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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, 17 Dec 2014 13:12:04 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2014/Dec/17/t1418821943vv278mfp7q6lqun.htm/, Retrieved Thu, 16 May 2024 04:37:54 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=270175, Retrieved Thu, 16 May 2024 04:37:54 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact89
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [willy] [2014-12-17 13:12:04] [52f27f122f36bfdf20d2404cd2faf7fa] [Current]
- R P     [Central Tendency] [Thomas boxplot st...] [2015-08-30 16:38:15] [69bf0eb8b9b38defaaf4848d8c317571]
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Dataseries X:
777.515
-149.351
164.173
182.104
-209.795
324.778
-145.883
43.353
194.123
15.228
0.500914
116.554
0.833391
-273.682
-0.411285
-298.507
43.786
-18.121
0.366955
-196.689
-147.678
-228.037
-356.621
168.472
125.273
-176.493
-315.821
-0.569257
-391.229
16.923
-319.868
18.125
180.082
0.294529
-456.566
-120.608
-0.613072
138.735
0.245001
-0.244272
-308.962
-192.195
-1.275
-224.218
-119.745
381.848
402.446
0.873424
102.278
-318.671
313.649
185.516




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 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=270175&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=270175&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=270175&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' @ jenkins.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean-20.649570615384632.2022573809259-0.641246058346698
Geometric MeanNaN
Harmonic Mean12.9916114034293
Quadratic Mean230.895342457134
Winsorized Mean ( 1 / 17 )-26.605955230769229.0464956371707-0.915978146317989
Winsorized Mean ( 2 / 17 )-26.067109076923128.505327782397-0.91446445646629
Winsorized Mean ( 3 / 17 )-27.239243692307727.1584988778123-1.00297309563605
Winsorized Mean ( 4 / 17 )-28.003243692307726.9237283412945-1.04009531433867
Winsorized Mean ( 5 / 17 )-39.222089846153824.3364543974174-1.61165998981002
Winsorized Mean ( 6 / 17 )-39.423782153846123.9763193471789-1.64427999072697
Winsorized Mean ( 7 / 17 )-38.47568623.5846866430571-1.63138423597952
Winsorized Mean ( 8 / 17 )-34.967532153846222.7207127640261-1.53901563375294
Winsorized Mean ( 9 / 17 )-29.076859076923120.7888610782926-1.39867494267325
Winsorized Mean ( 10 / 17 )-29.169166769230820.4979592814693-1.42302784236675
Winsorized Mean ( 11 / 17 )-31.499262923076918.959686275498-1.66138101998998
Winsorized Mean ( 12 / 17 )-31.581416769230817.865623704568-1.76771980040953
Winsorized Mean ( 13 / 17 )-32.637666769230817.290108837236-1.88764958488533
Winsorized Mean ( 14 / 17 )-32.253743692307715.8865776404568-2.03025122353414
Winsorized Mean ( 15 / 17 )-41.297012923076911.8741340645531-3.47789680481691
Winsorized Mean ( 16 / 17 )-40.915474461538511.7636898048338-3.47811572222229
Winsorized Mean ( 17 / 17 )-48.576262923076910.5651207716546-4.59779532794394
Trimmed Mean ( 1 / 17 )-27.8945334427.9968725613757-0.996344623094907
Trimmed Mean ( 2 / 17 )-29.290493166666726.6567398325885-1.09880252988996
Trimmed Mean ( 3 / 17 )-31.112405913043525.3167344571278-1.22892650178601
Trimmed Mean ( 4 / 17 )-32.638197090909124.2933911652937-1.3435010727336
Trimmed Mean ( 5 / 17 )-34.072825523809523.0484950856508-1.47831020624952
Trimmed Mean ( 6 / 17 )-32.734016822.4073073234297-1.46086347313014
Trimmed Mean ( 7 / 17 )-31.208280842105321.6534346093311-1.4412623865526
Trimmed Mean ( 8 / 17 )-29.708657555555620.7441186190345-1.43214846102429
Trimmed Mean ( 9 / 17 )-28.703284470588219.772137303493-1.45170367927383
