Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationTue, 11 Oct 2016 22:01:58 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Oct/11/t1476219969ngnvu3htabmbki7.htm/, Retrieved Mon, 29 Apr 2024 06:02:30 +0200
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Mon, 29 Apr 2024 06:02:30 +0200
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact0
Dataseries X:
85
93.96
87.38
85.78
88.17
90.32
90.63
89.19
88.49
88.03
85.96
81.14
90.38
92.65
94.01
87.48
88.74
91.83
91.35
90.49
90.77
90.37
92.77
92.3
94.46
99.2
99.21
94.09
96.74
101.26
100.79
100.96
97.54
97.46
98.07
98.73
96.94
100.44
106.19
94.62
98.18
103.34
100.48
100.38
98.61
98.15
100.64
102.04
102.89
102.14
104.81
103.3
102.55
102.04
100.82
101.02
102.69
103.41
102.31
102.8
102.57
104.28
96.59
102.03
102.33
102.05
100.86
102.05
101.94
101.7
102.56
102.27




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ wold.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 time2 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean96.91277777777780.707128254725791137.051202706302
Geometric Mean96.7243063937794
Harmonic Mean96.5305828986363
Quadratic Mean97.0957705195122
Winsorized Mean ( 1 / 24 )96.94722222222220.688819560850942140.744002830665
Winsorized Mean ( 2 / 24 )96.95416666666670.681371503931099142.292664291506
Winsorized Mean ( 3 / 24 )96.92541666666660.674445954078319143.711169265034
Winsorized Mean ( 4 / 24 )97.00041666666670.656735698496716147.700843564166
Winsorized Mean ( 5 / 24 )97.00458333333330.654931214581603148.114154851062
Winsorized Mean ( 6 / 24 )97.016250.641193699157745151.305682085519
Winsorized Mean ( 7 / 24 )97.02111111111110.637396085475247152.214789707677
Winsorized Mean ( 8 / 24 )97.04444444444450.628960033191665154.293499305498
Winsorized Mean ( 9 / 24 )97.06069444444440.621133338875883156.263862152534
Winsorized Mean ( 10 / 24 )97.12180555555550.609332170101573159.390575979873
Winsorized Mean ( 11 / 24 )97.29291666666670.578631332537846168.143187545592
Winsorized Mean ( 12 / 24 )97.26458333333330.57258685769484169.868696820789
Winsorized Mean ( 13 / 24 )97.26277777777780.571831277790124170.089992547549
Winsorized Mean ( 14 / 24 )97.27638888888890.567250572734336171.487511101107
Winsorized Mean ( 15 / 24 )97.27847222222220.559012433327838174.018441133978
Winsorized Mean ( 16 / 24 )97.28958333333330.551375057230835176.449010627992
Winsorized Mean ( 17 / 24 )97.42652777777780.528884805703768184.211243596109
Winsorized Mean ( 18 / 24 )97.54402777777780.509382303358733191.494732217036
Winsorized Mean ( 19 / 24 )97.66805555555560.49001160276931199.317842686954
Winsorized Mean ( 20 / 24 )97.76250.474786326621557205.908415045669
Winsorized Mean ( 21 / 24 )97.771250.466173109956797209.731638122716
Winsorized Mean ( 22 / 24 )98.06152777777780.403281127054406243.159228635434
Winsorized Mean ( 23 / 24 )97.93694444444440.383468573759807255.397576610252
Winsorized Mean ( 24 / 24 )97.88361111111110.369959674321728264.579136335785
Trimmed Mean ( 1 / 24 )97.00557142857140.67806586571589143.062165983174
Trimmed Mean ( 2 / 24 )97.06735294117650.665103239051897145.943287059533
Trimmed Mean ( 3 / 24 )97.12909090909090.654146634519566148.482138076621
Trimmed Mean ( 4 / 24 )97.205468750.64379532240239150.988156278097
Trimmed Mean ( 5 / 24 )97.2650.637444484367423152.585836704701
Trimmed Mean ( 6 / 24 )97.32750.629850427271796154.524782052741
Trimmed Mean ( 7 / 24 )97.39189655172410.62386824120914156.109720159766
Trimmed Mean ( 8 / 24 )97.460.616910715718921157.980721548051
Trimmed Mean ( 9 / 24 )97.52925925925930.609759312120618159.947141963396
Trimmed Mean ( 10 / 24 )97.60134615384620.602026368842563162.121380732029
Trimmed Mean ( 11 / 24 )97.67040.594396346845148164.318641119517
Trimmed Mean ( 12 / 24 )97.7218750.59087180572634165.385916290038
Trimmed Mean ( 13 / 24 )97.78152173913040.586559440743843166.703517064066
Trimmed Mean ( 14 / 24 )97.84681818181820.580110051227914168.669406735337
Trimmed Mean ( 15 / 24 )97.91666666666670.571699045550805171.273098020181
Trimmed Mean ( 16 / 24 )97.993250.561392201162112174.553992373155
Trimmed Mean ( 17 / 24 )98.07657894736840.548342293798933178.860139107437
Trimmed Mean ( 18 / 24 )98.15305555555560.535642000120201183.243762687634
Trimmed Mean ( 19 / 24 )98.22470588235290.522442541816651188.010542826018
Trimmed Mean ( 20 / 24 )98.2906250.508444801754774193.316215763783
Trimmed Mean ( 21 / 24 )98.3540.491920842150979199.938672185419
