Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationWed, 04 Aug 2010 16:47:43 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Aug/04/t1280940463d7drcu52izs9733.htm/, Retrieved Fri, 03 May 2024 07:23:33 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=78353, Retrieved Fri, 03 May 2024 07:23:33 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsMathias Goossenaerts
Estimated Impact133
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Tijdreeks 1 - Sta...] [2010-08-04 16:47:43] [f7fc4e1bbbe57039ee5ebdd2c8b864c0] [Current]
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Dataseries X:
36
35
34
32
52
51
36
26
27
27
28
30
28
29
25
28
55
53
42
32
37
41
37
38
39
32
36
39
83
83
66
53
72
77
69
72
81
71
63
66
114
116
109
97
111
120
110
106
115
110
103
112
163
166
156
140
166
176
163
162
171
167
163
168
222
216
197
178
204
220
196
195
213
218
216
225
280
272
252
230
248
259
240
237
252
250
255
255
313
291
271
247
268
283
259
259
267
270
279
269
334
326
301
276
301
313
291
287
289
298
320
312
385
380
351
322
350
363
344
345




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'George Udny Yule' @ 72.249.76.132

\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 & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78353&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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78353&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78353&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'George Udny Yule' @ 72.249.76.132







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean170.3259.8927240508192817.2171991379760
Geometric Mean127.190485633427
Harmonic Mean86.7201196875877
Quadratic Mean201.634963072711
Winsorized Mean ( 1 / 40 )170.2916666666679.8841850580799817.2287007645065
Winsorized Mean ( 2 / 40 )170.0259.8335194102415217.2903507794901
Winsorized Mean ( 3 / 40 )169.7259.7854287896156417.3446666108401
Winsorized Mean ( 4 / 40 )169.7259.7761784054755417.3610784255879
Winsorized Mean ( 5 / 40 )169.5166666666679.7442720611581617.3965449243131
Winsorized Mean ( 6 / 40 )169.4666666666679.7367228663209317.4048978278767
Winsorized Mean ( 7 / 40 )168.9416666666679.6437110015501417.5183253251275
Winsorized Mean ( 8 / 40 )168.4759.5603051480488617.6223454577058
Winsorized Mean ( 9 / 40 )168.3259.500974168687217.7166043198766
Winsorized Mean ( 10 / 40 )168.1583333333339.4784289659696217.7411608967131
Winsorized Mean ( 11 / 40 )167.5166666666679.393476067128517.8332989267811
Winsorized Mean ( 12 / 40 )167.7166666666679.3693596166716417.9005474790652
Winsorized Mean ( 13 / 40 )167.7166666666679.342308984481917.9523784693113
Winsorized Mean ( 14 / 40 )166.559.1659524804544818.170506595485
Winsorized Mean ( 15 / 40 )166.559.1659524804544818.170506595485
Winsorized Mean ( 16 / 40 )166.159.1169928607808718.2242108266573
Winsorized Mean ( 17 / 40 )165.38.9814046925912918.4046934369136
Winsorized Mean ( 18 / 40 )165.38.9814046925912918.4046934369136
Winsorized Mean ( 19 / 40 )165.1416666666678.925338429611518.5025663697836
Winsorized Mean ( 20 / 40 )164.9758.8667024374818118.6061279447711
Winsorized Mean ( 21 / 40 )164.2758.7864802762117318.6963374224778
Winsorized Mean ( 22 / 40 )164.0916666666678.6805829542051318.9033003350513
Winsorized Mean ( 23 / 40 )164.0916666666678.6363101934894619.0002052948918
Winsorized Mean ( 24 / 40 )165.2916666666678.3589918360094419.7741150977815
Winsorized Mean ( 25 / 40 )164.6666666666678.2430883817349919.9763315690676
Winsorized Mean ( 26 / 40 )164.6666666666678.1945730259420920.0945999438129
Winsorized Mean ( 27 / 40 )164.4416666666678.170091283045520.1272740988726
Winsorized Mean ( 28 / 40 )164.6758.0914604023363520.3517031304326
Winsorized Mean ( 29 / 40 )166.3666666666677.8480754062189921.1984031823693
Winsorized Mean ( 30 / 40 )166.8666666666677.7382958819063721.5637485582366
Winsorized Mean ( 31 / 40 )164.87.517063688608721.9234540010266
Winsorized Mean ( 32 / 40 )165.67.4291744530076322.2904982306558
Winsorized Mean ( 33 / 40 )166.157.3692871810930922.5462783464703
Winsorized Mean ( 34 / 40 )165.37.2193581191585922.8967724376119
Winsorized Mean ( 35 / 40 )165.37.2193581191585922.8967724376119