Trimmed Mean ( 10 / 17 )-28.635833519.0505378771107-1.50315091808542
Trimmed Mean ( 11 / 17 )-28.543389066666718.0863739575872-1.57817090001574
Trimmed Mean ( 12 / 17 )-28.044345428571417.2036719267943-1.63013719093847
Trimmed Mean ( 13 / 17 )-27.454833538461516.2572719934284-1.68877247975918
Trimmed Mean ( 14 / 17 )-26.59102814.9817827669333-1.77489077325896
Trimmed Mean ( 15 / 17 )-26.59102813.5481001229687-1.96271268728808
Trimmed Mean ( 16 / 17 )-22.920233613.0311617204452-1.75887876243906
Trimmed Mean ( 17 / 17 )-19.671092888888912.0431659020103-1.63338220605309
Median0.000364500000000004
Midrange160.4745
Midmean - Weighted Average at Xnp-33.7227656296296
Midmean - Weighted Average at X(n+1)p-27.4548335384615
Midmean - Empirical Distribution Function-33.7227656296296
Midmean - Empirical Distribution Function - Averaging-27.4548335384615
Midmean - Empirical Distribution Function - Interpolation-27.4548335384615
Midmean - Closest Observation-33.7227656296296
Midmean - True Basic - Statistics Graphics Toolkit-27.4548335384615
Midmean - MS Excel (old versions)-28.0443454285714
Number of observations52

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & -20.6495706153846 & 32.2022573809259 & -0.641246058346698 \tabularnewline
Geometric Mean & NaN &  &  \tabularnewline
Harmonic Mean & 12.9916114034293 &  &  \tabularnewline
Quadratic Mean & 230.895342457134 &  &  \tabularnewline
Winsorized Mean ( 1 / 17 ) & -26.6059552307692 & 29.0464956371707 & -0.915978146317989 \tabularnewline
Winsorized Mean ( 2 / 17 ) & -26.0671090769231 & 28.505327782397 & -0.91446445646629 \tabularnewline
Winsorized Mean ( 3 / 17 ) & -27.2392436923077 & 27.1584988778123 & -1.00297309563605 \tabularnewline
Winsorized Mean ( 4 / 17 ) & -28.0032436923077 & 26.9237283412945 & -1.04009531433867 \tabularnewline
Winsorized Mean ( 5 / 17 ) & -39.2220898461538 & 24.3364543974174 & -1.61165998981002 \tabularnewline
Winsorized Mean ( 6 / 17 ) & -39.4237821538461 & 23.9763193471789 & -1.64427999072697 \tabularnewline
Winsorized Mean ( 7 / 17 ) & -38.475686 & 23.5846866430571 & -1.63138423597952 \tabularnewline
Winsorized Mean ( 8 / 17 ) & -34.9675321538462 & 22.7207127640261 & -1.53901563375294 \tabularnewline
Winsorized Mean ( 9 / 17 ) & -29.0768590769231 & 20.7888610782926 & -1.39867494267325 \tabularnewline
Winsorized Mean ( 10 / 17 ) & -29.1691667692308 & 20.4979592814693 & -1.42302784236675 \tabularnewline
Winsorized Mean ( 11 / 17 ) & -31.4992629230769 & 18.959686275498 & -1.66138101998998 \tabularnewline
Winsorized Mean ( 12 / 17 ) & -31.5814167692308 & 17.865623704568 & -1.76771980040953 \tabularnewline
Winsorized Mean ( 13 / 17 ) & -32.6376667692308 & 17.290108837236 & -1.88764958488533 \tabularnewline
Winsorized Mean ( 14 / 17 ) & -32.2537436923077 & 15.8865776404568 & -2.03025122353414 \tabularnewline
Winsorized Mean ( 15 / 17 ) & -41.2970129230769 & 11.8741340645531 & -3.47789680481691 \tabularnewline
Winsorized Mean ( 16 / 17 ) & -40.9154744615385 & 11.7636898048338 & -3.47811572222229 \tabularnewline
Winsorized Mean ( 17 / 17 ) & -48.5762629230769 & 10.5651207716546 & -4.59779532794394 \tabularnewline
Trimmed Mean ( 1 / 17 ) & -27.89453344 & 27.9968725613757 & -0.996344623094907 \tabularnewline
Trimmed Mean ( 2 / 17 ) & -29.2904931666667 & 26.6567398325885 & -1.09880252988996 \tabularnewline
Trimmed Mean ( 3 / 17 ) & -31.1124059130435 & 25.3167344571278 & -1.22892650178601 \tabularnewline
Trimmed Mean ( 4 / 17 ) & -32.6381970909091 & 24.2933911652937 & -1.3435010727336 \tabularnewline
Trimmed Mean ( 5 / 17 ) & -34.0728255238095 & 23.0484950856508 & -1.47831020624952 \tabularnewline
