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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationWed, 07 Mar 2012 15:48:11 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/Mar/07/t1331153353hvcwymlwdpfik8x.htm/, Retrieved Sun, 28 Apr 2024 22:23:58 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=163708, Retrieved Sun, 28 Apr 2024 22:23:58 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDG2011W52a
Estimated Impact137
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Opgave 5 oef 2] [2012-03-07 20:48:11] [921480865c2f7a3cce0a5eeacc6bbad6] [Current]
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Dataseries X:
34,74
34,89
34,98
34,93
35,01
35,03
35,03
34,98
34,92
35,04
35,21
35,21
35,21
35,26
35,45
35,53
35,53
35,57
35,57
35,57
35,63
35,92
36,05
36,1
36,1
36,02
36,07
36,17
36,52
36,49
36,49
36,48
36,62
36,63
36,7
36,7
36,7
36,69
36,86
36,85
36,83
36,88
36,88
36,92
36,93
37,06
37,1
37,09
37,09
37,15
37,27
37,43
37,42
37,4
37,4
37,39
37,42
37,7
37,85
37,88




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Herman Ole Andreas Wold' @ wold.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 & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=163708&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]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=163708&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=163708&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'Herman Ole Andreas Wold' @ wold.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean36.27566666666670.117526380418023308.659779511967
Geometric Mean36.26440703453
Harmonic Mean36.2531229625943
Quadratic Mean36.2868974516514
Winsorized Mean ( 1 / 20 )36.27766666666670.116883100291317310.375636651056
Winsorized Mean ( 2 / 20 )36.27366666666670.115590101492682313.81291475865
Winsorized Mean ( 3 / 20 )36.26066666666670.112891094629755321.200416964593
Winsorized Mean ( 4 / 20 )36.26333333333330.112117943010963323.439160222442
Winsorized Mean ( 5 / 20 )36.26333333333330.112117943010963323.439160222442
Winsorized Mean ( 6 / 20 )36.26433333333330.111192144650668326.141144657879
Winsorized Mean ( 7 / 20 )36.26666666666670.110748268192876327.469379507638
Winsorized Mean ( 8 / 20 )36.26533333333330.110517648631943328.140652486262
Winsorized Mean ( 9 / 20 )36.24883333333330.107225695668884338.061069291365
Winsorized Mean ( 10 / 20 )36.25716666666670.0988187554153844366.905720622161
Winsorized Mean ( 11 / 20 )36.2480.0974374491516232372.013022873723
Winsorized Mean ( 12 / 20 )36.2460.0971419835691625373.123943615932
Winsorized Mean ( 13 / 20 )36.25683333333330.0952013897689315380.843529924661
Winsorized Mean ( 14 / 20 )36.29416666666670.0865461869006562419.36182247206
Winsorized Mean ( 15 / 20 )36.28166666666670.0785512056054619461.885548248592
Winsorized Mean ( 16 / 20 )36.2790.0781793895419537464.048136120728
Winsorized Mean ( 17 / 20 )36.2790.0747888553285578485.08564331706
Winsorized Mean ( 18 / 20 )36.2790.0747888553285578485.08564331706
Winsorized Mean ( 19 / 20 )36.27266666666670.0739311279237836490.627800296251
Winsorized Mean ( 20 / 20 )36.28933333333330.0702798548928956516.354699204163
Trimmed Mean ( 1 / 20 )36.27448275862070.115317802391148314.560995843303
Trimmed Mean ( 2 / 20 )36.27107142857140.11333798396184320.025733303881
Trimmed Mean ( 3 / 20 )36.26962962962960.111681125808448324.760601821281
Trimmed Mean ( 4 / 20 )36.27307692307690.110795675157473327.387119321421
Trimmed Mean ( 5 / 20 )36.2760.109855563800652330.215409624839
Trimmed Mean ( 6 / 20 )36.27916666666670.108541194476315334.243296673719
Trimmed Mean ( 7 / 20 )36.28239130434780.107025747402274339.006194163489
Trimmed Mean ( 8 / 20 )36.28545454545450.10508450970662345.297843105118
Trimmed Mean ( 9 / 20 )36.28904761904760.102512461792419353.996450622078
Trimmed Mean ( 10 / 20 )36.295750.0999101439243001363.283932685559
Trimmed Mean ( 11 / 20 )36.30184210526320.0985743722542227368.268559820406
Trimmed Mean ( 12 / 20 )36.310.0968979171561822374.724256884436
Trimmed Mean ( 13 / 20 )36.31941176470590.0944492820320844384.538780849262
Trimmed Mean ( 14 / 20 )36.32843750.0914170580527737397.392327797599
Trimmed Mean ( 15 / 20 )36.33333333333330.0895882449869777405.559159447923
Trimmed Mean ( 16 / 20 )36.34071428571430.0889368847179892408.612404189189
Trimmed Mean ( 17 / 20 )36.34961538461540.0875732322454594415.07678148422
Trimmed Mean ( 18 / 20 )36.360.0861116565355954422.242486822561
Trimmed Mean ( 19 / 20 )36.37227272727270.0831650208952754437.35061129936
Trimmed Mean ( 20 / 20 )36.3880.0779493762845982466.815794229643
Median36.49
Midrange36.31
Midmean - Weighted Average at Xnp36.3048387096774
Midmean - Weighted Average at X(n+1)p36.3333333333333
Midmean - Empirical Distribution Function36.3048387096774
Midmean - Empirical Distribution Function - Averaging36.3333333333333
Midmean - Empirical Distribution Function - Interpolation36.3333333333333