Winsorized Mean ( 36 / 40 )165.96.9636853149224223.8235923217975
Winsorized Mean ( 37 / 40 )167.1333333333336.8321916105703624.4626238343132
Winsorized Mean ( 38 / 40 )167.1333333333336.6992509022820924.9480629657265
Winsorized Mean ( 39 / 40 )166.4833333333336.6318979557035325.1034220437839
Winsorized Mean ( 40 / 40 )170.8166666666676.1132402495899327.9420830349543
Trimmed Mean ( 1 / 40 )169.7372881355939.8160720187735517.2917729017233
Trimmed Mean ( 2 / 40 )169.1637931034489.7393769750891217.3690569259334
Trimmed Mean ( 3 / 40 )168.7105263157899.6819690835712317.4252287793466
Trimmed Mean ( 4 / 40 )168.3482142857149.6355708788710817.4715350446821
Trimmed Mean ( 5 / 40 )167.9727272727279.5849170772608417.5246927979402
Trimmed Mean ( 6 / 40 )167.6296296296309.5348061860372717.5808114353814
Trimmed Mean ( 7 / 40 )167.2830188679259.4786349315065717.6484293441752
Trimmed Mean ( 8 / 40 )167.0096153846159.4323828380237417.7059835518304
Trimmed Mean ( 9 / 40 )166.7941176470599.3933161927164517.7566808382742
Trimmed Mean ( 10 / 40 )166.599.3567249623039617.8043065999216
Trimmed Mean ( 11 / 40 )166.3979591836739.3163958933596817.8607651594405
Trimmed Mean ( 12 / 40 )166.2708333333339.2807038919217917.9157567431993
Trimmed Mean ( 13 / 40 )166.1170212765969.2407473046715217.9765787116176
Trimmed Mean ( 14 / 40 )165.9565217391309.1961674987956318.0462700098563
Trimmed Mean ( 15 / 40 )165.99.1654926044183818.1005001215129
Trimmed Mean ( 16 / 40 )165.8409090909099.1270191273723218.1703255768957
Trimmed Mean ( 17 / 40 )165.8139534883729.0856919374922418.2500083239823
Trimmed Mean ( 18 / 40 )165.8571428571439.0511890169798518.3243486072380
Trimmed Mean ( 19 / 40 )165.9024390243909.0075850428154418.4180818982904
Trimmed Mean ( 20 / 40 )165.96258.9601516528686618.5222869466574
Trimmed Mean ( 21 / 40 )166.0384615384628.9083363007307518.6385488752643
Trimmed Mean ( 22 / 40 )166.1710526315798.8536520001416518.7686451454067
Trimmed Mean ( 23 / 40 )166.3243243243248.7984151771251618.9038958694229
Trimmed Mean ( 24 / 40 )166.4861111111118.7347674936013819.0601651655948
Trimmed Mean ( 25 / 40 )166.5714285714298.6894327062917319.1694250017978
Trimmed Mean ( 26 / 40 )166.7058823529418.6444260264793519.2847832629133
Trimmed Mean ( 27 / 40 )166.8484848484858.5912690115072719.4207031144067
Trimmed Mean ( 28 / 40 )167.0156258.5251871281043719.5908456307559
Trimmed Mean ( 29 / 40 )167.1774193548398.4507320781430819.7825960885951
Trimmed Mean ( 30 / 40 )167.2333333333338.3880587259631919.9370723068144
Trimmed Mean ( 31 / 40 )167.2586206896558.3203974738411820.1022392518514
Trimmed Mean ( 32 / 40 )167.4285714285718.261153701655420.2669720810329
Trimmed Mean ( 33 / 40 )167.5555555555568.1932744429989420.4503775286973
Trimmed Mean ( 34 / 40 )167.6538461538468.1102826849811620.6717635704995
Trimmed Mean ( 35 / 40 )167.828.0218930027106920.9202491161739
Trimmed Mean ( 36 / 40 )1687.9022171231239221.2598562381169
Trimmed Mean ( 37 / 40 )168.1521739130437.7875763434850621.5923628220629
Trimmed Mean ( 38 / 40 )168.2272727272737.6564626515397121.971931475881
Trimmed Mean ( 39 / 40 )168.3095238095247.503811504994222.4298709659091
Trimmed Mean ( 40 / 40 )168.457.3087539714635823.0477042540629
Median166.5
Midrange205
Midmean - Weighted Average at Xnp165.524590163934
Midmean - Weighted Average at X(n+1)p167.233333333333
Midmean - Empirical Distribution Function165.524590163934
Midmean - Empirical Distribution Function - Averaging167.233333333333
Midmean - Empirical Distribution Function - Interpolation167.233333333333
Midmean - Closest Observation165.524590163934
Midmean - True Basic - Statistics Graphics Toolkit167.233333333333
Midmean - MS Excel (old versions)167.177419354839
Number of observations120

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 170.325 & 9.89272405081928 & 17.2171991379760 \tabularnewline
Geometric Mean & 127.190485633427 &  &  \tabularnewline
Harmonic Mean & 86.7201196875877 &  &  \tabularnewline
Quadratic Mean & 201.634963072711 &  &  \tabularnewline
Winsorized Mean ( 1 / 40 ) & 170.291666666667 & 9.88418505807998 & 17.2287007645065 \tabularnewline
Winsorized Mean ( 2 / 40 ) & 170.025 & 9.83351941024152 & 17.2903507794901 \tabularnewline
