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Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationMon, 12 Dec 2016 22:37:11 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Dec/12/t1481578737l9lpjs7cpduag4s.htm/, Retrieved Fri, 03 May 2024 23:23:59 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=299001, Retrieved Fri, 03 May 2024 23:23:59 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact59

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2016-12-12 21:37:11] [9412b5b3b31fe4708efb1e5c8c74b28f] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
40548
40331
39814
39360
38915
38583
38191
37477
37110
36670
36330
36108
35341
34764
34253
33743
33296
32875
32622
32346
31780
31003
28467
28153
27682
27217
26780
26490
26020
25227
25343
24453
23958
23475
23102
22393
21557
20893
20376
19704
19016
18274
18020
17317
16919
16372
16069
15478
15018
14561
14047
13506
13035
12471
11815
11172
10594
9914
9319
8939
8073
7431
7022

Tables (Output of Computation)





Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R ServerBig Analytics Cloud Computing Center

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input view raw input (R code)  \tabularnewline
Raw Outputview raw output of R engine  \tabularnewline
Computing time1 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299001&T=0

[TABLE]
[ROW]
Summary of computational transaction[/C][/ROW] [ROW]Raw Input[/C] view raw input (R code) [/C][/ROW] [ROW]Raw Output[/C]view raw output of R engine [/C][/ROW] [ROW]Computing time[/C]1 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=299001&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299001&T=0

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R ServerBig Analytics Cloud Computing Center






Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean24398.91282.6919.0217
Geometric Mean21983.9
Harmonic Mean19364.7
Quadratic Mean26406.7
Winsorized Mean ( 1 / 21 )244021280.5919.0553
Winsorized Mean ( 2 / 21 )24405.91273.0519.1712
Winsorized Mean ( 3 / 21 )24425.61260.5219.3773
Winsorized Mean ( 4 / 21 )24421.41250.4419.5303
Winsorized Mean ( 5 / 21 )24442.31236.4719.7678
Winsorized Mean ( 6 / 21 )24469.71217.5520.0976
Winsorized Mean ( 7 / 21 )24454.61191.6720.5214
Winsorized Mean ( 8 / 21 )24489.71169.0220.9489
Winsorized Mean ( 9 / 21 )24520.51141.9821.4719
Winsorized Mean ( 10 / 21 )24556.11117.7121.9701
Winsorized Mean ( 11 / 21 )24599.61097.5922.4123
Winsorized Mean ( 12 / 21 )24556.51056.5423.2424
Winsorized Mean ( 13 / 21 )24543.51020.2424.0567
Winsorized Mean ( 14 / 21 )24531.5986.11624.8769
Winsorized Mean ( 15 / 21 )24519.6950.02225.8095
Winsorized Mean ( 16 / 21 )24556.2909.51426.9992
Winsorized Mean ( 17 / 21 )24524.3879.74927.8765
Winsorized Mean ( 18 / 21 )24608.3845.54529.1035
Winsorized Mean ( 19 / 21 )24645.1815.33730.2269
Winsorized Mean ( 20 / 21 )24688.6755.99132.6573
Winsorized Mean ( 21 / 21 )24514.3705.09934.7672
Trimmed Mean ( 1 / 21 )244191265.7419.2923
Trimmed Mean ( 2 / 21 )24437.31247.0819.5957
Trimmed Mean ( 3 / 21 )24454.61228.5319.9056
Trimmed Mean ( 4 / 21 )24465.71210.8820.2048
Trimmed Mean ( 5 / 21 )24478.91192.0920.5343
Trimmed Mean ( 6 / 21 )24487.91172.4720.8857
Trimmed Mean ( 7 / 21 )24491.81152.6121.249
Trimmed Mean ( 8 / 21 )24498.91133.6721.6103
Trimmed Mean ( 9 / 21 )24500.51114.3421.9865
Trimmed Mean ( 10 / 21 )24497.31095.1122.3697
Trimmed Mean ( 11 / 21 )24488.21074.7922.7843
Trimmed Mean ( 12 / 21 )24471.91051.5823.2715
Trimmed Mean ( 13 / 21 )24459.91029.623.7567
Trimmed Mean ( 14 / 21 )24448.31007.4724.267
Trimmed Mean ( 15 / 21 )24437984.14624.8306
Trimmed Mean ( 16 / 21 )24425.8959.34125.461
Trimmed Mean ( 17 / 21 )24408.1933.36326.1507
Trimmed Mean ( 18 / 21 )24392.1901.9727.0431
Trimmed Mean ( 19 / 21 )24361.8863.62728.2087
Trimmed Mean ( 20 / 21 )24321812.56929.931
Trimmed Mean ( 21 / 21 )24265.9753.86832.1885
Median24453
Midrange23785
Midmean - Weighted Average at Xnp24146.2
Midmean - Weighted Average at X(n+1)p24437
Midmean - Empirical Distribution Function24437
Midmean - Empirical Distribution Function - Averaging24437
Midmean - Empirical Distribution Function - Interpolation24425.8
Midmean - Closest Observation24146.2
Midmean - True Basic - Statistics Graphics Toolkit24437
Midmean - MS Excel (old versions)24437
Number of observations63

