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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 computationSun, 19 Oct 2008 07:49:09 -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/2008/Oct/19/t1224424300n728r22dfd1zbi6.htm/, Retrieved Sat, 18 May 2024 15:17:40 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=16843, Retrieved Sat, 18 May 2024 15:17:40 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact153
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Pearson Correlation] [Investigating ass...] [2007-10-22 22:08:56] [8cd6641b921d30ebe00b648d1481bba0]
-    D  [Pearson Correlation] [Verband inflatie ...] [2008-10-19 13:31:27] [e5d91604aae608e98a8ea24759233f66]
-    D    [Pearson Correlation] [Pearson correlati...] [2008-10-19 13:35:43] [e5d91604aae608e98a8ea24759233f66]
- RM D        [Central Tendency] [Central tendency ...] [2008-10-19 13:49:09] [55ca0ca4a201c9689dcf5fae352c92eb] [Current]
-    D          [Central Tendency] [Central tendency ...] [2008-10-19 13:52:59] [e5d91604aae608e98a8ea24759233f66]
-    D          [Central Tendency] [Central tendency ...] [2008-10-19 13:56:08] [e5d91604aae608e98a8ea24759233f66]
- RMPD          [Back to Back Histogram] [Back-to-back hist...] [2008-10-19 14:07:33] [e5d91604aae608e98a8ea24759233f66]
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Dataseries X:
1.21
1.74
1.76
1.48
1.04
1.62
1.49
1.79
1.8
1.58
1.86
1.74
1.59
1.26
1.13
1.92
2.61
2.26
2.41
2.26
2.03
2.86
2.55
2.27
2.26
2.57
3.07
2.76
2.51
2.87
3.14
3.11
3.16
2.47
2.57
2.89
2.63
2.38
1.69
1.96
2.19
1.87
1.6
1.63
1.22
1.21
1.49
1.64
1.66
1.77
1.82
1.78
1.28
1.29
1.37
1.12
1.51
2.24
2.94
3.09




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=16843&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=16843&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=16843&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 Mean2.0170.078325086715812525.7516471998084
Geometric Mean1.92767093053265
Harmonic Mean1.84087247740495
Quadratic Mean2.10481432276895
Winsorized Mean ( 1 / 20 )2.0180.077972108587071825.8810494748451
Winsorized Mean ( 2 / 20 )2.017333333333330.077666121091170825.9744313864371
Winsorized Mean ( 3 / 20 )2.020333333333330.07668298770024926.3465651759781
Winsorized Mean ( 4 / 20 )2.0190.07636986272217226.4371301457615
Winsorized Mean ( 5 / 20 )2.0090.073796061934646227.2236749134279
Winsorized Mean ( 6 / 20 )2.0080.072027850859476827.8781051501526
Winsorized Mean ( 7 / 20 )2.0080.071138362833752828.2266827631753
Winsorized Mean ( 8 / 20 )2.0080.070634653232589328.4279727882001
Winsorized Mean ( 9 / 20 )2.0050.065616373525030130.5563976228459
Winsorized Mean ( 10 / 20 )2.001666666666670.058635215632255134.1376192631507
Winsorized Mean ( 11 / 20 )1.999833333333330.057698070381949334.660315675981
Winsorized Mean ( 12 / 20 )1.991833333333330.0562844328593435.388707536791
Winsorized Mean ( 13 / 20 )1.996166666666670.055636071127876535.8790012702116
Winsorized Mean ( 14 / 20 )2.007833333333330.052479262337783438.25955708771
Winsorized Mean ( 15 / 20 )2.000333333333330.050401196440526439.688211284701
Winsorized Mean ( 16 / 20 )1.992333333333330.048223448047807541.3146179708715
Winsorized Mean ( 17 / 20 )1.9810.044630751223817244.3864363847597
Winsorized Mean ( 18 / 20 )1.9750.042764299488410546.183382485553
Winsorized Mean ( 19 / 20 )1.943333333333330.036905488289865152.6570280840047
Winsorized Mean ( 20 / 20 )1.946666666666670.035485070200808554.8587520230498
Trimmed Mean ( 1 / 20 )2.014137931034480.076713747537634426.2552410185199
Trimmed Mean ( 2 / 20 )2.010.07513580777758126.7515590695458
Trimmed Mean ( 3 / 20 )2.005925925925930.073360257359040527.3434963035708
Trimmed Mean ( 4 / 20 )2.000384615384620.071590928553595627.9418727456099
Trimmed Mean ( 5 / 20 )1.99480.069463976863066628.7170428484439
Trimmed Mean ( 6 / 20 )1.991250.067659468182596429.4304707602209
Trimmed Mean ( 7 / 20 )1.987608695652170.065881011744391230.1696747366875
Trimmed Mean ( 8 / 20 )1.983636363636360.063813028709631831.0851311048485
Trimmed Mean ( 9 / 20 )1.979285714285710.06122291560942932.3291645715233
Trimmed Mean ( 10 / 20 )1.9750.059231185479722933.3439215170886
Trimmed Mean ( 11 / 20 )1.970789473684210.058418441498424933.7357420556546
Trimmed Mean ( 12 / 20 )1.966388888888890.057444455957752734.2311343384480
Trimmed Mean ( 13 / 20 )1.962647058823530.056376485951033334.813220897241
Trimmed Mean ( 14 / 20 )1.95781250.054915136829695635.6516001420815
Trimmed Mean ( 15 / 20 )1.950666666666670.053569019467816436.4140819833113
Trimmed Mean ( 16 / 20 )1.943571428571430.052101890118235337.3032806326385
Trimmed Mean ( 17 / 20 )1.936538461538460.050471446025503638.3689910639753
Trimmed Mean ( 18 / 20 )1.930.049093226900828539.3129586673682
Trimmed Mean ( 19 / 20 )1.923181818181820.047374287341777340.5954775489751
Trimmed Mean ( 20 / 20 )1.920.046909767807882740.929641942874
Median1.84
Midrange2.1
Midmean - Weighted Average at Xnp1.93870967741935