Winsorized Mean ( 3 / 40 ) & 169.725 & 9.78542878961564 & 17.3446666108401 \tabularnewline
Winsorized Mean ( 4 / 40 ) & 169.725 & 9.77617840547554 & 17.3610784255879 \tabularnewline
Winsorized Mean ( 5 / 40 ) & 169.516666666667 & 9.74427206115816 & 17.3965449243131 \tabularnewline
Winsorized Mean ( 6 / 40 ) & 169.466666666667 & 9.73672286632093 & 17.4048978278767 \tabularnewline
Winsorized Mean ( 7 / 40 ) & 168.941666666667 & 9.64371100155014 & 17.5183253251275 \tabularnewline
Winsorized Mean ( 8 / 40 ) & 168.475 & 9.56030514804886 & 17.6223454577058 \tabularnewline
Winsorized Mean ( 9 / 40 ) & 168.325 & 9.5009741686872 & 17.7166043198766 \tabularnewline
Winsorized Mean ( 10 / 40 ) & 168.158333333333 & 9.47842896596962 & 17.7411608967131 \tabularnewline
Winsorized Mean ( 11 / 40 ) & 167.516666666667 & 9.3934760671285 & 17.8332989267811 \tabularnewline
Winsorized Mean ( 12 / 40 ) & 167.716666666667 & 9.36935961667164 & 17.9005474790652 \tabularnewline
Winsorized Mean ( 13 / 40 ) & 167.716666666667 & 9.3423089844819 & 17.9523784693113 \tabularnewline
Winsorized Mean ( 14 / 40 ) & 166.55 & 9.16595248045448 & 18.170506595485 \tabularnewline
Winsorized Mean ( 15 / 40 ) & 166.55 & 9.16595248045448 & 18.170506595485 \tabularnewline
Winsorized Mean ( 16 / 40 ) & 166.15 & 9.11699286078087 & 18.2242108266573 \tabularnewline
Winsorized Mean ( 17 / 40 ) & 165.3 & 8.98140469259129 & 18.4046934369136 \tabularnewline
Winsorized Mean ( 18 / 40 ) & 165.3 & 8.98140469259129 & 18.4046934369136 \tabularnewline
Winsorized Mean ( 19 / 40 ) & 165.141666666667 & 8.9253384296115 & 18.5025663697836 \tabularnewline
Winsorized Mean ( 20 / 40 ) & 164.975 & 8.86670243748181 & 18.6061279447711 \tabularnewline
Winsorized Mean ( 21 / 40 ) & 164.275 & 8.78648027621173 & 18.6963374224778 \tabularnewline
Winsorized Mean ( 22 / 40 ) & 164.091666666667 & 8.68058295420513 & 18.9033003350513 \tabularnewline
Winsorized Mean ( 23 / 40 ) & 164.091666666667 & 8.63631019348946 & 19.0002052948918 \tabularnewline
Winsorized Mean ( 24 / 40 ) & 165.291666666667 & 8.35899183600944 & 19.7741150977815 \tabularnewline
Winsorized Mean ( 25 / 40 ) & 164.666666666667 & 8.24308838173499 & 19.9763315690676 \tabularnewline
Winsorized Mean ( 26 / 40 ) & 164.666666666667 & 8.19457302594209 & 20.0945999438129 \tabularnewline
Winsorized Mean ( 27 / 40 ) & 164.441666666667 & 8.1700912830455 & 20.1272740988726 \tabularnewline
Winsorized Mean ( 28 / 40 ) & 164.675 & 8.09146040233635 & 20.3517031304326 \tabularnewline
Winsorized Mean ( 29 / 40 ) & 166.366666666667 & 7.84807540621899 & 21.1984031823693 \tabularnewline
Winsorized Mean ( 30 / 40 ) & 166.866666666667 & 7.73829588190637 & 21.5637485582366 \tabularnewline
Winsorized Mean ( 31 / 40 ) & 164.8 & 7.5170636886087 & 21.9234540010266 \tabularnewline
Winsorized Mean ( 32 / 40 ) & 165.6 & 7.42917445300763 & 22.2904982306558 \tabularnewline
Winsorized Mean ( 33 / 40 ) & 166.15 & 7.36928718109309 & 22.5462783464703 \tabularnewline
Winsorized Mean ( 34 / 40 ) & 165.3 & 7.21935811915859 & 22.8967724376119 \tabularnewline
Winsorized Mean ( 35 / 40 ) & 165.3 & 7.21935811915859 & 22.8967724376119 \tabularnewline
Winsorized Mean ( 36 / 40 ) & 165.9 & 6.96368531492242 & 23.8235923217975 \tabularnewline
Winsorized Mean ( 37 / 40 ) & 167.133333333333 & 6.83219161057036 & 24.4626238343132 \tabularnewline
Winsorized Mean ( 38 / 40 ) & 167.133333333333 & 6.69925090228209 & 24.9480629657265 \tabularnewline
Winsorized Mean ( 39 / 40 ) & 166.483333333333 & 6.63189795570353 & 25.1034220437839 \tabularnewline
Winsorized Mean ( 40 / 40 ) & 170.816666666667 & 6.11324024958993 & 27.9420830349543 \tabularnewline
Trimmed Mean ( 1 / 40 ) & 169.737288135593 & 9.81607201877355 & 17.2917729017233 \tabularnewline
Trimmed Mean ( 2 / 40 ) & 169.163793103448 & 9.73937697508912 & 17.3690569259334 \tabularnewline
Trimmed Mean ( 3 / 40 ) & 168.710526315789 & 9.68196908357123 & 17.4252287793466 \tabularnewline
Trimmed Mean ( 4 / 40 ) & 168.348214285714 & 9.63557087887108 & 17.4715350446821 \tabularnewline
Trimmed Mean ( 5 / 40 ) & 167.972727272727 & 9.58491707726084 & 17.5246927979402 \tabularnewline
Trimmed Mean ( 6 / 40 ) & 167.629629629630 & 9.53480618603727 & 17.5808114353814 \tabularnewline