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 24398.9 & 1282.69 & 19.0217 \tabularnewline
Geometric Mean & 21983.9 &  &  \tabularnewline
Harmonic Mean & 19364.7 &  &  \tabularnewline
Quadratic Mean & 26406.7 &  &  \tabularnewline
Winsorized Mean ( 1 / 21 ) & 24402 & 1280.59 & 19.0553 \tabularnewline
Winsorized Mean ( 2 / 21 ) & 24405.9 & 1273.05 & 19.1712 \tabularnewline
Winsorized Mean ( 3 / 21 ) & 24425.6 & 1260.52 & 19.3773 \tabularnewline
Winsorized Mean ( 4 / 21 ) & 24421.4 & 1250.44 & 19.5303 \tabularnewline
Winsorized Mean ( 5 / 21 ) & 24442.3 & 1236.47 & 19.7678 \tabularnewline
Winsorized Mean ( 6 / 21 ) & 24469.7 & 1217.55 & 20.0976 \tabularnewline
Winsorized Mean ( 7 / 21 ) & 24454.6 & 1191.67 & 20.5214 \tabularnewline
Winsorized Mean ( 8 / 21 ) & 24489.7 & 1169.02 & 20.9489 \tabularnewline
Winsorized Mean ( 9 / 21 ) & 24520.5 & 1141.98 & 21.4719 \tabularnewline
Winsorized Mean ( 10 / 21 ) & 24556.1 & 1117.71 & 21.9701 \tabularnewline
Winsorized Mean ( 11 / 21 ) & 24599.6 & 1097.59 & 22.4123 \tabularnewline
Winsorized Mean ( 12 / 21 ) & 24556.5 & 1056.54 & 23.2424 \tabularnewline
Winsorized Mean ( 13 / 21 ) & 24543.5 & 1020.24 & 24.0567 \tabularnewline
Winsorized Mean ( 14 / 21 ) & 24531.5 & 986.116 & 24.8769 \tabularnewline
Winsorized Mean ( 15 / 21 ) & 24519.6 & 950.022 & 25.8095 \tabularnewline
Winsorized Mean ( 16 / 21 ) & 24556.2 & 909.514 & 26.9992 \tabularnewline
Winsorized Mean ( 17 / 21 ) & 24524.3 & 879.749 & 27.8765 \tabularnewline
Winsorized Mean ( 18 / 21 ) & 24608.3 & 845.545 & 29.1035 \tabularnewline
Winsorized Mean ( 19 / 21 ) & 24645.1 & 815.337 & 30.2269 \tabularnewline
Winsorized Mean ( 20 / 21 ) & 24688.6 & 755.991 & 32.6573 \tabularnewline
Winsorized Mean ( 21 / 21 ) & 24514.3 & 705.099 & 34.7672 \tabularnewline
Trimmed Mean ( 1 / 21 ) & 24419 & 1265.74 & 19.2923 \tabularnewline
Trimmed Mean ( 2 / 21 ) & 24437.3 & 1247.08 & 19.5957 \tabularnewline
Trimmed Mean ( 3 / 21 ) & 24454.6 & 1228.53 & 19.9056 \tabularnewline
Trimmed Mean ( 4 / 21 ) & 24465.7 & 1210.88 & 20.2048 \tabularnewline
Trimmed Mean ( 5 / 21 ) & 24478.9 & 1192.09 & 20.5343 \tabularnewline
Trimmed Mean ( 6 / 21 ) & 24487.9 & 1172.47 & 20.8857 \tabularnewline
Trimmed Mean ( 7 / 21 ) & 24491.8 & 1152.61 & 21.249 \tabularnewline
Trimmed Mean ( 8 / 21 ) & 24498.9 & 1133.67 & 21.6103 \tabularnewline
Trimmed Mean ( 9 / 21 ) & 24500.5 & 1114.34 & 21.9865 \tabularnewline
Trimmed Mean ( 10 / 21 ) & 24497.3 & 1095.11 & 22.3697 \tabularnewline
Trimmed Mean ( 11 / 21 ) & 24488.2 & 1074.79 & 22.7843 \tabularnewline
Trimmed Mean ( 12 / 21 ) & 24471.9 & 1051.58 & 23.2715 \tabularnewline
Trimmed Mean ( 13 / 21 ) & 24459.9 & 1029.6 & 23.7567 \tabularnewline
Trimmed Mean ( 14 / 21 ) & 24448.3 & 1007.47 & 24.267 \tabularnewline
Trimmed Mean ( 15 / 21 ) & 24437 & 984.146 & 24.8306 \tabularnewline
Trimmed Mean ( 16 / 21 ) & 24425.8 & 959.341 & 25.461 \tabularnewline
Trimmed Mean ( 17 / 21 ) & 24408.1 & 933.363 & 26.1507 \tabularnewline
Trimmed Mean ( 18 / 21 ) & 24392.1 & 901.97 & 27.0431 \tabularnewline
Trimmed Mean ( 19 / 21 ) & 24361.8 & 863.627 & 28.2087 \tabularnewline
Trimmed Mean ( 20 / 21 ) & 24321 & 812.569 & 29.931 \tabularnewline
Trimmed Mean ( 21 / 21 ) & 24265.9 & 753.868 & 32.1885 \tabularnewline
Median & 24453 &  &  \tabularnewline
Midrange & 23785 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 24146.2 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 24437 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 24437 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 24437 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 24425.8 &  &  \tabularnewline
Midmean - Closest Observation & 24146.2 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 24437 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 24437 &  &  \tabularnewline
Number of observations & 63 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299001&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]24398.9[/C][C]1282.69[/C][C]19.0217[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]21983.9[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]19364.7[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]26406.7[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 21 )[/C][C]24402[/C][C]1280.59[/C][C]19.0553[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 21 )[/C][C]24405.9[/C][C]1273.05[/C][C]19.1712[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 21 )[/C][C]24425.6[/C][C]1260.52[/C][C]19.3773[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 21 )[/C][C]24421.4[/C][C]1250.44[/C][C]19.5303[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 