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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 computationMon, 18 Oct 2010 09:37:20 +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/Oct/18/t12873945619qes336qo1jbeix.htm/, Retrieved Sat, 04 May 2024 17:58:52 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=84550, Retrieved Sat, 04 May 2024 17:58:52 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP1W52
Estimated Impact114
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2010-10-18 09:37:20] [d05b5f5c1bde1241a89791f96cf6e071] [Current]
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Dataseries X:
47
19
52
136
80
42
54
66
81
63
137
72
107
58
36
52
79
77
54
84
48
96
83
66
61
53
30
74
69
59
42
65
70
100
63
105
82
81
75
102
121
98
76
77
63
37
35
23
40
29
37
51
20
28
13
22
25
13
16
13
16
17
9
17
25
14
8
7
10
7
10
3




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\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 & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=84550&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=84550&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=84550&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'Gwilym Jenkins' @ 72.249.127.135







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean52.77777777777783.9015276402092813.5274647893938
Geometric Mean40.1753847097589
Harmonic Mean26.3258893697183
Quadratic Mean62.1791765786585
Winsorized Mean ( 1 / 24 )52.81944444444443.8877202441467413.5862256354397
Winsorized Mean ( 2 / 24 )52.40277777777783.7714259953535013.8946854166937
Winsorized Mean ( 3 / 24 )51.86111111111113.6269350539519114.2988805533210
Winsorized Mean ( 4 / 24 )51.80555555555563.5940656448516214.4141929154147
Winsorized Mean ( 5 / 24 )51.66666666666673.5399022116764214.5955067618092
Winsorized Mean ( 6 / 24 )51.53.5069794037520614.6850021260179
Winsorized Mean ( 7 / 24 )51.59722222222223.4219819940631715.0781688248912
Winsorized Mean ( 8 / 24 )51.3753.3800967138518715.1992692367238
Winsorized Mean ( 9 / 24 )49.8753.1243113482215515.9635178575881
Winsorized Mean ( 10 / 24 )49.8753.0801714215146416.1922806151726
Winsorized Mean ( 11 / 24 )50.02777777777783.0077477043172316.6329701477186
Winsorized Mean ( 12 / 24 )49.86111111111112.9830182876874016.7149867357220
Winsorized Mean ( 13 / 24 )50.04166666666672.954363202571316.9382243263501
Winsorized Mean ( 14 / 24 )49.84722222222222.9259015251420817.0365344813858
Winsorized Mean ( 15 / 24 )50.05555555555562.8306317477048517.6835279248676
Winsorized Mean ( 16 / 24 )49.83333333333332.7332503136367318.2322610866282
Winsorized Mean ( 17 / 24 )50.30555555555562.6615736935447418.9006810811079
Winsorized Mean ( 18 / 24 )50.30555555555562.5891490563558819.4293779386957
Winsorized Mean ( 19 / 24 )50.56944444444442.4747414455999220.4342334567341
Winsorized Mean ( 20 / 24 )50.29166666666672.4363924994919420.6418574499609
Winsorized Mean ( 21 / 24 )50.58333333333332.2305278082999522.6777416291827
Winsorized Mean ( 22 / 24 )50.27777777777782.1053273048002123.8812167890203
Winsorized Mean ( 23 / 24 )50.27777777777782.0180350983435424.9142236520303
Winsorized Mean ( 24 / 24 )50.94444444444441.6572372800956130.7405855856111
Trimmed Mean ( 1 / 24 )52.28571428571433.7583939379215913.9117173849606
Trimmed Mean ( 2 / 24 )51.72058823529413.6030450971377614.3546880044273
Trimmed Mean ( 3 / 24 )51.34848484848493.4928159653702314.7011710200546
Trimmed Mean ( 4 / 24 )51.156253.4271918856740714.9265788746283
Trimmed Mean ( 5 / 24 )50.96774193548393.3593179835517515.1720504534068
Trimmed Mean ( 6 / 24 )50.83.293359180117715.4249801560316
Trimmed Mean ( 7 / 24 )50.65517241379313.2214638340672415.7242716426335
Trimmed Mean ( 8 / 24 )50.48214285714293.1544640674567416.0033976541200
Trimmed Mean ( 9 / 24 )50.33333333333333.0811298716240616.3359986207925
Trimmed Mean ( 10 / 24 )50.40384615384623.0482865665803816.5351403330790
Trimmed Mean ( 11 / 24 )50.483.0138781037875116.7491843603636
Trimmed Mean ( 12 / 24 )50.54166666666672.9828050861618716.9443410503572
Trimmed Mean ( 13 / 24 )50.63043478260872.9447995093704717.1931687102978
Trimmed Mean ( 14 / 24 )50.70454545454552.8986727927198517.4923315187186
Trimmed Mean ( 15 / 24 )50.80952380952382.8413812248772417.8819805539184
Trimmed Mean ( 16 / 24 )50.92.7845268437545618.2795867506769
Trimmed Mean ( 17 / 24 )51.02631578947372.7274190828757518.7086451472915
Trimmed Mean ( 18 / 24 )51.11111111111112.6639205436985819.1864247723202