Trimmed Mean ( 7 / 40 ) & 167.283018867925 & 9.47863493150657 & 17.6484293441752 \tabularnewline
Trimmed Mean ( 8 / 40 ) & 167.009615384615 & 9.43238283802374 & 17.7059835518304 \tabularnewline
Trimmed Mean ( 9 / 40 ) & 166.794117647059 & 9.39331619271645 & 17.7566808382742 \tabularnewline
Trimmed Mean ( 10 / 40 ) & 166.59 & 9.35672496230396 & 17.8043065999216 \tabularnewline
Trimmed Mean ( 11 / 40 ) & 166.397959183673 & 9.31639589335968 & 17.8607651594405 \tabularnewline
Trimmed Mean ( 12 / 40 ) & 166.270833333333 & 9.28070389192179 & 17.9157567431993 \tabularnewline
Trimmed Mean ( 13 / 40 ) & 166.117021276596 & 9.24074730467152 & 17.9765787116176 \tabularnewline
Trimmed Mean ( 14 / 40 ) & 165.956521739130 & 9.19616749879563 & 18.0462700098563 \tabularnewline
Trimmed Mean ( 15 / 40 ) & 165.9 & 9.16549260441838 & 18.1005001215129 \tabularnewline
Trimmed Mean ( 16 / 40 ) & 165.840909090909 & 9.12701912737232 & 18.1703255768957 \tabularnewline
Trimmed Mean ( 17 / 40 ) & 165.813953488372 & 9.08569193749224 & 18.2500083239823 \tabularnewline
Trimmed Mean ( 18 / 40 ) & 165.857142857143 & 9.05118901697985 & 18.3243486072380 \tabularnewline
Trimmed Mean ( 19 / 40 ) & 165.902439024390 & 9.00758504281544 & 18.4180818982904 \tabularnewline
Trimmed Mean ( 20 / 40 ) & 165.9625 & 8.96015165286866 & 18.5222869466574 \tabularnewline
Trimmed Mean ( 21 / 40 ) & 166.038461538462 & 8.90833630073075 & 18.6385488752643 \tabularnewline
Trimmed Mean ( 22 / 40 ) & 166.171052631579 & 8.85365200014165 & 18.7686451454067 \tabularnewline
Trimmed Mean ( 23 / 40 ) & 166.324324324324 & 8.79841517712516 & 18.9038958694229 \tabularnewline
Trimmed Mean ( 24 / 40 ) & 166.486111111111 & 8.73476749360138 & 19.0601651655948 \tabularnewline
Trimmed Mean ( 25 / 40 ) & 166.571428571429 & 8.68943270629173 & 19.1694250017978 \tabularnewline
Trimmed Mean ( 26 / 40 ) & 166.705882352941 & 8.64442602647935 & 19.2847832629133 \tabularnewline
Trimmed Mean ( 27 / 40 ) & 166.848484848485 & 8.59126901150727 & 19.4207031144067 \tabularnewline
Trimmed Mean ( 28 / 40 ) & 167.015625 & 8.52518712810437 & 19.5908456307559 \tabularnewline
Trimmed Mean ( 29 / 40 ) & 167.177419354839 & 8.45073207814308 & 19.7825960885951 \tabularnewline
Trimmed Mean ( 30 / 40 ) & 167.233333333333 & 8.38805872596319 & 19.9370723068144 \tabularnewline
Trimmed Mean ( 31 / 40 ) & 167.258620689655 & 8.32039747384118 & 20.1022392518514 \tabularnewline
Trimmed Mean ( 32 / 40 ) & 167.428571428571 & 8.2611537016554 & 20.2669720810329 \tabularnewline
Trimmed Mean ( 33 / 40 ) & 167.555555555556 & 8.19327444299894 & 20.4503775286973 \tabularnewline
Trimmed Mean ( 34 / 40 ) & 167.653846153846 & 8.11028268498116 & 20.6717635704995 \tabularnewline
Trimmed Mean ( 35 / 40 ) & 167.82 & 8.02189300271069 & 20.9202491161739 \tabularnewline
Trimmed Mean ( 36 / 40 ) & 168 & 7.90221712312392 & 21.2598562381169 \tabularnewline
Trimmed Mean ( 37 / 40 ) & 168.152173913043 & 7.78757634348506 & 21.5923628220629 \tabularnewline
Trimmed Mean ( 38 / 40 ) & 168.227272727273 & 7.65646265153971 & 21.971931475881 \tabularnewline
Trimmed Mean ( 39 / 40 ) & 168.309523809524 & 7.5038115049942 & 22.4298709659091 \tabularnewline
Trimmed Mean ( 40 / 40 ) & 168.45 & 7.30875397146358 & 23.0477042540629 \tabularnewline
Median & 166.5 &  &  \tabularnewline
Midrange & 205 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 165.524590163934 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 167.233333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 165.524590163934 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 167.233333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 167.233333333333 &  &  \tabularnewline
Midmean - Closest Observation & 165.524590163934 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 167.233333333333 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 167.177419354839 &  &  \tabularnewline