21 )[/C][C]24442.3[/C][C]1236.47[/C][C]19.7678[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 21 )[/C][C]24469.7[/C][C]1217.55[/C][C]20.0976[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 21 )[/C][C]24454.6[/C][C]1191.67[/C][C]20.5214[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 21 )[/C][C]24489.7[/C][C]1169.02[/C][C]20.9489[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 21 )[/C][C]24520.5[/C][C]1141.98[/C][C]21.4719[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 21 )[/C][C]24556.1[/C][C]1117.71[/C][C]21.9701[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 21 )[/C][C]24599.6[/C][C]1097.59[/C][C]22.4123[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 21 )[/C][C]24556.5[/C][C]1056.54[/C][C]23.2424[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 21 )[/C][C]24543.5[/C][C]1020.24[/C][C]24.0567[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 21 )[/C][C]24531.5[/C][C]986.116[/C][C]24.8769[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 21 )[/C][C]24519.6[/C][C]950.022[/C][C]25.8095[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 21 )[/C][C]24556.2[/C][C]909.514[/C][C]26.9992[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 21 )[/C][C]24524.3[/C][C]879.749[/C][C]27.8765[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 21 )[/C][C]24608.3[/C][C]845.545[/C][C]29.1035[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 21 )[/C][C]24645.1[/C][C]815.337[/C][C]30.2269[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 21 )[/C][C]24688.6[/C][C]755.991[/C][C]32.6573[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 21 )[/C][C]24514.3[/C][C]705.099[/C][C]34.7672[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 21 )[/C][C]24419[/C][C]1265.74[/C][C]19.2923[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 21 )[/C][C]24437.3[/C][C]1247.08[/C][C]19.5957[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 21 )[/C][C]24454.6[/C][C]1228.53[/C][C]19.9056[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 21 )[/C][C]24465.7[/C][C]1210.88[/C][C]20.2048[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 21 )[/C][C]24478.9[/C][C]1192.09[/C][C]20.5343[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 21 )[/C][C]24487.9[/C][C]1172.47[/C][C]20.8857[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 21 )[/C][C]24491.8[/C][C]1152.61[/C][C]21.249[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 21 )[/C][C]24498.9[/C][C]1133.67[/C][C]21.6103[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 21 )[/C][C]24500.5[/C][C]1114.34[/C][C]21.9865[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 21 )[/C][C]24497.3[/C][C]1095.11[/C][C]22.3697[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 21 )[/C][C]24488.2[/C][C]1074.79[/C][C]22.7843[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 21 )[/C][C]24471.9[/C][C]1051.58[/C][C]23.2715[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 21 )[/C][C]24459.9[/C][C]1029.6[/C][C]23.7567[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 21 )[/C][C]24448.3[/C][C]1007.47[/C][C]24.267[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 21 )[/C][C]24437[/C][C]984.146[/C][C]24.8306[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 21 )[/C][C]24425.8[/C][C]959.341[/C][C]25.461[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 21 )[/C][C]24408.1[/C][C]933.363[/C][C]26.1507[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 21 )[/C][C]24392.1[/C][C]901.97[/C][C]27.0431[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 21 )[/C][C]24361.8[/C][C]863.627[/C][C]28.2087[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 21 )[/C][C]24321[/C][C]812.569[/C][C]29.931[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 21 )[/C][C]24265.9[/C][C]753.868[/C][C]32.1885[/C][/ROW]
[ROW][C]Median[/C][C]24453[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]23785[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]24146.2[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]24437[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]24437[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]24437[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]24425.8[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]24146.2[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]24437[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]24437[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]63[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=299001&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299001&T=1

