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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationFri, 12 Dec 2008 06:49:21 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/Dec/12/t1229089858d0n53iyuk8feyua.htm/, Retrieved Fri, 17 May 2024 18:37:02 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=32730, Retrieved Fri, 17 May 2024 18:37:02 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact159
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [central tendency ...] [2008-12-12 13:49:21] [b0654df83a8a0e1de3ceb7bf60f0d58f] [Current]
-    D    [Central Tendency] [Central tendency ...] [2008-12-12 14:08:41] [005293453b571dbccb80b45226e44173]
-    D      [Central Tendency] [Central tendency ...] [2008-12-12 14:20:11] [005293453b571dbccb80b45226e44173]
-    D        [Central Tendency] [Central tendency ...] [2008-12-13 12:58:54] [005293453b571dbccb80b45226e44173]
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Dataseries X:
217859
208679
213188
216234
213587
209465
204045
200237
203666
241476
260307
243324
244460
233575
237217
235243
230354
227184
221678
217142
219452
256446
265845
248624
241114
229245
231805
219277
219313
212610
214771
211142
211457
240048
240636
230580
208795
197922
194596
194581
185686
178106
172608
167302
168053
202300
202388
182516
173476
166444
171297
169701
164182
161914
159612
151001
158114
186530
187069
174330




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

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=32730&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=32730&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=32730&T=0

As an alternative you can also use a QR Code:  

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

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







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean207496.83744.0122589011755.420972382419
Geometric Mean205450.479090557
Harmonic Mean203358.847990224
Quadratic Mean209480.218756171
Winsorized Mean ( 1 / 20 )207523.053692.0150266896656.2086146724244
Winsorized Mean ( 2 / 20 )207444.2833333333650.5679225449256.8252084976186
Winsorized Mean ( 3 / 20 )207168.2833333333541.9518636722858.4898641503676
Winsorized Mean ( 4 / 20 )207041.8833333333456.6607751088459.8965003520815
Winsorized Mean ( 5 / 20 )207135.7166666673400.5088602334760.913153054524
Winsorized Mean ( 6 / 20 )207036.7166666673350.415121517461.794347612931
Winsorized Mean ( 7 / 20 )207082.13325.5528871873762.2699764595062
Winsorized Mean ( 8 / 20 )207238.13271.2853070746563.3506651198586
Winsorized Mean ( 9 / 20 )207389.33209.9529421986864.6082057071988
Winsorized Mean ( 10 / 20 )207135.9666666673088.7736851293167.0609075905784
Winsorized Mean ( 11 / 20 )206933.22999.8319190956168.9815981631351
Winsorized Mean ( 12 / 20 )206770.42914.8917097851270.9358770707962
Winsorized Mean ( 13 / 20 )207205.0333333332703.5379020002376.6421780808146
Winsorized Mean ( 14 / 20 )207948.22475.7291740798083.9947285741754
Winsorized Mean ( 15 / 20 )208684.22331.5839137332589.5031908441426
Winsorized Mean ( 16 / 20 )208613.5333333332247.7274369398492.8108675032902
Winsorized Mean ( 17 / 20 )208182.32132.6508337514197.6166828180684
Winsorized Mean ( 18 / 20 )208784.11518.63890901975137.481068580526
Winsorized Mean ( 19 / 20 )208083.951419.21321591138146.619230759047
Winsorized Mean ( 20 / 20 )209146.2833333331238.09857020486168.925389598606
Trimmed Mean ( 1 / 20 )207464.8620689663607.56646575957.5082577238994
Trimmed Mean ( 2 / 20 )207402.5178571433503.1543569610959.2045044903644
Trimmed Mean ( 3 / 20 )207379.3148148153401.2377392952460.9717199179923
Trimmed Mean ( 4 / 20 )207460.4807692313326.1754572354662.3720797163421
Trimmed Mean ( 5 / 20 )207586.063263.7446544290663.6036461119271
Trimmed Mean ( 6 / 20 )207698.6458333333201.7693455218564.8699588943941
Trimmed Mean ( 7 / 20 )207842.5434782613135.6792352508166.2831010078224
Trimmed Mean ( 8 / 20 )207990.6818181823055.3456484450768.0743541811816
Trimmed Mean ( 9 / 20 )208125.0714285712964.1199498521270.2147939184967
Trimmed Mean ( 10 / 20 )208247.72859.2542579831772.8328722143416
Trimmed Mean ( 11 / 20 )208423.2368421052751.3016449904675.7544114516125
Trimmed Mean ( 12 / 20 )2086492627.7667293972279.4016446230984
Trimmed Mean ( 13 / 20 )208925.2647058822479.6506691136384.2559265739492
Trimmed Mean ( 14 / 20 )209173.3752338.2180683980489.4584546356315
Trimmed Mean ( 15 / 20 )209348.42211.1908107124894.6767682760697
Trimmed Mean ( 16 / 20 )209443.2857142862074.13871961195100.978436848944
Trimmed Mean ( 17 / 20 )209562.9615384621895.27832295927110.571074970800
Trimmed Mean ( 18 / 20 )2097661657.9754853872126.519361624344
Trimmed Mean ( 19 / 20 )209914.7727272731573.87790982322133.374241684890