Number of observations & 120 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78353&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]170.325[/C][C]9.89272405081928[/C][C]17.2171991379760[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]127.190485633427[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]86.7201196875877[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]201.634963072711[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 40 )[/C][C]170.291666666667[/C][C]9.88418505807998[/C][C]17.2287007645065[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 40 )[/C][C]170.025[/C][C]9.83351941024152[/C][C]17.2903507794901[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 40 )[/C][C]169.725[/C][C]9.78542878961564[/C][C]17.3446666108401[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 40 )[/C][C]169.725[/C][C]9.77617840547554[/C][C]17.3610784255879[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 40 )[/C][C]169.516666666667[/C][C]9.74427206115816[/C][C]17.3965449243131[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 40 )[/C][C]169.466666666667[/C][C]9.73672286632093[/C][C]17.4048978278767[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 40 )[/C][C]168.941666666667[/C][C]9.64371100155014[/C][C]17.5183253251275[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 40 )[/C][C]168.475[/C][C]9.56030514804886[/C][C]17.6223454577058[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 40 )[/C][C]168.325[/C][C]9.5009741686872[/C][C]17.7166043198766[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 40 )[/C][C]168.158333333333[/C][C]9.47842896596962[/C][C]17.7411608967131[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 40 )[/C][C]167.516666666667[/C][C]9.3934760671285[/C][C]17.8332989267811[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 40 )[/C][C]167.716666666667[/C][C]9.36935961667164[/C][C]17.9005474790652[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 40 )[/C][C]167.716666666667[/C][C]9.3423089844819[/C][C]17.9523784693113[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 40 )[/C][C]166.55[/C][C]9.16595248045448[/C][C]18.170506595485[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 40 )[/C][C]166.55[/C][C]9.16595248045448[/C][C]18.170506595485[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 40 )[/C][C]166.15[/C][C]9.11699286078087[/C][C]18.2242108266573[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 40 )[/C][C]165.3[/C][C]8.98140469259129[/C][C]18.4046934369136[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 40 )[/C][C]165.3[/C][C]8.98140469259129[/C][C]18.4046934369136[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 40 )[/C][C]165.141666666667[/C][C]8.9253384296115[/C][C]18.5025663697836[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 40 )[/C][C]164.975[/C][C]8.86670243748181[/C][C]18.6061279447711[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 40 )[/C][C]164.275[/C][C]8.78648027621173[/C][C]18.6963374224778[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 40 )[/C][C]164.091666666667[/C][C]8.68058295420513[/C][C]18.9033003350513[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 40 )[/C][C]164.091666666667[/C][C]8.63631019348946[/C][C]19.0002052948918[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 40 )[/C][C]165.291666666667[/C][C]8.35899183600944[/C][C]19.7741150977815[/C][/ROW]
[ROW][C]Winsorized Mean ( 25 / 40 )[/C][C]164.666666666667[/C][C]8.24308838173499[/C][C]19.9763315690676[/C][/ROW]
[ROW][C]Winsorized Mean ( 26 / 40 )[/C][C]164.666666666667[/C][C]8.19457302594209[/C][C]20.0945999438129[/C][/ROW]
[ROW][C]Winsorized Mean ( 27 / 40 )[/C][C]164.441666666667[/C][C]8.1700912830455[/C][C]20.1272740988726[/C][/ROW]
[ROW][C]Winsorized Mean ( 28 / 40 )[/C][C]164.675[/C][C]8.09146040233635[/C][C]20.3517031304326[/C][/ROW]
[ROW][C]Winsorized Mean ( 29 / 40 )[/C][C]166.366666666667[/C][C]7.84807540621899[/C][C]21.1984031823693[/C][/ROW]
[ROW][C]Winsorized Mean ( 30 / 40 )[/C][C]166.866666666667[/C][C]7.73829588190637[/C][C]21.5637485582366[/C][/ROW]
[ROW][C]Winsorized Mean ( 31 / 40 )[/C][C]164.8[/C][C]7.5170636886087[/C][C]21.9234540010266[/C][/ROW]
[ROW][C]Winsorized Mean ( 32 / 40 )[/C][C]165.6[/C][C]7.42917445300763[/C][C]22.2904982306558[/C][/ROW]
[ROW][C]Winsorized Mean ( 33 / 40 )[/C][C]166.15[/C][C]7.36928718109309[/C][C]22.5462783464703[/C][/ROW]
[ROW][C]Winsorized Mean ( 34 / 40 )[/C][C]165.3[/C][C]7.21935811915859[/C][C]22.8967724376119[/C][/ROW]
[ROW][C]Winsorized Mean ( 35 / 40 )[/C][C]165.3[/C][C]7.21935811915859[/C][C]22.8967724376119[/C][/ROW]