Trimmed Mean ( 6 / 17 ) & -32.7340168 & 22.4073073234297 & -1.46086347313014 \tabularnewline
Trimmed Mean ( 7 / 17 ) & -31.2082808421053 & 21.6534346093311 & -1.4412623865526 \tabularnewline
Trimmed Mean ( 8 / 17 ) & -29.7086575555556 & 20.7441186190345 & -1.43214846102429 \tabularnewline
Trimmed Mean ( 9 / 17 ) & -28.7032844705882 & 19.772137303493 & -1.45170367927383 \tabularnewline
Trimmed Mean ( 10 / 17 ) & -28.6358335 & 19.0505378771107 & -1.50315091808542 \tabularnewline
Trimmed Mean ( 11 / 17 ) & -28.5433890666667 & 18.0863739575872 & -1.57817090001574 \tabularnewline
Trimmed Mean ( 12 / 17 ) & -28.0443454285714 & 17.2036719267943 & -1.63013719093847 \tabularnewline
Trimmed Mean ( 13 / 17 ) & -27.4548335384615 & 16.2572719934284 & -1.68877247975918 \tabularnewline
Trimmed Mean ( 14 / 17 ) & -26.591028 & 14.9817827669333 & -1.77489077325896 \tabularnewline
Trimmed Mean ( 15 / 17 ) & -26.591028 & 13.5481001229687 & -1.96271268728808 \tabularnewline
Trimmed Mean ( 16 / 17 ) & -22.9202336 & 13.0311617204452 & -1.75887876243906 \tabularnewline
Trimmed Mean ( 17 / 17 ) & -19.6710928888889 & 12.0431659020103 & -1.63338220605309 \tabularnewline
Median & 0.000364500000000004 &  &  \tabularnewline
Midrange & 160.4745 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & -33.7227656296296 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & -27.4548335384615 &  &  \tabularnewline
Midmean - Empirical Distribution Function & -33.7227656296296 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & -27.4548335384615 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & -27.4548335384615 &  &  \tabularnewline
Midmean - Closest Observation & -33.7227656296296 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & -27.4548335384615 &  &  \tabularnewline
Midmean - MS Excel (old versions) & -28.0443454285714 &  &  \tabularnewline
Number of observations & 52 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=270175&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]-20.6495706153846[/C][C]32.2022573809259[/C][C]-0.641246058346698[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]NaN[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]12.9916114034293[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]230.895342457134[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 17 )[/C][C]-26.6059552307692[/C][C]29.0464956371707[/C][C]-0.915978146317989[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 17 )[/C][C]-26.0671090769231[/C][C]28.505327782397[/C][C]-0.91446445646629[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 17 )[/C][C]-27.2392436923077[/C][C]27.1584988778123[/C][C]-1.00297309563605[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 17 )[/C][C]-28.0032436923077[/C][C]26.9237283412945[/C][C]-1.04009531433867[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 17 )[/C][C]-39.2220898461538[/C][C]24.3364543974174[/C][C]-1.61165998981002[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 17 )[/C][C]-39.4237821538461[/C][C]23.9763193471789[/C][C]-1.64427999072697[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 17 )[/C][C]-38.475686[/C][C]23.5846866430571[/C][C]-1.63138423597952[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 17 )[/C][C]-34.9675321538462[/C][C]22.7207127640261[/C][C]-1.53901563375294[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 17 )[/C][C]-29.0768590769231[/C][C]20.7888610782926[/C][C]-1.39867494267325[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 17 )[/C][C]-29.1691667692308[/C][C]20.4979592814693[/C][C]-1.42302784236675[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 