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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationSun, 23 Feb 2014 14:35:05 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2014/Feb/23/t1393184131r9hvc6cf3i8ql53.htm/, Retrieved Wed, 15 May 2024 13:04:04 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=233986, Retrieved Wed, 15 May 2024 13:04:04 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact121
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2014-02-23 19:35:05] [e610340e7a3184c9e0a1f377a12e8a83] [Current]
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Dataseries X:
3477
2685
2438
1692
4054
3946
3623
2455
2362
2791
2369
3438
3682
2801
2563
3108
2890
3940
4036
1514
3461
2980
2728
3891
3715
2843
1416
2657
1856
2441
3172
2813
3335
2608
5784
4726
3817
2755
2541
3154
2684
3732
4286
2394
1698
3945
2549
3943
3899
2783
2660
1848
4482
4157
4404
2686
2593
3254
2664
4203
3985
2861
2758
1968
4666
4226
4748
2767
2723
3297
2758
4338




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 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 & 3 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=233986&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]3 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=233986&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=233986&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 time3 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean3173.83333333333102.99376472003130.8157813432766
Geometric Mean3052.42213976467
Harmonic Mean2926.59865893181
Quadratic Mean3290.34433355133
Winsorized Mean ( 1 / 24 )3160.8055555555698.44697944423532.1066788783092
Winsorized Mean ( 2 / 24 )3165.1388888888997.197935654232332.5638488881947
Winsorized Mean ( 3 / 24 )3162.8888888888996.587821081955132.746249511159
Winsorized Mean ( 4 / 24 )316192.717649872120234.0927536920939
Winsorized Mean ( 5 / 24 )3156.1388888888991.543073542445834.4770911304992
Winsorized Mean ( 6 / 24 )3159.9722222222288.682647021365235.6323624559936
Winsorized Mean ( 7 / 24 )3193.2222222222281.310366336623239.2720186378493
Winsorized Mean ( 8 / 24 )3187.3333333333379.957299832830339.8629435961096
Winsorized Mean ( 9 / 24 )3187.5833333333378.987637327291540.3554713268018
Winsorized Mean ( 10 / 24 )3187.3055555555676.991028070296441.3984023261178
Winsorized Mean ( 11 / 24 )3172.0277777777874.21366072544642.7418314468103
Winsorized Mean ( 12 / 24 )3171.3611111111173.391417739349443.2116071442337
Winsorized Mean ( 13 / 24 )3177.6805555555669.810773823097645.5184834880628
Winsorized Mean ( 14 / 24 )3171.6527777777868.388736156388846.3768298119293
Winsorized Mean ( 15 / 24 )3174.3611111111167.983768388504846.6929266552376
Winsorized Mean ( 16 / 24 )3180.5833333333367.079201167459347.4153430270166
Winsorized Mean ( 17 / 24 )3183.4166666666766.531581890774947.8482034576134
Winsorized Mean ( 18 / 24 )3185.4166666666763.433105714807850.2169431997883
Winsorized Mean ( 19 / 24 )3184.0972222222263.006241337391850.536219184568
Winsorized Mean ( 20 / 24 )3164.6527777777859.667634344850153.0380131963606
Winsorized Mean ( 21 / 24 )3145.6944444444455.21457871093256.9721714424967
Winsorized Mean ( 22 / 24 )3140.8055555555654.404021814105357.7311281560666
Winsorized Mean ( 23 / 24 )3130.5833333333352.807408184410459.2830332138424
Winsorized Mean ( 24 / 24 )3123.2548.484008100311364.4181478053162
Trimmed Mean ( 1 / 24 )3161.6571428571495.784129889027333.008152253616
Trimmed Mean ( 2 / 24 )3162.5588235294192.618245097827734.1461751967873
Trimmed Mean ( 3 / 24 )3161.1515151515289.64444203152935.2632181484235
Trimmed Mean ( 4 / 24 )3160.586.358156249387636.5975854194132
Trimmed Mean ( 5 / 24 )3160.3548387096883.865736219705937.6835043864683
Trimmed Mean ( 6 / 24 )3161.3666666666781.22038083913138.9233174482181
Trimmed Mean ( 7 / 24 )3161.6551724137978.829728945318240.1073962160511
Trimmed Mean ( 8 / 24 )3155.8571428571477.790967945369840.5684262094978
Trimmed Mean ( 9 / 24 )3150.6111111111176.781389949221141.033525352885
Trimmed Mean ( 10 / 24 )3144.9230769230875.684203618329541.5532294266148
Trimmed Mean ( 11 / 24 )3138.8274.68304558572342.0285484527701
Trimmed Mean ( 12 / 24 )3134.2916666666773.957062720081342.3798830211739
Trimmed Mean ( 13 / 24 )3129.4565217391373.10879132238542.8054747607478
Trimmed Mean ( 14 / 24 )3123.3863636363672.642934962072542.9964230556916
Trimmed Mean ( 15 / 24 )3117.4761904761972.197932848939543.1795768585081
Trimmed Mean ( 16 / 24 )3110.6571.530400117891443.4871047117483