Trimmed Mean ( 20 / 20 )210203.851466.39688975716143.347173925615
Median211299.5
Midrange208423
Midmean - Weighted Average at Xnp208482.838709677
Midmean - Weighted Average at X(n+1)p209348.4
Midmean - Empirical Distribution Function208482.838709677
Midmean - Empirical Distribution Function - Averaging209348.4
Midmean - Empirical Distribution Function - Interpolation209348.4
Midmean - Closest Observation208482.838709677
Midmean - True Basic - Statistics Graphics Toolkit209348.4
Midmean - MS Excel (old versions)209173.375
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 207496.8 & 3744.01225890117 & 55.420972382419 \tabularnewline
Geometric Mean & 205450.479090557 &  &  \tabularnewline
Harmonic Mean & 203358.847990224 &  &  \tabularnewline
Quadratic Mean & 209480.218756171 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 207523.05 & 3692.01502668966 & 56.2086146724244 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 207444.283333333 & 3650.56792254492 & 56.8252084976186 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 207168.283333333 & 3541.95186367228 & 58.4898641503676 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 207041.883333333 & 3456.66077510884 & 59.8965003520815 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 207135.716666667 & 3400.50886023347 & 60.913153054524 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 207036.716666667 & 3350.4151215174 & 61.794347612931 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 207082.1 & 3325.55288718737 & 62.2699764595062 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 207238.1 & 3271.28530707465 & 63.3506651198586 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 207389.3 & 3209.95294219868 & 64.6082057071988 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 207135.966666667 & 3088.77368512931 & 67.0609075905784 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 206933.2 & 2999.83191909561 & 68.9815981631351 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 206770.4 & 2914.89170978512 & 70.9358770707962 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 207205.033333333 & 2703.53790200023 & 76.6421780808146 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 207948.2 & 2475.72917407980 & 83.9947285741754 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 208684.2 & 2331.58391373325 & 89.5031908441426 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 208613.533333333 & 2247.72743693984 & 92.8108675032902 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 208182.3 & 2132.65083375141 & 97.6166828180684 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 208784.1 & 1518.63890901975 & 137.481068580526 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 208083.95 & 1419.21321591138 & 146.619230759047 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 209146.283333333 & 1238.09857020486 & 168.925389598606 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 207464.862068966 & 3607.566465759 & 57.5082577238994 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 207402.517857143 & 3503.15435696109 & 59.2045044903644 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 207379.314814815 & 3401.23773929524 & 60.9717199179923 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 207460.480769231 & 3326.17545723546 & 62.3720797163421 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 207586.06 & 3263.74465442906 & 63.6036461119271 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 207698.645833333 & 3201.76934552185 & 64.8699588943941 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 207842.543478261 & 3135.67923525081 & 66.2831010078224 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 207990.681818182 & 3055.34564844507 & 68.0743541811816 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 208125.071428571 & 2964.11994985212 & 70.2147939184967 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 208247.7 & 2859.25425798317 & 72.8328722143416 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 208423.236842105 & 2751.30164499046 & 75.7544114516125 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 208649 & 2627.76672939722 & 79.4016446230984 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 208925.264705882 & 2479.65066911363 & 84.2559265739492 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 209173.375 & 2338.21806839804 & 89.4584546356315 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 209348.4 & 2211.19081071248 & 94.6767682760697 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 209443.285714286 & 2074.13871961195 & 100.978436848944 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 209562.961538462 & 1895.27832295927 & 110.571074970800 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 209766 & 1657.9754853872 & 126.519361624344 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 209914.772727273 & 1573.87790982322 & 133.374241684890 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 210203.85 & 1466.39688975716 & 143.347173925615 \tabularnewline
