Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationWed, 15 Mar 2017 09:38:54 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2017/Mar/15/t1489570995nk2s3xkik90dbym.htm/, Retrieved Tue, 14 May 2024 09:13:24 +0200
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Tue, 14 May 2024 09:13:24 +0200
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact0
Dataseries X:
101,74
100,73
100,86
100,78
100,76
100,77
100,77
101,93
101,98
102,47
102,59
102,54
102,54
101,29
101,49
101,71
101,98
102,11
102,11
103,13
103,43
103,8
103,99
104,03
104,03
102,58
102,65
102,81
102,98
103,12
103,12
104,33
104,41
104,66
104,81
104,9
100,15
98,74
98,74
98,96
99,34
99,4
99,5
100,5
100,77
101,08
101,39
101,43
101,43
101,29
101,33
101,15
101,25
101,13
101,07
101,33
101,61
101,29
101,39
101,46
101,81
101,78
101,93
102,01
102,03
102,14
101,81
101,52
101,38
101,5
101,65
101,64




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&T=0

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean101.81750.161576344499192630.151030558247
Geometric Mean101.808407353045
Harmonic Mean101.799323993259
Quadratic Mean101.826602109774
Winsorized Mean ( 1 / 24 )101.816250.16124496540769631.438319593849
Winsorized Mean ( 2 / 24 )101.8181944444440.158577070413446642.073877257168
Winsorized Mean ( 3 / 24 )101.8236111111110.152180976186671669.095531271993
Winsorized Mean ( 4 / 24 )101.82250.150365718746069677.165652178695
Winsorized Mean ( 5 / 24 )101.8086111111110.144081640040278706.603638622177
Winsorized Mean ( 6 / 24 )101.8627777777780.133009616155806765.830176206636
Winsorized Mean ( 7 / 24 )101.8929166666670.12637064456706806.302104541345
Winsorized Mean ( 8 / 24 )101.8973611111110.11772308311435865.568233649924
Winsorized Mean ( 9 / 24 )101.8548611111110.107115763992782950.885820297888
Winsorized Mean ( 10 / 24 )101.8145833333330.09866914441042581031.87864799784
Winsorized Mean ( 11 / 24 )101.8130555555560.09838278355741071034.86658817844
Winsorized Mean ( 12 / 24 )101.8130555555560.09838278355741071034.86658817844
Winsorized Mean ( 13 / 24 )101.7895833333330.09347646584809021088.93273199645
Winsorized Mean ( 14 / 24 )101.7720833333330.08531927918945681192.83805841048
Winsorized Mean ( 15 / 24 )101.78250.07337406839179041387.17263783874
Winsorized Mean ( 16 / 24 )101.7713888888890.07087434757231351435.94110386767
Winsorized Mean ( 17 / 24 )101.7808333333330.06889263550566981477.38336015548
Winsorized Mean ( 18 / 24 )101.7758333333330.06660406391657681528.07242304028
Winsorized Mean ( 19 / 24 )101.8022222222220.06323170194419811609.98706490713
Winsorized Mean ( 20 / 24 )101.7938888888890.05870057290697421734.12087562087
Winsorized Mean ( 21 / 24 )101.6976388888890.04392628492885352315.18870884725
Winsorized Mean ( 22 / 24 )101.6884722222220.04263781839174492384.93609799487
Winsorized Mean ( 23 / 24 )101.701250.04098118652100992481.65703908696
Winsorized Mean ( 24 / 24 )101.6745833333330.03731550206084892724.72773292817
Trimmed Mean ( 1 / 24 )101.8174285714290.153957952598407661.332700604398
Trimmed Mean ( 2 / 24 )101.8186764705880.145203968498085701.211389218547
Trimmed Mean ( 3 / 24 )101.8189393939390.136399271438128746.477149917369
Trimmed Mean ( 4 / 24 )101.81718750.128864367594828790.11125728821
Trimmed Mean ( 5 / 24 )101.815645161290.120371279361707845.846664596309
Trimmed Mean ( 6 / 24 )101.8173333333330.112159809983425907.788033417499
Trimmed Mean ( 7 / 24 )101.8079310344830.10557873767957964.284412487183
Trimmed Mean ( 8 / 24 )101.7923214285710.09929262507481931025.17504549677
Trimmed Mean ( 9 / 24 )101.7748148148150.09381641257847391084.82953054386
Trimmed Mean ( 10 / 24 )101.76250.08985612557398331132.50487209371
Trimmed Mean ( 11 / 24 )101.7550.08702486156617711169.26356639616
Trimmed Mean ( 12 / 24 )101.7470833333330.08347025542185171218.96216585312
Trimmed Mean ( 13 / 24 )101.738478260870.07886634409584311290.01134041703
Trimmed Mean ( 14 / 24 )101.7320454545450.0741880499781591371.27267106354
Trimmed Mean ( 15 / 24 )101.7271428571430.07021560103593021448.78262603047
Trimmed Mean ( 16 / 24 )101.72050.067958273396821496.80818707733
Trimmed Mean ( 17 / 24 )101.7144736842110.06552631578947381552.26907630522
Trimmed Mean ( 18 / 24 )101.7066666666670.062640318675831623.66138641486
Trimmed Mean ( 19 / 24 )101.6985294117650.05923928387932271716.74137079267
Trimmed Mean ( 20 / 24 )101.686250.05520626644538381841.93310918063
Trimmed Mean ( 21 / 24 )101.6733333333330.05082160218885432000.59283757944
