Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationWed, 20 Oct 2010 12:13:29 +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/20/t1287576839vnmbppp10fs724q.htm/, Retrieved Sat, 04 May 2024 05:20:09 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=87181, Retrieved Sat, 04 May 2024 05:20:09 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP1W52 - PAUWELS
Estimated Impact93
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Faillissementen d...] [2010-10-20 12:13:29] [0879bbcec85a2f8393668d46994b687b] [Current]
Feedback Forum

Post a new message
Dataseries X:
12
13
23
24
21
20
18
13
12
25
21
17
10
15
23
12
10
21
9
13
17
14
20
12
13
14
23
14
21
21
21
7
15
28
28
18
22
30
1
26
29
24
26
19
19
41
36
54
49
33
50
43
51
46
45
23
56
41
48
43




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 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 & 1 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=87181&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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=87181&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=87181&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'George Udny Yule' @ 72.249.76.132







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean24.551.7086395619153814.3681561326366
Geometric Mean20.8769800772255
Harmonic Mean14.8670274617938
Quadratic Mean27.8379237731552
Winsorized Mean ( 1 / 20 )24.61666666666671.6778873699880314.6712271079568
Winsorized Mean ( 2 / 20 )24.58333333333331.6380523895422615.0076600054305
Winsorized Mean ( 3 / 20 )24.58333333333331.6167016129952315.2058568728636
Winsorized Mean ( 4 / 20 )24.51666666666671.5991685104048415.3308838356629
Winsorized Mean ( 5 / 20 )24.61.5534179555524515.8360471578631
Winsorized Mean ( 6 / 20 )24.41.5035175329045616.2286102197046
Winsorized Mean ( 7 / 20 )24.28333333333331.47542805560616.4585004609794
Winsorized Mean ( 8 / 20 )24.01666666666671.4133127463589616.9931720551870
Winsorized Mean ( 9 / 20 )24.16666666666671.3923046509491417.3573123168066
Winsorized Mean ( 10 / 20 )23.83333333333331.3172404528202718.0933809634416
Winsorized Mean ( 11 / 20 )23.83333333333331.3172404528202718.0933809634416
Winsorized Mean ( 12 / 20 )22.83333333333331.1049878355714320.6638775543854
Winsorized Mean ( 13 / 20 )22.40.94456518559097223.7146152978159
Winsorized Mean ( 14 / 20 )21.70.81729193174465826.5511002337652
Winsorized Mean ( 15 / 20 )21.450.7751161749994427.6732710422609
Winsorized Mean ( 16 / 20 )21.450.68865914096117131.1474846178066
Winsorized Mean ( 17 / 20 )21.450.68865914096117131.1474846178066
Winsorized Mean ( 18 / 20 )21.450.50052232604555942.8552311931188
Winsorized Mean ( 19 / 20 )21.450.50052232604555942.8552311931188
Winsorized Mean ( 20 / 20 )21.450.40015886675677753.6037103809514
Trimmed Mean ( 1 / 20 )24.41379310344831.6305897824319514.9723697317889
Trimmed Mean ( 2 / 20 )24.19642857142861.5717513688531215.3945649744109
Trimmed Mean ( 3 / 20 )23.98148148148151.5251194499599815.7243299743576
Trimmed Mean ( 4 / 20 )23.751.4765321055850916.0849871873181
Trimmed Mean ( 5 / 20 )23.521.4217666503907316.5427990546383
Trimmed Mean ( 6 / 20 )23.251.3672006395012017.0055508520552
Trimmed Mean ( 7 / 20 )231.3132546139874917.5137401041861
Trimmed Mean ( 8 / 20 )22.751.2512678559594218.1815587219382
Trimmed Mean ( 9 / 20 )22.52380952380951.1890118752700518.9433007291822
Trimmed Mean ( 10 / 20 )22.251.1098336673712720.0480492294858
Trimmed Mean ( 11 / 20 )221.0266713466606821.4284737482511
Trimmed Mean ( 12 / 20 )21.72222222222220.9072994212821423.9416246860664
Trimmed Mean ( 13 / 20 )21.55882352941180.82105880999249326.257343891857
Trimmed Mean ( 14 / 20 )21.43750.7566073202770228.3337200493262
Trimmed Mean ( 15 / 20 )21.40.71051219990011230.1191168892083
Trimmed Mean ( 16 / 20 )21.39285714285710.65735417582278732.5438826277789
Trimmed Mean ( 17 / 20 )21.38461538461540.61036413615007335.0358320845992
Trimmed Mean ( 18 / 20 )21.3750.53437115961837340.0002874692287
Trimmed Mean ( 19 / 20 )21.36363636363640.50343174926776242.4360132127336
Trimmed Mean ( 20 / 20 )21.350.44882888545753547.5682396827822
Median21
Midrange28.5
Midmean - Weighted Average at Xnp20.9375
Midmean - Weighted Average at X(n+1)p20.9375
Midmean - Empirical Distribution Function20.9375
Midmean - Empirical Distribution Function - Averaging20.9375
Midmean - Empirical Distribution Function - Interpolation20.9375
Midmean - Closest Observation20.9375
Midmean - True Basic - Statistics Graphics Toolkit20.9375
Midmean - MS Excel (old versions)21.2121212121212
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 24.55 & 1.70863956191538 & 14.3681561326366 \tabularnewline
