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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 computationTue, 05 Mar 2013 07:34:19 -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/2013/Mar/05/t1362487027fj1fpkce03axod6.htm/, Retrieved Sat, 04 May 2024 16:28:32 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=207374, Retrieved Sat, 04 May 2024 16:28:32 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact113
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [opdracht 5] [2013-03-05 12:34:19] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataseries X:
59
57
62
50
40
46
39
35
31
35
33
47
34
31
36
24
22
17
8
12
5
6
5
8
15
16
17
23
24
27
31
40
47
43
60
64
65
65
55
57
57
57
65
69
70
71
71
73
68
65
57
41
21
21
17
9
11
6
-2
0
5
3
7
4
8
9
14
12
12
7
15
14
19
39
12




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Maurice George Kendall' @ kendall.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Sir Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=207374&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]'Sir Maurice George Kendall' @ kendall.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=207374&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=207374&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'Sir Maurice George Kendall' @ kendall.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean32.242.6179450024849712.3150027863067
Geometric MeanNaN
Harmonic Mean0
Quadratic Mean39.3266661015991
Winsorized Mean ( 1 / 25 )32.242.6078771871818312.3625453523905
Winsorized Mean ( 2 / 25 )32.322.5950861396246712.4543072025634
Winsorized Mean ( 3 / 25 )32.322.5810927220151612.5218283420545
Winsorized Mean ( 4 / 25 )32.322.5628784493116212.6108204658247
Winsorized Mean ( 5 / 25 )32.25333333333332.5501169966683312.6477857194284
Winsorized Mean ( 6 / 25 )32.01333333333332.5060282875055112.7745299176967
Winsorized Mean ( 7 / 25 )32.10666666666672.4926250379027312.8806644314545
Winsorized Mean ( 8 / 25 )32.10666666666672.4926250379027312.8806644314545
Winsorized Mean ( 9 / 25 )32.22666666666672.4758708238388213.0162956630748
Winsorized Mean ( 10 / 25 )32.09333333333332.4522226236204213.0874468835751
Winsorized Mean ( 11 / 25 )31.94666666666672.381300525383613.4156383564903
Winsorized Mean ( 12 / 25 )31.62666666666672.3276460934464113.5874034956229
Winsorized Mean ( 13 / 25 )31.45333333333332.2993374159858613.679303052548
Winsorized Mean ( 14 / 25 )31.26666666666672.2142318809968414.1207734090571
Winsorized Mean ( 15 / 25 )31.26666666666672.2142318809968414.1207734090571
Winsorized Mean ( 16 / 25 )31.69333333333332.1575739907418114.6893378717625
Winsorized Mean ( 17 / 25 )31.922.1285498172052114.9961254098864
Winsorized Mean ( 18 / 25 )31.922.1285498172052114.9961254098864
Winsorized Mean ( 19 / 25 )31.41333333333332.0487828364936915.3326808355611
Winsorized Mean ( 20 / 25 )30.081.8475949792114116.2806244541965
Winsorized Mean ( 21 / 25 )29.81.6540422775297718.0164681428246
Winsorized Mean ( 22 / 25 )29.81.6540422775297718.0164681428246
Winsorized Mean ( 23 / 25 )29.81.5718239820764418.9588658398207
Winsorized Mean ( 24 / 25 )28.841.4411006804422720.0124810094109
Winsorized Mean ( 25 / 25 )28.50666666666671.3107144511190721.7489527504088
Trimmed Mean ( 1 / 25 )32.15068493150692.5880000000644512.4229849036732
Trimmed Mean ( 2 / 25 )32.0563380281692.563470933900212.505052272778
Trimmed Mean ( 3 / 25 )31.91304347826092.5411145303687712.5586797040705
Trimmed Mean ( 4 / 25 )31.76119402985072.5193138663954512.6070810205533
Trimmed Mean ( 5 / 25 )31.62.498153163993212.6493445059584
Trimmed Mean ( 6 / 25 )31.44444444444442.4750447018960912.7045965757125
Trimmed Mean ( 7 / 25 )31.3278688524592.4573655660882912.7485585721492
Trimmed Mean ( 8 / 25 )31.18644067796612.4371077530633712.7964964367151