Trimmed Mean ( 17 / 24 )3102.3684210526370.652913381893943.9099857678009
Trimmed Mean ( 18 / 24 )3092.8333333333369.403461557695244.5630990719715
Trimmed Mean ( 19 / 24 )3081.9411764705968.243364204077245.1610381817381
Trimmed Mean ( 20 / 24 )3069.8437566.508823532001346.1569395904728
Trimmed Mean ( 21 / 24 )3058.4666666666764.871238217662547.1467286689455
Trimmed Mean ( 22 / 24 )3047.7857142857163.663869238443847.8730832848169
Trimmed Mean ( 23 / 24 )3036.0769230769261.815878544567249.1148390115981
Trimmed Mean ( 24 / 24 )3023.7559.288726413291651.0004208712792
Median2875.5
Midrange3600
Midmean - Weighted Average at Xnp3079.72972972973
Midmean - Weighted Average at X(n+1)p3092.83333333333
Midmean - Empirical Distribution Function3079.72972972973
Midmean - Empirical Distribution Function - Averaging3092.83333333333
Midmean - Empirical Distribution Function - Interpolation3092.83333333333
Midmean - Closest Observation3079.72972972973
Midmean - True Basic - Statistics Graphics Toolkit3092.83333333333
Midmean - MS Excel (old versions)3102.36842105263
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 3173.83333333333 & 102.993764720031 & 30.8157813432766 \tabularnewline
Geometric Mean & 3052.42213976467 &  &  \tabularnewline
Harmonic Mean & 2926.59865893181 &  &  \tabularnewline
Quadratic Mean & 3290.34433355133 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 3160.80555555556 & 98.446979444235 & 32.1066788783092 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 3165.13888888889 & 97.1979356542323 & 32.5638488881947 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 3162.88888888889 & 96.5878210819551 & 32.746249511159 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 3161 & 92.7176498721202 & 34.0927536920939 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 3156.13888888889 & 91.5430735424458 & 34.4770911304992 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 3159.97222222222 & 88.6826470213652 & 35.6323624559936 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 3193.22222222222 & 81.3103663366232 & 39.2720186378493 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 3187.33333333333 & 79.9572998328303 & 39.8629435961096 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 3187.58333333333 & 78.9876373272915 & 40.3554713268018 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 3187.30555555556 & 76.9910280702964 & 41.3984023261178 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 3172.02777777778 & 74.213660725446 & 42.7418314468103 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 3171.36111111111 & 73.3914177393494 & 43.2116071442337 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 3177.68055555556 & 69.8107738230976 & 45.5184834880628 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 3171.65277777778 & 68.3887361563888 & 46.3768298119293 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 3174.36111111111 & 67.9837683885048 & 46.6929266552376 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 3180.58333333333 & 67.0792011674593 & 47.4153430270166 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 3183.41666666667 & 66.5315818907749 & 47.8482034576134 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 3185.41666666667 & 63.4331057148078 & 50.2169431997883 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 3184.09722222222 & 63.0062413373918 & 50.536219184568 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 3164.65277777778 & 59.6676343448501 & 53.0380131963606 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 3145.69444444444 & 55.214578710932 & 56.9721714424967 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 3140.80555555556 & 54.4040218141053 & 57.7311281560666 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 3130.58333333333 & 52.8074081844104 & 59.2830332138424 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 3123.25 & 48.4840081003113 & 64.4181478053162 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 3161.65714285714 & 95.7841298890273 & 33.008152253616 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 3162.55882352941 & 92.6182450978277 & 34.1461751967873 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 3161.15151515152 & 89.644442031529 & 35.2632181484235 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 3160.5 & 86.3581562493876 & 36.5975854194132 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 3160.35483870968 & 83.8657362197059 & 37.6835043864683 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 