Geometric Mean & 20.8769800772255 &  &  \tabularnewline
Harmonic Mean & 14.8670274617938 &  &  \tabularnewline
Quadratic Mean & 27.8379237731552 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 24.6166666666667 & 1.67788736998803 & 14.6712271079568 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 24.5833333333333 & 1.63805238954226 & 15.0076600054305 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 24.5833333333333 & 1.61670161299523 & 15.2058568728636 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 24.5166666666667 & 1.59916851040484 & 15.3308838356629 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 24.6 & 1.55341795555245 & 15.8360471578631 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 24.4 & 1.50351753290456 & 16.2286102197046 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 24.2833333333333 & 1.475428055606 & 16.4585004609794 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 24.0166666666667 & 1.41331274635896 & 16.9931720551870 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 24.1666666666667 & 1.39230465094914 & 17.3573123168066 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 23.8333333333333 & 1.31724045282027 & 18.0933809634416 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 23.8333333333333 & 1.31724045282027 & 18.0933809634416 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 22.8333333333333 & 1.10498783557143 & 20.6638775543854 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 22.4 & 0.944565185590972 & 23.7146152978159 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 21.7 & 0.817291931744658 & 26.5511002337652 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 21.45 & 0.77511617499944 & 27.6732710422609 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 21.45 & 0.688659140961171 & 31.1474846178066 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 21.45 & 0.688659140961171 & 31.1474846178066 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 21.45 & 0.500522326045559 & 42.8552311931188 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 21.45 & 0.500522326045559 & 42.8552311931188 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 21.45 & 0.400158866756777 & 53.6037103809514 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 24.4137931034483 & 1.63058978243195 & 14.9723697317889 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 24.1964285714286 & 1.57175136885312 & 15.3945649744109 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 23.9814814814815 & 1.52511944995998 & 15.7243299743576 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 23.75 & 1.47653210558509 & 16.0849871873181 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 23.52 & 1.42176665039073 & 16.5427990546383 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 23.25 & 1.36720063950120 & 17.0055508520552 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 23 & 1.31325461398749 & 17.5137401041861 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 22.75 & 1.25126785595942 & 18.1815587219382 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 22.5238095238095 & 1.18901187527005 & 18.9433007291822 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 22.25 & 1.10983366737127 & 20.0480492294858 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 22 & 1.02667134666068 & 21.4284737482511 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 21.7222222222222 & 0.90729942128214 & 23.9416246860664 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 21.5588235294118 & 0.821058809992493 & 26.257343891857 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 21.4375 & 0.75660732027702 & 28.3337200493262 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 21.4 & 0.710512199900112 & 30.1191168892083 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 21.3928571428571 & 0.657354175822787 & 32.5438826277789 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 21.3846153846154 & 0.610364136150073 & 35.0358320845992 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 21.375 & 0.534371159618373 & 40.0002874692287 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 21.3636363636364 & 0.503431749267762 & 42.4360132127336 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 21.35 & 0.448828885457535 & 47.5682396827822 \tabularnewline
Median & 21 &  &  \tabularnewline
Midrange & 28.5 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 20.9375 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 20.9375 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 20.9375 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 20.9375 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 20.9375 &  &  \tabularnewline