Trimmed Mean ( 9 / 25 )31.03508771929822.4104207913045612.8753816890625
Trimmed Mean ( 10 / 25 )30.85454545454552.3792619999747912.9681159346354
Trimmed Mean ( 11 / 25 )30.67924528301892.3440895603902113.0879151553884
Trimmed Mean ( 12 / 25 )30.50980392156862.3133665391219613.1884867380976
Trimmed Mean ( 13 / 25 )30.36734693877552.283982580163213.295787455877
Trimmed Mean ( 14 / 25 )30.23404255319152.2503392212078713.4353266690892
Trimmed Mean ( 15 / 25 )30.11111111111112.2225252318669113.5481526505856
Trimmed Mean ( 16 / 25 )29.97674418604652.1835710873126513.7283115535933
Trimmed Mean ( 17 / 25 )29.7804878048782.1412078296281613.9082658828357
Trimmed Mean ( 18 / 25 )29.53846153846152.0877659685255814.1483585726432
Trimmed Mean ( 19 / 25 )29.27027027027032.0125912392906414.5435743229146
Trimmed Mean ( 20 / 25 )29.02857142857141.9300741111236615.0401330504721
Trimmed Mean ( 21 / 25 )28.90909090909091.8725305133471115.438515262118
Trimmed Mean ( 22 / 25 )28.80645161290321.8412357671386815.6451727296548
Trimmed Mean ( 23 / 25 )28.68965517241381.7901643210180416.026269117071
Trimmed Mean ( 24 / 25 )28.55555555555561.7356110390903716.4527390713771
Trimmed Mean ( 25 / 25 )28.521.6942254867637916.8336506697684
Median31
Midrange35.5
Midmean - Weighted Average at Xnp28.3846153846154
Midmean - Weighted Average at X(n+1)p31.6363636363636
Midmean - Empirical Distribution Function31.6363636363636
Midmean - Empirical Distribution Function - Averaging31.6363636363636
Midmean - Empirical Distribution Function - Interpolation28.3846153846154
Midmean - Closest Observation28.3846153846154
Midmean - True Basic - Statistics Graphics Toolkit31.6363636363636
Midmean - MS Excel (old versions)31.6363636363636
Number of observations75

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 32.24 & 2.61794500248497 & 12.3150027863067 \tabularnewline
Geometric Mean & NaN &  &  \tabularnewline
Harmonic Mean & 0 &  &  \tabularnewline
Quadratic Mean & 39.3266661015991 &  &  \tabularnewline
Winsorized Mean ( 1 / 25 ) & 32.24 & 2.60787718718183 & 12.3625453523905 \tabularnewline
Winsorized Mean ( 2 / 25 ) & 32.32 & 2.59508613962467 & 12.4543072025634 \tabularnewline
Winsorized Mean ( 3 / 25 ) & 32.32 & 2.58109272201516 & 12.5218283420545 \tabularnewline
Winsorized Mean ( 4 / 25 ) & 32.32 & 2.56287844931162 & 12.6108204658247 \tabularnewline
Winsorized Mean ( 5 / 25 ) & 32.2533333333333 & 2.55011699666833 & 12.6477857194284 \tabularnewline
Winsorized Mean ( 6 / 25 ) & 32.0133333333333 & 2.50602828750551 & 12.7745299176967 \tabularnewline
Winsorized Mean ( 7 / 25 ) & 32.1066666666667 & 2.49262503790273 & 12.8806644314545 \tabularnewline
Winsorized Mean ( 8 / 25 ) & 32.1066666666667 & 2.49262503790273 & 12.8806644314545 \tabularnewline
Winsorized Mean ( 9 / 25 ) & 32.2266666666667 & 2.47587082383882 & 13.0162956630748 \tabularnewline
Winsorized Mean ( 10 / 25 ) & 32.0933333333333 & 2.45222262362042 & 13.0874468835751 \tabularnewline
Winsorized Mean ( 11 / 25 ) & 31.9466666666667 & 2.3813005253836 & 13.4156383564903 \tabularnewline
Winsorized Mean ( 12 / 25 ) & 31.6266666666667 & 2.32764609344641 & 13.5874034956229 \tabularnewline
Winsorized Mean ( 13 / 25 ) & 31.4533333333333 & 2.29933741598586 & 13.679303052548 \tabularnewline
Winsorized Mean ( 14 / 25 ) & 31.2666666666667 & 2.21423188099684 & 14.1207734090571 \tabularnewline
Winsorized Mean ( 15 / 25 ) & 31.2666666666667 & 2.21423188099684 & 14.1207734090571 \tabularnewline
Winsorized Mean ( 16 / 25 ) & 31.6933333333333 & 2.15757399074181 & 14.6893378717625 \tabularnewline
Winsorized Mean ( 17 / 25 ) & 31.92 & 2.12854981720521 & 14.9961254098864 \tabularnewline
Winsorized Mean ( 18 / 25 ) & 31.92 & 2.12854981720521 & 14.9961254098864 \tabularnewline
Winsorized Mean ( 19 / 25 ) & 31.4133333333333 & 2.04878283649369 & 15.3326808355611 \tabularnewline
