Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationMon, 13 Mar 2017 13:44:28 +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/13/t14894128764yzjgcy9008pgah.htm/, Retrieved Tue, 14 May 2024 01:51:50 +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 01:51:50 +0200
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact0
Dataseries X:
93,55
94,11
94,34
94,38
94,39
94,42
94,42
94,47
94,59
94,63
94,84
94,98
95,19
95,76
96,04
96,08
96,2
96,29
96,3
96,31
96,46
96,66
96,83
97
97,1
97,16
97,31
97,33
97,4
97,4
97,52
97,77
98
98,2
98,48
98,53
98,71
99,03
99,52
99,65
99,94
99,98
100,12
100,17
100,38
100,75
100,84
100,9
100,91
101,15
101,25
101,39
101,4
101,53
101,55
101,58
101,58
101,65
101,7
101,71
101,71
101,73
101,73
101,75
101,84
101,95
101,95
101,98
101,99
102,03
102,11
102,14
102,18
102,2
102,28
102,29
102,32
102,33
102,33
102,36
102,54
102,58
102,79
103,01




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gertrude Mary Cox' @ cox.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 & 'Gertrude Mary Cox' @ cox.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]'Gertrude Mary Cox' @ cox.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'Gertrude Mary Cox' @ cox.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean99.16607142857140.316920197050069312.905495931219
Geometric Mean99.123684484589
Harmonic Mean99.0809576005231
Quadratic Mean99.208094985814
Winsorized Mean ( 1 / 28 )99.17011904761910.31519100084277314.634995232904
Winsorized Mean ( 2 / 28 )99.17059523809520.313479416477527316.354408057935
Winsorized Mean ( 3 / 28 )99.17059523809520.313028868652986316.809742388433
Winsorized Mean ( 4 / 28 )99.16250.3118558018775317.975485474379
Winsorized Mean ( 5 / 28 )99.16250.311307547035209318.535483461263
Winsorized Mean ( 6 / 28 )99.16250.311307547035209318.535483461263
Winsorized Mean ( 7 / 28 )99.16583333333330.310443402857739319.432889926078
Winsorized Mean ( 8 / 28 )99.17440476190480.308028326814611321.965209458134
Winsorized Mean ( 9 / 28 )99.1776190476190.307131324639949322.91600071691
Winsorized Mean ( 10 / 28 )99.19309523809520.301575371048656328.916432708596
Winsorized Mean ( 11 / 28 )99.20880952380950.298099757508005332.804059799161
Winsorized Mean ( 12 / 28 )99.23309523809520.292350700685582339.431699685984
Winsorized Mean ( 13 / 28 )99.31666666666670.277620014484096357.743179472229
Winsorized Mean ( 14 / 28 )99.350.268947663437309369.402725906776
Winsorized Mean ( 15 / 28 )99.350.267036981114687372.045847677297
Winsorized Mean ( 16 / 28 )99.37095238095240.263466379186755377.167487888519
Winsorized Mean ( 17 / 28 )99.38309523809520.26011780597085382.069558318636
Winsorized Mean ( 18 / 28 )99.38523809523810.259811015002543382.528962808852
Winsorized Mean ( 19 / 28 )99.3626190476190.256559953472826387.288108306206
Winsorized Mean ( 20 / 28 )99.37690476190480.249002195587999399.100516070687
Winsorized Mean ( 21 / 28 )99.42190476190470.241452116140471411.766549621224
Winsorized Mean ( 22 / 28 )99.46642857142860.235379031914195422.579818442316
Winsorized Mean ( 23 / 28 )99.50750.228525347881173435.433097127332
Winsorized Mean ( 24 / 28 )99.53607142857140.224771192250401442.832866756722
Winsorized Mean ( 25 / 28 )99.55095238095240.222100338812226448.225126144978
Winsorized Mean ( 26 / 28 )99.58190476190480.214322002409648464.636871820408
Winsorized Mean ( 27 / 28 )99.56583333333330.210898428425293472.10324930706
Winsorized Mean ( 28 / 28 )99.58916666666670.207928283811135478.959210557065
Trimmed Mean ( 1 / 28 )99.18768292682930.313766796351426316.119118020814
Trimmed Mean ( 2 / 28 )99.2061250.311975001724416317.9938278761