Midmean - Closest Observation36.3048387096774
Midmean - True Basic - Statistics Graphics Toolkit36.3333333333333
Midmean - MS Excel (old versions)36.3284375
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 36.2756666666667 & 0.117526380418023 & 308.659779511967 \tabularnewline
Geometric Mean & 36.26440703453 &  &  \tabularnewline
Harmonic Mean & 36.2531229625943 &  &  \tabularnewline
Quadratic Mean & 36.2868974516514 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 36.2776666666667 & 0.116883100291317 & 310.375636651056 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 36.2736666666667 & 0.115590101492682 & 313.81291475865 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 36.2606666666667 & 0.112891094629755 & 321.200416964593 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 36.2633333333333 & 0.112117943010963 & 323.439160222442 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 36.2633333333333 & 0.112117943010963 & 323.439160222442 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 36.2643333333333 & 0.111192144650668 & 326.141144657879 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 36.2666666666667 & 0.110748268192876 & 327.469379507638 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 36.2653333333333 & 0.110517648631943 & 328.140652486262 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 36.2488333333333 & 0.107225695668884 & 338.061069291365 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 36.2571666666667 & 0.0988187554153844 & 366.905720622161 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 36.248 & 0.0974374491516232 & 372.013022873723 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 36.246 & 0.0971419835691625 & 373.123943615932 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 36.2568333333333 & 0.0952013897689315 & 380.843529924661 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 36.2941666666667 & 0.0865461869006562 & 419.36182247206 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 36.2816666666667 & 0.0785512056054619 & 461.885548248592 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 36.279 & 0.0781793895419537 & 464.048136120728 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 36.279 & 0.0747888553285578 & 485.08564331706 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 36.279 & 0.0747888553285578 & 485.08564331706 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 36.2726666666667 & 0.0739311279237836 & 490.627800296251 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 36.2893333333333 & 0.0702798548928956 & 516.354699204163 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 36.2744827586207 & 0.115317802391148 & 314.560995843303 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 36.2710714285714 & 0.11333798396184 & 320.025733303881 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 36.2696296296296 & 0.111681125808448 & 324.760601821281 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 36.2730769230769 & 0.110795675157473 & 327.387119321421 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 36.276 & 0.109855563800652 & 330.215409624839 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 36.2791666666667 & 0.108541194476315 & 334.243296673719 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 36.2823913043478 & 0.107025747402274 & 339.006194163489 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 36.2854545454545 & 0.10508450970662 & 345.297843105118 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 36.2890476190476 & 0.102512461792419 & 353.996450622078 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 36.29575 & 0.0999101439243001 & 363.283932685559 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 36.3018421052632 & 0.0985743722542227 & 368.268559820406 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 36.31 & 0.0968979171561822 & 374.724256884436 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 36.3194117647059 & 0.0944492820320844 & 384.538780849262 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 36.3284375 & 0.0914170580527737 & 397.392327797599 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 36.3333333333333 & 0.0895882449869777 & 405.559159447923 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 36.3407142857143 & 0.0889368847179892 & 408.612404189189 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 36.3496153846154 & 0.0875732322454594 & 415.07678148422 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 36.36 & 0.0861116565355954 & 422.242486822561 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 36.3722727272727 & 0.0831650208952754 & 437.35061129936 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 36.388 & 0.0779493762845982 & 466.815794229643 \tabularnewline
Median & 36.49 &  &  \tabularnewline