Winsorized Mean ( 20 / 25 ) & 30.08 & 1.84759497921141 & 16.2806244541965 \tabularnewline
Winsorized Mean ( 21 / 25 ) & 29.8 & 1.65404227752977 & 18.0164681428246 \tabularnewline
Winsorized Mean ( 22 / 25 ) & 29.8 & 1.65404227752977 & 18.0164681428246 \tabularnewline
Winsorized Mean ( 23 / 25 ) & 29.8 & 1.57182398207644 & 18.9588658398207 \tabularnewline
Winsorized Mean ( 24 / 25 ) & 28.84 & 1.44110068044227 & 20.0124810094109 \tabularnewline
Winsorized Mean ( 25 / 25 ) & 28.5066666666667 & 1.31071445111907 & 21.7489527504088 \tabularnewline
Trimmed Mean ( 1 / 25 ) & 32.1506849315069 & 2.58800000006445 & 12.4229849036732 \tabularnewline
Trimmed Mean ( 2 / 25 ) & 32.056338028169 & 2.5634709339002 & 12.505052272778 \tabularnewline
Trimmed Mean ( 3 / 25 ) & 31.9130434782609 & 2.54111453036877 & 12.5586797040705 \tabularnewline
Trimmed Mean ( 4 / 25 ) & 31.7611940298507 & 2.51931386639545 & 12.6070810205533 \tabularnewline
Trimmed Mean ( 5 / 25 ) & 31.6 & 2.4981531639932 & 12.6493445059584 \tabularnewline
Trimmed Mean ( 6 / 25 ) & 31.4444444444444 & 2.47504470189609 & 12.7045965757125 \tabularnewline
Trimmed Mean ( 7 / 25 ) & 31.327868852459 & 2.45736556608829 & 12.7485585721492 \tabularnewline
Trimmed Mean ( 8 / 25 ) & 31.1864406779661 & 2.43710775306337 & 12.7964964367151 \tabularnewline
Trimmed Mean ( 9 / 25 ) & 31.0350877192982 & 2.41042079130456 & 12.8753816890625 \tabularnewline
Trimmed Mean ( 10 / 25 ) & 30.8545454545455 & 2.37926199997479 & 12.9681159346354 \tabularnewline
Trimmed Mean ( 11 / 25 ) & 30.6792452830189 & 2.34408956039021 & 13.0879151553884 \tabularnewline
Trimmed Mean ( 12 / 25 ) & 30.5098039215686 & 2.31336653912196 & 13.1884867380976 \tabularnewline
Trimmed Mean ( 13 / 25 ) & 30.3673469387755 & 2.2839825801632 & 13.295787455877 \tabularnewline
Trimmed Mean ( 14 / 25 ) & 30.2340425531915 & 2.25033922120787 & 13.4353266690892 \tabularnewline
Trimmed Mean ( 15 / 25 ) & 30.1111111111111 & 2.22252523186691 & 13.5481526505856 \tabularnewline
Trimmed Mean ( 16 / 25 ) & 29.9767441860465 & 2.18357108731265 & 13.7283115535933 \tabularnewline
Trimmed Mean ( 17 / 25 ) & 29.780487804878 & 2.14120782962816 & 13.9082658828357 \tabularnewline
Trimmed Mean ( 18 / 25 ) & 29.5384615384615 & 2.08776596852558 & 14.1483585726432 \tabularnewline
Trimmed Mean ( 19 / 25 ) & 29.2702702702703 & 2.01259123929064 & 14.5435743229146 \tabularnewline
Trimmed Mean ( 20 / 25 ) & 29.0285714285714 & 1.93007411112366 & 15.0401330504721 \tabularnewline
Trimmed Mean ( 21 / 25 ) & 28.9090909090909 & 1.87253051334711 & 15.438515262118 \tabularnewline
Trimmed Mean ( 22 / 25 ) & 28.8064516129032 & 1.84123576713868 & 15.6451727296548 \tabularnewline
Trimmed Mean ( 23 / 25 ) & 28.6896551724138 & 1.79016432101804 & 16.026269117071 \tabularnewline
Trimmed Mean ( 24 / 25 ) & 28.5555555555556 & 1.73561103909037 & 16.4527390713771 \tabularnewline
Trimmed Mean ( 25 / 25 ) & 28.52 & 1.69422548676379 & 16.8336506697684 \tabularnewline
Median & 31 &  &  \tabularnewline
Midrange & 35.5 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 28.3846153846154 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 31.6363636363636 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 31.6363636363636 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 31.6363636363636 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 28.3846153846154 &  &  \tabularnewline
Midmean - Closest Observation & 28.3846153846154 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 31.6363636363636 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 31.6363636363636 &  &  \tabularnewline
