Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationWed, 12 Oct 2016 08:55:24 +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/Oct/12/t1476258958g8gofcw4yi4sa60.htm/, Retrieved Sun, 05 May 2024 17:15:32 +0200
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Sun, 05 May 2024 17:15:32 +0200
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact0
Dataseries X:
209305
161498
126542
100278
168677
143277
127573
90760
160404
132039
117053
101248
152336
135356
119590
81695
155847
129364
111902
86772
150695
123177
114397
76927
160032
126833
110054
87080
161472
133737
121069
89365
163837
136276
120950
78858
124634
96579
94974
71028
145065
125041
120555
92507
180404
147940
125532
101901
166452
164909
95859
75225
115418
95535
90178
115685
107032
91924
85095
103517
109702
91594
99712
148342




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

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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'Herman Ole Andreas Wold' @ wold.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean121072.093753738.852461455432.3821533473591
Geometric Mean117531.454282247
Harmonic Mean114108.209568098
Quadratic Mean124656.046792389
Winsorized Mean ( 1 / 21 )120686.093753580.3779956348733.7076403377348
Winsorized Mean ( 2 / 21 )120372.81253480.7594900277434.5823412519205
Winsorized Mean ( 3 / 21 )120359.031253440.5470044695934.9825278055037
Winsorized Mean ( 4 / 21 )120439.906253387.1646750742435.5577356885845
Winsorized Mean ( 5 / 21 )120621.781253323.1266296905936.2976782685019
Winsorized Mean ( 6 / 21 )120559.718753252.2737440419937.0693638476342
Winsorized Mean ( 7 / 21 )120590.56253246.1677973403637.1485918253523
Winsorized Mean ( 8 / 21 )120742.68753173.7589117477638.0440641074114
Winsorized Mean ( 9 / 21 )120804.7031253145.5871548803538.4045003927399
Winsorized Mean ( 10 / 21 )120241.7343753005.2009869302140.0112121944383
Winsorized Mean ( 11 / 21 )119781.6252871.7838791527341.7098326477616
Winsorized Mean ( 12 / 21 )119535.81252807.3416502640142.5797168252602
Winsorized Mean ( 13 / 21 )119176.281252705.8225975292644.04438094309
Winsorized Mean ( 14 / 21 )1196282607.9901863319945.8698045057642
Winsorized Mean ( 15 / 21 )119085.656252473.928864558248.1362491686949
Winsorized Mean ( 16 / 21 )118719.656252387.9033709589449.7171107063366
Winsorized Mean ( 17 / 21 )117051.2656252068.3742777596956.5909501406977
Winsorized Mean ( 18 / 21 )117673.6718751894.4733278690662.1141876974121
Winsorized Mean ( 19 / 21 )117361.06251798.8110816530165.2436843963355
Winsorized Mean ( 20 / 21 )117133.56251677.3852872025969.8310420352775
Winsorized Mean ( 21 / 21 )116470.093751524.05225684976.4213255986404
Trimmed Mean ( 1 / 21 )120456.145161293489.4424159633434.5201699303686
Trimmed Mean ( 2 / 21 )120210.8666666673378.5301097553635.5808185102637
Trimmed Mean ( 3 / 21 )120121.5172413793308.3281573565636.3088277607139
Trimmed Mean ( 4 / 21 )120031.0357142863240.1016300964137.045453944824
Trimmed Mean ( 5 / 21 )119909.8888888893174.9676348974337.7672791277958
Trimmed Mean ( 6 / 21 )119734.6538461543113.4225176915338.4575666058111
Trimmed Mean ( 7 / 21 )119558.643055.5826142418639.1279356816423
Trimmed Mean ( 8 / 21 )119362.0833333332982.0077534898440.0274221935352
Trimmed Mean ( 9 / 21 )119121.978260872905.4564204442340.9994028554923
Trimmed Mean ( 10 / 21 )118850.0227272732811.9002461278842.2667990768644
Trimmed Mean ( 11 / 21 )118637.9523809522726.3840606932743.5147615816038
Trimmed Mean ( 12 / 21 )118471.62647.1898648402344.7537222673488
Trimmed Mean ( 13 / 21 )118322.2368421052556.3225655106946.286113669097
Trimmed Mean ( 14 / 21 )118205.4444444442459.1591192359548.0674241531676
Trimmed Mean ( 15 / 21 )118014.1764705882349.7101237648450.2249938309408
Trimmed Mean ( 16 / 21 )117871.31252235.392300869252.7295868623005
Trimmed Mean ( 17 / 21 )117758.22097.2418166966756.1490806937461
Trimmed Mean ( 18 / 21 )117853.252003.6038368367158.8206350143883