Trimmed Mean ( 22 / 24 )101.6703571428570.04989534587953492037.67215860825
Trimmed Mean ( 23 / 24 )101.6680769230770.04873797833870842086.01342092047
Trimmed Mean ( 24 / 24 )101.663750.04728043265024382150.22884312536
Median101.645
Midrange101.82
Midmean - Weighted Average at Xnp101.691081081081
Midmean - Weighted Average at X(n+1)p101.706666666667
Midmean - Empirical Distribution Function101.691081081081
Midmean - Empirical Distribution Function - Averaging101.706666666667
Midmean - Empirical Distribution Function - Interpolation101.706666666667
Midmean - Closest Observation101.691081081081
Midmean - True Basic - Statistics Graphics Toolkit101.706666666667
Midmean - MS Excel (old versions)101.714473684211
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 101.8175 & 0.161576344499192 & 630.151030558247 \tabularnewline
Geometric Mean & 101.808407353045 &  &  \tabularnewline
Harmonic Mean & 101.799323993259 &  &  \tabularnewline
Quadratic Mean & 101.826602109774 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 101.81625 & 0.16124496540769 & 631.438319593849 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 101.818194444444 & 0.158577070413446 & 642.073877257168 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 101.823611111111 & 0.152180976186671 & 669.095531271993 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 101.8225 & 0.150365718746069 & 677.165652178695 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 101.808611111111 & 0.144081640040278 & 706.603638622177 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 101.862777777778 & 0.133009616155806 & 765.830176206636 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 101.892916666667 & 0.12637064456706 & 806.302104541345 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 101.897361111111 & 0.11772308311435 & 865.568233649924 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 101.854861111111 & 0.107115763992782 & 950.885820297888 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 101.814583333333 & 0.0986691444104258 & 1031.87864799784 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 101.813055555556 & 0.0983827835574107 & 1034.86658817844 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 101.813055555556 & 0.0983827835574107 & 1034.86658817844 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 101.789583333333 & 0.0934764658480902 & 1088.93273199645 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 101.772083333333 & 0.0853192791894568 & 1192.83805841048 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 101.7825 & 0.0733740683917904 & 1387.17263783874 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 101.771388888889 & 0.0708743475723135 & 1435.94110386767 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 101.780833333333 & 0.0688926355056698 & 1477.38336015548 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 101.775833333333 & 0.0666040639165768 & 1528.07242304028 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 101.802222222222 & 0.0632317019441981 & 1609.98706490713 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 101.793888888889 & 0.0587005729069742 & 1734.12087562087 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 101.697638888889 & 0.0439262849288535 & 2315.18870884725 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 101.688472222222 & 0.0426378183917449 & 2384.93609799487 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 101.70125 & 0.0409811865210099 & 2481.65703908696 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 101.674583333333 & 0.0373155020608489 & 2724.72773292817 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 101.817428571429 & 0.153957952598407 & 661.332700604398 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 101.818676470588 & 0.145203968498085 & 701.211389218547 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 101.818939393939 & 0.136399271438128 & 746.477149917369 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 101.8171875 & 0.128864367594828 & 790.11125728821 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 101.81564516129 & 0.120371279361707 & 845.846664596309 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 101.817333333333 & 0.112159809983425 & 907.788033417499 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 101.807931034483 & 0.10557873767957 & 964.284412487183 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 101.792321428571 & 0.0992926250748193 & 1025.17504549677 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 101.774814814815 & 0.0938164125784739 & 1084.82953054386 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 101.7625 & 0.0898561255739833 & 1132.50487209371 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 101.755 & 0.0870248615661771 & 1169.26356639616 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 101.747083333333 & 0.0834702554218517 & 1218.96216585312 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 101.73847826087 & 0.0788663440958431 & 1290.01134041703 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 101.732045454545 & 0.074188049978159 & 1371.27267106354 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 101.727142857143 & 0.0702156010359302 & 1448.78262603047 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 101.7205 & 0.06795827339682 & 1496.80818707733 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 101.714473684211 & 0.0655263157894738 & 1552.26907630522 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 101.706666666667 & 0.06264031867583 & 1623.66138641486 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 101.698529411765 & 0.0592392838793227 & 1716.74137079267 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 101.68625 & 0.0552062664453838 & 1841.93310918063 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 101.673333333333 & 0.0508216021888543 & 2000.59283757944 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 101.670357142857 & 0.0498953458795349 & 2037.67215860825 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 101.668076923077 & 0.0487379783387084 & 2086.01342092047 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 101.66375 & 0.0472804326502438 & 2150.22884312536 \tabularnewline
Median & 101.645 &  &  \tabularnewline
Midrange & 101.82 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 101.691081081081 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 101.706666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 101.691081081081 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 101.706666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 101.706666666667 &  &  \tabularnewline
Midmean - Closest Observation & 101.691081081081 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 101.706666666667 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 101.714473684211 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]101.8175[/C][C]0.161576344499192[/C][C]630.151030558247[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]101.808407353045[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]101.799323993259[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]101.826602109774[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]101.81625[/C][C]0.16124496540769[/C][C]631.438319593849[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]101.818194444444[/C][C]0.158577070413446[/C][C]642.073877257168[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]101.823611111111[/C][C]0.152180976186671[/C][C]669.095531271993[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]101.8225[/C][C]0.150365718746069[/C][C]677.165652178695[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]101.808611111111[/C][C]0.144081640040278[/C][C]706.603638622177[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]101.862777777778[/C][C]0.133009616155806[/C][C]765.830176206636[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]101.892916666667[/C][C]0.12637064456706[/C][C]806.302104541345[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]101.897361111111[/C][C]0.11772308311435[/C][C]865.568233649924[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]101.854861111111[/C][C]0.107115763992782[/C][C]950.885820297888[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]101.814583333333[/C][C]0.0986691444104258[/C][C]1031.87864799784[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]101.813055555556[/C][C]0.0983827835574107[/C][C]1034.86658817844[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]101.813055555556[/C][C]0.0983827835574107[/C][C]1034.86658817844[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]101.789583333333[/C][C]0.0934764658480902[/C][C]1088.93273199645[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]101.772083333333[/C][C]0.0853192791894568[/C][C]1192.83805841048[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]101.7825[/C][C]0.0733740683917904[/C][C]1387.17263783874