Number of observations & 75 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=207374&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]32.24[/C][C]2.61794500248497[/C][C]12.3150027863067[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]NaN[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]0[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]39.3266661015991[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 25 )[/C][C]32.24[/C][C]2.60787718718183[/C][C]12.3625453523905[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 25 )[/C][C]32.32[/C][C]2.59508613962467[/C][C]12.4543072025634[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 25 )[/C][C]32.32[/C][C]2.58109272201516[/C][C]12.5218283420545[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 25 )[/C][C]32.32[/C][C]2.56287844931162[/C][C]12.6108204658247[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 25 )[/C][C]32.2533333333333[/C][C]2.55011699666833[/C][C]12.6477857194284[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 25 )[/C][C]32.0133333333333[/C][C]2.50602828750551[/C][C]12.7745299176967[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 25 )[/C][C]32.1066666666667[/C][C]2.49262503790273[/C][C]12.8806644314545[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 25 )[/C][C]32.1066666666667[/C][C]2.49262503790273[/C][C]12.8806644314545[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 25 )[/C][C]32.2266666666667[/C][C]2.47587082383882[/C][C]13.0162956630748[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 25 )[/C][C]32.0933333333333[/C][C]2.45222262362042[/C][C]13.0874468835751[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 25 )[/C][C]31.9466666666667[/C][C]2.3813005253836[/C][C]13.4156383564903[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 25 )[/C][C]31.6266666666667[/C][C]2.32764609344641[/C][C]13.5874034956229[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 25 )[/C][C]31.4533333333333[/C][C]2.29933741598586[/C][C]13.679303052548[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 25 )[/C][C]31.2666666666667[/C][C]2.21423188099684[/C][C]14.1207734090571[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 25 )[/C][C]31.2666666666667[/C][C]2.21423188099684[/C][C]14.1207734090571[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 25 )[/C][C]31.6933333333333[/C][C]2.15757399074181[/C][C]14.6893378717625[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 25 )[/C][C]31.92[/C][C]2.12854981720521[/C][C]14.9961254098864[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 25 )[/C][C]31.92[/C][C]2.12854981720521[/C][C]14.9961254098864[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 25 )[/C][C]31.4133333333333[/C][C]2.04878283649369[/C][C]15.3326808355611[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 25 )[/C][C]30.08[/C][C]1.84759497921141[/C][C]16.2806244541965[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 25 )[/C][C]29.8[/C][C]1.65404227752977[/C][C]18.0164681428246[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 25 )[/C][C]29.8[/C][C]1.65404227752977[/C][C]18.0164681428246[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 25 )[/C][C]29.8[/C][C]1.57182398207644[/C][C]18.9588658398207[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 25 )[/C][C]28.84[/C][C]1.44110068044227[/C][C]20.0124810094109[/C][/ROW]
[ROW][C]Winsorized Mean ( 25 / 25 )[/C][C]28.5066666666667[/C][C]1.31071445111907[/C][C]21.7489527504088[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 25 )[/C][C]32.1506849315069[/C][C]2.58800000006445[/C][C]12.4229849036732[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 25 )[/C][C]32.056338028169[/C][C]2.5634709339002[/C][C]12.505052272778[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 25 )[/C][C]31.9130434782609[/C][C]2.54111453036877[/C][C]12.5586797040705[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 25 )[/C][C]31.7611940298507[/C][C]2.51931386639545[/C][C]12.6070810205533[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 25 )[/C][C]31.6[/C][C]2.4981531639932[/C][C]12.6493445059584[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 