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean24398.91282.6919.0217
Geometric Mean21983.9
Harmonic Mean19364.7
Quadratic Mean26406.7
Winsorized Mean ( 1 / 21 )244021280.5919.0553
Winsorized Mean ( 2 / 21 )24405.91273.0519.1712
Winsorized Mean ( 3 / 21 )24425.61260.5219.3773
Winsorized Mean ( 4 / 21 )24421.41250.4419.5303
Winsorized Mean ( 5 / 21 )24442.31236.4719.7678
Winsorized Mean ( 6 / 21 )24469.71217.5520.0976
Winsorized Mean ( 7 / 21 )24454.61191.6720.5214
Winsorized Mean ( 8 / 21 )24489.71169.0220.9489
Winsorized Mean ( 9 / 21 )24520.51141.9821.4719
Winsorized Mean ( 10 / 21 )24556.11117.7121.9701
Winsorized Mean ( 11 / 21 )24599.61097.5922.4123
Winsorized Mean ( 12 / 21 )24556.51056.5423.2424
Winsorized Mean ( 13 / 21 )24543.51020.2424.0567
Winsorized Mean ( 14 / 21 )24531.5986.11624.8769
Winsorized Mean ( 15 / 21 )24519.6950.02225.8095
Winsorized Mean ( 16 / 21 )24556.2909.51426.9992
Winsorized Mean ( 17 / 21 )24524.3879.74927.8765
Winsorized Mean ( 18 / 21 )24608.3845.54529.1035
Winsorized Mean ( 19 / 21 )24645.1815.33730.2269
Winsorized Mean ( 20 / 21 )24688.6755.99132.6573
Winsorized Mean ( 21 / 21 )24514.3705.09934.7672
Trimmed Mean ( 1 / 21 )244191265.7419.2923
Trimmed Mean ( 2 / 21 )24437.31247.0819.5957
Trimmed Mean ( 3 / 21 )24454.61228.5319.9056
Trimmed Mean ( 4 / 21 )24465.71210.8820.2048
Trimmed Mean ( 5 / 21 )24478.91192.0920.5343
Trimmed Mean ( 6 / 21 )24487.91172.4720.8857
Trimmed Mean ( 7 / 21 )24491.81152.6121.249
Trimmed Mean ( 8 / 21 )24498.91133.6721.6103
Trimmed Mean ( 9 / 21 )24500.51114.3421.9865
Trimmed Mean ( 10 / 21 )24497.31095.1122.3697
Trimmed Mean ( 11 / 21 )24488.21074.7922.7843
Trimmed Mean ( 12 / 21 )24471.91051.5823.2715
Trimmed Mean ( 13 / 21 )24459.91029.623.7567
Trimmed Mean ( 14 / 21 )24448.31007.4724.267
Trimmed Mean ( 15 / 21 )24437984.14624.8306
Trimmed Mean ( 16 / 21 )24425.8959.34125.461
Trimmed Mean ( 17 / 21 )24408.1933.36326.1507
Trimmed Mean ( 18 / 21 )24392.1901.9727.0431
Trimmed Mean ( 19 / 21 )24361.8863.62728.2087
Trimmed Mean ( 20 / 21 )24321812.56929.931
Trimmed Mean ( 21 / 21 )24265.9753.86832.1885
Median24453
Midrange23785
Midmean - Weighted Average at Xnp24146.2
Midmean - Weighted Average at X(n+1)p24437
Midmean - Empirical Distribution Function24437
Midmean - Empirical Distribution Function - Averaging24437
Midmean - Empirical Distribution Function - Interpolation24425.8
Midmean - Closest Observation24146.2
Midmean - True Basic - Statistics Graphics Toolkit24437
Midmean - MS Excel (old versions)24437
Number of observations63


