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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationMon, 04 Mar 2013 14:44:33 -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/2013/Mar/04/t1362426371izh2fz778f5k3mf.htm/, Retrieved Sun, 28 Apr 2024 05:09:36 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=207338, Retrieved Sun, 28 Apr 2024 05:09:36 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact103
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [centrummaten] [2013-03-04 19:44:33] [8907525eeb8291a8059cdce9cf2ca306] [Current]
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Dataseries X:
8,27
8,25
8,22
8,21
8,12
8,16
8,15
8,1
8,09
8,02
8,03
7,98
7,95
7,92
7,96
7,96
7,94
7,83
7,77
7,8
7,78
7,78
7,8
7,81
7,95
8,02
7,99
8,01
8,03
8,05
8,05
8,06
8,07
7,99
8
8,01
8
8,09
8,1
8,12
8,29
8,32
8,36
8,38
8,48
8,45
8,41
8,38
8,38
8,34
8,41
8,34
8,22
8,27
8,18
8,19
8,19
8,13
8,06
7,99
8
7,98
7,92
7,93
7,9
7,86
7,88
7,88
7,93
7,91
7,89
7,93




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Maurice George Kendall' @ kendall.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 & 2 seconds \tabularnewline
R Server & 'Sir Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=207338&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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Maurice George Kendall' @ kendall.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=207338&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=207338&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 time2 seconds
R Server'Sir Maurice George Kendall' @ kendall.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean8.07250.0216158215254265373.453305510706
Geometric Mean8.07045774031594
Harmonic Mean8.06842809864638
Quadratic Mean8.07455451127525
Winsorized Mean ( 1 / 24 )8.072222222222220.0214818974470906375.768585717529
Winsorized Mean ( 2 / 24 )8.071111111111110.0212192477985062380.367446940287
Winsorized Mean ( 3 / 24 )8.071944444444440.0210629495525495383.229538878491
Winsorized Mean ( 4 / 24 )8.070277777777780.0206988355404767389.890424608492
Winsorized Mean ( 5 / 24 )8.070972222222220.0205729357538722392.310184544427
Winsorized Mean ( 6 / 24 )8.072638888888890.0202835851975092397.988758411417
Winsorized Mean ( 7 / 24 )8.073611111111110.0194015567712215416.132128277808
Winsorized Mean ( 8 / 24 )8.073611111111110.0186111111111111433.805970149254
Winsorized Mean ( 9 / 24 )8.073611111111110.0186111111111111433.805970149254
Winsorized Mean ( 10 / 24 )8.072222222222220.0178579228286823452.024700725949
Winsorized Mean ( 11 / 24 )8.069166666666670.0167658434168194481.286056779685
Winsorized Mean ( 12 / 24 )8.06750.0159232681784729506.648503911193
Winsorized Mean ( 13 / 24 )8.069305555555560.0156763609863704514.743540453764
Winsorized Mean ( 14 / 24 )8.065416666666670.0149881767435878538.118598722635
Winsorized Mean ( 15 / 24 )8.061250.0136493327323192590.596636340501
Winsorized Mean ( 16 / 24 )8.061250.0136493327323192590.596636340501
Winsorized Mean ( 17 / 24 )8.058888888888890.0132664926079653607.461906250207
Winsorized Mean ( 18 / 24 )8.056388888888890.0121372329600396663.774759487073
Winsorized Mean ( 19 / 24 )8.059027777777780.0117870378565946683.719512554967
Winsorized Mean ( 20 / 24 )8.056250.0113564344442428709.399595405946
Winsorized Mean ( 21 / 24 )8.053333333333330.0100915217208124798.029628844226
Winsorized Mean ( 22 / 24 )8.050277777777780.00964140340984417834.9694993115
Winsorized Mean ( 23 / 24 )8.050277777777780.007896960207898121019.41475781103
Winsorized Mean ( 24 / 24 )8.046944444444440.00742895113066141083.18715561776
Trimmed Mean ( 1 / 24 )8.0710.0210039432362111384.261179400136
Trimmed Mean ( 2 / 24 )8.069705882352940.020434235277806394.911078033715
Trimmed Mean ( 3 / 24 )8.068939393939390.0199219090694986405.028422014702
Trimmed Mean ( 4 / 24 )8.06781250.0193770400231698416.359386694409
Trimmed Mean ( 5 / 24 )8.067096774193550.0188559446092204427.827772163099
Trimmed Mean ( 6 / 24 )8.066166666666670.0182622015038297441.686434407985
Trimmed Mean ( 7 / 24 )8.06482758620690.0176187379273623457.741503361715
Trimmed Mean ( 8 / 24 )8.063214285714290.0170657763832224472.478608921733
Trimmed Mean ( 9 / 24 )8.061481481481480.0165792411592001486.239472848735
Trimmed Mean ( 10 / 24 )8.059615384615380.0159655585625997504.812616045611
Trimmed Mean ( 11 / 24 )8.05780.0153763401606069524.038875040206
Trimmed Mean ( 12 / 24 )8.056250.0148921209354963540.973984491184
Trimmed Mean ( 13 / 24 )8.054782608695650.0144654815865194556.827822186165
Trimmed Mean ( 14 / 24 )8.052954545454550.0139562118954565577.015783779852
