Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationMon, 10 Oct 2016 18:13:58 +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/10/t1476119666hc3p2q933ahhvwp.htm/, Retrieved Wed, 08 May 2024 21:41:04 +0200
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Wed, 08 May 2024 21:41:04 +0200
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact0
Dataseries X:
75,8
75,7
112,3
110,9
99,6
107,5
90
88,8
129,7
120,4
93,3
96
81,1
78
111,9
117,6
101
98,3
91
86,8
108,8
110,1
93,8
100,6
75,7
69
116
94,5
105,1
95,3
79,7
76,1
111,1
106,3
89,5
96,8
67,8
62,5
90,1
93,6
94,2
93,2
81
73,7
97,7
97,5
82,7
88,8
68,5
61,1
89,6
87,6
90,8
84,3
75
78,4
83,5
93
79,3
83,9
65
60,3
80,6
86,5
78,7
80,7
70,6
67,2
88
89,1
69
84,1




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Sir Ronald Aylmer Fisher' @ fisher.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 & 'Sir Ronald Aylmer Fisher' @ fisher.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]'Sir Ronald Aylmer Fisher' @ fisher.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'Sir Ronald Aylmer Fisher' @ fisher.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean89.05138888888891.7873851485428249.8221600204571
Geometric Mean87.7826909210854
Harmonic Mean86.5174382660609
Quadratic Mean90.3159831123791
Winsorized Mean ( 1 / 24 )88.93333333333331.747768530349750.8839310177642
Winsorized Mean ( 2 / 24 )88.89444444444441.7201965723745451.6769105764091
Winsorized Mean ( 3 / 24 )88.93194444444451.6831134825856852.8377589298512
Winsorized Mean ( 4 / 24 )88.84861111111111.6149753907527255.0154582044124
Winsorized Mean ( 5 / 24 )88.86251.6015280720277655.4860708045457
Winsorized Mean ( 6 / 24 )88.85416666666671.577448834637756.3277646257694
Winsorized Mean ( 7 / 24 )88.88333333333331.5648238587522256.8008551481368
Winsorized Mean ( 8 / 24 )88.79444444444441.5473965829777857.38312041091
Winsorized Mean ( 9 / 24 )88.83194444444441.4808292763885559.9879715108606
Winsorized Mean ( 10 / 24 )89.08194444444441.3752810587537664.7736285448213
Winsorized Mean ( 11 / 24 )89.09722222222221.3103267046263367.9961889715363
Winsorized Mean ( 12 / 24 )89.01388888888891.2562415464341770.8573037896686
Winsorized Mean ( 13 / 24 )88.27361111111111.1303675518395778.092838888956
Winsorized Mean ( 14 / 24 )88.21527777777781.115069033916779.111942933183
Winsorized Mean ( 15 / 24 )88.06944444444441.0731913104228882.0631359843399
Winsorized Mean ( 16 / 24 )88.20277777777780.96534224517612691.3694373353414
Winsorized Mean ( 17 / 24 )88.15555555555560.93066959103202194.7227205068554
Winsorized Mean ( 18 / 24 )88.18055555555560.91243718863051996.6428776186842
Winsorized Mean ( 19 / 24 )88.15416666666670.863083821821397102.138592379859
Winsorized Mean ( 20 / 24 )88.04305555555560.816110346082644107.881312837369
Winsorized Mean ( 21 / 24 )88.10138888888890.750916219327406117.325191041686
Winsorized Mean ( 22 / 24 )87.88750.714145410851582123.066673347657
Winsorized Mean ( 23 / 24 )87.88750.688156963104018127.714322040094
Winsorized Mean ( 24 / 24 )87.78750.666364184606152131.741023944566
Trimmed Mean ( 1 / 24 )88.88142857142861.6934024857382652.486889159537
Trimmed Mean ( 2 / 24 )88.82647058823531.6286728165333254.5391742813669
Trimmed Mean ( 3 / 24 )88.78939393939391.5692293608296656.5815273125213
Trimmed Mean ( 4 / 24 )88.73593751.5152586465059458.561578054425
Trimmed Mean ( 5 / 24 )88.70322580645161.4759108683401960.1006657713737
Trimmed Mean ( 6 / 24 )88.6651.4323991667413661.8996450561392
Trimmed Mean ( 7 / 24 )88.62586206896551.3862616918136863.9315524567473
Trimmed Mean ( 8 / 24 )88.57857142857141.3328728719440566.4568791916186
Trimmed Mean ( 9 / 24 )88.54259259259261.271250125767269.6500167810464
Trimmed Mean ( 10 / 24 )88.49807692307691.2115597390934873.0447489030076
Trimmed Mean ( 11 / 24 )88.4141.16275538340376.038349305459
Trimmed Mean ( 12 / 24 )88.32083333333331.1164746249071179.1068882023913
Trimmed Mean ( 13 / 24 )88.23043478260871.0702244541555982.441056583988
Trimmed Mean ( 14 / 24 )88.2251.0411365811216584.7391222244368
Trimmed Mean ( 15 / 24 )88.22619047619051.0061775480084387.6845151741066
Trimmed Mean ( 16 / 24 )88.2450.96970752926214491.0016652826715
Trimmed Mean ( 17 / 24 )88.250.94697804901700793.1911780759927
Trimmed Mean ( 18 / 24 )88.26111111111110.92347066004542295.5754361560008
Trimmed Mean ( 19 / 24 )88.27058823529410.89450221582366998.6812404416612