Trimmed Mean ( 22 / 24 )98.42535714285710.469076680068221209.827862533141
Trimmed Mean ( 23 / 24 )98.47115384615380.456790922354595215.571608425513
Trimmed Mean ( 24 / 24 )98.54083333333330.441980849422278222.952721734749
Median98.67
Midrange93.665
Midmean - Weighted Average at Xnp97.9691891891892
Midmean - Weighted Average at X(n+1)p98.1530555555556
Midmean - Empirical Distribution Function97.9691891891892
Midmean - Empirical Distribution Function - Averaging98.1530555555556
Midmean - Empirical Distribution Function - Interpolation98.1530555555556
Midmean - Closest Observation97.9691891891892
Midmean - True Basic - Statistics Graphics Toolkit98.1530555555556
Midmean - MS Excel (old versions)98.1784615384616
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 96.9127777777778 & 0.707128254725791 & 137.051202706302 \tabularnewline
Geometric Mean & 96.7243063937794 &  &  \tabularnewline
Harmonic Mean & 96.5305828986363 &  &  \tabularnewline
Quadratic Mean & 97.0957705195122 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 96.9472222222222 & 0.688819560850942 & 140.744002830665 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 96.9541666666667 & 0.681371503931099 & 142.292664291506 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 96.9254166666666 & 0.674445954078319 & 143.711169265034 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 97.0004166666667 & 0.656735698496716 & 147.700843564166 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 97.0045833333333 & 0.654931214581603 & 148.114154851062 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 97.01625 & 0.641193699157745 & 151.305682085519 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 97.0211111111111 & 0.637396085475247 & 152.214789707677 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 97.0444444444445 & 0.628960033191665 & 154.293499305498 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 97.0606944444444 & 0.621133338875883 & 156.263862152534 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 97.1218055555555 & 0.609332170101573 & 159.390575979873 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 97.2929166666667 & 0.578631332537846 & 168.143187545592 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 97.2645833333333 & 0.57258685769484 & 169.868696820789 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 97.2627777777778 & 0.571831277790124 & 170.089992547549 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 97.2763888888889 & 0.567250572734336 & 171.487511101107 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 97.2784722222222 & 0.559012433327838 & 174.018441133978 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 97.2895833333333 & 0.551375057230835 & 176.449010627992 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 97.4265277777778 & 0.528884805703768 & 184.211243596109 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 97.5440277777778 & 0.509382303358733 & 191.494732217036 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 97.6680555555556 & 0.49001160276931 & 199.317842686954 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 97.7625 & 0.474786326621557 & 205.908415045669 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 97.77125 & 0.466173109956797 & 209.731638122716 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 98.0615277777778 & 0.403281127054406 & 243.159228635434 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 97.9369444444444 & 0.383468573759807 & 255.397576610252 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 97.8836111111111 & 0.369959674321728 & 264.579136335785 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 97.0055714285714 & 0.67806586571589 & 143.062165983174 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 97.0673529411765 & 0.665103239051897 & 145.943287059533 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 97.1290909090909 & 0.654146634519566 & 148.482138076621 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 97.20546875 & 0.64379532240239 & 150.988156278097 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 97.265 & 0.637444484367423 & 152.585836704701 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 97.3275 & 0.629850427271796 & 154.524782052741 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 97.3918965517241 & 0.62386824120914 & 156.109720159766 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 