Trimmed Mean ( 3 / 28 )99.22525641025640.310763924217999319.294643546367
Trimmed Mean ( 4 / 28 )99.24539473684210.309365476293716320.803070613533
Trimmed Mean ( 5 / 28 )99.26891891891890.307927262669985322.377817599439
Trimmed Mean ( 6 / 28 )99.293750.306197937192597324.27961765642
Trimmed Mean ( 7 / 28 )99.320.303964896632972326.748256460435
Trimmed Mean ( 8 / 28 )99.34720588235290.301333504347472329.691867811002
Trimmed Mean ( 9 / 28 )99.3746969696970.298540522892147332.868369114493
Trimmed Mean ( 10 / 28 )99.40343750.295194079515246336.739265446095
Trimmed Mean ( 11 / 28 )99.4319354838710.292082444435502340.424210280901
Trimmed Mean ( 12 / 28 )99.46033333333330.288787937236014344.406121271086
Trimmed Mean ( 13 / 28 )99.48775862068970.285657671151902348.276166432044
Trimmed Mean ( 14 / 28 )99.50750.284317621227141349.987100941956
Trimmed Mean ( 15 / 28 )99.5250.283837478472953350.640798161839
Trimmed Mean ( 16 / 28 )99.54384615384620.283142934053698351.567474168251
Trimmed Mean ( 17 / 28 )99.5620.282465818773724352.474506233112
Trimmed Mean ( 18 / 28 )99.58041666666670.281722468925778353.469913302875
Trimmed Mean ( 19 / 28 )99.60021739130440.280319949900323355.309058191258
Trimmed Mean ( 20 / 28 )99.62409090909090.278541830978479357.66294261485
Trimmed Mean ( 21 / 28 )99.64880952380950.277113083660803359.596191588642
Trimmed Mean ( 22 / 28 )99.67150.276134385251002360.952874121056
Trimmed Mean ( 23 / 28 )99.69210526315790.275379773431498362.016803270981
Trimmed Mean ( 24 / 28 )99.71083333333330.275004581491418362.578807933224
Trimmed Mean ( 25 / 28 )99.72882352941180.274375896802446363.475161964455
Trimmed Mean ( 26 / 28 )99.74750.273070577548334365.281023300083
Trimmed Mean ( 27 / 28 )99.76533333333330.27207281536059366.686150548007
Trimmed Mean ( 28 / 28 )99.78750.270123734630228369.41403959411
Median100.05
Midrange98.28
Midmean - Weighted Average at Xnp99.5746511627907
Midmean - Weighted Average at X(n+1)p99.6488095238095
Midmean - Empirical Distribution Function99.5746511627907
Midmean - Empirical Distribution Function - Averaging99.6488095238095
Midmean - Empirical Distribution Function - Interpolation99.6488095238095
Midmean - Closest Observation99.5746511627907
Midmean - True Basic - Statistics Graphics Toolkit99.6488095238095
Midmean - MS Excel (old versions)99.6240909090909
Number of observations84

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 99.1660714285714 & 0.316920197050069 & 312.905495931219 \tabularnewline
Geometric Mean & 99.123684484589 &  &  \tabularnewline
Harmonic Mean & 99.0809576005231 &  &  \tabularnewline
Quadratic Mean & 99.208094985814 &  &  \tabularnewline
Winsorized Mean ( 1 / 28 ) & 99.1701190476191 & 0.31519100084277 & 314.634995232904 \tabularnewline
Winsorized Mean ( 2 / 28 ) & 99.1705952380952 & 0.313479416477527 & 316.354408057935 \tabularnewline
Winsorized Mean ( 3 / 28 ) & 99.1705952380952 & 0.313028868652986 & 316.809742388433 \tabularnewline
Winsorized Mean ( 4 / 28 ) & 99.1625 & 0.3118558018775 & 317.975485474379 \tabularnewline
Winsorized Mean ( 5 / 28 ) & 99.1625 & 0.311307547035209 & 318.535483461263 \tabularnewline
Winsorized Mean ( 6 / 28 ) & 99.1625 & 0.311307547035209 & 318.535483461263 \tabularnewline
Winsorized Mean ( 7 / 28 ) & 99.1658333333333 & 0.310443402857739 & 319.432889926078 \tabularnewline
Winsorized Mean ( 8 / 28 ) & 99.1744047619048 & 0.308028326814611 & 321.965209458134 \tabularnewline
Winsorized Mean ( 9 / 28 ) & 99.177619047619 & 0.307131324639949 & 322.91600071691 \tabularnewline
Winsorized Mean ( 10 / 28 ) & 99.1930952380952 & 0.301575371048656 & 328.916432708596 \tabularnewline
