 20 )-18439.5666666667630.330851769951-29.2537904735091
Winsorized Mean ( 7 / 20 )-18487.6333333333620.466816681309-29.7963288870437
Winsorized Mean ( 8 / 20 )-18421.1597.04542157505-30.8537664544915
Winsorized Mean ( 9 / 20 )-18410.6593.785844805621-31.0054545103324
Winsorized Mean ( 10 / 20 )-18426.7666666667577.932745078763-31.8839290965515
Winsorized Mean ( 11 / 20 )-18116.9333333333519.921232553801-34.8455346675203
Winsorized Mean ( 12 / 20 )-18123.5333333333516.621566174443-35.0808687053798
Winsorized Mean ( 13 / 20 )-18031.0166666667492.150214478376-36.6372220029967
Winsorized Mean ( 14 / 20 )-18087.7166666667481.380889804257-37.574646293129
Winsorized Mean ( 15 / 20 )-18112.7166666667472.236641155183-38.3551700316168
Winsorized Mean ( 16 / 20 )-18084.7166666667434.661017405275-41.6064840013122
Winsorized Mean ( 17 / 20 )-18182.75408.755704965457-44.4831711927704
Winsorized Mean ( 18 / 20 )-18237.65391.802780165223-46.5480362143148
Winsorized Mean ( 19 / 20 )-18308.5833333333366.72583879889-49.9244432661142
Winsorized Mean ( 20 / 20 )-18333.9166666667362.283497234104-50.6065465488743
Trimmed Mean ( 1 / 20 )-18196.6034482759709.292882516055-25.6545693560713
Trimmed Mean ( 2 / 20 )-18256.6607142857677.629045685288-26.9419689585807
Trimmed Mean ( 3 / 20 )-18297.5555555556650.163798458866-28.1429935024492
Trimmed Mean ( 4 / 20 )-18325.9615384615632.132847886206-28.9906806769208
Trimmed Mean ( 5 / 20 )-18344.82614.535053509429-29.8515436918336
Trimmed Mean ( 6 / 20 )-18321.5833333333604.032778390359-30.3321011521215
Trimmed Mean ( 7 / 20 )-18295.9347826087592.103207319503-30.8999082532179
Trimmed Mean ( 8 / 20 )-18258.5909090909579.020569216021-31.5335790813314
Trimmed Mean ( 9 / 20 )-18229.5714285714568.04305154816-32.0918834917319
Trimmed Mean ( 10 / 20 )-18199.4553.800294700406-32.8627488539808
Trimmed Mean ( 11 / 20 )-18163.5538.484026305386-33.7308055814066
Trimmed Mean ( 12 / 20 )-18170.5555555556532.847073633768-34.1008827009987
Trimmed Mean ( 13 / 20 )-18177.4705882353524.626554617466-34.6483997583566
Trimmed Mean ( 14 / 20 )-18198.59375518.310647330186-35.1113638968075
Trimmed Mean ( 15 / 20 )-18214.4333333333510.665623066969-35.6680232829079
Trimmed Mean ( 16 / 20 )-18228.9642857143500.431307313004-36.4265065341179
Trimmed Mean ( 17 / 20 )-18249.7692307692495.004286874032-36.8679013792327
Trimmed Mean ( 18 / 20 )-18259.625492.38288835107-37.0841989678993
Trimmed Mean ( 19 / 20 )-18262.9545454545490.317939422774-37.2471677600754
Trimmed Mean ( 20 / 20 )-18255.75491.643794219694-37.132066375361
Median-18289.5
Midrange-16565
Midmean - Weighted Average at Xnp-18349.6129032258
Midmean - Weighted Average at X(n+1)p-18214.4333333333
Midmean - Empirical Distribution Function-18349.6129032258
Midmean - Empirical Distribution Function - Averaging-18214.4333333333
Midmean - Empirical Distribution Function - Interpolation-18214.4333333333
Midmean - Closest Observation-18349.6129032258
Midmean - True Basic - Statistics Graphics Toolkit-18214.4333333333
Midmean - MS Excel (old versions)-18198.59375
Number of observations60



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')