Trimmed Mean ( 19 / 24 )51.20588235294122.5908722994983519.7639545425901
Trimmed Mean ( 20 / 24 )51.281252.5157705703223420.3839136227074
Trimmed Mean ( 21 / 24 )51.42.4143250645348921.2895938310205
Trimmed Mean ( 22 / 24 )51.52.3285097534598522.1171502174203
Trimmed Mean ( 23 / 24 )51.65384615384622.2360282836330823.1007123353196
Trimmed Mean ( 24 / 24 )51.83333333333332.1193267548256524.4574524505531
Median52.5
Midrange70
Midmean - Weighted Average at Xnp50.3243243243243
Midmean - Weighted Average at X(n+1)p51.1111111111111
Midmean - Empirical Distribution Function50.3243243243243
Midmean - Empirical Distribution Function - Averaging51.1111111111111
Midmean - Empirical Distribution Function - Interpolation51.1111111111111
Midmean - Closest Observation50.3243243243243
Midmean - True Basic - Statistics Graphics Toolkit51.1111111111111
Midmean - MS Excel (old versions)51.6923076923077
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 52.7777777777778 & 3.90152764020928 & 13.5274647893938 \tabularnewline
Geometric Mean & 40.1753847097589 &  &  \tabularnewline
Harmonic Mean & 26.3258893697183 &  &  \tabularnewline
Quadratic Mean & 62.1791765786585 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 52.8194444444444 & 3.88772024414674 & 13.5862256354397 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 52.4027777777778 & 3.77142599535350 & 13.8946854166937 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 51.8611111111111 & 3.62693505395191 & 14.2988805533210 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 51.8055555555556 & 3.59406564485162 & 14.4141929154147 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 51.6666666666667 & 3.53990221167642 & 14.5955067618092 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 51.5 & 3.50697940375206 & 14.6850021260179 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 51.5972222222222 & 3.42198199406317 & 15.0781688248912 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 51.375 & 3.38009671385187 & 15.1992692367238 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 49.875 & 3.12431134822155 & 15.9635178575881 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 49.875 & 3.08017142151464 & 16.1922806151726 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 50.0277777777778 & 3.00774770431723 & 16.6329701477186 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 49.8611111111111 & 2.98301828768740 & 16.7149867357220 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 50.0416666666667 & 2.9543632025713 & 16.9382243263501 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 49.8472222222222 & 2.92590152514208 & 17.0365344813858 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 50.0555555555556 & 2.83063174770485 & 17.6835279248676 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 49.8333333333333 & 2.73325031363673 & 18.2322610866282 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 50.3055555555556 & 2.66157369354474 & 18.9006810811079 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 50.3055555555556 & 2.58914905635588 & 19.4293779386957 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 50.5694444444444 & 2.47474144559992 & 20.4342334567341 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 50.2916666666667 & 2.43639249949194 & 20.6418574499609 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 50.5833333333333 & 2.23052780829995 & 22.6777416291827 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 50.2777777777778 & 2.10532730480021 & 23.8812167890203 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 50.2777777777778 & 2.01803509834354 & 24.9142236520303 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 50.9444444444444 & 1.65723728009561 & 30.7405855856111 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 52.2857142857143 & 3.75839393792159 & 13.9117173849606 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 51.7205882352941 & 3.60304509713776 & 14.3546880044273 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 51.3484848484849 & 3.49281596537023 & 14.7011710200546 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 51.15625 & 3.42719188567407 & 14.9265788746283 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 50.9677419354839 & 3.35931798355175 & 15.1720504534068 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 50.8 & 3.2933591801177 & 15.4249801560316 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 