Trimmed Mean ( 19 / 21 )117877.8076923081921.3140263245661.3527024095098
Trimmed Mean ( 20 / 21 )117950.3333333331824.7729069217864.6383628811679
Trimmed Mean ( 21 / 21 )118069.1363636361715.9037744535168.8087165034881
Median120072.5
Midrange140166.5
Midmean - Weighted Average at Xnp117194.454545455
Midmean - Weighted Average at X(n+1)p117871.3125
Midmean - Empirical Distribution Function117194.454545455
Midmean - Empirical Distribution Function - Averaging117871.3125
Midmean - Empirical Distribution Function - Interpolation117871.3125
Midmean - Closest Observation117194.454545455
Midmean - True Basic - Statistics Graphics Toolkit117871.3125
Midmean - MS Excel (old versions)118014.176470588
Number of observations64

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 121072.09375 & 3738.8524614554 & 32.3821533473591 \tabularnewline
Geometric Mean & 117531.454282247 &  &  \tabularnewline
Harmonic Mean & 114108.209568098 &  &  \tabularnewline
Quadratic Mean & 124656.046792389 &  &  \tabularnewline
Winsorized Mean ( 1 / 21 ) & 120686.09375 & 3580.37799563487 & 33.7076403377348 \tabularnewline
Winsorized Mean ( 2 / 21 ) & 120372.8125 & 3480.75949002774 & 34.5823412519205 \tabularnewline
Winsorized Mean ( 3 / 21 ) & 120359.03125 & 3440.54700446959 & 34.9825278055037 \tabularnewline
Winsorized Mean ( 4 / 21 ) & 120439.90625 & 3387.16467507424 & 35.5577356885845 \tabularnewline
Winsorized Mean ( 5 / 21 ) & 120621.78125 & 3323.12662969059 & 36.2976782685019 \tabularnewline
Winsorized Mean ( 6 / 21 ) & 120559.71875 & 3252.27374404199 & 37.0693638476342 \tabularnewline
Winsorized Mean ( 7 / 21 ) & 120590.5625 & 3246.16779734036 & 37.1485918253523 \tabularnewline
Winsorized Mean ( 8 / 21 ) & 120742.6875 & 3173.75891174776 & 38.0440641074114 \tabularnewline
Winsorized Mean ( 9 / 21 ) & 120804.703125 & 3145.58715488035 & 38.4045003927399 \tabularnewline
Winsorized Mean ( 10 / 21 ) & 120241.734375 & 3005.20098693021 & 40.0112121944383 \tabularnewline
Winsorized Mean ( 11 / 21 ) & 119781.625 & 2871.78387915273 & 41.7098326477616 \tabularnewline
Winsorized Mean ( 12 / 21 ) & 119535.8125 & 2807.34165026401 & 42.5797168252602 \tabularnewline
Winsorized Mean ( 13 / 21 ) & 119176.28125 & 2705.82259752926 & 44.04438094309 \tabularnewline
Winsorized Mean ( 14 / 21 ) & 119628 & 2607.99018633199 & 45.8698045057642 \tabularnewline
Winsorized Mean ( 15 / 21 ) & 119085.65625 & 2473.9288645582 & 48.1362491686949 \tabularnewline
Winsorized Mean ( 16 / 21 ) & 118719.65625 & 2387.90337095894 & 49.7171107063366 \tabularnewline
Winsorized Mean ( 17 / 21 ) & 117051.265625 & 2068.37427775969 & 56.5909501406977 \tabularnewline
Winsorized Mean ( 18 / 21 ) & 117673.671875 & 1894.47332786906 & 62.1141876974121 \tabularnewline
Winsorized Mean ( 19 / 21 ) & 117361.0625 & 1798.81108165301 & 65.2436843963355 \tabularnewline
Winsorized Mean ( 20 / 21 ) & 117133.5625 & 1677.38528720259 & 69.8310420352775 \tabularnewline
Winsorized Mean ( 21 / 21 ) & 116470.09375 & 1524.052256849 & 76.4213255986404 \tabularnewline
Trimmed Mean ( 1 / 21 ) & 120456.14516129 & 3489.44241596334 & 34.5201699303686 \tabularnewline
Trimmed Mean ( 2 / 21 ) & 120210.866666667 & 3378.53010975536 & 35.5808185102637 \tabularnewline
Trimmed Mean ( 3 / 21 ) & 120121.517241379 & 3308.32815735656 & 36.3088277607139 \tabularnewline
Trimmed Mean ( 4 / 21 ) & 120031.035714286 & 3240.10163009641 & 37.045453944824 \tabularnewline
Trimmed Mean ( 5 / 21 ) & 119909.888888889 & 3174.96763489743 & 37.7672791277958 \tabularnewline
Trimmed Mean ( 6 / 21 ) & 119734.653846154 & 3113.42251769153 & 38.4575666058111 \tabularnewline
Trimmed Mean ( 7 / 21 ) & 119558.64 & 3055.58261424186 & 39.1279356816423 \tabularnewline
Trimmed Mean ( 8 / 21 ) & 119362.083333333 & 2982.00775348984 & 40.0274221935352 \tabularnewline
Trimmed Mean ( 9 / 21 ) & 119121.97826087 & 2905.45642044423 & 40.9994028554923 \tabularnewline