3161.36666666667 & 81.220380839131 & 38.9233174482181 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 3161.65517241379 & 78.8297289453182 & 40.1073962160511 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 3155.85714285714 & 77.7909679453698 & 40.5684262094978 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 3150.61111111111 & 76.7813899492211 & 41.033525352885 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 3144.92307692308 & 75.6842036183295 & 41.5532294266148 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 3138.82 & 74.683045585723 & 42.0285484527701 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 3134.29166666667 & 73.9570627200813 & 42.3798830211739 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 3129.45652173913 & 73.108791322385 & 42.8054747607478 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 3123.38636363636 & 72.6429349620725 & 42.9964230556916 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 3117.47619047619 & 72.1979328489395 & 43.1795768585081 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 3110.65 & 71.5304001178914 & 43.4871047117483 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 3102.36842105263 & 70.6529133818939 & 43.9099857678009 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 3092.83333333333 & 69.4034615576952 & 44.5630990719715 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 3081.94117647059 & 68.2433642040772 & 45.1610381817381 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 3069.84375 & 66.5088235320013 & 46.1569395904728 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 3058.46666666667 & 64.8712382176625 & 47.1467286689455 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 3047.78571428571 & 63.6638692384438 & 47.8730832848169 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 3036.07692307692 & 61.8158785445672 & 49.1148390115981 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 3023.75 & 59.2887264132916 & 51.0004208712792 \tabularnewline
Median & 2875.5 &  &  \tabularnewline
Midrange & 3600 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 3079.72972972973 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 3092.83333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 3079.72972972973 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 3092.83333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 3092.83333333333 &  &  \tabularnewline
Midmean - Closest Observation & 3079.72972972973 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 3092.83333333333 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 3102.36842105263 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=233986&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]3173.83333333333[/C][C]102.993764720031[/C][C]30.8157813432766[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]3052.42213976467[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]2926.59865893181[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]3290.34433355133[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]3160.80555555556[/C][C]98.446979444235[/C][C]32.1066788783092[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]3165.13888888889[/C][C]97.1979356542323[/C][C]32.5638488881947[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]3162.88888888889[/C][C]96.5878210819551[/C][C]32.746249511159[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]3161[/C][C]92.7176498721202[/C][C]34.0927536920939[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]3156.13888888889[/C][C]91.5430735424458[/C][C]34.4770911304992[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]3159.97222222222[/C][C]88.6826470213652[/C][C]35.6323624559936[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]3193.22222222222[/C][C]81.3103663366232[/C][C]39.2720186378493[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]3187.33333333333[/C][C]79.9572998328303[/C][C]39.8629435961096[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]3187.58333333333[/C][C]78.9876373272915[/C][C]40.3554713268018[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]3187.30555555556[/C][C]76.9910280702964[/C][C]41.3984023261178[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]3172.02777777778[/C][C]74.213660725446[/C][C]42.7418314468103[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]3171.36111111111[/C][C]73.3914177393494[/C][C]43.2116071442337[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]3177.68055555556[/C][C]69.8107738230976[/C][C]45.5184834880628[