50.6551724137931 & 3.22146383406724 & 15.7242716426335 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 50.4821428571429 & 3.15446406745674 & 16.0033976541200 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 50.3333333333333 & 3.08112987162406 & 16.3359986207925 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 50.4038461538462 & 3.04828656658038 & 16.5351403330790 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 50.48 & 3.01387810378751 & 16.7491843603636 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 50.5416666666667 & 2.98280508616187 & 16.9443410503572 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 50.6304347826087 & 2.94479950937047 & 17.1931687102978 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 50.7045454545455 & 2.89867279271985 & 17.4923315187186 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 50.8095238095238 & 2.84138122487724 & 17.8819805539184 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 50.9 & 2.78452684375456 & 18.2795867506769 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 51.0263157894737 & 2.72741908287575 & 18.7086451472915 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 51.1111111111111 & 2.66392054369858 & 19.1864247723202 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 51.2058823529412 & 2.59087229949835 & 19.7639545425901 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 51.28125 & 2.51577057032234 & 20.3839136227074 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 51.4 & 2.41432506453489 & 21.2895938310205 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 51.5 & 2.32850975345985 & 22.1171502174203 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 51.6538461538462 & 2.23602828363308 & 23.1007123353196 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 51.8333333333333 & 2.11932675482565 & 24.4574524505531 \tabularnewline
Median & 52.5 &  &  \tabularnewline
Midrange & 70 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 50.3243243243243 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 51.1111111111111 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 50.3243243243243 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 51.1111111111111 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 51.1111111111111 &  &  \tabularnewline
Midmean - Closest Observation & 50.3243243243243 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 51.1111111111111 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 51.6923076923077 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=84550&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]52.7777777777778[/C][C]3.90152764020928[/C][C]13.5274647893938[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]40.1753847097589[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]26.3258893697183[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]62.1791765786585[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]52.8194444444444[/C][C]3.88772024414674[/C][C]13.5862256354397[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]52.4027777777778[/C][C]3.77142599535350[/C][C]13.8946854166937[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]51.8611111111111[/C][C]3.62693505395191[/C][C]14.2988805533210[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]51.8055555555556[/C][C]3.59406564485162[/C][C]14.4141929154147[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]51.6666666666667[/C][C]3.53990221167642[/C][C]14.5955067618092[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]51.5[/C][C]3.50697940375206[/C][C]14.6850021260179[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]51.5972222222222[/C][C]3.42198199406317[/C][C]15.0781688248912[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]51.375[/C][C]3.38009671385187[/C][C]15.1992692367238[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]49.875[/C][C]3.12431134822155[/C][C]15.9635178575881[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]49.875[/C][C]3.08017142151464[/C][C]16.1922806151726[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]50.0277777777778[/C][C]3.00774770431723[/C][C]16.6329701477186[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]49.8611111111111[/C][C]2.98301828768740[/C][C]16.7149867357220[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]50.0416666666667[/C][C]2.9543632025713[/C][C]16.9382243263501[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]49.8472222222222[/C][C]2.92590152514