Trimmed Mean ( 20 / 24 )88.2843750.866329266901169101.906259401567
Trimmed Mean ( 21 / 24 )88.31333333333330.838221068326831105.358045353853
Trimmed Mean ( 22 / 24 )88.33928571428570.815643013871324108.30631074126
Trimmed Mean ( 23 / 24 )88.39615384615390.790860889629499111.772063842436
Trimmed Mean ( 24 / 24 )88.46250.759071049833711116.540474069429
Median88.95
Midrange95
Midmean - Weighted Average at Xnp87.9945945945946
Midmean - Weighted Average at X(n+1)p88.2611111111111
Midmean - Empirical Distribution Function87.9945945945946
Midmean - Empirical Distribution Function - Averaging88.2611111111111
Midmean - Empirical Distribution Function - Interpolation88.2611111111111
Midmean - Closest Observation87.9945945945946
Midmean - True Basic - Statistics Graphics Toolkit88.2611111111111
Midmean - MS Excel (old versions)88.25
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 89.0513888888889 & 1.78738514854282 & 49.8221600204571 \tabularnewline
Geometric Mean & 87.7826909210854 &  &  \tabularnewline
Harmonic Mean & 86.5174382660609 &  &  \tabularnewline
Quadratic Mean & 90.3159831123791 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 88.9333333333333 & 1.7477685303497 & 50.8839310177642 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 88.8944444444444 & 1.72019657237454 & 51.6769105764091 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 88.9319444444445 & 1.68311348258568 & 52.8377589298512 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 88.8486111111111 & 1.61497539075272 & 55.0154582044124 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 88.8625 & 1.60152807202776 & 55.4860708045457 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 88.8541666666667 & 1.5774488346377 & 56.3277646257694 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 88.8833333333333 & 1.56482385875222 & 56.8008551481368 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 88.7944444444444 & 1.54739658297778 & 57.38312041091 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 88.8319444444444 & 1.48082927638855 & 59.9879715108606 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 89.0819444444444 & 1.37528105875376 & 64.7736285448213 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 89.0972222222222 & 1.31032670462633 & 67.9961889715363 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 89.0138888888889 & 1.25624154643417 & 70.8573037896686 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 88.2736111111111 & 1.13036755183957 & 78.092838888956 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 88.2152777777778 & 1.1150690339167 & 79.111942933183 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 88.0694444444444 & 1.07319131042288 & 82.0631359843399 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 88.2027777777778 & 0.965342245176126 & 91.3694373353414 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 88.1555555555556 & 0.930669591032021 & 94.7227205068554 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 88.1805555555556 & 0.912437188630519 & 96.6428776186842 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 88.1541666666667 & 0.863083821821397 & 102.138592379859 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 88.0430555555556 & 0.816110346082644 & 107.881312837369 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 88.1013888888889 & 0.750916219327406 & 117.325191041686 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 87.8875 & 0.714145410851582 & 123.066673347657 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 87.8875 & 0.688156963104018 & 127.714322040094 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 87.7875 & 0.666364184606152 & 131.741023944566 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 88.8814285714286 & 1.69340248573826 & 52.486889159537 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 88.8264705882353 & 1.62867281653332 & 54.5391742813669 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 88.7893939393939 & 1.56922936082966 & 56.5815273125213 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 88.7359375 & 1.51525864650594 & 58.561578054425 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 88.7032258064516 & 1.47591086834019 & 60.1006657713737 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 88.665 & 1.43239916674136 & 61.8996450561392 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 88.6258620689655 & 1.38626169181368 & 63.9315524567473 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 88.5785714285714 & 1.33287287194405 & 66.4568791916186 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 88.5425925925926 & 1.2712501257672 & 69.6500167810464 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 88.4980769230769 & 1.21155973909348 & 73.0447489030076 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 88.414 & 1.162755383403 & 76.038349305459 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 88.3208333333333 & 1.11647462490711 & 79.1068882023913 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 88.2304347826087 & 1.07022445415559 & 82.441056583988 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 88.225 & 1.04113658112165 & 84.7391222244368 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 88.2261904761905 & 1.00617754800843 & 87.6845151741066 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 88.245 & 0.969707529262144 & 91.0016652826715 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 88.25 & 0.946978049017007 & 93.1911780759927 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 88.2611111111111 & 0.923470660045422 & 95.5754361560008 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 88.2705882352941 & 0.894502215823669 & 98.6812404416612 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 88.284375 & 0.866329266901169 & 101.906259401567 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 88.3133333333333 & 0.838221068326831 & 105.358045353853 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 88.3392857142857 & 0.815643013871324 & 108.30631074126 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 88.3961538461539 & 0.790860889629499 & 111.772063842436 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 88.4625 & 0.759071049833711 & 116.540474069429 \tabularnewline
Median & 88.95 &  &  \tabularnewline
Midrange & 95 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 87.9945945945946 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 88.2611111111111 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 87.9945945945946 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 88.2611111111111 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 88.2611111111111 &  &  \tabularnewline
Midmean - Closest Observation & 87.9945945945946 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 88.2611111111111 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 88.25 &  &  \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]89.0513888888889[/C][C]1.78738514854282[/C][C]49.8221600204571[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]87.7826909210854[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]86.5174382660609[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]90.3159831123791[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]88.9333333333333[/C][C]1.7477685303497[/C][C]50.8839310177642[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]88.8944444444444[/C][C]1.72019657237454[/C][C]51.6769105764091[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]88.9319444444445[/C][C]1.68311348258568[/C][C]52.8377589298512[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]88.8486111111111[/C][C]1.61497539075272[/C][C]55.0154582044124[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]88.8625[/C][C]1.60152807202776[/C][C]55.4860708045457[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]88.8541666666667[/C][C]1.5774488346377[/C][C]56.3277646257694[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]88.8833333333333[/C][C]1.56482385875222[/C][C]56.8008551481368[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]88.7944444444444[/C][C]1.54739658297778[/C][C]57.38312041091[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]88.8319444444444[/C][C]1.48082927638855[/C][C]59.9879715108606[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]89.0819444444444[/C][C]1.37528105875376[/C][C]64.7736285448213[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]89.0972222222222[/C][C]1.31032670462633[/C][C]67.9961889715363[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]89.0138888888889[/C][C]1.25624154643417[/C][C]70.8573037896686[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]88.2736111111111[/C][C]1.13036755183957[/C][C]78.092838888956[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]88.2152777777778[/C