Trimmed Mean ( 10 / 21 ) & 118850.022727273 & 2811.90024612788 & 42.2667990768644 \tabularnewline
Trimmed Mean ( 11 / 21 ) & 118637.952380952 & 2726.38406069327 & 43.5147615816038 \tabularnewline
Trimmed Mean ( 12 / 21 ) & 118471.6 & 2647.18986484023 & 44.7537222673488 \tabularnewline
Trimmed Mean ( 13 / 21 ) & 118322.236842105 & 2556.32256551069 & 46.286113669097 \tabularnewline
Trimmed Mean ( 14 / 21 ) & 118205.444444444 & 2459.15911923595 & 48.0674241531676 \tabularnewline
Trimmed Mean ( 15 / 21 ) & 118014.176470588 & 2349.71012376484 & 50.2249938309408 \tabularnewline
Trimmed Mean ( 16 / 21 ) & 117871.3125 & 2235.3923008692 & 52.7295868623005 \tabularnewline
Trimmed Mean ( 17 / 21 ) & 117758.2 & 2097.24181669667 & 56.1490806937461 \tabularnewline
Trimmed Mean ( 18 / 21 ) & 117853.25 & 2003.60383683671 & 58.8206350143883 \tabularnewline
Trimmed Mean ( 19 / 21 ) & 117877.807692308 & 1921.31402632456 & 61.3527024095098 \tabularnewline
Trimmed Mean ( 20 / 21 ) & 117950.333333333 & 1824.77290692178 & 64.6383628811679 \tabularnewline
Trimmed Mean ( 21 / 21 ) & 118069.136363636 & 1715.90377445351 & 68.8087165034881 \tabularnewline
Median & 120072.5 &  &  \tabularnewline
Midrange & 140166.5 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 117194.454545455 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 117871.3125 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 117194.454545455 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 117871.3125 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 117871.3125 &  &  \tabularnewline
Midmean - Closest Observation & 117194.454545455 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 117871.3125 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 118014.176470588 &  &  \tabularnewline
Number of observations & 64 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]121072.09375[/C][C]3738.8524614554[/C][C]32.3821533473591[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]117531.454282247[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]114108.209568098[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]124656.046792389[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 21 )[/C][C]120686.09375[/C][C]3580.37799563487[/C][C]33.7076403377348[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 21 )[/C][C]120372.8125[/C][C]3480.75949002774[/C][C]34.5823412519205[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 21 )[/C][C]120359.03125[/C][C]3440.54700446959[/C][C]34.9825278055037[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 21 )[/C][C]120439.90625[/C][C]3387.16467507424[/C][C]35.5577356885845[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 21 )[/C][C]120621.78125[/C][C]3323.12662969059[/C][C]36.2976782685019[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 21 )[/C][C]120559.71875[/C][C]3252.27374404199[/C][C]37.0693638476342[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 21 )[/C][C]120590.5625[/C][C]3246.16779734036[/C][C]37.1485918253523[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 21 )[/C][C]120742.6875[/C][C]3173.75891174776[/C][C]38.0440641074114[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 21 )[/C][C]120804.703125[/C][C]3145.58715488035[/C][C]38.4045003927399[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 21 )[/C][C]120241.734375[/C][C]3005.20098693021[/C][C]40.0112121944383[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 21 )[/C][C]119781.625[/C][C]2871.78387915273[/C][C]41.7098326477616[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 21 )[/C][C]119535.8125[/C][C]2807.34165026401[/C][C]42.5797168252602[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 21 )[/C][C]119176.28125[/C][C]2705.82259752926[/C][C]44.04438094309[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 21 )[/C][C]119628[/C][C]2607.99018633199[/C][C]45.8698045057642[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 21 )[/C][C]119085.65625[/C][C]2473.9288645582[/C][C]48.1362491686949[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 