Midrange & 36.31 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 36.3048387096774 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 36.3333333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 36.3048387096774 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 36.3333333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 36.3333333333333 &  &  \tabularnewline
Midmean - Closest Observation & 36.3048387096774 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 36.3333333333333 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 36.3284375 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=163708&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]36.2756666666667[/C][C]0.117526380418023[/C][C]308.659779511967[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]36.26440703453[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]36.2531229625943[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]36.2868974516514[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]36.2776666666667[/C][C]0.116883100291317[/C][C]310.375636651056[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]36.2736666666667[/C][C]0.115590101492682[/C][C]313.81291475865[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]36.2606666666667[/C][C]0.112891094629755[/C][C]321.200416964593[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]36.2633333333333[/C][C]0.112117943010963[/C][C]323.439160222442[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]36.2633333333333[/C][C]0.112117943010963[/C][C]323.439160222442[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]36.2643333333333[/C][C]0.111192144650668[/C][C]326.141144657879[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]36.2666666666667[/C][C]0.110748268192876[/C][C]327.469379507638[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]36.2653333333333[/C][C]0.110517648631943[/C][C]328.140652486262[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]36.2488333333333[/C][C]0.107225695668884[/C][C]338.061069291365[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]36.2571666666667[/C][C]0.0988187554153844[/C][C]366.905720622161[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]36.248[/C][C]0.0974374491516232[/C][C]372.013022873723[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]36.246[/C][C]0.0971419835691625[/C][C]373.123943615932[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]36.2568333333333[/C][C]0.0952013897689315[/C][C]380.843529924661[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]36.2941666666667[/C][C]0.0865461869006562[/C][C]419.36182247206[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]36.2816666666667[/C][C]0.0785512056054619[/C][C]461.885548248592[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]36.279[/C][C]0.0781793895419537[/C][C]464.048136120728[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]36.279[/C][C]0.0747888553285578[/C][C]485.08564331706[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]36.279[/C][C]0.0747888553285578[/C][C]485.08564331706[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]36.2726666666667[/C][C]0.0739311279237836[/C][C]490.627800296251[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]36.2893333333333[/C][C]0.0702798548928956[/C][C]516.354699204163[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]36.2744827586207[/C][C]0.115317802391148[/C][C]314.560995843303[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]36.2710714285714[/C][C]0.11333798396184[/C][C]320.025733303881[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]36.2696296296296[/C][C]0.111681125808448[/C][C]324.760601821281[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]36.2730769230769[/C][C]0.110795675157473[/C][C]327.387119321421[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]36.276[/C][C]0.109855563800652[/C][C]330.215409624839[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]36.2791666666667[/C][C]0.108541194476315[/C][C]334.243296673719[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]36.2823913043478[/C][C]0.107025747402274[/C][C]339.006194163489[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]36.2854545454545[/C][C]0.10508450970662[/C][C]345.297843105118[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]36.2890476190476[/C][C]0.102512461792419[/C][C]353.996450622078[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]36.29575[/C][C]0.0999101439243001[/C][C]363.283932685559[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]36.3018421052632[/C][C]0.0985743722542227[/C][C]368.268559820406[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]36.31[/C][C]0.0968979171561822[/C][C]374.724256884436[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]36.3194117647059[/C][C]0.0944492820320844[/C][C]384.538780849262[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]36.3284375[/C][C]0.0914170580527737[/C][C]397.392327797599[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]36.3333333333333[/C][C]0.0895882449869777[/C][C]405.559159447923[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]36.3407142857143[/C][C]0.0889368847179892[/C][C]408.612404189189[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]36.3496153846154[/C][C]0.0875732322454594[/C][C]415.07678148422[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]36.36[/C][C]0.0861116565355954[/C][C]422.242486822561[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]36.3722727272727[/C][C]0.0831650208952754[/C][C]437.35061129936[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]36.388[/C][C]0.0779493762845982[/C][C]466.815794229643[/C][/ROW]