[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]101.771388888889[/C][C]0.0708743475723135[/C][C]1435.94110386767[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]101.780833333333[/C][C]0.0688926355056698[/C][C]1477.38336015548[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]101.775833333333[/C][C]0.0666040639165768[/C][C]1528.07242304028[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]101.802222222222[/C][C]0.0632317019441981[/C][C]1609.98706490713[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]101.793888888889[/C][C]0.0587005729069742[/C][C]1734.12087562087[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]101.697638888889[/C][C]0.0439262849288535[/C][C]2315.18870884725[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]101.688472222222[/C][C]0.0426378183917449[/C][C]2384.93609799487[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]101.70125[/C][C]0.0409811865210099[/C][C]2481.65703908696[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]101.674583333333[/C][C]0.0373155020608489[/C][C]2724.72773292817[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]101.817428571429[/C][C]0.153957952598407[/C][C]661.332700604398[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]101.818676470588[/C][C]0.145203968498085[/C][C]701.211389218547[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]101.818939393939[/C][C]0.136399271438128[/C][C]746.477149917369[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]101.8171875[/C][C]0.128864367594828[/C][C]790.11125728821[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]101.81564516129[/C][C]0.120371279361707[/C][C]845.846664596309[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]101.817333333333[/C][C]0.112159809983425[/C][C]907.788033417499[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]101.807931034483[/C][C]0.10557873767957[/C][C]964.284412487183[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]101.792321428571[/C][C]0.0992926250748193[/C][C]1025.17504549677[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]101.774814814815[/C][C]0.0938164125784739[/C][C]1084.82953054386[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]101.7625[/C][C]0.0898561255739833[/C][C]1132.50487209371[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]101.755[/C][C]0.0870248615661771[/C][C]1169.26356639616[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]101.747083333333[/C][C]0.0834702554218517[/C][C]1218.96216585312[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]101.73847826087[/C][C]0.0788663440958431[/C][C]1290.01134041703[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]101.732045454545[/C][C]0.074188049978159[/C][C]1371.27267106354[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]101.727142857143[/C][C]0.0702156010359302[/C][C]1448.78262603047[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]101.7205[/C][C]0.06795827339682[/C][C]1496.80818707733[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]101.714473684211[/C][C]0.0655263157894738[/C][C]1552.26907630522[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]101.706666666667[/C][C]0.06264031867583[/C][C]1623.66138641486[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]101.698529411765[/C][C]0.0592392838793227[/C][C]1716.74137079267[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]101.68625[/C][C]0.0552062664453838[/C][C]1841.93310918063[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]101.673333333333[/C][C]0.0508216021888543[/C][C]2000.59283757944[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]101.670357142857[/C][C]0.0498953458795349[/C][C]2037.67215860825[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]101.668076923077[/C][C]0.0487379783387084[/C][C]2086.01342092047[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]101.66375[/C][C]0.0472804326502438[/C][C]2150.22884312536[/C][/ROW]
[ROW][C]Median[/C][C]101.645[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]101.82[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]101.691081081081[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]101.706666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]101.691081081081[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]101.706666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]101.706666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]101.691081081081[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]101.706666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]101.714473684211[/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=&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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 Mean101.81750.161576344499192630.151030558247