21 )[/C][C]118719.65625[/C][C]2387.90337095894[/C][C]49.7171107063366[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 21 )[/C][C]117051.265625[/C][C]2068.37427775969[/C][C]56.5909501406977[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 21 )[/C][C]117673.671875[/C][C]1894.47332786906[/C][C]62.1141876974121[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 21 )[/C][C]117361.0625[/C][C]1798.81108165301[/C][C]65.2436843963355[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 21 )[/C][C]117133.5625[/C][C]1677.38528720259[/C][C]69.8310420352775[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 21 )[/C][C]116470.09375[/C][C]1524.052256849[/C][C]76.4213255986404[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 21 )[/C][C]120456.14516129[/C][C]3489.44241596334[/C][C]34.5201699303686[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 21 )[/C][C]120210.866666667[/C][C]3378.53010975536[/C][C]35.5808185102637[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 21 )[/C][C]120121.517241379[/C][C]3308.32815735656[/C][C]36.3088277607139[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 21 )[/C][C]120031.035714286[/C][C]3240.10163009641[/C][C]37.045453944824[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 21 )[/C][C]119909.888888889[/C][C]3174.96763489743[/C][C]37.7672791277958[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 21 )[/C][C]119734.653846154[/C][C]3113.42251769153[/C][C]38.4575666058111[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 21 )[/C][C]119558.64[/C][C]3055.58261424186[/C][C]39.1279356816423[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 21 )[/C][C]119362.083333333[/C][C]2982.00775348984[/C][C]40.0274221935352[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 21 )[/C][C]119121.97826087[/C][C]2905.45642044423[/C][C]40.9994028554923[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 21 )[/C][C]118850.022727273[/C][C]2811.90024612788[/C][C]42.2667990768644[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 21 )[/C][C]118637.952380952[/C][C]2726.38406069327[/C][C]43.5147615816038[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 21 )[/C][C]118471.6[/C][C]2647.18986484023[/C][C]44.7537222673488[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 21 )[/C][C]118322.236842105[/C][C]2556.32256551069[/C][C]46.286113669097[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 21 )[/C][C]118205.444444444[/C][C]2459.15911923595[/C][C]48.0674241531676[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 21 )[/C][C]118014.176470588[/C][C]2349.71012376484[/C][C]50.2249938309408[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 21 )[/C][C]117871.3125[/C][C]2235.3923008692[/C][C]52.7295868623005[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 21 )[/C][C]117758.2[/C][C]2097.24181669667[/C][C]56.1490806937461[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 21 )[/C][C]117853.25[/C][C]2003.60383683671[/C][C]58.8206350143883[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 21 )[/C][C]117877.807692308[/C][C]1921.31402632456[/C][C]61.3527024095098[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 21 )[/C][C]117950.333333333[/C][C]1824.77290692178[/C][C]64.6383628811679[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 21 )[/C][C]118069.136363636[/C][C]1715.90377445351[/C][C]68.8087165034881[/C][/ROW]
[ROW][C]Median[/C][C]120072.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]140166.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]117194.454545455[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]117871.3125[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]117194.454545455[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]117871.3125[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]117871.3125[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]117194.454545455[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]117871.3125[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]118014.176470588[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]64[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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 Mean121072.093753738.852461455432.3821533473591