Figures (Output of Computation)

Input Parameters & R Code

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,'Arithmetic Mean',header=TRUE)
a<-table.element(a,signif(arm,6))
a<-table.element(a, signif(armse,6))
a<-table.element(a,signif(armose,6))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Geometric Mean',header=TRUE)
a<-table.element(a,signif(geo,6))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Harmonic Mean',header=TRUE)
a<-table.element(a,signif(har,6))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Quadratic Mean',header=TRUE)
a<-table.element(a,signif(qua,6))
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, mylabel,header=TRUE)
a<-table.element(a,signif(win[j,1],6))
a<-table.element(a,signif(win[j,2],6))
a<-table.element(a,signif(win[j,1]/win[j,2],6))
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, mylabel,header=TRUE)
a<-table.element(a,signif(tri[j,1],6))
a<-table.element(a,signif(tri[j,2],6))
a<-table.element(a,signif(tri[j,1]/tri[j,2],6))
a<-table.row.end(a)
}
a<-table.row.start(a)
a<-table.element(a, 'Median',header=TRUE)
a<-table.element(a,signif(median(x),6))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Midrange',header=TRUE)
a<-table.element(a,signif(midr,6))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <-  'Midmean'
mylabel <- paste(mymid,'Weighted Average at Xnp',sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,signif(midm[1],6))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <-  'Midmean'
mylabel <- paste(mymid,'Weighted Average at X(n+1)p',sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,signif(midm[2],6))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <-  'Midmean'
mylabel <- paste(mymid,'Empirical Distribution Function',sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,signif(midm[3],6))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <-  'Midmean'
mylabel <- paste(mymid,'Empirical Distribution Function - Averaging',sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,signif(midm[4],6))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <-  'Midmean'
mylabel <- paste(mymid,'Empirical Distribution Function - Interpolation',sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,signif(midm[5],6))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <-  'Midmean'
mylabel <- paste(mymid,'Closest Observation',sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,signif(midm[6],6))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <-  'Midmean'
mylabel <- paste(mymid,'True Basic - Statistics Graphics Toolkit',sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,signif(midm[7],6))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <-  'Midmean'
mylabel <- paste(mymid,'MS Excel (old versions)',sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,signif(midm[8],6))
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,signif(length(x),6))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')