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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationWed, 16 Apr 2008 11:50:46 -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/Apr/16/t1208368324erixrtakpxsqu8c.htm/, Retrieved Fri, 10 May 2024 21:30:02 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=10160, Retrieved Fri, 10 May 2024 21:30:02 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact307
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Centrummaten - Ei...] [2008-04-16 17:50:46] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataseries X:
77.5 
77.7 
76.6 
77
76.5 
77.6 
77.8 
76.9 
76.9 
77
77
76.3 
76.5 
77.1 
76.4 
75.4 
75.4 
75.5 
75.5 
75.8 
75.7 
75.9 
76.1 
76
76
75.89 
74.87 
74.9 
74.79 
74.64 
74.09 
74.33 
73.93 
73.78 
72.85 
71.51 
71.5 
71.5 
71.31 
70.85 
70.62 
70.07 
68.83 
68.82 
68.4 
68.21 
67.75 
67.7 
67.42 
66.27 
64.8 
62.69 
62.75 
62.31 
62.4 
61.75 
61.69 
60.39 
59.9 
59.62 
58.97 
58.54 
58.32 
56.03 
53.63 
53.61 
53.48 
53.48 
52.81 
52.8 
52.57 
52.36




Summary of compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'George Udny Yule' @ 72.249.76.132

\begin{tabular}{lllllllll}
\hline
Summary of compuational 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 & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=10160&T=0

[TABLE]
[ROW][C]Summary of compuational 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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=10160&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=10160&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 compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'George Udny Yule' @ 72.249.76.132







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean69.05319444444440.97017968638836771.1756754065887
Geometric Mean68.5330632341875
Harmonic Mean67.9773076118395
Quadratic Mean69.5354033228957
Winsorized Mean ( 1 / 24 )69.05472222222220.96930153232731271.2417342995636
Winsorized Mean ( 2 / 24 )69.05833333333330.9674330376393671.3830628545031
Winsorized Mean ( 3 / 24 )69.05458333333330.96681903318986571.4245178909012
Winsorized Mean ( 4 / 24 )69.06958333333330.95545434950430772.2897785427079
Winsorized Mean ( 5 / 24 )69.06263888888890.95463669549498572.3444208826264
Winsorized Mean ( 6 / 24 )69.07347222222220.95215237105429372.5445572810358
Winsorized Mean ( 7 / 24 )69.07541666666670.95170775458484872.5804915783193
Winsorized Mean ( 8 / 24 )69.33097222222220.89182696026902377.7403860960968
Winsorized Mean ( 9 / 24 )69.61722222222220.83437583200763283.4362880031087
Winsorized Mean ( 10 / 24 )69.60611111111110.82351710413104684.522969543611
Winsorized Mean ( 11 / 24 )69.65652777777780.80936749971684586.0629167864375
Winsorized Mean ( 12 / 24 )69.76486111111110.78948766079747588.3672596486694
Winsorized Mean ( 13 / 24 )69.79736111111110.77822095561180389.6883598517847
Winsorized Mean ( 14 / 24 )69.87319444444440.75898088810777592.0618628733145
Winsorized Mean ( 15 / 24 )70.10236111111110.70745818605612599.090465688031
Winsorized Mean ( 16 / 24 )70.09347222222220.70258421266704899.7652252334899
Winsorized Mean ( 17 / 24 )70.22569444444440.680694774931675103.167670783860
Winsorized Mean ( 18 / 24 )70.22319444444440.674036808479918104.183026150769
Winsorized Mean ( 19 / 24 )70.29708333333330.661267823568848106.306523359842
Winsorized Mean ( 20 / 24 )70.288750.655598853499381107.213045942379
Winsorized Mean ( 21 / 24 )70.85750.5577253977784127.047289369013
Winsorized Mean ( 22 / 24 )71.24555555555560.483145296468428147.461966568500
Winsorized Mean ( 23 / 24 )71.61291666666670.431266488310592166.052588382643
Winsorized Mean ( 24 / 24 )71.67291666666670.414344818973488172.97891365996
Trimmed Mean ( 1 / 24 )69.16671428571430.96045964068471272.0141808732383
Trimmed Mean ( 2 / 24 )69.28529411764710.94937337752161972.980026360671
Trimmed Mean ( 3 / 24 )69.40909090909090.93674742853193974.0958435486374
Trimmed Mean ( 4 / 24 )69.542031250.92129957975628275.482538772455
Trimmed Mean ( 5 / 24 )69.67919354838710.90624119240088876.8881332394385
Trimmed Mean ( 6 / 24 )69.82716666666670.88756841358552678.67243313063
Trimmed Mean ( 7 / 24 )69.98310344827590.86486794612852180.9176750757696
Trimmed Mean ( 8 / 24 )70.14982142857140.83639984888355383.871155072791
Trimmed Mean ( 9 / 24 )70.28629629629630.81665046389164886.0665601796827
Trimmed Mean ( 10 / 24 )70.38923076923080.805625715718987.3721250399994
Trimmed Mean ( 11 / 24 )70.5020.79324217163306688.8782802039582
Trimmed Mean ( 12 / 24 )70.61729166666670.77984931825508490.5524824009247
Trimmed Mean ( 13 / 24 )70.72847826086960.766416088060492.2846993463628