Winsorized Mean ( 11 / 28 ) & 99.2088095238095 & 0.298099757508005 & 332.804059799161 \tabularnewline
Winsorized Mean ( 12 / 28 ) & 99.2330952380952 & 0.292350700685582 & 339.431699685984 \tabularnewline
Winsorized Mean ( 13 / 28 ) & 99.3166666666667 & 0.277620014484096 & 357.743179472229 \tabularnewline
Winsorized Mean ( 14 / 28 ) & 99.35 & 0.268947663437309 & 369.402725906776 \tabularnewline
Winsorized Mean ( 15 / 28 ) & 99.35 & 0.267036981114687 & 372.045847677297 \tabularnewline
Winsorized Mean ( 16 / 28 ) & 99.3709523809524 & 0.263466379186755 & 377.167487888519 \tabularnewline
Winsorized Mean ( 17 / 28 ) & 99.3830952380952 & 0.26011780597085 & 382.069558318636 \tabularnewline
Winsorized Mean ( 18 / 28 ) & 99.3852380952381 & 0.259811015002543 & 382.528962808852 \tabularnewline
Winsorized Mean ( 19 / 28 ) & 99.362619047619 & 0.256559953472826 & 387.288108306206 \tabularnewline
Winsorized Mean ( 20 / 28 ) & 99.3769047619048 & 0.249002195587999 & 399.100516070687 \tabularnewline
Winsorized Mean ( 21 / 28 ) & 99.4219047619047 & 0.241452116140471 & 411.766549621224 \tabularnewline
Winsorized Mean ( 22 / 28 ) & 99.4664285714286 & 0.235379031914195 & 422.579818442316 \tabularnewline
Winsorized Mean ( 23 / 28 ) & 99.5075 & 0.228525347881173 & 435.433097127332 \tabularnewline
Winsorized Mean ( 24 / 28 ) & 99.5360714285714 & 0.224771192250401 & 442.832866756722 \tabularnewline
Winsorized Mean ( 25 / 28 ) & 99.5509523809524 & 0.222100338812226 & 448.225126144978 \tabularnewline
Winsorized Mean ( 26 / 28 ) & 99.5819047619048 & 0.214322002409648 & 464.636871820408 \tabularnewline
Winsorized Mean ( 27 / 28 ) & 99.5658333333333 & 0.210898428425293 & 472.10324930706 \tabularnewline
Winsorized Mean ( 28 / 28 ) & 99.5891666666667 & 0.207928283811135 & 478.959210557065 \tabularnewline
Trimmed Mean ( 1 / 28 ) & 99.1876829268293 & 0.313766796351426 & 316.119118020814 \tabularnewline
Trimmed Mean ( 2 / 28 ) & 99.206125 & 0.311975001724416 & 317.9938278761 \tabularnewline
Trimmed Mean ( 3 / 28 ) & 99.2252564102564 & 0.310763924217999 & 319.294643546367 \tabularnewline
Trimmed Mean ( 4 / 28 ) & 99.2453947368421 & 0.309365476293716 & 320.803070613533 \tabularnewline
Trimmed Mean ( 5 / 28 ) & 99.2689189189189 & 0.307927262669985 & 322.377817599439 \tabularnewline
Trimmed Mean ( 6 / 28 ) & 99.29375 & 0.306197937192597 & 324.27961765642 \tabularnewline
Trimmed Mean ( 7 / 28 ) & 99.32 & 0.303964896632972 & 326.748256460435 \tabularnewline
Trimmed Mean ( 8 / 28 ) & 99.3472058823529 & 0.301333504347472 & 329.691867811002 \tabularnewline
Trimmed Mean ( 9 / 28 ) & 99.374696969697 & 0.298540522892147 & 332.868369114493 \tabularnewline
Trimmed Mean ( 10 / 28 ) & 99.4034375 & 0.295194079515246 & 336.739265446095 \tabularnewline
Trimmed Mean ( 11 / 28 ) & 99.431935483871 & 0.292082444435502 & 340.424210280901 \tabularnewline
Trimmed Mean ( 12 / 28 ) & 99.4603333333333 & 0.288787937236014 & 344.406121271086 \tabularnewline
Trimmed Mean ( 13 / 28 ) & 99.4877586206897 & 0.285657671151902 & 348.276166432044 \tabularnewline
Trimmed Mean ( 14 / 28 ) & 99.5075 & 0.284317621227141 & 349.987100941956 \tabularnewline
Trimmed Mean ( 15 / 28 ) & 99.525 & 0.283837478472953 & 350.640798161839 \tabularnewline
Trimmed Mean ( 16 / 28 ) & 99.5438461538462 & 0.283142934053698 & 351.567474168251 \tabularnewline
Trimmed Mean ( 17 / 28 ) & 99.562 & 0.282465818773724 & 352.474506233112 \tabularnewline
Trimmed Mean ( 18 / 28 ) & 99.5804166666667 & 0.281722468925778 & 353.469913302875 \tabularnewline
Trimmed Mean ( 19 / 28 ) & 99.6002173913044 & 0.280319949900323 & 355.309058191258 \tabularnewline