[ROW][C]Median[/C][C]36.49[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]36.31[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]36.3048387096774[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]36.3333333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]36.3048387096774[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]36.3333333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]36.3333333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]36.3048387096774[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]36.3333333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]36.3284375[/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=163708&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=163708&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 Mean36.27566666666670.117526380418023308.659779511967
Geometric Mean36.26440703453
Harmonic Mean36.2531229625943
Quadratic Mean36.2868974516514
Winsorized Mean ( 1 / 20 )36.27766666666670.116883100291317310.375636651056
Winsorized Mean ( 2 / 20 )36.27366666666670.115590101492682313.81291475865
Winsorized Mean ( 3 / 20 )36.26066666666670.112891094629755321.200416964593
Winsorized Mean ( 4 / 20 )36.26333333333330.112117943010963323.439160222442
Winsorized Mean ( 5 / 20 )36.26333333333330.112117943010963323.439160222442
Winsorized Mean ( 6 / 20 )36.26433333333330.111192144650668326.141144657879
Winsorized Mean ( 7 / 20 )36.26666666666670.110748268192876327.469379507638
Winsorized Mean ( 8 / 20 )36.26533333333330.110517648631943328.140652486262
Winsorized Mean ( 9 / 20 )36.24883333333330.107225695668884338.061069291365
Winsorized Mean ( 10 / 20 )36.25716666666670.0988187554153844366.905720622161
Winsorized Mean ( 11 / 20 )36.2480.0974374491516232372.013022873723
Winsorized Mean ( 12 / 20 )36.2460.0971419835691625373.123943615932
Winsorized Mean ( 13 / 20 )36.25683333333330.0952013897689315380.843529924661
Winsorized Mean ( 14 / 20 )36.29416666666670.0865461869006562419.36182247206
Winsorized Mean ( 15 / 20 )36.28166666666670.0785512056054619461.885548248592
Winsorized Mean ( 16 / 20 )36.2790.0781793895419537464.048136120728
Winsorized Mean ( 17 / 20 )36.2790.0747888553285578485.08564331706
Winsorized Mean ( 18 / 20 )36.2790.0747888553285578485.08564331706
Winsorized Mean ( 19 / 20 )36.27266666666670.0739311279237836490.627800296251
Winsorized Mean ( 20 / 20 )36.28933333333330.0702798548928956516.354699204163
Trimmed Mean ( 1 / 20 )36.27448275862070.115317802391148314.560995843303
Trimmed Mean ( 2 / 20 )36.27107142857140.11333798396184320.025733303881
Trimmed Mean ( 3 / 20 )36.26962962962960.111681125808448324.760601821281
Trimmed Mean ( 4 / 20 )36.27307692307690.110795675157473327.387119321421
Trimmed Mean ( 5 / 20 )36.2760.109855563800652330.215409624839
Trimmed Mean ( 6 / 20 )36.27916666666670.108541194476315334.243296673719
Trimmed Mean ( 7 / 20 )36.28239130434780.107025747402274339.006194163489
Trimmed Mean ( 8 / 20 )36.28545454545450.10508450970662345.297843105118
Trimmed Mean ( 9 / 20 )36.28904761904760.102512461792419353.996450622078
Trimmed Mean ( 10 / 20 )36.295750.0999101439243001363.283932685559
Trimmed Mean ( 11 / 20 )36.30184210526320.0985743722542227368.268559820406
Trimmed Mean ( 12 / 20 )36.310.0968979171561822374.724256884436
Trimmed Mean ( 13 / 20 )36.31941176470590.0944492820320844384.538780849262
Trimmed Mean ( 14 / 20 )36.32843750.0914170580527737397.392327797599
Trimmed Mean ( 15 / 20 )36.33333333333330.0895882449869777405.559159447923
Trimmed Mean ( 16 / 20 )36.34071428571430.0889368847179892408.612404189189
Trimmed Mean ( 17 / 20 )36.34961538461540.0875732322454594415.07678148422
Trimmed Mean ( 18 / 20 )36.360.0861116565355954422.242486822561
Trimmed Mean ( 19 / 20 )36.37227272727270.0831650208952754437.35061129936
Trimmed Mean ( 20 / 20 )36.3880.0779493762845982466.815794229643
Median36.49
Midrange36.31
Midmean - Weighted Average at Xnp36.3048387096774
Midmean - Weighted Average at X(n+1)p36.3333333333333
Midmean - Empirical Distribution Function36.3048387096774
Midmean - Empirical Distribution Function - Averaging36.3333333333333
Midmean - Empirical Distribution Function - Interpolation36.3333333333333
Midmean - Closest Observation36.3048387096774
Midmean - True Basic - Statistics Graphics Toolkit36.3333333333333
Midmean - MS Excel (old versions)36.3284375
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')