Trimmed Mean ( 14 / 24 )70.84568181818180.75057352262624994.388730327568
Trimmed Mean ( 15 / 24 )70.96476190476190.73339609366869996.7618487709307
Trimmed Mean ( 16 / 24 )71.068250.72208369139026798.4210706423356
Trimmed Mean ( 17 / 24 )71.18368421052630.7064694361125100.759750630161
Trimmed Mean ( 18 / 24 )71.29638888888890.689684095245474103.375428519216
Trimmed Mean ( 19 / 24 )71.42264705882350.666525739403676107.156622522520
Trimmed Mean ( 20 / 24 )71.55593750.636325587970695112.451768171384
Trimmed Mean ( 21 / 24 )71.7080.592501690186251121.025815095074
Trimmed Mean ( 22 / 24 )71.81214285714290.565147908050894127.067873443629
Trimmed Mean ( 23 / 24 )71.88346153846150.550541814888596130.568577344134
Trimmed Mean ( 24 / 24 )71.918750.545038328827712131.951729256703
Median71.505
Midrange65.08
Midmean - Weighted Average at Xnp71.0535135135135
Midmean - Weighted Average at X(n+1)p71.2963888888889
Midmean - Empirical Distribution Function71.0535135135135
Midmean - Empirical Distribution Function - Averaging71.2963888888889
Midmean - Empirical Distribution Function - Interpolation71.2963888888889
Midmean - Closest Observation71.0535135135135
Midmean - True Basic - Statistics Graphics Toolkit71.2963888888889
Midmean - MS Excel (old versions)71.3071794871795
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 69.0531944444444 & 0.970179686388367 & 71.1756754065887 \tabularnewline
Geometric Mean & 68.5330632341875 &  &  \tabularnewline
Harmonic Mean & 67.9773076118395 &  &  \tabularnewline
Quadratic Mean & 69.5354033228957 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 69.0547222222222 & 0.969301532327312 & 71.2417342995636 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 69.0583333333333 & 0.96743303763936 & 71.3830628545031 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 69.0545833333333 & 0.966819033189865 & 71.4245178909012 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 69.0695833333333 & 0.955454349504307 & 72.2897785427079 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 69.0626388888889 & 0.954636695494985 & 72.3444208826264 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 69.0734722222222 & 0.952152371054293 & 72.5445572810358 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 69.0754166666667 & 0.951707754584848 & 72.5804915783193 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 69.3309722222222 & 0.891826960269023 & 77.7403860960968 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 69.6172222222222 & 0.834375832007632 & 83.4362880031087 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 69.6061111111111 & 0.823517104131046 & 84.522969543611 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 69.6565277777778 & 0.809367499716845 & 86.0629167864375 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 69.7648611111111 & 0.789487660797475 & 88.3672596486694 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 69.7973611111111 & 0.778220955611803 & 89.6883598517847 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 69.8731944444444 & 0.758980888107775 & 92.0618628733145 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 70.1023611111111 & 0.707458186056125 & 99.090465688031 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 70.0934722222222 & 0.702584212667048 & 99.7652252334899 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 70.2256944444444 & 0.680694774931675 & 103.167670783860 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 70.2231944444444 & 0.674036808479918 & 104.183026150769 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 70.2970833333333 & 0.661267823568848 & 106.306523359842 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 70.28875 & 0.655598853499381 & 107.213045942379 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 70.8575 & 0.5577253977784 & 127.047289369013 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 71.2455555555556 & 0.483145296468428 & 147.461966568500 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 71.6129166666667 & 0.431266488310592 & 166.052588382643 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 71.6729166666667 & 0.414344818973488 & 172.97891365996 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 69.1667142857143 & 0.960459640684712 & 72.0141808732383 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 69.2852941176471 & 0.949373377521619 & 72.980026360671 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 69.4090909090909 & 0.936747428531939 & 74.0958435486374 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 69.54203125 & 0.921299579756282 & 