Trimmed Mean ( 20 / 28 ) & 99.6240909090909 & 0.278541830978479 & 357.66294261485 \tabularnewline
Trimmed Mean ( 21 / 28 ) & 99.6488095238095 & 0.277113083660803 & 359.596191588642 \tabularnewline
Trimmed Mean ( 22 / 28 ) & 99.6715 & 0.276134385251002 & 360.952874121056 \tabularnewline
Trimmed Mean ( 23 / 28 ) & 99.6921052631579 & 0.275379773431498 & 362.016803270981 \tabularnewline
Trimmed Mean ( 24 / 28 ) & 99.7108333333333 & 0.275004581491418 & 362.578807933224 \tabularnewline
Trimmed Mean ( 25 / 28 ) & 99.7288235294118 & 0.274375896802446 & 363.475161964455 \tabularnewline
Trimmed Mean ( 26 / 28 ) & 99.7475 & 0.273070577548334 & 365.281023300083 \tabularnewline
Trimmed Mean ( 27 / 28 ) & 99.7653333333333 & 0.27207281536059 & 366.686150548007 \tabularnewline
Trimmed Mean ( 28 / 28 ) & 99.7875 & 0.270123734630228 & 369.41403959411 \tabularnewline
Median & 100.05 &  &  \tabularnewline
Midrange & 98.28 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 99.5746511627907 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 99.6488095238095 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 99.5746511627907 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 99.6488095238095 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 99.6488095238095 &  &  \tabularnewline
Midmean - Closest Observation & 99.5746511627907 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 99.6488095238095 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 99.6240909090909 &  &  \tabularnewline
Number of observations & 84 &  &  \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]99.1660714285714[/C][C]0.316920197050069[/C][C]312.905495931219[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]99.123684484589[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]99.0809576005231[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]99.208094985814[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 28 )[/C][C]99.1701190476191[/C][C]0.31519100084277[/C][C]314.634995232904[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 28 )[/C][C]99.1705952380952[/C][C]0.313479416477527[/C][C]316.354408057935[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 28 )[/C][C]99.1705952380952[/C][C]0.313028868652986[/C][C]316.809742388433[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 28 )[/C][C]99.1625[/C][C]0.3118558018775[/C][C]317.975485474379[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 28 )[/C][C]99.1625[/C][C]0.311307547035209[/C][C]318.535483461263[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 28 )[/C][C]99.1625[/C][C]0.311307547035209[/C][C]318.535483461263[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 28 )[/C][C]99.1658333333333[/C][C]0.310443402857739[/C][C]319.432889926078[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 28 )[/C][C]99.1744047619048[/C][C]0.308028326814611[/C][C]321.965209458134[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 28 )[/C][C]99.177619047619[/C][C]0.307131324639949[/C][C]322.91600071691[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 28 )[/C][C]99.1930952380952[/C][C]0.301575371048656[/C][C]328.916432708596[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 28 )[/C][C]99.2088095238095[/C][C]0.298099757508005[/C][C]332.804059799161[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 28 )[/C][C]99.2330952380952[/C][C]0.292350700685582[/C][C]339.431699685984[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 28 )[/C][C]99.3166666666667[/C][C]0.277620014484096[/C][C]357.743179472229[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 