Midmean - Weighted Average at X(n+1)p1.95066666666667
Midmean - Empirical Distribution Function1.93870967741935
Midmean - Empirical Distribution Function - Averaging1.95066666666667
Midmean - Empirical Distribution Function - Interpolation1.95066666666667
Midmean - Closest Observation1.93870967741935
Midmean - True Basic - Statistics Graphics Toolkit1.95066666666667
Midmean - MS Excel (old versions)1.9578125
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 2.017 & 0.0783250867158125 & 25.7516471998084 \tabularnewline
Geometric Mean & 1.92767093053265 &  &  \tabularnewline
Harmonic Mean & 1.84087247740495 &  &  \tabularnewline
Quadratic Mean & 2.10481432276895 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 2.018 & 0.0779721085870718 & 25.8810494748451 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 2.01733333333333 & 0.0776661210911708 & 25.9744313864371 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 2.02033333333333 & 0.076682987700249 & 26.3465651759781 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 2.019 & 0.076369862722172 & 26.4371301457615 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 2.009 & 0.0737960619346462 & 27.2236749134279 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 2.008 & 0.0720278508594768 & 27.8781051501526 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 2.008 & 0.0711383628337528 & 28.2266827631753 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 2.008 & 0.0706346532325893 & 28.4279727882001 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 2.005 & 0.0656163735250301 & 30.5563976228459 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 2.00166666666667 & 0.0586352156322551 & 34.1376192631507 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 1.99983333333333 & 0.0576980703819493 & 34.660315675981 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 1.99183333333333 & 0.05628443285934 & 35.388707536791 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 1.99616666666667 & 0.0556360711278765 & 35.8790012702116 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 2.00783333333333 & 0.0524792623377834 & 38.25955708771 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 2.00033333333333 & 0.0504011964405264 & 39.688211284701 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 1.99233333333333 & 0.0482234480478075 & 41.3146179708715 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 1.981 & 0.0446307512238172 & 44.3864363847597 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 1.975 & 0.0427642994884105 & 46.183382485553 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 1.94333333333333 & 0.0369054882898651 & 52.6570280840047 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 1.94666666666667 & 0.0354850702008085 & 54.8587520230498 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 2.01413793103448 & 0.0767137475376344 & 26.2552410185199 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 2.01 & 0.075135807777581 & 26.7515590695458 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 2.00592592592593 & 0.0733602573590405 & 27.3434963035708 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 2.00038461538462 & 0.0715909285535956 & 27.9418727456099 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 1.9948 & 0.0694639768630666 & 28.7170428484439 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 1.99125 & 0.0676594681825964 & 29.4304707602209 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 1.98760869565217 & 0.0658810117443912 & 30.1696747366875 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 1.98363636363636 & 0.0638130287096318 & 31.0851311048485 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 1.97928571428571 & 0.061222915609429 & 32.3291645715233 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 1.975 & 0.0592311854797229 & 33.3439215170886 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 1.97078947368421 & 0.0584184414984249 & 33.7357420556546 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 1.96638888888889 & 0.0574444559577527 & 34.2311343384480 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 1.96264705882353 & 0.0563764859510333 & 34.813220897241 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 1.9578125 & 0.0549151368296956 & 35.6516001420815 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 1.95066666666667 & 0.0535690194678164 & 36.4140819833113 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 1.94357142857143 & 0.0521018901182353 & 37.3032806326385 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 1.93653846153846 & 0.0504714460255036 & 38.3689910639753 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 1.93 & 0.0490932269008285 & 39.3129586673682 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 1.92318181818182 & 0.0473742873417773 & 40.5954775489751 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 1.92 & 0.0469097678078827 & 40.929641942874 \tabularnewline