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]3171.65277777778[/C][C]68.3887361563888[/C][C]46.3768298119293[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]3174.36111111111[/C][C]67.9837683885048[/C][C]46.6929266552376[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]3180.58333333333[/C][C]67.0792011674593[/C][C]47.4153430270166[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]3183.41666666667[/C][C]66.5315818907749[/C][C]47.8482034576134[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]3185.41666666667[/C][C]63.4331057148078[/C][C]50.2169431997883[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]3184.09722222222[/C][C]63.0062413373918[/C][C]50.536219184568[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]3164.65277777778[/C][C]59.6676343448501[/C][C]53.0380131963606[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]3145.69444444444[/C][C]55.214578710932[/C][C]56.9721714424967[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]3140.80555555556[/C][C]54.4040218141053[/C][C]57.7311281560666[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]3130.58333333333[/C][C]52.8074081844104[/C][C]59.2830332138424[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]3123.25[/C][C]48.4840081003113[/C][C]64.4181478053162[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]3161.65714285714[/C][C]95.7841298890273[/C][C]33.008152253616[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]3162.55882352941[/C][C]92.6182450978277[/C][C]34.1461751967873[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]3161.15151515152[/C][C]89.644442031529[/C][C]35.2632181484235[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]3160.5[/C][C]86.3581562493876[/C][C]36.5975854194132[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]3160.35483870968[/C][C]83.8657362197059[/C][C]37.6835043864683[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]3161.36666666667[/C][C]81.220380839131[/C][C]38.9233174482181[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]3161.65517241379[/C][C]78.8297289453182[/C][C]40.1073962160511[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]3155.85714285714[/C][C]77.7909679453698[/C][C]40.5684262094978[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]3150.61111111111[/C][C]76.7813899492211[/C][C]41.033525352885[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]3144.92307692308[/C][C]75.6842036183295[/C][C]41.5532294266148[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]3138.82[/C][C]74.683045585723[/C][C]42.0285484527701[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]3134.29166666667[/C][C]73.9570627200813[/C][C]42.3798830211739[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]3129.45652173913[/C][C]73.108791322385[/C][C]42.8054747607478[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]3123.38636363636[/C][C]72.6429349620725[/C][C]42.9964230556916[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]3117.47619047619[/C][C]72.1979328489395[/C][C]43.1795768585081[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]3110.65[/C][C]71.5304001178914[/C][C]43.4871047117483[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]3102.36842105263[/C][C]70.6529133818939[/C][C]43.9099857678009[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]3092.83333333333[/C][C]69.4034615576952[/C][C]44.5630990719715[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]3081.94117647059[/C][C]68.2433642040772[/C][C]45.1610381817381[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]3069.84375[/C][C]66.5088235320013[/C][C]46.1569395904728[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]3058.46666666667[/C][C]64.8712382176625[/C][C]47.1467286689455[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]3047.78571428571[/C][C]63.6638692384438[/C][C]47.8730832848169[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]3036.07692307692[/C][C]61.8158785445672[/C][C]49.1148390115981[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]3023.75[/C][C]59.2887264132916[/C][C]51.0004208712792[/C][/ROW]
[ROW][C]Median[/C][C]2875.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]3600[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]3079.72972972973[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]3092.83333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]3079.72972972973[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]3092.83333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]3092.83333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]3079.72972972973[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]3092.83333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]3102.36842105263[/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=233986&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=233986&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 Mean3173.83333333333102.99376472003130.8157813432766