28 )[/C][C]99.35[/C][C]0.268947663437309[/C][C]369.402725906776[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 28 )[/C][C]99.35[/C][C]0.267036981114687[/C][C]372.045847677297[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 28 )[/C][C]99.3709523809524[/C][C]0.263466379186755[/C][C]377.167487888519[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 28 )[/C][C]99.3830952380952[/C][C]0.26011780597085[/C][C]382.069558318636[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 28 )[/C][C]99.3852380952381[/C][C]0.259811015002543[/C][C]382.528962808852[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 28 )[/C][C]99.362619047619[/C][C]0.256559953472826[/C][C]387.288108306206[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 28 )[/C][C]99.3769047619048[/C][C]0.249002195587999[/C][C]399.100516070687[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 28 )[/C][C]99.4219047619047[/C][C]0.241452116140471[/C][C]411.766549621224[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 28 )[/C][C]99.4664285714286[/C][C]0.235379031914195[/C][C]422.579818442316[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 28 )[/C][C]99.5075[/C][C]0.228525347881173[/C][C]435.433097127332[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 28 )[/C][C]99.5360714285714[/C][C]0.224771192250401[/C][C]442.832866756722[/C][/ROW]
[ROW][C]Winsorized Mean ( 25 / 28 )[/C][C]99.5509523809524[/C][C]0.222100338812226[/C][C]448.225126144978[/C][/ROW]
[ROW][C]Winsorized Mean ( 26 / 28 )[/C][C]99.5819047619048[/C][C]0.214322002409648[/C][C]464.636871820408[/C][/ROW]
[ROW][C]Winsorized Mean ( 27 / 28 )[/C][C]99.5658333333333[/C][C]0.210898428425293[/C][C]472.10324930706[/C][/ROW]
[ROW][C]Winsorized Mean ( 28 / 28 )[/C][C]99.5891666666667[/C][C]0.207928283811135[/C][C]478.959210557065[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 28 )[/C][C]99.1876829268293[/C][C]0.313766796351426[/C][C]316.119118020814[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 28 )[/C][C]99.206125[/C][C]0.311975001724416[/C][C]317.9938278761[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 28 )[/C][C]99.2252564102564[/C][C]0.310763924217999[/C][C]319.294643546367[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 28 )[/C][C]99.2453947368421[/C][C]0.309365476293716[/C][C]320.803070613533[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 28 )[/C][C]99.2689189189189[/C][C]0.307927262669985[/C][C]322.377817599439[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 28 )[/C][C]99.29375[/C][C]0.306197937192597[/C][C]324.27961765642[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 28 )[/C][C]99.32[/C][C]0.303964896632972[/C][C]326.748256460435[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 28 )[/C][C]99.3472058823529[/C][C]0.301333504347472[/C][C]329.691867811002[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 28 )[/C][C]99.374696969697[/C][C]0.298540522892147[/C][C]332.868369114493[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 28 )[/C][C]99.4034375[/C][C]0.295194079515246[/C][C]336.739265446095[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 28 )[/C][C]99.431935483871[/C][C]0.292082444435502[/C][C]340.424210280901[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 28 )[/C][C]99.4603333333333[/C][C]0.288787937236014[/C][C]344.406121271086[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 28 )[/C][C]99.4877586206897[/C][C]0.285657671151902[/C][C]348.276166432044[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 28 )[/C][C]99.5075[/C][C]0.284317621227141[/C][C]349.987100941956[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 