[ROW][C]Winsorized Mean ( 36 / 40 )[/C][C]165.9[/C][C]6.96368531492242[/C][C]23.8235923217975[/C][/ROW]
[ROW][C]Winsorized Mean ( 37 / 40 )[/C][C]167.133333333333[/C][C]6.83219161057036[/C][C]24.4626238343132[/C][/ROW]
[ROW][C]Winsorized Mean ( 38 / 40 )[/C][C]167.133333333333[/C][C]6.69925090228209[/C][C]24.9480629657265[/C][/ROW]
[ROW][C]Winsorized Mean ( 39 / 40 )[/C][C]166.483333333333[/C][C]6.63189795570353[/C][C]25.1034220437839[/C][/ROW]
[ROW][C]Winsorized Mean ( 40 / 40 )[/C][C]170.816666666667[/C][C]6.11324024958993[/C][C]27.9420830349543[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 40 )[/C][C]169.737288135593[/C][C]9.81607201877355[/C][C]17.2917729017233[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 40 )[/C][C]169.163793103448[/C][C]9.73937697508912[/C][C]17.3690569259334[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 40 )[/C][C]168.710526315789[/C][C]9.68196908357123[/C][C]17.4252287793466[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 40 )[/C][C]168.348214285714[/C][C]9.63557087887108[/C][C]17.4715350446821[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 40 )[/C][C]167.972727272727[/C][C]9.58491707726084[/C][C]17.5246927979402[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 40 )[/C][C]167.629629629630[/C][C]9.53480618603727[/C][C]17.5808114353814[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 40 )[/C][C]167.283018867925[/C][C]9.47863493150657[/C][C]17.6484293441752[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 40 )[/C][C]167.009615384615[/C][C]9.43238283802374[/C][C]17.7059835518304[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 40 )[/C][C]166.794117647059[/C][C]9.39331619271645[/C][C]17.7566808382742[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 40 )[/C][C]166.59[/C][C]9.35672496230396[/C][C]17.8043065999216[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 40 )[/C][C]166.397959183673[/C][C]9.31639589335968[/C][C]17.8607651594405[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 40 )[/C][C]166.270833333333[/C][C]9.28070389192179[/C][C]17.9157567431993[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 40 )[/C][C]166.117021276596[/C][C]9.24074730467152[/C][C]17.9765787116176[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 40 )[/C][C]165.956521739130[/C][C]9.19616749879563[/C][C]18.0462700098563[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 40 )[/C][C]165.9[/C][C]9.16549260441838[/C][C]18.1005001215129[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 40 )[/C][C]165.840909090909[/C][C]9.12701912737232[/C][C]18.1703255768957[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 40 )[/C][C]165.813953488372[/C][C]9.08569193749224[/C][C]18.2500083239823[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 40 )[/C][C]165.857142857143[/C][C]9.05118901697985[/C][C]18.3243486072380[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 40 )[/C][C]165.902439024390[/C][C]9.00758504281544[/C][C]18.4180818982904[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 40 )[/C][C]165.9625[/C][C]8.96015165286866[/C][C]18.5222869466574[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 40 )[/C][C]166.038461538462[/C][C]8.90833630073075[/C][C]18.6385488752643[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 40 )[/C][C]166.171052631579[/C][C]8.85365200014165[/C][C]18.7686451454067[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 40 )[/C][C]166.324324324324[/C][C]8.79841517712516[/C][C]18.9038958694229[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 40 )[/C][C]166.486111111111[/C][C]8.73476749360138[/C][C]19.0601651655948[/C][/ROW]
[ROW][C]Trimmed Mean ( 25 / 40 )[/C][C]166.571428571429[/C][C]8.68943270629173[/C][C]19.1694250017978[/C][/ROW]
[ROW][C]Trimmed Mean ( 26 / 40 )[/C][C]166.705882352941[/C][C]8.64442602647935[/C][C]19.2847832629133[/C][/ROW]
[ROW][C]Trimmed Mean ( 27 / 40 )[/C][C]166.848484848485[/C][C]8.59126901150727[/C][C]19.4207031144067[/C][/ROW]
[ROW][C]Trimmed Mean ( 28 / 40 )[/C][C]167.015625[/C][C]8.52518712810437[/C][C]19.5908456307559[/C][/ROW]
[ROW][C]Trimmed Mean ( 29 / 40 )[/C][C]167.177419354839[/C][C]8.45073207814308[/C][C]19.7825960885951[/C][/ROW]