][C]1.1150690339167[/C][C]79.111942933183[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]88.0694444444444[/C][C]1.07319131042288[/C][C]82.0631359843399[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]88.2027777777778[/C][C]0.965342245176126[/C][C]91.3694373353414[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]88.1555555555556[/C][C]0.930669591032021[/C][C]94.7227205068554[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]88.1805555555556[/C][C]0.912437188630519[/C][C]96.6428776186842[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]88.1541666666667[/C][C]0.863083821821397[/C][C]102.138592379859[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]88.0430555555556[/C][C]0.816110346082644[/C][C]107.881312837369[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]88.1013888888889[/C][C]0.750916219327406[/C][C]117.325191041686[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]87.8875[/C][C]0.714145410851582[/C][C]123.066673347657[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]87.8875[/C][C]0.688156963104018[/C][C]127.714322040094[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]87.7875[/C][C]0.666364184606152[/C][C]131.741023944566[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]88.8814285714286[/C][C]1.69340248573826[/C][C]52.486889159537[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]88.8264705882353[/C][C]1.62867281653332[/C][C]54.5391742813669[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]88.7893939393939[/C][C]1.56922936082966[/C][C]56.5815273125213[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]88.7359375[/C][C]1.51525864650594[/C][C]58.561578054425[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]88.7032258064516[/C][C]1.47591086834019[/C][C]60.1006657713737[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]88.665[/C][C]1.43239916674136[/C][C]61.8996450561392[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]88.6258620689655[/C][C]1.38626169181368[/C][C]63.9315524567473[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]88.5785714285714[/C][C]1.33287287194405[/C][C]66.4568791916186[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]88.5425925925926[/C][C]1.2712501257672[/C][C]69.6500167810464[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]88.4980769230769[/C][C]1.21155973909348[/C][C]73.0447489030076[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]88.414[/C][C]1.162755383403[/C][C]76.038349305459[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]88.3208333333333[/C][C]1.11647462490711[/C][C]79.1068882023913[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]88.2304347826087[/C][C]1.07022445415559[/C][C]82.441056583988[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]88.225[/C][C]1.04113658112165[/C][C]84.7391222244368[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]88.2261904761905[/C][C]1.00617754800843[/C][C]87.6845151741066[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]88.245[/C][C]0.969707529262144[/C][C]91.0016652826715[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]88.25[/C][C]0.946978049017007[/C][C]93.1911780759927[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]88.2611111111111[/C][C]0.923470660045422[/C][C]95.5754361560008[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]88.2705882352941[/C][C]0.894502215823669[/C][C]98.6812404416612[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]88.284375[/C][C]0.866329266901169[/C][C]101.906259401567[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]88.3133333333333[/C][C]0.838221068326831[/C][C]105.358045353853[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]88.3392857142857[/C][C]0.815643013871324[/C][C]108.30631074126[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]88.3961538461539[/C][C]0.790860889629499[/C][C]111.772063842436[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]88.4625[/C][C]0.759071049833711[/C][C]116.540474069429[/C][/ROW]
[ROW][C]Median[/C][C]88.95[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]95[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]87.9945945945946[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]88.2611111111111[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]87.9945945945946[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]88.2611111111111[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]88.2611111111111[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]87.9945945945946[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]88.2611111111111[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]88.25[/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 Mean89.05138888888891.7873851485428249.8221600204571