Trimmed Mean ( 15 / 24 )8.051428571428570.0134586363715491598.235092260084
Trimmed Mean ( 16 / 24 )8.050250.0131240994807067613.394466556305
Trimmed Mean ( 17 / 24 )8.048947368421050.0126602921640505635.763161238601
Trimmed Mean ( 18 / 24 )8.047777777777780.0121244283852242663.765541935607
Trimmed Mean ( 19 / 24 )8.046764705882350.0116906089056059688.310144566018
Trimmed Mean ( 20 / 24 )8.04531250.0111531166535955721.351058173177
Trimmed Mean ( 21 / 24 )8.0440.0105110779000391765.287830277626
Trimmed Mean ( 22 / 24 )8.042857142857140.00999811017668159804.437738805414
Trimmed Mean ( 23 / 24 )8.041923076923080.00938114690002043857.243060217462
Trimmed Mean ( 24 / 24 )8.040833333333330.00908727145052124884.845729228449
Median8.03
Midrange8.125
Midmean - Weighted Average at Xnp8.03871794871795
Midmean - Weighted Average at X(n+1)p8.04777777777778
Midmean - Empirical Distribution Function8.03871794871795
Midmean - Empirical Distribution Function - Averaging8.04777777777778
Midmean - Empirical Distribution Function - Interpolation8.04777777777778
Midmean - Closest Observation8.03871794871795
Midmean - True Basic - Statistics Graphics Toolkit8.04777777777778
Midmean - MS Excel (old versions)8.043
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 8.0725 & 0.0216158215254265 & 373.453305510706 \tabularnewline
Geometric Mean & 8.07045774031594 &  &  \tabularnewline
Harmonic Mean & 8.06842809864638 &  &  \tabularnewline
Quadratic Mean & 8.07455451127525 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 8.07222222222222 & 0.0214818974470906 & 375.768585717529 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 8.07111111111111 & 0.0212192477985062 & 380.367446940287 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 8.07194444444444 & 0.0210629495525495 & 383.229538878491 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 8.07027777777778 & 0.0206988355404767 & 389.890424608492 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 8.07097222222222 & 0.0205729357538722 & 392.310184544427 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 8.07263888888889 & 0.0202835851975092 & 397.988758411417 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 8.07361111111111 & 0.0194015567712215 & 416.132128277808 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 8.07361111111111 & 0.0186111111111111 & 433.805970149254 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 8.07361111111111 & 0.0186111111111111 & 433.805970149254 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 8.07222222222222 & 0.0178579228286823 & 452.024700725949 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 8.06916666666667 & 0.0167658434168194 & 481.286056779685 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 8.0675 & 0.0159232681784729 & 506.648503911193 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 8.06930555555556 & 0.0156763609863704 & 514.743540453764 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 8.06541666666667 & 0.0149881767435878 & 538.118598722635 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 8.06125 & 0.0136493327323192 & 590.596636340501 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 8.06125 & 0.0136493327323192 & 590.596636340501 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 8.05888888888889 & 0.0132664926079653 & 607.461906250207 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 8.05638888888889 & 0.0121372329600396 & 663.774759487073 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 8.05902777777778 & 0.0117870378565946 & 683.719512554967 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 8.05625 & 0.0113564344442428 & 709.399595405946 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 8.05333333333333 & 0.0100915217208124 & 798.029628844226 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 8.05027777777778 & 0.00964140340984417 & 834.9694993115 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 8.05027777777778 & 0.00789696020789812 & 1019.41475781103 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 8.04694444444444 & 0.0074289511306614 & 1083.18715561776 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 8.071 & 0.0210039432362111 & 384.261179400136 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 8.06970588235294 & 0.020434235277806 & 394.911078033715 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 8.06893939393939 & 0.0199219090694986 & 405.028422014702 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 8.0678125 & 0.0193770400231698 & 416.359386694409 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 8.06709677419355 & 0.0188559446092204 & 427.827772163099 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 8.06616666666667 & 0.0182622015038297 & 441.686434407985 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 8.0648275862069 & 0.0176187379273623 & 457.741503361715 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 8.06321428571429 & 0.0170657763832224 & 472.478608921733 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 8.06148148148148 & 0.0165792411592001 & 486.239472848735 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 8.05961538461538 & 0.0159655585625997 & 504.812616045611 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 8.0578 & 0.0153763401606069 & 524.038875040206 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 8.05625 & 0.0148921209354963 & 540.973984491184 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 8.05478260869565 & 0.0144654815865194 & 556.827822186165 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 8.05295454545455 & 0.0139562118954565 & 577.015783779852 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 8.05142857142857 & 0.0134586363715491 & 598.235092260084 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 8.05025 & 0.0131240994807067 & 613.394466556305 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 8.04894736842105 & 0.0126602921640505 & 635.763161238601 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 8.04777777777778 & 0.0121244283852242 & 663.765541935607 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 8.04676470588235 & 0.0116906089056059 & 688.310144566018 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 8.0453125 & 0.0111531166535955 & 721.351058173177 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 8.044 & 0.0105110779000391 & 765.287830277626 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 8.04285714285714 & 0.00999811017668159 & 804.437738805414 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 8.04192307692308 & 0.00938114690002043 & 857.243060217462 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 8.04083333333333 & 0.00908727145052124 & 884.845729228449 \tabularnewline
Median & 8.03 &  &  \tabularnewline
Midrange & 8.125 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 8.03871794871795 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 8.04777777777778 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 8.03871794871795 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 8.04777777777778 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 8.04777777777778 &  &  \tabularnewline
Midmean - Closest Observation & 8.03871794871795 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 8.04777777777778 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 8.043 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=207338&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]8.0725[/C][C]0.0216158215254265[/C][C]373.453305510706[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]8.07045774031594[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]8.06842809864638[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]8.07455451127525[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]8.07222222222222[/C][C]0.0214818974470906[/C][C]375.768585717529[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]8.07111111111111[/C][C]0.0212192477985062[/C][C]380.367446940287[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]8.07194444444444[/C][C]0.0210629495525495[/C][C]383.229538878491[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]8.07027777777778[/C][C]0.0206988355404767[/C][C]389.890424608492[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]8.07097222222222[/C][C]0.0205729357538722[/C][C]392.310184544427[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]8.07263888888889[/C][C]0.0202835851975092[/C][C]397.988758411417[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]8.07361111111111[/C][C]0.0194015567712215[/C][C]416.132128277808[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]8.07361111111111[/C][C]0.0186111111111111[/C][C]433.805970149254[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]8.07361111111111[/C][C]0.0186111111111111[/C][C]433.805970149254[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]8.07222222222222[/C][C]0.0178579228286823[/C][C]452.024700725949[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]8.06916666666667[/C][C]0.0167658434168194[/C][C]481.286056779685[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]8.0675[/C][C]0.0159232681784729[/C][C]506.648503911193[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]8.06930555555556[/C][C]0.0156763609863704[/C][C]514