97.46 & 0.616910715718921 & 157.980721548051 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 97.5292592592593 & 0.609759312120618 & 159.947141963396 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 97.6013461538462 & 0.602026368842563 & 162.121380732029 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 97.6704 & 0.594396346845148 & 164.318641119517 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 97.721875 & 0.59087180572634 & 165.385916290038 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 97.7815217391304 & 0.586559440743843 & 166.703517064066 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 97.8468181818182 & 0.580110051227914 & 168.669406735337 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 97.9166666666667 & 0.571699045550805 & 171.273098020181 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 97.99325 & 0.561392201162112 & 174.553992373155 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 98.0765789473684 & 0.548342293798933 & 178.860139107437 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 98.1530555555556 & 0.535642000120201 & 183.243762687634 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 98.2247058823529 & 0.522442541816651 & 188.010542826018 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 98.290625 & 0.508444801754774 & 193.316215763783 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 98.354 & 0.491920842150979 & 199.938672185419 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 98.4253571428571 & 0.469076680068221 & 209.827862533141 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 98.4711538461538 & 0.456790922354595 & 215.571608425513 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 98.5408333333333 & 0.441980849422278 & 222.952721734749 \tabularnewline
Median & 98.67 &  &  \tabularnewline
Midrange & 93.665 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 97.9691891891892 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 98.1530555555556 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 97.9691891891892 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 98.1530555555556 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 98.1530555555556 &  &  \tabularnewline
Midmean - Closest Observation & 97.9691891891892 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 98.1530555555556 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 98.1784615384616 &  &  \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]96.9127777777778[/C][C]0.707128254725791[/C][C]137.051202706302[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]96.7243063937794[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]96.5305828986363[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]97.0957705195122[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]96.9472222222222[/C][C]0.688819560850942[/C][C]140.744002830665[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]96.9541666666667[/C][C]0.681371503931099[/C][C]142.292664291506[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]96.9254166666666[/C][C]0.674445954078319[/C][C]143.711169265034[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]97.0004166666667[/C][C]0.656735698496716[/C][C]147.700843564166[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]97.0045833333333[/C][C]0.654931214581603[/C][C]148.114154851062[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]97.01625[/C][C]0.641193699157745[/C][C]151.305682085519[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]97.0211111111111[/C][C]0.637396085475247[/C][C]152.214789707677[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]97.0444444444445[/C][C]0.628960033191665[/C][C]154.293499305498[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]97.0606944444444[/C][C]0.621133338875883[/C][C]156.263862152534[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]97.1218055555555[/C][C]0.609332170101573[/C][C]159.390575979873[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]97.2929166666667[/C][C]0.578631332537846[/C][C]168.143187545592[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]97.2645833333333[/C][C]0.57258685769484[/C][C]169.868696820789[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]97.2627777777778[/C][C]0.571831277790124[/C][C]170.089992547549[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]97.2763888888889[/C][C]0.567250572734336[/C][C]171.487511101107[