Median & 1.84 &  &  \tabularnewline
Midrange & 2.1 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 1.93870967741935 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 1.95066666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 1.93870967741935 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 1.95066666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 1.95066666666667 &  &  \tabularnewline
Midmean - Closest Observation & 1.93870967741935 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 1.95066666666667 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 1.9578125 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=16843&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]2.017[/C][C]0.0783250867158125[/C][C]25.7516471998084[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]1.92767093053265[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]1.84087247740495[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]2.10481432276895[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]2.018[/C][C]0.0779721085870718[/C][C]25.8810494748451[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]2.01733333333333[/C][C]0.0776661210911708[/C][C]25.9744313864371[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]2.02033333333333[/C][C]0.076682987700249[/C][C]26.3465651759781[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]2.019[/C][C]0.076369862722172[/C][C]26.4371301457615[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]2.009[/C][C]0.0737960619346462[/C][C]27.2236749134279[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]2.008[/C][C]0.0720278508594768[/C][C]27.8781051501526[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]2.008[/C][C]0.0711383628337528[/C][C]28.2266827631753[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]2.008[/C][C]0.0706346532325893[/C][C]28.4279727882001[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]2.005[/C][C]0.0656163735250301[/C][C]30.5563976228459[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]2.00166666666667[/C][C]0.0586352156322551[/C][C]34.1376192631507[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]1.99983333333333[/C][C]0.0576980703819493[/C][C]34.660315675981[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]1.99183333333333[/C][C]0.05628443285934[/C][C]35.388707536791[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]1.99616666666667[/C][C]0.0556360711278765[/C][C]35.8790012702116[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]2.00783333333333[/C][C]0.0524792623377834[/C][C]38.25955708771[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]2.00033333333333[/C][C]0.0504011964405264[/C][C]39.688211284701[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]1.99233333333333[/C][C]0.0482234480478075[/C][C]41.3146179708715[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]1.981[/C][C]0.0446307512238172[/C][C]44.3864363847597[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]1.975[/C][C]0.0427642994884105[/C][C]46.183382485553[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]1.94333333333333[/C][C]0.0369054882898651[/C][C]52.6570280840047[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]1.94666666666667[/C][C]0.0354850702008085[/C][C]54.8587520230498[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]2.01413793103448[/C][C]0.0767137475376344[/C][C]26.2552410185199[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]2.01[/C][C]0.075135807777581[/C][C]26.7515590695458[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]2.00592592592593[/C][C]0.0733602573590405[/C][C]27.3434963035708[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]2.00038461538462[/C][C]0.0715909285535956[/C][C]27.9418727456099[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]1.9948[/C][C]0.0694639768630666[/C][C]28.7170428484439[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]1.99125[/C][C]0.0676594681825964[/C][C]29.4304707602209[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]1.98760869565217[/C][C]0.0658810117443912[/C][C]30.1696747366875[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]1.98363636363636[/C][C]0.0638130287096318[/C][C]31.0851311048485[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]1.97928571428571[/C][C]0.061222915609429[/C][C]32.3291645715233[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]1.975[/C][C]0.0592311854797229[/C][C]33.3439215170886[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]1.97078947368421[/C][C]0.0584184414984249[/C][C]33.7357420556546[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]1.96638888888889[/C][C]0.0574444559577527[/C][C]34.2311343384480[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]1.96264705882353[/C][C]0.0563764859510333[/C][C]34.813220897241[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]1.9578125[/C][C]0.0549151368296956[/C][C]35.6516001420815[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]1.95066666666667[/C][C]0.0535690194678164[/C][C]36.4140819833113[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]1.94357142857143[/C][C]0.0521018901182353[/C][C]37.3032806326385[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]1.93653846153846[/C][C]0.0504714460255036[/C][C]38.3689910639753[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]1.93[/C][C]0.0490932269008285[/C][C]39.3129586673682[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]1.92318181818182[/C][C]0.0473742873417773[/C][C]40.5954775489751[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]1.92[/C][C]0.0469097678078827[/C][C]40.929641942874[/C][/ROW]