Median & 211299.5 &  &  \tabularnewline
Midrange & 208423 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 208482.838709677 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 209348.4 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 208482.838709677 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 209348.4 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 209348.4 &  &  \tabularnewline
Midmean - Closest Observation & 208482.838709677 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 209348.4 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 209173.375 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=32730&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]207496.8[/C][C]3744.01225890117[/C][C]55.420972382419[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]205450.479090557[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]203358.847990224[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]209480.218756171[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]207523.05[/C][C]3692.01502668966[/C][C]56.2086146724244[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]207444.283333333[/C][C]3650.56792254492[/C][C]56.8252084976186[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]207168.283333333[/C][C]3541.95186367228[/C][C]58.4898641503676[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]207041.883333333[/C][C]3456.66077510884[/C][C]59.8965003520815[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]207135.716666667[/C][C]3400.50886023347[/C][C]60.913153054524[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]207036.716666667[/C][C]3350.4151215174[/C][C]61.794347612931[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]207082.1[/C][C]3325.55288718737[/C][C]62.2699764595062[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]207238.1[/C][C]3271.28530707465[/C][C]63.3506651198586[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]207389.3[/C][C]3209.95294219868[/C][C]64.6082057071988[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]207135.966666667[/C][C]3088.77368512931[/C][C]67.0609075905784[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]206933.2[/C][C]2999.83191909561[/C][C]68.9815981631351[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]206770.4[/C][C]2914.89170978512[/C][C]70.9358770707962[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]207205.033333333[/C][C]2703.53790200023[/C][C]76.6421780808146[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]207948.2[/C][C]2475.72917407980[/C][C]83.9947285741754[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]208684.2[/C][C]2331.58391373325[/C][C]89.5031908441426[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]208613.533333333[/C][C]2247.72743693984[/C][C]92.8108675032902[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]208182.3[/C][C]2132.65083375141[/C][C]97.6166828180684[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]208784.1[/C][C]1518.63890901975[/C][C]137.481068580526[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]208083.95[/C][C]1419.21321591138[/C][C]146.619230759047[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]209146.283333333[/C][C]1238.09857020486[/C][C]168.925389598606[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]207464.862068966[/C][C]3607.566465759[/C][C]57.5082577238994[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]207402.517857143[/C][C]3503.15435696109[/C][C]59.2045044903644[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]207379.314814815[/C][C]3401.23773929524[/C][C]60.9717199179923[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]207460.480769231[/C][C]3326.17545723546[/C][C]62.3720797163421[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]207586.06[/C][C]3263.74465442906[/C][C]63.6036461119271[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]207698.645833333[/C][C]3201.76934552185[/C][C]64.8699588943941[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]207842.543478261[/C][C]3135.67923525081[/C][C]66.2831010078224[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]207990.681818182[/C][C]3055.34564844507[/C][C]68.0743541811816[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]208125.071428571[/C][C]2964.11994985212[/C][C]70.2147939184967[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]208247.7[/C][C]2859.25425