Geometric Mean3052.42213976467
Harmonic Mean2926.59865893181
Quadratic Mean3290.34433355133
Winsorized Mean ( 1 / 24 )3160.8055555555698.44697944423532.1066788783092
Winsorized Mean ( 2 / 24 )3165.1388888888997.197935654232332.5638488881947
Winsorized Mean ( 3 / 24 )3162.8888888888996.587821081955132.746249511159
Winsorized Mean ( 4 / 24 )316192.717649872120234.0927536920939
Winsorized Mean ( 5 / 24 )3156.1388888888991.543073542445834.4770911304992
Winsorized Mean ( 6 / 24 )3159.9722222222288.682647021365235.6323624559936
Winsorized Mean ( 7 / 24 )3193.2222222222281.310366336623239.2720186378493
Winsorized Mean ( 8 / 24 )3187.3333333333379.957299832830339.8629435961096
Winsorized Mean ( 9 / 24 )3187.5833333333378.987637327291540.3554713268018
Winsorized Mean ( 10 / 24 )3187.3055555555676.991028070296441.3984023261178
Winsorized Mean ( 11 / 24 )3172.0277777777874.21366072544642.7418314468103
Winsorized Mean ( 12 / 24 )3171.3611111111173.391417739349443.2116071442337
Winsorized Mean ( 13 / 24 )3177.6805555555669.810773823097645.5184834880628
Winsorized Mean ( 14 / 24 )3171.6527777777868.388736156388846.3768298119293
Winsorized Mean ( 15 / 24 )3174.3611111111167.983768388504846.6929266552376
Winsorized Mean ( 16 / 24 )3180.5833333333367.079201167459347.4153430270166
Winsorized Mean ( 17 / 24 )3183.4166666666766.531581890774947.8482034576134
Winsorized Mean ( 18 / 24 )3185.4166666666763.433105714807850.2169431997883
Winsorized Mean ( 19 / 24 )3184.0972222222263.006241337391850.536219184568
Winsorized Mean ( 20 / 24 )3164.6527777777859.667634344850153.0380131963606
Winsorized Mean ( 21 / 24 )3145.6944444444455.21457871093256.9721714424967
Winsorized Mean ( 22 / 24 )3140.8055555555654.404021814105357.7311281560666
Winsorized Mean ( 23 / 24 )3130.5833333333352.807408184410459.2830332138424
Winsorized Mean ( 24 / 24 )3123.2548.484008100311364.4181478053162
Trimmed Mean ( 1 / 24 )3161.6571428571495.784129889027333.008152253616
Trimmed Mean ( 2 / 24 )3162.5588235294192.618245097827734.1461751967873
Trimmed Mean ( 3 / 24 )3161.1515151515289.64444203152935.2632181484235
Trimmed Mean ( 4 / 24 )3160.586.358156249387636.5975854194132
Trimmed Mean ( 5 / 24 )3160.3548387096883.865736219705937.6835043864683
Trimmed Mean ( 6 / 24 )3161.3666666666781.22038083913138.9233174482181
Trimmed Mean ( 7 / 24 )3161.6551724137978.829728945318240.1073962160511
Trimmed Mean ( 8 / 24 )3155.8571428571477.790967945369840.5684262094978
Trimmed Mean ( 9 / 24 )3150.6111111111176.781389949221141.033525352885
Trimmed Mean ( 10 / 24 )3144.9230769230875.684203618329541.5532294266148
Trimmed Mean ( 11 / 24 )3138.8274.68304558572342.0285484527701
Trimmed Mean ( 12 / 24 )3134.2916666666773.957062720081342.3798830211739
Trimmed Mean ( 13 / 24 )3129.4565217391373.10879132238542.8054747607478
Trimmed Mean ( 14 / 24 )3123.3863636363672.642934962072542.9964230556916
Trimmed Mean ( 15 / 24 )3117.4761904761972.197932848939543.1795768585081
Trimmed Mean ( 16 / 24 )3110.6571.530400117891443.4871047117483
Trimmed Mean ( 17 / 24 )3102.3684210526370.652913381893943.9099857678009
Trimmed Mean ( 18 / 24 )3092.8333333333369.403461557695244.5630990719715
Trimmed Mean ( 19 / 24 )3081.9411764705968.243364204077245.1610381817381
Trimmed Mean ( 20 / 24 )3069.8437566.508823532001346.1569395904728
Trimmed Mean ( 21 / 24 )3058.4666666666764.871238217662547.1467286689455
Trimmed Mean ( 22 / 24 )3047.7857142857163.663869238443847.8730832848169
Trimmed Mean ( 23 / 24 )3036.0769230769261.815878544567249.1148390115981
Trimmed Mean ( 24 / 24 )3023.7559.288726413291651.0004208712792
Median2875.5
Midrange3600
Midmean - Weighted Average at Xnp3079.72972972973
Midmean - Weighted Average at X(n+1)p3092.83333333333
Midmean - Empirical Distribution Function3079.72972972973
Midmean - Empirical Distribution Function - Averaging3092.83333333333
Midmean - Empirical Distribution Function - Interpolation3092.83333333333
Midmean - Closest Observation3079.72972972973
Midmean - True Basic - Statistics Graphics Toolkit3092.83333333333
Midmean - MS Excel (old versions)3102.36842105263
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')