208[/C][C]17.0365344813858[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]50.0555555555556[/C][C]2.83063174770485[/C][C]17.6835279248676[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]49.8333333333333[/C][C]2.73325031363673[/C][C]18.2322610866282[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]50.3055555555556[/C][C]2.66157369354474[/C][C]18.9006810811079[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]50.3055555555556[/C][C]2.58914905635588[/C][C]19.4293779386957[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]50.5694444444444[/C][C]2.47474144559992[/C][C]20.4342334567341[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]50.2916666666667[/C][C]2.43639249949194[/C][C]20.6418574499609[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]50.5833333333333[/C][C]2.23052780829995[/C][C]22.6777416291827[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]50.2777777777778[/C][C]2.10532730480021[/C][C]23.8812167890203[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]50.2777777777778[/C][C]2.01803509834354[/C][C]24.9142236520303[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]50.9444444444444[/C][C]1.65723728009561[/C][C]30.7405855856111[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]52.2857142857143[/C][C]3.75839393792159[/C][C]13.9117173849606[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]51.7205882352941[/C][C]3.60304509713776[/C][C]14.3546880044273[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]51.3484848484849[/C][C]3.49281596537023[/C][C]14.7011710200546[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]51.15625[/C][C]3.42719188567407[/C][C]14.9265788746283[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]50.9677419354839[/C][C]3.35931798355175[/C][C]15.1720504534068[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]50.8[/C][C]3.2933591801177[/C][C]15.4249801560316[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]50.6551724137931[/C][C]3.22146383406724[/C][C]15.7242716426335[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]50.4821428571429[/C][C]3.15446406745674[/C][C]16.0033976541200[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]50.3333333333333[/C][C]3.08112987162406[/C][C]16.3359986207925[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]50.4038461538462[/C][C]3.04828656658038[/C][C]16.5351403330790[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]50.48[/C][C]3.01387810378751[/C][C]16.7491843603636[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]50.5416666666667[/C][C]2.98280508616187[/C][C]16.9443410503572[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]50.6304347826087[/C][C]2.94479950937047[/C][C]17.1931687102978[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]50.7045454545455[/C][C]2.89867279271985[/C][C]17.4923315187186[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]50.8095238095238[/C][C]2.84138122487724[/C][C]17.8819805539184[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]50.9[/C][C]2.78452684375456[/C][C]18.2795867506769[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]51.0263157894737[/C][C]2.72741908287575[/C][C]18.7086451472915[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]51.1111111111111[/C][C]2.66392054369858[/C][C]19.1864247723202[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]51.2058823529412[/C][C]2.59087229949835[/C][C]19.7639545425901[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]51.28125[/C][C]2.51577057032234[/C][C]20.3839136227074[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]51.4[/C][C]2.41432506453489[/C][C]21.2895938310205[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]51.5[/C][C]2.32850975345985[/C][C]22.1171502174203[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]51.6538461538462[/C][C]2.23602828363308[/C][C]23.1007123353196[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]51.8333333333333[/C][C]2.11932675482565[/C][C]24.4574524505531[/C][/ROW]
[ROW][C]Median[/C][C]52.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]70[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]50.3243243243243[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]51.1111111111111[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]50.3243243243243[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]51.1111111111111[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]51.1111111111111[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]50.3243243243243[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]51.1111111111111[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]51.6923076923077[/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=84550&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=84550&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 Mean52.77777777777783.9015276402092813.5274647893938