Midmean - Closest Observation & 20.9375 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 20.9375 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 21.2121212121212 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=87181&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]24.55[/C][C]1.70863956191538[/C][C]14.3681561326366[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]20.8769800772255[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]14.8670274617938[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]27.8379237731552[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]24.6166666666667[/C][C]1.67788736998803[/C][C]14.6712271079568[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]24.5833333333333[/C][C]1.63805238954226[/C][C]15.0076600054305[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]24.5833333333333[/C][C]1.61670161299523[/C][C]15.2058568728636[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]24.5166666666667[/C][C]1.59916851040484[/C][C]15.3308838356629[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]24.6[/C][C]1.55341795555245[/C][C]15.8360471578631[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]24.4[/C][C]1.50351753290456[/C][C]16.2286102197046[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]24.2833333333333[/C][C]1.475428055606[/C][C]16.4585004609794[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]24.0166666666667[/C][C]1.41331274635896[/C][C]16.9931720551870[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]24.1666666666667[/C][C]1.39230465094914[/C][C]17.3573123168066[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]23.8333333333333[/C][C]1.31724045282027[/C][C]18.0933809634416[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]23.8333333333333[/C][C]1.31724045282027[/C][C]18.0933809634416[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]22.8333333333333[/C][C]1.10498783557143[/C][C]20.6638775543854[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]22.4[/C][C]0.944565185590972[/C][C]23.7146152978159[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]21.7[/C][C]0.817291931744658[/C][C]26.5511002337652[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]21.45[/C][C]0.77511617499944[/C][C]27.6732710422609[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]21.45[/C][C]0.688659140961171[/C][C]31.1474846178066[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]21.45[/C][C]0.688659140961171[/C][C]31.1474846178066[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]21.45[/C][C]0.500522326045559[/C][C]42.8552311931188[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]21.45[/C][C]0.500522326045559[/C][C]42.8552311931188[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]21.45[/C][C]0.400158866756777[/C][C]53.6037103809514[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]24.4137931034483[/C][C]1.63058978243195[/C][C]14.9723697317889[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]24.1964285714286[/C][C]1.57175136885312[/C][C]15.3945649744109[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]23.9814814814815[/C][C]1.52511944995998[/C][C]15.7243299743576[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]23.75[/C][C]1.47653210558509[/C][C]16.0849871873181[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]23.52[/C][C]1.42176665039073[/C][C]16.5427990546383[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]23.25[/C][C]1.36720063950120[/C][C]17.0055508520552[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]23[/C][C]1.31325461398749[/C][C]17.5137401041861[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]22.75[/C][C]1.25126785595942[/C][C]18.1815587219382[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]22.5238095238095[/C][C]1.18901187527005[/C][C]18.9433007291822[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]22.25[/C][C]1.10983366737127[/C][C]20.0480492294858[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]22[/C][C]1.02667134666068[/C][C]21.4284737482511[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]21.7222222222222[/C][C]0.90729942128214[/C][C]23.9416246860664[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]21.5588235294118[/C][C]0.821058809992493[/C][C]26.257343891857[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]21.4375[/C][C]0.75660732027702[/C][C]28.3337200493262[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]21.4[/C][C]0.710512199900112[/C][C]30.1191168892083[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]21.3928571428571[/C][C]0.657354175822787[/C][C]32.5438826277789[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]21.3846153846154[/C][C]0.610364136150073[/C][C]35.0358320845992[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]21.375[/C][C]0.534371159618373[/C][C]40.0002874692287[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]21.3636363636364[/C][C]0.503431749267762[/C][C]42.4360132127336[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]21.35[/C][C]0.448828885457535[/C][C]47.5682396827822[/C][/ROW]