17 )[/C][C]-31.4992629230769[/C][C]18.959686275498[/C][C]-1.66138101998998[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 17 )[/C][C]-31.5814167692308[/C][C]17.865623704568[/C][C]-1.76771980040953[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 17 )[/C][C]-32.6376667692308[/C][C]17.290108837236[/C][C]-1.88764958488533[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 17 )[/C][C]-32.2537436923077[/C][C]15.8865776404568[/C][C]-2.03025122353414[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 17 )[/C][C]-41.2970129230769[/C][C]11.8741340645531[/C][C]-3.47789680481691[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 17 )[/C][C]-40.9154744615385[/C][C]11.7636898048338[/C][C]-3.47811572222229[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 17 )[/C][C]-48.5762629230769[/C][C]10.5651207716546[/C][C]-4.59779532794394[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 17 )[/C][C]-27.89453344[/C][C]27.9968725613757[/C][C]-0.996344623094907[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 17 )[/C][C]-29.2904931666667[/C][C]26.6567398325885[/C][C]-1.09880252988996[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 17 )[/C][C]-31.1124059130435[/C][C]25.3167344571278[/C][C]-1.22892650178601[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 17 )[/C][C]-32.6381970909091[/C][C]24.2933911652937[/C][C]-1.3435010727336[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 17 )[/C][C]-34.0728255238095[/C][C]23.0484950856508[/C][C]-1.47831020624952[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 17 )[/C][C]-32.7340168[/C][C]22.4073073234297[/C][C]-1.46086347313014[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 17 )[/C][C]-31.2082808421053[/C][C]21.6534346093311[/C][C]-1.4412623865526[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 17 )[/C][C]-29.7086575555556[/C][C]20.7441186190345[/C][C]-1.43214846102429[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 17 )[/C][C]-28.7032844705882[/C][C]19.772137303493[/C][C]-1.45170367927383[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 17 )[/C][C]-28.6358335[/C][C]19.0505378771107[/C][C]-1.50315091808542[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 17 )[/C][C]-28.5433890666667[/C][C]18.0863739575872[/C][C]-1.57817090001574[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 17 )[/C][C]-28.0443454285714[/C][C]17.2036719267943[/C][C]-1.63013719093847[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 17 )[/C][C]-27.4548335384615[/C][C]16.2572719934284[/C][C]-1.68877247975918[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 17 )[/C][C]-26.591028[/C][C]14.9817827669333[/C][C]-1.77489077325896[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 17 )[/C][C]-26.591028[/C][C]13.5481001229687[/C][C]-1.96271268728808[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 17 )[/C][C]-22.9202336[/C][C]13.0311617204452[/C][C]-1.75887876243906[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 17 )[/C][C]-19.6710928888889[/C][C]12.0431659020103[/C][C]-1.63338220605309[/C][/ROW]
[ROW][C]Median[/C][C]0.000364500000000004[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]160.4745[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]-33.7227656296296[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]-27.4548335384615[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]-33.7227656296296[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]-27.4548335384615[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]-27.4548335384615[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]-33.7227656296296[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]-27.4548335384615[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]-28.0443454285714[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]52[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=270175&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=270175&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-20.649570615384632.2022573809259-0.641246058346698