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]97.2784722222222[/C][C]0.559012433327838[/C][C]174.018441133978[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]97.2895833333333[/C][C]0.551375057230835[/C][C]176.449010627992[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]97.4265277777778[/C][C]0.528884805703768[/C][C]184.211243596109[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]97.5440277777778[/C][C]0.509382303358733[/C][C]191.494732217036[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]97.6680555555556[/C][C]0.49001160276931[/C][C]199.317842686954[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]97.7625[/C][C]0.474786326621557[/C][C]205.908415045669[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]97.77125[/C][C]0.466173109956797[/C][C]209.731638122716[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]98.0615277777778[/C][C]0.403281127054406[/C][C]243.159228635434[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]97.9369444444444[/C][C]0.383468573759807[/C][C]255.397576610252[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]97.8836111111111[/C][C]0.369959674321728[/C][C]264.579136335785[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]97.0055714285714[/C][C]0.67806586571589[/C][C]143.062165983174[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]97.0673529411765[/C][C]0.665103239051897[/C][C]145.943287059533[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]97.1290909090909[/C][C]0.654146634519566[/C][C]148.482138076621[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]97.20546875[/C][C]0.64379532240239[/C][C]150.988156278097[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]97.265[/C][C]0.637444484367423[/C][C]152.585836704701[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]97.3275[/C][C]0.629850427271796[/C][C]154.524782052741[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]97.3918965517241[/C][C]0.62386824120914[/C][C]156.109720159766[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]97.46[/C][C]0.616910715718921[/C][C]157.980721548051[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]97.5292592592593[/C][C]0.609759312120618[/C][C]159.947141963396[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]97.6013461538462[/C][C]0.602026368842563[/C][C]162.121380732029[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]97.6704[/C][C]0.594396346845148[/C][C]164.318641119517[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]97.721875[/C][C]0.59087180572634[/C][C]165.385916290038[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]97.7815217391304[/C][C]0.586559440743843[/C][C]166.703517064066[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]97.8468181818182[/C][C]0.580110051227914[/C][C]168.669406735337[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]97.9166666666667[/C][C]0.571699045550805[/C][C]171.273098020181[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]97.99325[/C][C]0.561392201162112[/C][C]174.553992373155[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]98.0765789473684[/C][C]0.548342293798933[/C][C]178.860139107437[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]98.1530555555556[/C][C]0.535642000120201[/C][C]183.243762687634[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]98.2247058823529[/C][C]0.522442541816651[/C][C]188.010542826018[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]98.290625[/C][C]0.508444801754774[/C][C]193.316215763783[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]98.354[/C][C]0.491920842150979[/C][C]199.938672185419[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]98.4253571428571[/C][C]0.469076680068221[/C][C]209.827862533141[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]98.4711538461538[/C][C]0.456790922354595[/C][C]215.571608425513[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]98.5408333333333[/C][C]0.441980849422278[/C][C]222.952721734749[/C][/ROW]
[ROW][C]Median[/C][C]98.67[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]93.665[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]97.9691891891892[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]98.1530555555556[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]97.9691891891892[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]98.1530555555556[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]98.1530555555556[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]97.9691891891892[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]98.1530555555556[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]98.1784615384616[/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 Mean96.91277777777780.707128254725791137.051202706302