Geometric Mean117531.454282247
Harmonic Mean114108.209568098
Quadratic Mean124656.046792389
Winsorized Mean ( 1 / 21 )120686.093753580.3779956348733.7076403377348
Winsorized Mean ( 2 / 21 )120372.81253480.7594900277434.5823412519205
Winsorized Mean ( 3 / 21 )120359.031253440.5470044695934.9825278055037
Winsorized Mean ( 4 / 21 )120439.906253387.1646750742435.5577356885845
Winsorized Mean ( 5 / 21 )120621.781253323.1266296905936.2976782685019
Winsorized Mean ( 6 / 21 )120559.718753252.2737440419937.0693638476342
Winsorized Mean ( 7 / 21 )120590.56253246.1677973403637.1485918253523
Winsorized Mean ( 8 / 21 )120742.68753173.7589117477638.0440641074114
Winsorized Mean ( 9 / 21 )120804.7031253145.5871548803538.4045003927399
Winsorized Mean ( 10 / 21 )120241.7343753005.2009869302140.0112121944383
Winsorized Mean ( 11 / 21 )119781.6252871.7838791527341.7098326477616
Winsorized Mean ( 12 / 21 )119535.81252807.3416502640142.5797168252602
Winsorized Mean ( 13 / 21 )119176.281252705.8225975292644.04438094309
Winsorized Mean ( 14 / 21 )1196282607.9901863319945.8698045057642
Winsorized Mean ( 15 / 21 )119085.656252473.928864558248.1362491686949
Winsorized Mean ( 16 / 21 )118719.656252387.9033709589449.7171107063366
Winsorized Mean ( 17 / 21 )117051.2656252068.3742777596956.5909501406977
Winsorized Mean ( 18 / 21 )117673.6718751894.4733278690662.1141876974121
Winsorized Mean ( 19 / 21 )117361.06251798.8110816530165.2436843963355
Winsorized Mean ( 20 / 21 )117133.56251677.3852872025969.8310420352775
Winsorized Mean ( 21 / 21 )116470.093751524.05225684976.4213255986404
Trimmed Mean ( 1 / 21 )120456.145161293489.4424159633434.5201699303686
Trimmed Mean ( 2 / 21 )120210.8666666673378.5301097553635.5808185102637
Trimmed Mean ( 3 / 21 )120121.5172413793308.3281573565636.3088277607139
Trimmed Mean ( 4 / 21 )120031.0357142863240.1016300964137.045453944824
Trimmed Mean ( 5 / 21 )119909.8888888893174.9676348974337.7672791277958
Trimmed Mean ( 6 / 21 )119734.6538461543113.4225176915338.4575666058111
Trimmed Mean ( 7 / 21 )119558.643055.5826142418639.1279356816423
Trimmed Mean ( 8 / 21 )119362.0833333332982.0077534898440.0274221935352
Trimmed Mean ( 9 / 21 )119121.978260872905.4564204442340.9994028554923
Trimmed Mean ( 10 / 21 )118850.0227272732811.9002461278842.2667990768644
Trimmed Mean ( 11 / 21 )118637.9523809522726.3840606932743.5147615816038
Trimmed Mean ( 12 / 21 )118471.62647.1898648402344.7537222673488
Trimmed Mean ( 13 / 21 )118322.2368421052556.3225655106946.286113669097
Trimmed Mean ( 14 / 21 )118205.4444444442459.1591192359548.0674241531676
Trimmed Mean ( 15 / 21 )118014.1764705882349.7101237648450.2249938309408
Trimmed Mean ( 16 / 21 )117871.31252235.392300869252.7295868623005
Trimmed Mean ( 17 / 21 )117758.22097.2418166966756.1490806937461
Trimmed Mean ( 18 / 21 )117853.252003.6038368367158.8206350143883
Trimmed Mean ( 19 / 21 )117877.8076923081921.3140263245661.3527024095098
Trimmed Mean ( 20 / 21 )117950.3333333331824.7729069217864.6383628811679
Trimmed Mean ( 21 / 21 )118069.1363636361715.9037744535168.8087165034881
Median120072.5
Midrange140166.5
Midmean - Weighted Average at Xnp117194.454545455
Midmean - Weighted Average at X(n+1)p117871.3125
Midmean - Empirical Distribution Function117194.454545455
Midmean - Empirical Distribution Function - Averaging117871.3125
Midmean - Empirical Distribution Function - Interpolation117871.3125
Midmean - Closest Observation117194.454545455
Midmean - True Basic - Statistics Graphics Toolkit117871.3125
Midmean - MS Excel (old versions)118014.176470588
Number of observations64



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')