Geometric MeanNaN
Harmonic Mean12.9916114034293
Quadratic Mean230.895342457134
Winsorized Mean ( 1 / 17 )-26.605955230769229.0464956371707-0.915978146317989
Winsorized Mean ( 2 / 17 )-26.067109076923128.505327782397-0.91446445646629
Winsorized Mean ( 3 / 17 )-27.239243692307727.1584988778123-1.00297309563605
Winsorized Mean ( 4 / 17 )-28.003243692307726.9237283412945-1.04009531433867
Winsorized Mean ( 5 / 17 )-39.222089846153824.3364543974174-1.61165998981002
Winsorized Mean ( 6 / 17 )-39.423782153846123.9763193471789-1.64427999072697
Winsorized Mean ( 7 / 17 )-38.47568623.5846866430571-1.63138423597952
Winsorized Mean ( 8 / 17 )-34.967532153846222.7207127640261-1.53901563375294
Winsorized Mean ( 9 / 17 )-29.076859076923120.7888610782926-1.39867494267325
Winsorized Mean ( 10 / 17 )-29.169166769230820.4979592814693-1.42302784236675
Winsorized Mean ( 11 / 17 )-31.499262923076918.959686275498-1.66138101998998
Winsorized Mean ( 12 / 17 )-31.581416769230817.865623704568-1.76771980040953
Winsorized Mean ( 13 / 17 )-32.637666769230817.290108837236-1.88764958488533
Winsorized Mean ( 14 / 17 )-32.253743692307715.8865776404568-2.03025122353414
Winsorized Mean ( 15 / 17 )-41.297012923076911.8741340645531-3.47789680481691
Winsorized Mean ( 16 / 17 )-40.915474461538511.7636898048338-3.47811572222229
Winsorized Mean ( 17 / 17 )-48.576262923076910.5651207716546-4.59779532794394
Trimmed Mean ( 1 / 17 )-27.8945334427.9968725613757-0.996344623094907
Trimmed Mean ( 2 / 17 )-29.290493166666726.6567398325885-1.09880252988996
Trimmed Mean ( 3 / 17 )-31.112405913043525.3167344571278-1.22892650178601
Trimmed Mean ( 4 / 17 )-32.638197090909124.2933911652937-1.3435010727336
Trimmed Mean ( 5 / 17 )-34.072825523809523.0484950856508-1.47831020624952
Trimmed Mean ( 6 / 17 )-32.734016822.4073073234297-1.46086347313014
Trimmed Mean ( 7 / 17 )-31.208280842105321.6534346093311-1.4412623865526
Trimmed Mean ( 8 / 17 )-29.708657555555620.7441186190345-1.43214846102429
Trimmed Mean ( 9 / 17 )-28.703284470588219.772137303493-1.45170367927383
Trimmed Mean ( 10 / 17 )-28.635833519.0505378771107-1.50315091808542
Trimmed Mean ( 11 / 17 )-28.543389066666718.0863739575872-1.57817090001574
Trimmed Mean ( 12 / 17 )-28.044345428571417.2036719267943-1.63013719093847
Trimmed Mean ( 13 / 17 )-27.454833538461516.2572719934284-1.68877247975918
Trimmed Mean ( 14 / 17 )-26.59102814.9817827669333-1.77489077325896
Trimmed Mean ( 15 / 17 )-26.59102813.5481001229687-1.96271268728808
Trimmed Mean ( 16 / 17 )-22.920233613.0311617204452-1.75887876243906
Trimmed Mean ( 17 / 17 )-19.671092888888912.0431659020103-1.63338220605309
Median0.000364500000000004
Midrange160.4745
Midmean - Weighted Average at Xnp-33.7227656296296
Midmean - Weighted Average at X(n+1)p-27.4548335384615
Midmean - Empirical Distribution Function-33.7227656296296
Midmean - Empirical Distribution Function - Averaging-27.4548335384615
Midmean - Empirical Distribution Function - Interpolation-27.4548335384615
Midmean - Closest Observation-33.7227656296296
Midmean - True Basic - Statistics Graphics Toolkit-27.4548335384615
Midmean - MS Excel (old versions)-28.0443454285714
Number of observations52



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')