[ROW][C]Median[/C][C]21[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]28.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]20.9375[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]20.9375[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]20.9375[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]20.9375[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]20.9375[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]20.9375[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]20.9375[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]21.2121212121212[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]60[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=87181&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=87181&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 Mean24.551.7086395619153814.3681561326366
Geometric Mean20.8769800772255
Harmonic Mean14.8670274617938
Quadratic Mean27.8379237731552
Winsorized Mean ( 1 / 20 )24.61666666666671.6778873699880314.6712271079568
Winsorized Mean ( 2 / 20 )24.58333333333331.6380523895422615.0076600054305
Winsorized Mean ( 3 / 20 )24.58333333333331.6167016129952315.2058568728636
Winsorized Mean ( 4 / 20 )24.51666666666671.5991685104048415.3308838356629
Winsorized Mean ( 5 / 20 )24.61.5534179555524515.8360471578631
Winsorized Mean ( 6 / 20 )24.41.5035175329045616.2286102197046
Winsorized Mean ( 7 / 20 )24.28333333333331.47542805560616.4585004609794
Winsorized Mean ( 8 / 20 )24.01666666666671.4133127463589616.9931720551870
Winsorized Mean ( 9 / 20 )24.16666666666671.3923046509491417.3573123168066
Winsorized Mean ( 10 / 20 )23.83333333333331.3172404528202718.0933809634416
Winsorized Mean ( 11 / 20 )23.83333333333331.3172404528202718.0933809634416
Winsorized Mean ( 12 / 20 )22.83333333333331.1049878355714320.6638775543854
Winsorized Mean ( 13 / 20 )22.40.94456518559097223.7146152978159
Winsorized Mean ( 14 / 20 )21.70.81729193174465826.5511002337652
Winsorized Mean ( 15 / 20 )21.450.7751161749994427.6732710422609
Winsorized Mean ( 16 / 20 )21.450.68865914096117131.1474846178066
Winsorized Mean ( 17 / 20 )21.450.68865914096117131.1474846178066
Winsorized Mean ( 18 / 20 )21.450.50052232604555942.8552311931188
Winsorized Mean ( 19 / 20 )21.450.50052232604555942.8552311931188
Winsorized Mean ( 20 / 20 )21.450.40015886675677753.6037103809514
Trimmed Mean ( 1 / 20 )24.41379310344831.6305897824319514.9723697317889
Trimmed Mean ( 2 / 20 )24.19642857142861.5717513688531215.3945649744109
Trimmed Mean ( 3 / 20 )23.98148148148151.5251194499599815.7243299743576
Trimmed Mean ( 4 / 20 )23.751.4765321055850916.0849871873181
Trimmed Mean ( 5 / 20 )23.521.4217666503907316.5427990546383
Trimmed Mean ( 6 / 20 )23.251.3672006395012017.0055508520552
Trimmed Mean ( 7 / 20 )231.3132546139874917.5137401041861
Trimmed Mean ( 8 / 20 )22.751.2512678559594218.1815587219382
Trimmed Mean ( 9 / 20 )22.52380952380951.1890118752700518.9433007291822
Trimmed Mean ( 10 / 20 )22.251.1098336673712720.0480492294858
Trimmed Mean ( 11 / 20 )221.0266713466606821.4284737482511
Trimmed Mean ( 12 / 20 )21.72222222222220.9072994212821423.9416246860664
Trimmed Mean ( 13 / 20 )21.55882352941180.82105880999249326.257343891857
Trimmed Mean ( 14 / 20 )21.43750.7566073202770228.3337200493262
Trimmed Mean ( 15 / 20 )21.40.71051219990011230.1191168892083
Trimmed Mean ( 16 / 20 )21.39285714285710.65735417582278732.5438826277789
Trimmed Mean ( 17 / 20 )21.38461538461540.61036413615007335.0358320845992
Trimmed Mean ( 18 / 20 )21.3750.53437115961837340.0002874692287
Trimmed Mean ( 19 / 20 )21.36363636363640.50343174926776242.4360132127336
Trimmed Mean ( 20 / 20 )21.350.44882888545753547.5682396827822
Median21
Midrange28.5
Midmean - Weighted Average at Xnp20.9375
Midmean - Weighted Average at X(n+1)p20.9375
Midmean - Empirical Distribution Function20.9375
Midmean - Empirical Distribution Function - Averaging20.9375
Midmean - Empirical Distribution Function - Interpolation20.9375
Midmean - Closest Observation20.9375
Midmean - True Basic - Statistics Graphics Toolkit20.9375
Midmean - MS Excel (old versions)21.2121212121212
Number of observations60



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')