.743540453764[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]8.06541666666667[/C][C]0.0149881767435878[/C][C]538.118598722635[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]8.06125[/C][C]0.0136493327323192[/C][C]590.596636340501[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]8.06125[/C][C]0.0136493327323192[/C][C]590.596636340501[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]8.05888888888889[/C][C]0.0132664926079653[/C][C]607.461906250207[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]8.05638888888889[/C][C]0.0121372329600396[/C][C]663.774759487073[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]8.05902777777778[/C][C]0.0117870378565946[/C][C]683.719512554967[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]8.05625[/C][C]0.0113564344442428[/C][C]709.399595405946[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]8.05333333333333[/C][C]0.0100915217208124[/C][C]798.029628844226[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]8.05027777777778[/C][C]0.00964140340984417[/C][C]834.9694993115[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]8.05027777777778[/C][C]0.00789696020789812[/C][C]1019.41475781103[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]8.04694444444444[/C][C]0.0074289511306614[/C][C]1083.18715561776[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]8.071[/C][C]0.0210039432362111[/C][C]384.261179400136[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]8.06970588235294[/C][C]0.020434235277806[/C][C]394.911078033715[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]8.06893939393939[/C][C]0.0199219090694986[/C][C]405.028422014702[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]8.0678125[/C][C]0.0193770400231698[/C][C]416.359386694409[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]8.06709677419355[/C][C]0.0188559446092204[/C][C]427.827772163099[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]8.06616666666667[/C][C]0.0182622015038297[/C][C]441.686434407985[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]8.0648275862069[/C][C]0.0176187379273623[/C][C]457.741503361715[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]8.06321428571429[/C][C]0.0170657763832224[/C][C]472.478608921733[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]8.06148148148148[/C][C]0.0165792411592001[/C][C]486.239472848735[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]8.05961538461538[/C][C]0.0159655585625997[/C][C]504.812616045611[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]8.0578[/C][C]0.0153763401606069[/C][C]524.038875040206[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]8.05625[/C][C]0.0148921209354963[/C][C]540.973984491184[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]8.05478260869565[/C][C]0.0144654815865194[/C][C]556.827822186165[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]8.05295454545455[/C][C]0.0139562118954565[/C][C]577.015783779852[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]8.05142857142857[/C][C]0.0134586363715491[/C][C]598.235092260084[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]8.05025[/C][C]0.0131240994807067[/C][C]613.394466556305[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]8.04894736842105[/C][C]0.0126602921640505[/C][C]635.763161238601[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]8.04777777777778[/C][C]0.0121244283852242[/C][C]663.765541935607[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]8.04676470588235[/C][C]0.0116906089056059[/C][C]688.310144566018[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]8.0453125[/C][C]0.0111531166535955[/C][C]721.351058173177[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]8.044[/C][C]0.0105110779000391[/C][C]765.287830277626[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]8.04285714285714[/C][C]0.00999811017668159[/C][C]804.437738805414[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]8.04192307692308[/C][C]0.00938114690002043[/C][C]857.243060217462[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]8.04083333333333[/C][C]0.00908727145052124[/C][C]884.845729228449[/C][/ROW]
[ROW][C]Median[/C][C]8.03[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]8.125[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]8.03871794871795[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]8.04777777777778[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]8.03871794871795[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]8.04777777777778[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]8.04777777777778[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]8.03871794871795[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]8.04777777777778[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]8.043[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]72[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=207338&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=207338&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 Mean8.07250.0216158215254265373.453305510706