Geometric Mean96.7243063937794
Harmonic Mean96.5305828986363
Quadratic Mean97.0957705195122
Winsorized Mean ( 1 / 24 )96.94722222222220.688819560850942140.744002830665
Winsorized Mean ( 2 / 24 )96.95416666666670.681371503931099142.292664291506
Winsorized Mean ( 3 / 24 )96.92541666666660.674445954078319143.711169265034
Winsorized Mean ( 4 / 24 )97.00041666666670.656735698496716147.700843564166
Winsorized Mean ( 5 / 24 )97.00458333333330.654931214581603148.114154851062
Winsorized Mean ( 6 / 24 )97.016250.641193699157745151.305682085519
Winsorized Mean ( 7 / 24 )97.02111111111110.637396085475247152.214789707677
Winsorized Mean ( 8 / 24 )97.04444444444450.628960033191665154.293499305498
Winsorized Mean ( 9 / 24 )97.06069444444440.621133338875883156.263862152534
Winsorized Mean ( 10 / 24 )97.12180555555550.609332170101573159.390575979873
Winsorized Mean ( 11 / 24 )97.29291666666670.578631332537846168.143187545592
Winsorized Mean ( 12 / 24 )97.26458333333330.57258685769484169.868696820789
Winsorized Mean ( 13 / 24 )97.26277777777780.571831277790124170.089992547549
Winsorized Mean ( 14 / 24 )97.27638888888890.567250572734336171.487511101107
Winsorized Mean ( 15 / 24 )97.27847222222220.559012433327838174.018441133978
Winsorized Mean ( 16 / 24 )97.28958333333330.551375057230835176.449010627992
Winsorized Mean ( 17 / 24 )97.42652777777780.528884805703768184.211243596109
Winsorized Mean ( 18 / 24 )97.54402777777780.509382303358733191.494732217036
Winsorized Mean ( 19 / 24 )97.66805555555560.49001160276931199.317842686954
Winsorized Mean ( 20 / 24 )97.76250.474786326621557205.908415045669
Winsorized Mean ( 21 / 24 )97.771250.466173109956797209.731638122716
Winsorized Mean ( 22 / 24 )98.06152777777780.403281127054406243.159228635434
Winsorized Mean ( 23 / 24 )97.93694444444440.383468573759807255.397576610252
Winsorized Mean ( 24 / 24 )97.88361111111110.369959674321728264.579136335785
Trimmed Mean ( 1 / 24 )97.00557142857140.67806586571589143.062165983174
Trimmed Mean ( 2 / 24 )97.06735294117650.665103239051897145.943287059533
Trimmed Mean ( 3 / 24 )97.12909090909090.654146634519566148.482138076621
Trimmed Mean ( 4 / 24 )97.205468750.64379532240239150.988156278097
Trimmed Mean ( 5 / 24 )97.2650.637444484367423152.585836704701
Trimmed Mean ( 6 / 24 )97.32750.629850427271796154.524782052741
Trimmed Mean ( 7 / 24 )97.39189655172410.62386824120914156.109720159766
Trimmed Mean ( 8 / 24 )97.460.616910715718921157.980721548051
Trimmed Mean ( 9 / 24 )97.52925925925930.609759312120618159.947141963396
Trimmed Mean ( 10 / 24 )97.60134615384620.602026368842563162.121380732029
Trimmed Mean ( 11 / 24 )97.67040.594396346845148164.318641119517
Trimmed Mean ( 12 / 24 )97.7218750.59087180572634165.385916290038
Trimmed Mean ( 13 / 24 )97.78152173913040.586559440743843166.703517064066
Trimmed Mean ( 14 / 24 )97.84681818181820.580110051227914168.669406735337
Trimmed Mean ( 15 / 24 )97.91666666666670.571699045550805171.273098020181
Trimmed Mean ( 16 / 24 )97.993250.561392201162112174.553992373155
Trimmed Mean ( 17 / 24 )98.07657894736840.548342293798933178.860139107437
Trimmed Mean ( 18 / 24 )98.15305555555560.535642000120201183.243762687634
Trimmed Mean ( 19 / 24 )98.22470588235290.522442541816651188.010542826018
Trimmed Mean ( 20 / 24 )98.2906250.508444801754774193.316215763783
Trimmed Mean ( 21 / 24 )98.3540.491920842150979199.938672185419
Trimmed Mean ( 22 / 24 )98.42535714285710.469076680068221209.827862533141
Trimmed Mean ( 23 / 24 )98.47115384615380.456790922354595215.571608425513
Trimmed Mean ( 24 / 24 )98.54083333333330.441980849422278222.952721734749
Median98.67
Midrange93.665
Midmean - Weighted Average at Xnp97.9691891891892
Midmean - Weighted Average at X(n+1)p98.1530555555556
Midmean - Empirical Distribution Function97.9691891891892
Midmean - Empirical Distribution Function - Averaging98.1530555555556
Midmean - Empirical Distribution Function - Interpolation98.1530555555556
Midmean - Closest Observation97.9691891891892
Midmean - True Basic - Statistics Graphics Toolkit98.1530555555556
Midmean - MS Excel (old versions)98.1784615384616
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')