28 )[/C][C]99.525[/C][C]0.283837478472953[/C][C]350.640798161839[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 28 )[/C][C]99.5438461538462[/C][C]0.283142934053698[/C][C]351.567474168251[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 28 )[/C][C]99.562[/C][C]0.282465818773724[/C][C]352.474506233112[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 28 )[/C][C]99.5804166666667[/C][C]0.281722468925778[/C][C]353.469913302875[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 28 )[/C][C]99.6002173913044[/C][C]0.280319949900323[/C][C]355.309058191258[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 28 )[/C][C]99.6240909090909[/C][C]0.278541830978479[/C][C]357.66294261485[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 28 )[/C][C]99.6488095238095[/C][C]0.277113083660803[/C][C]359.596191588642[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 28 )[/C][C]99.6715[/C][C]0.276134385251002[/C][C]360.952874121056[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 28 )[/C][C]99.6921052631579[/C][C]0.275379773431498[/C][C]362.016803270981[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 28 )[/C][C]99.7108333333333[/C][C]0.275004581491418[/C][C]362.578807933224[/C][/ROW]
[ROW][C]Trimmed Mean ( 25 / 28 )[/C][C]99.7288235294118[/C][C]0.274375896802446[/C][C]363.475161964455[/C][/ROW]
[ROW][C]Trimmed Mean ( 26 / 28 )[/C][C]99.7475[/C][C]0.273070577548334[/C][C]365.281023300083[/C][/ROW]
[ROW][C]Trimmed Mean ( 27 / 28 )[/C][C]99.7653333333333[/C][C]0.27207281536059[/C][C]366.686150548007[/C][/ROW]
[ROW][C]Trimmed Mean ( 28 / 28 )[/C][C]99.7875[/C][C]0.270123734630228[/C][C]369.41403959411[/C][/ROW]
[ROW][C]Median[/C][C]100.05[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]98.28[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]99.5746511627907[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]99.6488095238095[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]99.5746511627907[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]99.6488095238095[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]99.6488095238095[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]99.5746511627907[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]99.6488095238095[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]99.6240909090909[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]84[/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 Mean99.16607142857140.316920197050069312.905495931219
Geometric Mean99.123684484589
Harmonic Mean99.0809576005231
Quadratic Mean99.208094985814
Winsorized Mean ( 1 / 28 )99.17011904761910.31519100084277314.634995232904
Winsorized Mean ( 2 / 28 )99.17059523809520.313479416477527316.354408057935
Winsorized Mean ( 3 / 28 )99.17059523809520.313028868652986316.809742388433
Winsorized Mean ( 4 / 28 )99.16250.3118558018775317.975485474379
Winsorized Mean ( 5 / 28 )99.16250.311307547035209318.535483461263
Winsorized Mean ( 6 / 28 )99.16250.311307547035209318.535483461263
Winsorized Mean ( 7 / 28 )99.16583333333330.310443402857739319.432889926078
Winsorized Mean ( 8 / 28 )99.17440476190480.308028326814611321.965209458134
Winsorized Mean ( 9 / 28 )99.1776190476190.307131324639949322.91600071691
Winsorized Mean ( 10 / 28 )99.19309523809520.301575371048656328.916432708596
Winsorized Mean ( 11 / 28 )99.20880952380950.298099757508005332.804059799161
Winsorized Mean ( 12 / 28 )99.23309523809520.292350700685582339.431699685984
Winsorized Mean ( 13 / 28 )99.31666666666670.277620014484096357.743179472229
Winsorized Mean ( 14 / 28 )99.350.268947663437309369.402725906776