25 )[/C][C]31.4444444444444[/C][C]2.47504470189609[/C][C]12.7045965757125[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 25 )[/C][C]31.327868852459[/C][C]2.45736556608829[/C][C]12.7485585721492[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 25 )[/C][C]31.1864406779661[/C][C]2.43710775306337[/C][C]12.7964964367151[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 25 )[/C][C]31.0350877192982[/C][C]2.41042079130456[/C][C]12.8753816890625[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 25 )[/C][C]30.8545454545455[/C][C]2.37926199997479[/C][C]12.9681159346354[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 25 )[/C][C]30.6792452830189[/C][C]2.34408956039021[/C][C]13.0879151553884[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 25 )[/C][C]30.5098039215686[/C][C]2.31336653912196[/C][C]13.1884867380976[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 25 )[/C][C]30.3673469387755[/C][C]2.2839825801632[/C][C]13.295787455877[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 25 )[/C][C]30.2340425531915[/C][C]2.25033922120787[/C][C]13.4353266690892[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 25 )[/C][C]30.1111111111111[/C][C]2.22252523186691[/C][C]13.5481526505856[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 25 )[/C][C]29.9767441860465[/C][C]2.18357108731265[/C][C]13.7283115535933[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 25 )[/C][C]29.780487804878[/C][C]2.14120782962816[/C][C]13.9082658828357[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 25 )[/C][C]29.5384615384615[/C][C]2.08776596852558[/C][C]14.1483585726432[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 25 )[/C][C]29.2702702702703[/C][C]2.01259123929064[/C][C]14.5435743229146[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 25 )[/C][C]29.0285714285714[/C][C]1.93007411112366[/C][C]15.0401330504721[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 25 )[/C][C]28.9090909090909[/C][C]1.87253051334711[/C][C]15.438515262118[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 25 )[/C][C]28.8064516129032[/C][C]1.84123576713868[/C][C]15.6451727296548[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 25 )[/C][C]28.6896551724138[/C][C]1.79016432101804[/C][C]16.026269117071[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 25 )[/C][C]28.5555555555556[/C][C]1.73561103909037[/C][C]16.4527390713771[/C][/ROW]
[ROW][C]Trimmed Mean ( 25 / 25 )[/C][C]28.52[/C][C]1.69422548676379[/C][C]16.8336506697684[/C][/ROW]
[ROW][C]Median[/C][C]31[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]35.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]28.3846153846154[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]31.6363636363636[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]31.6363636363636[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]31.6363636363636[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]28.3846153846154[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]28.3846153846154[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]31.6363636363636[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]31.6363636363636[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]75[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=207374&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=207374&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 Mean32.242.6179450024849712.3150027863067
Geometric MeanNaN
Harmonic Mean0
Quadratic Mean39.3266661015991
Winsorized Mean ( 1 / 25 )32.242.6078771871818312.3625453523905
Winsorized Mean ( 2 / 25 )32.322.5950861396246712.4543072025634
Winsorized Mean ( 3 / 25 )32.322.5810927220151612.5218283420545
Winsorized Mean ( 4 / 25 )32.322.5628784493116212.6108204658247
Winsorized Mean ( 5 / 25 )32.25333333333332.5501169966683312.6477857194284