Geometric Mean101.808407353045
Harmonic Mean101.799323993259
Quadratic Mean101.826602109774
Winsorized Mean ( 1 / 24 )101.816250.16124496540769631.438319593849
Winsorized Mean ( 2 / 24 )101.8181944444440.158577070413446642.073877257168
Winsorized Mean ( 3 / 24 )101.8236111111110.152180976186671669.095531271993
Winsorized Mean ( 4 / 24 )101.82250.150365718746069677.165652178695
Winsorized Mean ( 5 / 24 )101.8086111111110.144081640040278706.603638622177
Winsorized Mean ( 6 / 24 )101.8627777777780.133009616155806765.830176206636
Winsorized Mean ( 7 / 24 )101.8929166666670.12637064456706806.302104541345
Winsorized Mean ( 8 / 24 )101.8973611111110.11772308311435865.568233649924
Winsorized Mean ( 9 / 24 )101.8548611111110.107115763992782950.885820297888
Winsorized Mean ( 10 / 24 )101.8145833333330.09866914441042581031.87864799784
Winsorized Mean ( 11 / 24 )101.8130555555560.09838278355741071034.86658817844
Winsorized Mean ( 12 / 24 )101.8130555555560.09838278355741071034.86658817844
Winsorized Mean ( 13 / 24 )101.7895833333330.09347646584809021088.93273199645
Winsorized Mean ( 14 / 24 )101.7720833333330.08531927918945681192.83805841048
Winsorized Mean ( 15 / 24 )101.78250.07337406839179041387.17263783874
Winsorized Mean ( 16 / 24 )101.7713888888890.07087434757231351435.94110386767
Winsorized Mean ( 17 / 24 )101.7808333333330.06889263550566981477.38336015548
Winsorized Mean ( 18 / 24 )101.7758333333330.06660406391657681528.07242304028
Winsorized Mean ( 19 / 24 )101.8022222222220.06323170194419811609.98706490713
Winsorized Mean ( 20 / 24 )101.7938888888890.05870057290697421734.12087562087
Winsorized Mean ( 21 / 24 )101.6976388888890.04392628492885352315.18870884725
Winsorized Mean ( 22 / 24 )101.6884722222220.04263781839174492384.93609799487
Winsorized Mean ( 23 / 24 )101.701250.04098118652100992481.65703908696
Winsorized Mean ( 24 / 24 )101.6745833333330.03731550206084892724.72773292817
Trimmed Mean ( 1 / 24 )101.8174285714290.153957952598407661.332700604398
Trimmed Mean ( 2 / 24 )101.8186764705880.145203968498085701.211389218547
Trimmed Mean ( 3 / 24 )101.8189393939390.136399271438128746.477149917369
Trimmed Mean ( 4 / 24 )101.81718750.128864367594828790.11125728821
Trimmed Mean ( 5 / 24 )101.815645161290.120371279361707845.846664596309
Trimmed Mean ( 6 / 24 )101.8173333333330.112159809983425907.788033417499
Trimmed Mean ( 7 / 24 )101.8079310344830.10557873767957964.284412487183
Trimmed Mean ( 8 / 24 )101.7923214285710.09929262507481931025.17504549677
Trimmed Mean ( 9 / 24 )101.7748148148150.09381641257847391084.82953054386
Trimmed Mean ( 10 / 24 )101.76250.08985612557398331132.50487209371
Trimmed Mean ( 11 / 24 )101.7550.08702486156617711169.26356639616
Trimmed Mean ( 12 / 24 )101.7470833333330.08347025542185171218.96216585312
Trimmed Mean ( 13 / 24 )101.738478260870.07886634409584311290.01134041703
Trimmed Mean ( 14 / 24 )101.7320454545450.0741880499781591371.27267106354
Trimmed Mean ( 15 / 24 )101.7271428571430.07021560103593021448.78262603047
Trimmed Mean ( 16 / 24 )101.72050.067958273396821496.80818707733
Trimmed Mean ( 17 / 24 )101.7144736842110.06552631578947381552.26907630522
Trimmed Mean ( 18 / 24 )101.7066666666670.062640318675831623.66138641486
Trimmed Mean ( 19 / 24 )101.6985294117650.05923928387932271716.74137079267
Trimmed Mean ( 20 / 24 )101.686250.05520626644538381841.93310918063
Trimmed Mean ( 21 / 24 )101.6733333333330.05082160218885432000.59283757944
Trimmed Mean ( 22 / 24 )101.6703571428570.04989534587953492037.67215860825
Trimmed Mean ( 23 / 24 )101.6680769230770.04873797833870842086.01342092047
Trimmed Mean ( 24 / 24 )101.663750.04728043265024382150.22884312536
Median101.645
Midrange101.82
Midmean - Weighted Average at Xnp101.691081081081
Midmean - Weighted Average at X(n+1)p101.706666666667
Midmean - Empirical Distribution Function101.691081081081
Midmean - Empirical Distribution Function - Averaging101.706666666667
Midmean - Empirical Distribution Function - Interpolation101.706666666667
Midmean - Closest Observation101.691081081081
Midmean - True Basic - Statistics Graphics Toolkit101.706666666667
Midmean - MS Excel (old versions)101.714473684211
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')