Geometric Mean87.7826909210854
Harmonic Mean86.5174382660609
Quadratic Mean90.3159831123791
Winsorized Mean ( 1 / 24 )88.93333333333331.747768530349750.8839310177642
Winsorized Mean ( 2 / 24 )88.89444444444441.7201965723745451.6769105764091
Winsorized Mean ( 3 / 24 )88.93194444444451.6831134825856852.8377589298512
Winsorized Mean ( 4 / 24 )88.84861111111111.6149753907527255.0154582044124
Winsorized Mean ( 5 / 24 )88.86251.6015280720277655.4860708045457
Winsorized Mean ( 6 / 24 )88.85416666666671.577448834637756.3277646257694
Winsorized Mean ( 7 / 24 )88.88333333333331.5648238587522256.8008551481368
Winsorized Mean ( 8 / 24 )88.79444444444441.5473965829777857.38312041091
Winsorized Mean ( 9 / 24 )88.83194444444441.4808292763885559.9879715108606
Winsorized Mean ( 10 / 24 )89.08194444444441.3752810587537664.7736285448213
Winsorized Mean ( 11 / 24 )89.09722222222221.3103267046263367.9961889715363
Winsorized Mean ( 12 / 24 )89.01388888888891.2562415464341770.8573037896686
Winsorized Mean ( 13 / 24 )88.27361111111111.1303675518395778.092838888956
Winsorized Mean ( 14 / 24 )88.21527777777781.115069033916779.111942933183
Winsorized Mean ( 15 / 24 )88.06944444444441.0731913104228882.0631359843399
Winsorized Mean ( 16 / 24 )88.20277777777780.96534224517612691.3694373353414
Winsorized Mean ( 17 / 24 )88.15555555555560.93066959103202194.7227205068554
Winsorized Mean ( 18 / 24 )88.18055555555560.91243718863051996.6428776186842
Winsorized Mean ( 19 / 24 )88.15416666666670.863083821821397102.138592379859
Winsorized Mean ( 20 / 24 )88.04305555555560.816110346082644107.881312837369
Winsorized Mean ( 21 / 24 )88.10138888888890.750916219327406117.325191041686
Winsorized Mean ( 22 / 24 )87.88750.714145410851582123.066673347657
Winsorized Mean ( 23 / 24 )87.88750.688156963104018127.714322040094
Winsorized Mean ( 24 / 24 )87.78750.666364184606152131.741023944566
Trimmed Mean ( 1 / 24 )88.88142857142861.6934024857382652.486889159537
Trimmed Mean ( 2 / 24 )88.82647058823531.6286728165333254.5391742813669
Trimmed Mean ( 3 / 24 )88.78939393939391.5692293608296656.5815273125213
Trimmed Mean ( 4 / 24 )88.73593751.5152586465059458.561578054425
Trimmed Mean ( 5 / 24 )88.70322580645161.4759108683401960.1006657713737
Trimmed Mean ( 6 / 24 )88.6651.4323991667413661.8996450561392
Trimmed Mean ( 7 / 24 )88.62586206896551.3862616918136863.9315524567473
Trimmed Mean ( 8 / 24 )88.57857142857141.3328728719440566.4568791916186
Trimmed Mean ( 9 / 24 )88.54259259259261.271250125767269.6500167810464
Trimmed Mean ( 10 / 24 )88.49807692307691.2115597390934873.0447489030076
Trimmed Mean ( 11 / 24 )88.4141.16275538340376.038349305459
Trimmed Mean ( 12 / 24 )88.32083333333331.1164746249071179.1068882023913
Trimmed Mean ( 13 / 24 )88.23043478260871.0702244541555982.441056583988
Trimmed Mean ( 14 / 24 )88.2251.0411365811216584.7391222244368
Trimmed Mean ( 15 / 24 )88.22619047619051.0061775480084387.6845151741066
Trimmed Mean ( 16 / 24 )88.2450.96970752926214491.0016652826715
Trimmed Mean ( 17 / 24 )88.250.94697804901700793.1911780759927
Trimmed Mean ( 18 / 24 )88.26111111111110.92347066004542295.5754361560008
Trimmed Mean ( 19 / 24 )88.27058823529410.89450221582366998.6812404416612
Trimmed Mean ( 20 / 24 )88.2843750.866329266901169101.906259401567
Trimmed Mean ( 21 / 24 )88.31333333333330.838221068326831105.358045353853
Trimmed Mean ( 22 / 24 )88.33928571428570.815643013871324108.30631074126
Trimmed Mean ( 23 / 24 )88.39615384615390.790860889629499111.772063842436
Trimmed Mean ( 24 / 24 )88.46250.759071049833711116.540474069429
Median88.95
Midrange95
Midmean - Weighted Average at Xnp87.9945945945946
Midmean - Weighted Average at X(n+1)p88.2611111111111
Midmean - Empirical Distribution Function87.9945945945946
Midmean - Empirical Distribution Function - Averaging88.2611111111111
Midmean - Empirical Distribution Function - Interpolation88.2611111111111
Midmean - Closest Observation87.9945945945946
Midmean - True Basic - Statistics Graphics Toolkit88.2611111111111
Midmean - MS Excel (old versions)88.25
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')