Winsorized Mean ( 6 / 25 )32.01333333333332.5060282875055112.7745299176967
Winsorized Mean ( 7 / 25 )32.10666666666672.4926250379027312.8806644314545
Winsorized Mean ( 8 / 25 )32.10666666666672.4926250379027312.8806644314545
Winsorized Mean ( 9 / 25 )32.22666666666672.4758708238388213.0162956630748
Winsorized Mean ( 10 / 25 )32.09333333333332.4522226236204213.0874468835751
Winsorized Mean ( 11 / 25 )31.94666666666672.381300525383613.4156383564903
Winsorized Mean ( 12 / 25 )31.62666666666672.3276460934464113.5874034956229
Winsorized Mean ( 13 / 25 )31.45333333333332.2993374159858613.679303052548
Winsorized Mean ( 14 / 25 )31.26666666666672.2142318809968414.1207734090571
Winsorized Mean ( 15 / 25 )31.26666666666672.2142318809968414.1207734090571
Winsorized Mean ( 16 / 25 )31.69333333333332.1575739907418114.6893378717625
Winsorized Mean ( 17 / 25 )31.922.1285498172052114.9961254098864
Winsorized Mean ( 18 / 25 )31.922.1285498172052114.9961254098864
Winsorized Mean ( 19 / 25 )31.41333333333332.0487828364936915.3326808355611
Winsorized Mean ( 20 / 25 )30.081.8475949792114116.2806244541965
Winsorized Mean ( 21 / 25 )29.81.6540422775297718.0164681428246
Winsorized Mean ( 22 / 25 )29.81.6540422775297718.0164681428246
Winsorized Mean ( 23 / 25 )29.81.5718239820764418.9588658398207
Winsorized Mean ( 24 / 25 )28.841.4411006804422720.0124810094109
Winsorized Mean ( 25 / 25 )28.50666666666671.3107144511190721.7489527504088
Trimmed Mean ( 1 / 25 )32.15068493150692.5880000000644512.4229849036732
Trimmed Mean ( 2 / 25 )32.0563380281692.563470933900212.505052272778
Trimmed Mean ( 3 / 25 )31.91304347826092.5411145303687712.5586797040705
Trimmed Mean ( 4 / 25 )31.76119402985072.5193138663954512.6070810205533
Trimmed Mean ( 5 / 25 )31.62.498153163993212.6493445059584
Trimmed Mean ( 6 / 25 )31.44444444444442.4750447018960912.7045965757125
Trimmed Mean ( 7 / 25 )31.3278688524592.4573655660882912.7485585721492
Trimmed Mean ( 8 / 25 )31.18644067796612.4371077530633712.7964964367151
Trimmed Mean ( 9 / 25 )31.03508771929822.4104207913045612.8753816890625
Trimmed Mean ( 10 / 25 )30.85454545454552.3792619999747912.9681159346354
Trimmed Mean ( 11 / 25 )30.67924528301892.3440895603902113.0879151553884
Trimmed Mean ( 12 / 25 )30.50980392156862.3133665391219613.1884867380976
Trimmed Mean ( 13 / 25 )30.36734693877552.283982580163213.295787455877
Trimmed Mean ( 14 / 25 )30.23404255319152.2503392212078713.4353266690892
Trimmed Mean ( 15 / 25 )30.11111111111112.2225252318669113.5481526505856
Trimmed Mean ( 16 / 25 )29.97674418604652.1835710873126513.7283115535933
Trimmed Mean ( 17 / 25 )29.7804878048782.1412078296281613.9082658828357
Trimmed Mean ( 18 / 25 )29.53846153846152.0877659685255814.1483585726432
Trimmed Mean ( 19 / 25 )29.27027027027032.0125912392906414.5435743229146
Trimmed Mean ( 20 / 25 )29.02857142857141.9300741111236615.0401330504721
Trimmed Mean ( 21 / 25 )28.90909090909091.8725305133471115.438515262118
Trimmed Mean ( 22 / 25 )28.80645161290321.8412357671386815.6451727296548
Trimmed Mean ( 23 / 25 )28.68965517241381.7901643210180416.026269117071
Trimmed Mean ( 24 / 25 )28.55555555555561.7356110390903716.4527390713771
Trimmed Mean ( 25 / 25 )28.521.6942254867637916.8336506697684
Median31
Midrange35.5
Midmean - Weighted Average at Xnp28.3846153846154
Midmean - Weighted Average at X(n+1)p31.6363636363636
Midmean - Empirical Distribution Function31.6363636363636
Midmean - Empirical Distribution Function - Averaging31.6363636363636
Midmean - Empirical Distribution Function - Interpolation28.3846153846154
Midmean - Closest Observation28.3846153846154
Midmean - True Basic - Statistics Graphics Toolkit31.6363636363636
Midmean - MS Excel (old versions)31.6363636363636
Number of observations75



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')