Geometric Mean40.1753847097589
Harmonic Mean26.3258893697183
Quadratic Mean62.1791765786585
Winsorized Mean ( 1 / 24 )52.81944444444443.8877202441467413.5862256354397
Winsorized Mean ( 2 / 24 )52.40277777777783.7714259953535013.8946854166937
Winsorized Mean ( 3 / 24 )51.86111111111113.6269350539519114.2988805533210
Winsorized Mean ( 4 / 24 )51.80555555555563.5940656448516214.4141929154147
Winsorized Mean ( 5 / 24 )51.66666666666673.5399022116764214.5955067618092
Winsorized Mean ( 6 / 24 )51.53.5069794037520614.6850021260179
Winsorized Mean ( 7 / 24 )51.59722222222223.4219819940631715.0781688248912
Winsorized Mean ( 8 / 24 )51.3753.3800967138518715.1992692367238
Winsorized Mean ( 9 / 24 )49.8753.1243113482215515.9635178575881
Winsorized Mean ( 10 / 24 )49.8753.0801714215146416.1922806151726
Winsorized Mean ( 11 / 24 )50.02777777777783.0077477043172316.6329701477186
Winsorized Mean ( 12 / 24 )49.86111111111112.9830182876874016.7149867357220
Winsorized Mean ( 13 / 24 )50.04166666666672.954363202571316.9382243263501
Winsorized Mean ( 14 / 24 )49.84722222222222.9259015251420817.0365344813858
Winsorized Mean ( 15 / 24 )50.05555555555562.8306317477048517.6835279248676
Winsorized Mean ( 16 / 24 )49.83333333333332.7332503136367318.2322610866282
Winsorized Mean ( 17 / 24 )50.30555555555562.6615736935447418.9006810811079
Winsorized Mean ( 18 / 24 )50.30555555555562.5891490563558819.4293779386957
Winsorized Mean ( 19 / 24 )50.56944444444442.4747414455999220.4342334567341
Winsorized Mean ( 20 / 24 )50.29166666666672.4363924994919420.6418574499609
Winsorized Mean ( 21 / 24 )50.58333333333332.2305278082999522.6777416291827
Winsorized Mean ( 22 / 24 )50.27777777777782.1053273048002123.8812167890203
Winsorized Mean ( 23 / 24 )50.27777777777782.0180350983435424.9142236520303
Winsorized Mean ( 24 / 24 )50.94444444444441.6572372800956130.7405855856111
Trimmed Mean ( 1 / 24 )52.28571428571433.7583939379215913.9117173849606
Trimmed Mean ( 2 / 24 )51.72058823529413.6030450971377614.3546880044273
Trimmed Mean ( 3 / 24 )51.34848484848493.4928159653702314.7011710200546
Trimmed Mean ( 4 / 24 )51.156253.4271918856740714.9265788746283
Trimmed Mean ( 5 / 24 )50.96774193548393.3593179835517515.1720504534068
Trimmed Mean ( 6 / 24 )50.83.293359180117715.4249801560316
Trimmed Mean ( 7 / 24 )50.65517241379313.2214638340672415.7242716426335
Trimmed Mean ( 8 / 24 )50.48214285714293.1544640674567416.0033976541200
Trimmed Mean ( 9 / 24 )50.33333333333333.0811298716240616.3359986207925
Trimmed Mean ( 10 / 24 )50.40384615384623.0482865665803816.5351403330790
Trimmed Mean ( 11 / 24 )50.483.0138781037875116.7491843603636
Trimmed Mean ( 12 / 24 )50.54166666666672.9828050861618716.9443410503572
Trimmed Mean ( 13 / 24 )50.63043478260872.9447995093704717.1931687102978
Trimmed Mean ( 14 / 24 )50.70454545454552.8986727927198517.4923315187186
Trimmed Mean ( 15 / 24 )50.80952380952382.8413812248772417.8819805539184
Trimmed Mean ( 16 / 24 )50.92.7845268437545618.2795867506769
Trimmed Mean ( 17 / 24 )51.02631578947372.7274190828757518.7086451472915
Trimmed Mean ( 18 / 24 )51.11111111111112.6639205436985819.1864247723202
Trimmed Mean ( 19 / 24 )51.20588235294122.5908722994983519.7639545425901
Trimmed Mean ( 20 / 24 )51.281252.5157705703223420.3839136227074
Trimmed Mean ( 21 / 24 )51.42.4143250645348921.2895938310205
Trimmed Mean ( 22 / 24 )51.52.3285097534598522.1171502174203
Trimmed Mean ( 23 / 24 )51.65384615384622.2360282836330823.1007123353196
Trimmed Mean ( 24 / 24 )51.83333333333332.1193267548256524.4574524505531
Median52.5
Midrange70
Midmean - Weighted Average at Xnp50.3243243243243
Midmean - Weighted Average at X(n+1)p51.1111111111111
Midmean - Empirical Distribution Function50.3243243243243
Midmean - Empirical Distribution Function - Averaging51.1111111111111
Midmean - Empirical Distribution Function - Interpolation51.1111111111111
Midmean - Closest Observation50.3243243243243
Midmean - True Basic - Statistics Graphics Toolkit51.1111111111111
Midmean - MS Excel (old versions)51.6923076923077
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')