[ROW][C]Trimmed Mean ( 30 / 40 )[/C][C]167.233333333333[/C][C]8.38805872596319[/C][C]19.9370723068144[/C][/ROW]
[ROW][C]Trimmed Mean ( 31 / 40 )[/C][C]167.258620689655[/C][C]8.32039747384118[/C][C]20.1022392518514[/C][/ROW]
[ROW][C]Trimmed Mean ( 32 / 40 )[/C][C]167.428571428571[/C][C]8.2611537016554[/C][C]20.2669720810329[/C][/ROW]
[ROW][C]Trimmed Mean ( 33 / 40 )[/C][C]167.555555555556[/C][C]8.19327444299894[/C][C]20.4503775286973[/C][/ROW]
[ROW][C]Trimmed Mean ( 34 / 40 )[/C][C]167.653846153846[/C][C]8.11028268498116[/C][C]20.6717635704995[/C][/ROW]
[ROW][C]Trimmed Mean ( 35 / 40 )[/C][C]167.82[/C][C]8.02189300271069[/C][C]20.9202491161739[/C][/ROW]
[ROW][C]Trimmed Mean ( 36 / 40 )[/C][C]168[/C][C]7.90221712312392[/C][C]21.2598562381169[/C][/ROW]
[ROW][C]Trimmed Mean ( 37 / 40 )[/C][C]168.152173913043[/C][C]7.78757634348506[/C][C]21.5923628220629[/C][/ROW]
[ROW][C]Trimmed Mean ( 38 / 40 )[/C][C]168.227272727273[/C][C]7.65646265153971[/C][C]21.971931475881[/C][/ROW]
[ROW][C]Trimmed Mean ( 39 / 40 )[/C][C]168.309523809524[/C][C]7.5038115049942[/C][C]22.4298709659091[/C][/ROW]
[ROW][C]Trimmed Mean ( 40 / 40 )[/C][C]168.45[/C][C]7.30875397146358[/C][C]23.0477042540629[/C][/ROW]
[ROW][C]Median[/C][C]166.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]205[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]165.524590163934[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]167.233333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]165.524590163934[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]167.233333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]167.233333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]165.524590163934[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]167.233333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]167.177419354839[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]120[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78353&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78353&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 Mean170.3259.8927240508192817.2171991379760
Geometric Mean127.190485633427
Harmonic Mean86.7201196875877
Quadratic Mean201.634963072711
Winsorized Mean ( 1 / 40 )170.2916666666679.8841850580799817.2287007645065
Winsorized Mean ( 2 / 40 )170.0259.8335194102415217.2903507794901
Winsorized Mean ( 3 / 40 )169.7259.7854287896156417.3446666108401
Winsorized Mean ( 4 / 40 )169.7259.7761784054755417.3610784255879
Winsorized Mean ( 5 / 40 )169.5166666666679.7442720611581617.3965449243131
Winsorized Mean ( 6 / 40 )169.4666666666679.7367228663209317.4048978278767
Winsorized Mean ( 7 / 40 )168.9416666666679.6437110015501417.5183253251275
Winsorized Mean ( 8 / 40 )168.4759.5603051480488617.6223454577058
Winsorized Mean ( 9 / 40 )168.3259.500974168687217.7166043198766
Winsorized Mean ( 10 / 40 )168.1583333333339.4784289659696217.7411608967131
Winsorized Mean ( 11 / 40 )167.5166666666679.393476067128517.8332989267811
Winsorized Mean ( 12 / 40 )167.7166666666679.3693596166716417.9005474790652
Winsorized Mean ( 13 / 40 )167.7166666666679.342308984481917.9523784693113
Winsorized Mean ( 14 / 40 )166.559.1659524804544818.170506595485
Winsorized Mean ( 15 / 40 )166.559.1659524804544818.170506595485
Winsorized Mean ( 16 / 40 )166.159.1169928607808718.2242108266573
Winsorized Mean ( 17 / 40 )165.38.9814046925912918.4046934369136
Winsorized Mean ( 18 / 40 )165.38.9814046925912918.4046934369136
Winsorized Mean ( 19 / 40 )165.1416666666678.925338429611518.5025663697836
Winsorized Mean ( 20 / 40 )164.9758.8667024374818118.6061279447711
Winsorized Mean ( 21 / 40 )164.2758.7864802762117318.6963374224778
Winsorized Mean ( 22 / 40 )164.0916666666678.6805829542051318.9033003350513
Winsorized Mean ( 23 / 40 )164.0916666666678.6363101934894619.0002052948918
Winsorized Mean ( 24 / 40 )165.2916666666678.3589918360094419.7741150977815
Winsorized Mean ( 25 / 40 )164.6666666666678.2430883817349919.9763315690676
Winsorized Mean ( 26 / 40 )164.6666666666678.1945730259420920.0945999438129
Winsorized Mean ( 27 / 40 )164.4416666666678.170091283045520.1272740988726
Winsorized Mean ( 28 / 40 )164.6758.0914604023363520.3517031304326
Winsorized Mean ( 29 / 40 )166.3666666666677.8480754062189921.1984031823693