75.482538772455 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 69.6791935483871 & 0.906241192400888 & 76.8881332394385 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 69.8271666666667 & 0.887568413585526 & 78.67243313063 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 69.9831034482759 & 0.864867946128521 & 80.9176750757696 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 70.1498214285714 & 0.836399848883553 & 83.871155072791 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 70.2862962962963 & 0.816650463891648 & 86.0665601796827 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 70.3892307692308 & 0.8056257157189 & 87.3721250399994 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 70.502 & 0.793242171633066 & 88.8782802039582 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 70.6172916666667 & 0.779849318255084 & 90.5524824009247 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 70.7284782608696 & 0.7664160880604 & 92.2846993463628 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 70.8456818181818 & 0.750573522626249 & 94.388730327568 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 70.9647619047619 & 0.733396093668699 & 96.7618487709307 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 71.06825 & 0.722083691390267 & 98.4210706423356 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 71.1836842105263 & 0.7064694361125 & 100.759750630161 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 71.2963888888889 & 0.689684095245474 & 103.375428519216 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 71.4226470588235 & 0.666525739403676 & 107.156622522520 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 71.5559375 & 0.636325587970695 & 112.451768171384 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 71.708 & 0.592501690186251 & 121.025815095074 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 71.8121428571429 & 0.565147908050894 & 127.067873443629 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 71.8834615384615 & 0.550541814888596 & 130.568577344134 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 71.91875 & 0.545038328827712 & 131.951729256703 \tabularnewline
Median & 71.505 &  &  \tabularnewline
Midrange & 65.08 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 71.0535135135135 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 71.2963888888889 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 71.0535135135135 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 71.2963888888889 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 71.2963888888889 &  &  \tabularnewline
Midmean - Closest Observation & 71.0535135135135 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 71.2963888888889 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 71.3071794871795 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=10160&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]69.0531944444444[/C][C]0.970179686388367[/C][C]71.1756754065887[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]68.5330632341875[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]67.9773076118395[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]69.5354033228957[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]69.0547222222222[/C][C]0.969301532327312[/C][C]71.2417342995636[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]69.0583333333333[/C][C]0.96743303763936[/C][C]71.3830628545031[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]69.0545833333333[/C][C]0.966819033189865[/C][C]71.4245178909012[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]69.0695833333333[/C][C]0.955454349504307[/C][C]72.2897785427079[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]69.0626388888889[/C][C]0.954636695494985[/C][C]72.3444208826264[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]69.0734722222222[/C][C]0.952152371054293[/C][C]72.5445572810358[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]69.0754166666667[/C][C]0.951707754584848[/C][C]72.5804915783193[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]69.3309722222222[/C][C]0.891826960269023[/C][C]77.7403860960968[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]69.6172222222222[/C][C]0.834375832007632[/C][C]83.4362880031087[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]69.6061111111111[/C][C]0.823517104131046[/C][C]84.522969543611[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]69.6565277777778[/C][C]0.809367499716845[/C][C]86.0629167864375[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]69.7648611111111[/C][C]0.789487660797475[/C][C]88.3672596486694[