Geometric Mean8.07045774031594
Harmonic Mean8.06842809864638
Quadratic Mean8.07455451127525
Winsorized Mean ( 1 / 24 )8.072222222222220.0214818974470906375.768585717529
Winsorized Mean ( 2 / 24 )8.071111111111110.0212192477985062380.367446940287
Winsorized Mean ( 3 / 24 )8.071944444444440.0210629495525495383.229538878491
Winsorized Mean ( 4 / 24 )8.070277777777780.0206988355404767389.890424608492
Winsorized Mean ( 5 / 24 )8.070972222222220.0205729357538722392.310184544427
Winsorized Mean ( 6 / 24 )8.072638888888890.0202835851975092397.988758411417
Winsorized Mean ( 7 / 24 )8.073611111111110.0194015567712215416.132128277808
Winsorized Mean ( 8 / 24 )8.073611111111110.0186111111111111433.805970149254
Winsorized Mean ( 9 / 24 )8.073611111111110.0186111111111111433.805970149254
Winsorized Mean ( 10 / 24 )8.072222222222220.0178579228286823452.024700725949
Winsorized Mean ( 11 / 24 )8.069166666666670.0167658434168194481.286056779685
Winsorized Mean ( 12 / 24 )8.06750.0159232681784729506.648503911193
Winsorized Mean ( 13 / 24 )8.069305555555560.0156763609863704514.743540453764
Winsorized Mean ( 14 / 24 )8.065416666666670.0149881767435878538.118598722635
Winsorized Mean ( 15 / 24 )8.061250.0136493327323192590.596636340501
Winsorized Mean ( 16 / 24 )8.061250.0136493327323192590.596636340501
Winsorized Mean ( 17 / 24 )8.058888888888890.0132664926079653607.461906250207
Winsorized Mean ( 18 / 24 )8.056388888888890.0121372329600396663.774759487073
Winsorized Mean ( 19 / 24 )8.059027777777780.0117870378565946683.719512554967
Winsorized Mean ( 20 / 24 )8.056250.0113564344442428709.399595405946
Winsorized Mean ( 21 / 24 )8.053333333333330.0100915217208124798.029628844226
Winsorized Mean ( 22 / 24 )8.050277777777780.00964140340984417834.9694993115
Winsorized Mean ( 23 / 24 )8.050277777777780.007896960207898121019.41475781103
Winsorized Mean ( 24 / 24 )8.046944444444440.00742895113066141083.18715561776
Trimmed Mean ( 1 / 24 )8.0710.0210039432362111384.261179400136
Trimmed Mean ( 2 / 24 )8.069705882352940.020434235277806394.911078033715
Trimmed Mean ( 3 / 24 )8.068939393939390.0199219090694986405.028422014702
Trimmed Mean ( 4 / 24 )8.06781250.0193770400231698416.359386694409
Trimmed Mean ( 5 / 24 )8.067096774193550.0188559446092204427.827772163099
Trimmed Mean ( 6 / 24 )8.066166666666670.0182622015038297441.686434407985
Trimmed Mean ( 7 / 24 )8.06482758620690.0176187379273623457.741503361715
Trimmed Mean ( 8 / 24 )8.063214285714290.0170657763832224472.478608921733
Trimmed Mean ( 9 / 24 )8.061481481481480.0165792411592001486.239472848735
Trimmed Mean ( 10 / 24 )8.059615384615380.0159655585625997504.812616045611
Trimmed Mean ( 11 / 24 )8.05780.0153763401606069524.038875040206
Trimmed Mean ( 12 / 24 )8.056250.0148921209354963540.973984491184
Trimmed Mean ( 13 / 24 )8.054782608695650.0144654815865194556.827822186165
Trimmed Mean ( 14 / 24 )8.052954545454550.0139562118954565577.015783779852
Trimmed Mean ( 15 / 24 )8.051428571428570.0134586363715491598.235092260084
Trimmed Mean ( 16 / 24 )8.050250.0131240994807067613.394466556305
Trimmed Mean ( 17 / 24 )8.048947368421050.0126602921640505635.763161238601
Trimmed Mean ( 18 / 24 )8.047777777777780.0121244283852242663.765541935607
Trimmed Mean ( 19 / 24 )8.046764705882350.0116906089056059688.310144566018
Trimmed Mean ( 20 / 24 )8.04531250.0111531166535955721.351058173177
Trimmed Mean ( 21 / 24 )8.0440.0105110779000391765.287830277626
Trimmed Mean ( 22 / 24 )8.042857142857140.00999811017668159804.437738805414
Trimmed Mean ( 23 / 24 )8.041923076923080.00938114690002043857.243060217462
Trimmed Mean ( 24 / 24 )8.040833333333330.00908727145052124884.845729228449
Median8.03
Midrange8.125
Midmean - Weighted Average at Xnp8.03871794871795
Midmean - Weighted Average at X(n+1)p8.04777777777778
Midmean - Empirical Distribution Function8.03871794871795
Midmean - Empirical Distribution Function - Averaging8.04777777777778
Midmean - Empirical Distribution Function - Interpolation8.04777777777778
Midmean - Closest Observation8.03871794871795
Midmean - True Basic - Statistics Graphics Toolkit8.04777777777778
Midmean - MS Excel (old versions)8.043
Number of observations72



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')