Winsorized Mean ( 15 / 28 )99.350.267036981114687372.045847677297
Winsorized Mean ( 16 / 28 )99.37095238095240.263466379186755377.167487888519
Winsorized Mean ( 17 / 28 )99.38309523809520.26011780597085382.069558318636
Winsorized Mean ( 18 / 28 )99.38523809523810.259811015002543382.528962808852
Winsorized Mean ( 19 / 28 )99.3626190476190.256559953472826387.288108306206
Winsorized Mean ( 20 / 28 )99.37690476190480.249002195587999399.100516070687
Winsorized Mean ( 21 / 28 )99.42190476190470.241452116140471411.766549621224
Winsorized Mean ( 22 / 28 )99.46642857142860.235379031914195422.579818442316
Winsorized Mean ( 23 / 28 )99.50750.228525347881173435.433097127332
Winsorized Mean ( 24 / 28 )99.53607142857140.224771192250401442.832866756722
Winsorized Mean ( 25 / 28 )99.55095238095240.222100338812226448.225126144978
Winsorized Mean ( 26 / 28 )99.58190476190480.214322002409648464.636871820408
Winsorized Mean ( 27 / 28 )99.56583333333330.210898428425293472.10324930706
Winsorized Mean ( 28 / 28 )99.58916666666670.207928283811135478.959210557065
Trimmed Mean ( 1 / 28 )99.18768292682930.313766796351426316.119118020814
Trimmed Mean ( 2 / 28 )99.2061250.311975001724416317.9938278761
Trimmed Mean ( 3 / 28 )99.22525641025640.310763924217999319.294643546367
Trimmed Mean ( 4 / 28 )99.24539473684210.309365476293716320.803070613533
Trimmed Mean ( 5 / 28 )99.26891891891890.307927262669985322.377817599439
Trimmed Mean ( 6 / 28 )99.293750.306197937192597324.27961765642
Trimmed Mean ( 7 / 28 )99.320.303964896632972326.748256460435
Trimmed Mean ( 8 / 28 )99.34720588235290.301333504347472329.691867811002
Trimmed Mean ( 9 / 28 )99.3746969696970.298540522892147332.868369114493
Trimmed Mean ( 10 / 28 )99.40343750.295194079515246336.739265446095
Trimmed Mean ( 11 / 28 )99.4319354838710.292082444435502340.424210280901
Trimmed Mean ( 12 / 28 )99.46033333333330.288787937236014344.406121271086
Trimmed Mean ( 13 / 28 )99.48775862068970.285657671151902348.276166432044
Trimmed Mean ( 14 / 28 )99.50750.284317621227141349.987100941956
Trimmed Mean ( 15 / 28 )99.5250.283837478472953350.640798161839
Trimmed Mean ( 16 / 28 )99.54384615384620.283142934053698351.567474168251
Trimmed Mean ( 17 / 28 )99.5620.282465818773724352.474506233112
Trimmed Mean ( 18 / 28 )99.58041666666670.281722468925778353.469913302875
Trimmed Mean ( 19 / 28 )99.60021739130440.280319949900323355.309058191258
Trimmed Mean ( 20 / 28 )99.62409090909090.278541830978479357.66294261485
Trimmed Mean ( 21 / 28 )99.64880952380950.277113083660803359.596191588642
Trimmed Mean ( 22 / 28 )99.67150.276134385251002360.952874121056
Trimmed Mean ( 23 / 28 )99.69210526315790.275379773431498362.016803270981
Trimmed Mean ( 24 / 28 )99.71083333333330.275004581491418362.578807933224
Trimmed Mean ( 25 / 28 )99.72882352941180.274375896802446363.475161964455
Trimmed Mean ( 26 / 28 )99.74750.273070577548334365.281023300083
Trimmed Mean ( 27 / 28 )99.76533333333330.27207281536059366.686150548007
Trimmed Mean ( 28 / 28 )99.78750.270123734630228369.41403959411
Median100.05
Midrange98.28
Midmean - Weighted Average at Xnp99.5746511627907
Midmean - Weighted Average at X(n+1)p99.6488095238095
Midmean - Empirical Distribution Function99.5746511627907
Midmean - Empirical Distribution Function - Averaging99.6488095238095
Midmean - Empirical Distribution Function - Interpolation99.6488095238095
Midmean - Closest Observation99.5746511627907
Midmean - True Basic - Statistics Graphics Toolkit99.6488095238095
Midmean - MS Excel (old versions)99.6240909090909
Number of observations84



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')