[ROW][C]Median[/C][C]1.84[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]2.1[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]1.93870967741935[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]1.95066666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]1.93870967741935[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]1.95066666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]1.95066666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]1.93870967741935[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]1.95066666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]1.9578125[/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=16843&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=16843&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 Mean2.0170.078325086715812525.7516471998084
Geometric Mean1.92767093053265
Harmonic Mean1.84087247740495
Quadratic Mean2.10481432276895
Winsorized Mean ( 1 / 20 )2.0180.077972108587071825.8810494748451
Winsorized Mean ( 2 / 20 )2.017333333333330.077666121091170825.9744313864371
Winsorized Mean ( 3 / 20 )2.020333333333330.07668298770024926.3465651759781
Winsorized Mean ( 4 / 20 )2.0190.07636986272217226.4371301457615
Winsorized Mean ( 5 / 20 )2.0090.073796061934646227.2236749134279
Winsorized Mean ( 6 / 20 )2.0080.072027850859476827.8781051501526
Winsorized Mean ( 7 / 20 )2.0080.071138362833752828.2266827631753
Winsorized Mean ( 8 / 20 )2.0080.070634653232589328.4279727882001
Winsorized Mean ( 9 / 20 )2.0050.065616373525030130.5563976228459
Winsorized Mean ( 10 / 20 )2.001666666666670.058635215632255134.1376192631507
Winsorized Mean ( 11 / 20 )1.999833333333330.057698070381949334.660315675981
Winsorized Mean ( 12 / 20 )1.991833333333330.0562844328593435.388707536791
Winsorized Mean ( 13 / 20 )1.996166666666670.055636071127876535.8790012702116
Winsorized Mean ( 14 / 20 )2.007833333333330.052479262337783438.25955708771
Winsorized Mean ( 15 / 20 )2.000333333333330.050401196440526439.688211284701
Winsorized Mean ( 16 / 20 )1.992333333333330.048223448047807541.3146179708715
Winsorized Mean ( 17 / 20 )1.9810.044630751223817244.3864363847597
Winsorized Mean ( 18 / 20 )1.9750.042764299488410546.183382485553
Winsorized Mean ( 19 / 20 )1.943333333333330.036905488289865152.6570280840047
Winsorized Mean ( 20 / 20 )1.946666666666670.035485070200808554.8587520230498
Trimmed Mean ( 1 / 20 )2.014137931034480.076713747537634426.2552410185199
Trimmed Mean ( 2 / 20 )2.010.07513580777758126.7515590695458
Trimmed Mean ( 3 / 20 )2.005925925925930.073360257359040527.3434963035708
Trimmed Mean ( 4 / 20 )2.000384615384620.071590928553595627.9418727456099
Trimmed Mean ( 5 / 20 )1.99480.069463976863066628.7170428484439
Trimmed Mean ( 6 / 20 )1.991250.067659468182596429.4304707602209
Trimmed Mean ( 7 / 20 )1.987608695652170.065881011744391230.1696747366875
Trimmed Mean ( 8 / 20 )1.983636363636360.063813028709631831.0851311048485
Trimmed Mean ( 9 / 20 )1.979285714285710.06122291560942932.3291645715233
Trimmed Mean ( 10 / 20 )1.9750.059231185479722933.3439215170886
Trimmed Mean ( 11 / 20 )1.970789473684210.058418441498424933.7357420556546
Trimmed Mean ( 12 / 20 )1.966388888888890.057444455957752734.2311343384480
Trimmed Mean ( 13 / 20 )1.962647058823530.056376485951033334.813220897241
Trimmed Mean ( 14 / 20 )1.95781250.054915136829695635.6516001420815
Trimmed Mean ( 15 / 20 )1.950666666666670.053569019467816436.4140819833113
Trimmed Mean ( 16 / 20 )1.943571428571430.052101890118235337.3032806326385
Trimmed Mean ( 17 / 20 )1.936538461538460.050471446025503638.3689910639753
Trimmed Mean ( 18 / 20 )1.930.049093226900828539.3129586673682
Trimmed Mean ( 19 / 20 )1.923181818181820.047374287341777340.5954775489751
Trimmed Mean ( 20 / 20 )1.920.046909767807882740.929641942874
Median1.84
Midrange2.1
Midmean - Weighted Average at Xnp1.93870967741935
Midmean - Weighted Average at X(n+1)p1.95066666666667
Midmean - Empirical Distribution Function1.93870967741935
Midmean - Empirical Distribution Function - Averaging1.95066666666667
Midmean - Empirical Distribution Function - Interpolation1.95066666666667
Midmean - Closest Observation1.93870967741935
Midmean - True Basic - Statistics Graphics Toolkit1.95066666666667
Midmean - MS Excel (old versions)1.9578125
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')