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]69.7973611111111[/C][C]0.778220955611803[/C][C]89.6883598517847[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]69.8731944444444[/C][C]0.758980888107775[/C][C]92.0618628733145[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]70.1023611111111[/C][C]0.707458186056125[/C][C]99.090465688031[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]70.0934722222222[/C][C]0.702584212667048[/C][C]99.7652252334899[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]70.2256944444444[/C][C]0.680694774931675[/C][C]103.167670783860[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]70.2231944444444[/C][C]0.674036808479918[/C][C]104.183026150769[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]70.2970833333333[/C][C]0.661267823568848[/C][C]106.306523359842[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]70.28875[/C][C]0.655598853499381[/C][C]107.213045942379[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]70.8575[/C][C]0.5577253977784[/C][C]127.047289369013[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]71.2455555555556[/C][C]0.483145296468428[/C][C]147.461966568500[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]71.6129166666667[/C][C]0.431266488310592[/C][C]166.052588382643[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]71.6729166666667[/C][C]0.414344818973488[/C][C]172.97891365996[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]69.1667142857143[/C][C]0.960459640684712[/C][C]72.0141808732383[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]69.2852941176471[/C][C]0.949373377521619[/C][C]72.980026360671[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]69.4090909090909[/C][C]0.936747428531939[/C][C]74.0958435486374[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]69.54203125[/C][C]0.921299579756282[/C][C]75.482538772455[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]69.6791935483871[/C][C]0.906241192400888[/C][C]76.8881332394385[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]69.8271666666667[/C][C]0.887568413585526[/C][C]78.67243313063[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]69.9831034482759[/C][C]0.864867946128521[/C][C]80.9176750757696[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]70.1498214285714[/C][C]0.836399848883553[/C][C]83.871155072791[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]70.2862962962963[/C][C]0.816650463891648[/C][C]86.0665601796827[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]70.3892307692308[/C][C]0.8056257157189[/C][C]87.3721250399994[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]70.502[/C][C]0.793242171633066[/C][C]88.8782802039582[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]70.6172916666667[/C][C]0.779849318255084[/C][C]90.5524824009247[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]70.7284782608696[/C][C]0.7664160880604[/C][C]92.2846993463628[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]70.8456818181818[/C][C]0.750573522626249[/C][C]94.388730327568[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]70.9647619047619[/C][C]0.733396093668699[/C][C]96.7618487709307[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]71.06825[/C][C]0.722083691390267[/C][C]98.4210706423356[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]71.1836842105263[/C][C]0.7064694361125[/C][C]100.759750630161[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]71.2963888888889[/C][C]0.689684095245474[/C][C]103.375428519216[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]71.4226470588235[/C][C]0.666525739403676[/C][C]107.156622522520[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]71.5559375[/C][C]0.636325587970695[/C][C]112.451768171384[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]71.708[/C][C]0.592501690186251[/C][C]121.025815095074[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]71.8121428571429[/C][C]0.565147908050894[/C][C]127.067873443629[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]71.8834615384615[/C][C]0.550541814888596[/C][C]130.568577344134[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]71.91875[/C][C]0.545038328827712[/C][C]131.951729256703[/C][/ROW]