Winsorized Mean ( 30 / 40 )166.8666666666677.7382958819063721.5637485582366
Winsorized Mean ( 31 / 40 )164.87.517063688608721.9234540010266
Winsorized Mean ( 32 / 40 )165.67.4291744530076322.2904982306558
Winsorized Mean ( 33 / 40 )166.157.3692871810930922.5462783464703
Winsorized Mean ( 34 / 40 )165.37.2193581191585922.8967724376119
Winsorized Mean ( 35 / 40 )165.37.2193581191585922.8967724376119
Winsorized Mean ( 36 / 40 )165.96.9636853149224223.8235923217975
Winsorized Mean ( 37 / 40 )167.1333333333336.8321916105703624.4626238343132
Winsorized Mean ( 38 / 40 )167.1333333333336.6992509022820924.9480629657265
Winsorized Mean ( 39 / 40 )166.4833333333336.6318979557035325.1034220437839
Winsorized Mean ( 40 / 40 )170.8166666666676.1132402495899327.9420830349543
Trimmed Mean ( 1 / 40 )169.7372881355939.8160720187735517.2917729017233
Trimmed Mean ( 2 / 40 )169.1637931034489.7393769750891217.3690569259334
Trimmed Mean ( 3 / 40 )168.7105263157899.6819690835712317.4252287793466
Trimmed Mean ( 4 / 40 )168.3482142857149.6355708788710817.4715350446821
Trimmed Mean ( 5 / 40 )167.9727272727279.5849170772608417.5246927979402
Trimmed Mean ( 6 / 40 )167.6296296296309.5348061860372717.5808114353814
Trimmed Mean ( 7 / 40 )167.2830188679259.4786349315065717.6484293441752
Trimmed Mean ( 8 / 40 )167.0096153846159.4323828380237417.7059835518304
Trimmed Mean ( 9 / 40 )166.7941176470599.3933161927164517.7566808382742
Trimmed Mean ( 10 / 40 )166.599.3567249623039617.8043065999216
Trimmed Mean ( 11 / 40 )166.3979591836739.3163958933596817.8607651594405
Trimmed Mean ( 12 / 40 )166.2708333333339.2807038919217917.9157567431993
Trimmed Mean ( 13 / 40 )166.1170212765969.2407473046715217.9765787116176
Trimmed Mean ( 14 / 40 )165.9565217391309.1961674987956318.0462700098563
Trimmed Mean ( 15 / 40 )165.99.1654926044183818.1005001215129
Trimmed Mean ( 16 / 40 )165.8409090909099.1270191273723218.1703255768957
Trimmed Mean ( 17 / 40 )165.8139534883729.0856919374922418.2500083239823
Trimmed Mean ( 18 / 40 )165.8571428571439.0511890169798518.3243486072380
Trimmed Mean ( 19 / 40 )165.9024390243909.0075850428154418.4180818982904
Trimmed Mean ( 20 / 40 )165.96258.9601516528686618.5222869466574
Trimmed Mean ( 21 / 40 )166.0384615384628.9083363007307518.6385488752643
Trimmed Mean ( 22 / 40 )166.1710526315798.8536520001416518.7686451454067
Trimmed Mean ( 23 / 40 )166.3243243243248.7984151771251618.9038958694229
Trimmed Mean ( 24 / 40 )166.4861111111118.7347674936013819.0601651655948
Trimmed Mean ( 25 / 40 )166.5714285714298.6894327062917319.1694250017978
Trimmed Mean ( 26 / 40 )166.7058823529418.6444260264793519.2847832629133
Trimmed Mean ( 27 / 40 )166.8484848484858.5912690115072719.4207031144067
Trimmed Mean ( 28 / 40 )167.0156258.5251871281043719.5908456307559
Trimmed Mean ( 29 / 40 )167.1774193548398.4507320781430819.7825960885951
Trimmed Mean ( 30 / 40 )167.2333333333338.3880587259631919.9370723068144
Trimmed Mean ( 31 / 40 )167.2586206896558.3203974738411820.1022392518514
Trimmed Mean ( 32 / 40 )167.4285714285718.261153701655420.2669720810329
Trimmed Mean ( 33 / 40 )167.5555555555568.1932744429989420.4503775286973
Trimmed Mean ( 34 / 40 )167.6538461538468.1102826849811620.6717635704995
Trimmed Mean ( 35 / 40 )167.828.0218930027106920.9202491161739
Trimmed Mean ( 36 / 40 )1687.9022171231239221.2598562381169
Trimmed Mean ( 37 / 40 )168.1521739130437.7875763434850621.5923628220629
Trimmed Mean ( 38 / 40 )168.2272727272737.6564626515397121.971931475881
Trimmed Mean ( 39 / 40 )168.3095238095247.503811504994222.4298709659091
Trimmed Mean ( 40 / 40 )168.457.3087539714635823.0477042540629
Median166.5
Midrange205
Midmean - Weighted Average at Xnp165.524590163934
Midmean - Weighted Average at X(n+1)p167.233333333333
Midmean - Empirical Distribution Function165.524590163934
Midmean - Empirical Distribution Function - Averaging167.233333333333
Midmean - Empirical Distribution Function - Interpolation167.233333333333
Midmean - Closest Observation165.524590163934
Midmean - True Basic - Statistics Graphics Toolkit167.233333333333
Midmean - MS Excel (old versions)167.177419354839
Number of observations120



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')