[ROW][C]Median[/C][C]71.505[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]65.08[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]71.0535135135135[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]71.2963888888889[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]71.0535135135135[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]71.2963888888889[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]71.2963888888889[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]71.0535135135135[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]71.2963888888889[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]71.3071794871795[/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=10160&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=10160&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 Mean69.05319444444440.97017968638836771.1756754065887
Geometric Mean68.5330632341875
Harmonic Mean67.9773076118395
Quadratic Mean69.5354033228957
Winsorized Mean ( 1 / 24 )69.05472222222220.96930153232731271.2417342995636
Winsorized Mean ( 2 / 24 )69.05833333333330.9674330376393671.3830628545031
Winsorized Mean ( 3 / 24 )69.05458333333330.96681903318986571.4245178909012
Winsorized Mean ( 4 / 24 )69.06958333333330.95545434950430772.2897785427079
Winsorized Mean ( 5 / 24 )69.06263888888890.95463669549498572.3444208826264
Winsorized Mean ( 6 / 24 )69.07347222222220.95215237105429372.5445572810358
Winsorized Mean ( 7 / 24 )69.07541666666670.95170775458484872.5804915783193
Winsorized Mean ( 8 / 24 )69.33097222222220.89182696026902377.7403860960968
Winsorized Mean ( 9 / 24 )69.61722222222220.83437583200763283.4362880031087
Winsorized Mean ( 10 / 24 )69.60611111111110.82351710413104684.522969543611
Winsorized Mean ( 11 / 24 )69.65652777777780.80936749971684586.0629167864375
Winsorized Mean ( 12 / 24 )69.76486111111110.78948766079747588.3672596486694
Winsorized Mean ( 13 / 24 )69.79736111111110.77822095561180389.6883598517847
Winsorized Mean ( 14 / 24 )69.87319444444440.75898088810777592.0618628733145
Winsorized Mean ( 15 / 24 )70.10236111111110.70745818605612599.090465688031
Winsorized Mean ( 16 / 24 )70.09347222222220.70258421266704899.7652252334899
Winsorized Mean ( 17 / 24 )70.22569444444440.680694774931675103.167670783860
Winsorized Mean ( 18 / 24 )70.22319444444440.674036808479918104.183026150769
Winsorized Mean ( 19 / 24 )70.29708333333330.661267823568848106.306523359842
Winsorized Mean ( 20 / 24 )70.288750.655598853499381107.213045942379
Winsorized Mean ( 21 / 24 )70.85750.5577253977784127.047289369013
Winsorized Mean ( 22 / 24 )71.24555555555560.483145296468428147.461966568500
Winsorized Mean ( 23 / 24 )71.61291666666670.431266488310592166.052588382643
Winsorized Mean ( 24 / 24 )71.67291666666670.414344818973488172.97891365996
Trimmed Mean ( 1 / 24 )69.16671428571430.96045964068471272.0141808732383
Trimmed Mean ( 2 / 24 )69.28529411764710.94937337752161972.980026360671
Trimmed Mean ( 3 / 24 )69.40909090909090.93674742853193974.0958435486374
Trimmed Mean ( 4 / 24 )69.542031250.92129957975628275.482538772455
Trimmed Mean ( 5 / 24 )69.67919354838710.90624119240088876.8881332394385
Trimmed Mean ( 6 / 24 )69.82716666666670.88756841358552678.67243313063
Trimmed Mean ( 7 / 24 )69.98310344827590.86486794612852180.9176750757696
Trimmed Mean ( 8 / 24 )70.14982142857140.83639984888355383.871155072791
Trimmed Mean ( 9 / 24 )70.28629629629630.81665046389164886.0665601796827
Trimmed Mean ( 10 / 24 )70.38923076923080.805625715718987.3721250399994
Trimmed Mean ( 11 / 24 )70.5020.79324217163306688.8782802039582
Trimmed Mean ( 12 / 24 )70.61729166666670.77984931825508490.5524824009247
Trimmed Mean ( 13 / 24 )70.72847826086960.766416088060492.2846993463628
Trimmed Mean ( 14 / 24 )70.84568181818180.75057352262624994.388730327568
Trimmed Mean ( 15 / 24 )70.96476190476190.73339609366869996.7618487709307
Trimmed Mean ( 16 / 24 )71.068250.72208369139026798.4210706423356
Trimmed Mean ( 17 / 24 )71.18368421052630.7064694361125100.759750630161
Trimmed Mean ( 18 / 24 )71.29638888888890.689684095245474103.375428519216
Trimmed Mean ( 19 / 24 )71.42264705882350.666525739403676107.156622522520
Trimmed Mean ( 20 / 24 )71.55593750.636325587970695112.451768171384
Trimmed Mean ( 21 / 24 )71.7080.592501690186251121.025815095074
Trimmed Mean ( 22 / 24 )71.81214285714290.565147908050894127.067873443629
Trimmed Mean ( 23 / 24 )71.88346153846150.550541814888596130.568577344134
Trimmed Mean ( 24 / 24 )71.918750.545038328827712131.951729256703
Median71.505
Midrange65.08
Midmean - Weighted Average at Xnp71.0535135135135
Midmean - Weighted Average at X(n+1)p71.2963888888889
Midmean - Empirical Distribution Function71.0535135135135
Midmean - Empirical Distribution Function - Averaging71.2963888888889
Midmean - Empirical Distribution Function - Interpolation71.2963888888889
Midmean - Closest Observation71.0535135135135
Midmean - True Basic - Statistics Graphics Toolkit71.2963888888889
Midmean - MS Excel (old versions)71.3071794871795
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')