798317[/C][C]72.8328722143416[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]208423.236842105[/C][C]2751.30164499046[/C][C]75.7544114516125[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]208649[/C][C]2627.76672939722[/C][C]79.4016446230984[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]208925.264705882[/C][C]2479.65066911363[/C][C]84.2559265739492[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]209173.375[/C][C]2338.21806839804[/C][C]89.4584546356315[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]209348.4[/C][C]2211.19081071248[/C][C]94.6767682760697[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]209443.285714286[/C][C]2074.13871961195[/C][C]100.978436848944[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]209562.961538462[/C][C]1895.27832295927[/C][C]110.571074970800[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]209766[/C][C]1657.9754853872[/C][C]126.519361624344[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]209914.772727273[/C][C]1573.87790982322[/C][C]133.374241684890[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]210203.85[/C][C]1466.39688975716[/C][C]143.347173925615[/C][/ROW]
[ROW][C]Median[/C][C]211299.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]208423[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]208482.838709677[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]209348.4[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]208482.838709677[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]209348.4[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]209348.4[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]208482.838709677[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]209348.4[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]209173.375[/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=32730&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=32730&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 Mean207496.83744.0122589011755.420972382419
Geometric Mean205450.479090557
Harmonic Mean203358.847990224
Quadratic Mean209480.218756171
Winsorized Mean ( 1 / 20 )207523.053692.0150266896656.2086146724244
Winsorized Mean ( 2 / 20 )207444.2833333333650.5679225449256.8252084976186
Winsorized Mean ( 3 / 20 )207168.2833333333541.9518636722858.4898641503676
Winsorized Mean ( 4 / 20 )207041.8833333333456.6607751088459.8965003520815
Winsorized Mean ( 5 / 20 )207135.7166666673400.5088602334760.913153054524
Winsorized Mean ( 6 / 20 )207036.7166666673350.415121517461.794347612931
Winsorized Mean ( 7 / 20 )207082.13325.5528871873762.2699764595062
Winsorized Mean ( 8 / 20 )207238.13271.2853070746563.3506651198586
Winsorized Mean ( 9 / 20 )207389.33209.9529421986864.6082057071988
Winsorized Mean ( 10 / 20 )207135.9666666673088.7736851293167.0609075905784
Winsorized Mean ( 11 / 20 )206933.22999.8319190956168.9815981631351
Winsorized Mean ( 12 / 20 )206770.42914.8917097851270.9358770707962
Winsorized Mean ( 13 / 20 )207205.0333333332703.5379020002376.6421780808146
Winsorized Mean ( 14 / 20 )207948.22475.7291740798083.9947285741754
Winsorized Mean ( 15 / 20 )208684.22331.5839137332589.5031908441426
Winsorized Mean ( 16 / 20 )208613.5333333332247.7274369398492.8108675032902
Winsorized Mean ( 17 / 20 )208182.32132.6508337514197.6166828180684
Winsorized Mean ( 18 / 20 )208784.11518.63890901975137.481068580526
Winsorized Mean ( 19 / 20 )208083.951419.21321591138146.619230759047
Winsorized Mean ( 20 / 20 )209146.2833333331238.09857020486168.925389598606
Trimmed Mean ( 1 / 20 )207464.8620689663607.56646575957.5082577238994
Trimmed Mean ( 2 / 20 )207402.5178571433503.1543569610959.2045044903644
Trimmed Mean ( 3 / 20 )207379.3148148153401.2377392952460.9717199179923
Trimmed Mean ( 4 / 20 )207460.4807692313326.1754572354662.3720797163421
Trimmed Mean ( 5 / 20 )207586.063263.7446544290663.6036461119271
Trimmed Mean ( 6 / 20 )207698.6458333333201.7693455218564.8699588943941
Trimmed Mean ( 7 / 20 )207842.5434782613135.6792352508166.2831010078224
Trimmed Mean ( 8 / 20 )207990.6818181823055.3456484450768.0743541811816
Trimmed Mean ( 9 / 20 )208125.0714285712964.1199498521270.2147939184967
Trimmed Mean ( 10 / 20 )208247.72859.2542579831772.8328722143416
Trimmed Mean ( 11 / 20 )208423.2368421052751.3016449904675.7544114516125
Trimmed Mean ( 12 / 20 )2086492627.7667293972279.4016446230984
Trimmed Mean ( 13 / 20 )208925.2647058822479.6506691136384.2559265739492
Trimmed Mean ( 14 / 20 )209173.3752338.2180683980489.4584546356315
Trimmed Mean ( 15 / 20 )209348.42211.1908107124894.6767682760697
Trimmed Mean ( 16 / 20 )209443.2857142862074.13871961195100.978436848944
Trimmed Mean ( 17 / 20 )209562.9615384621895.27832295927110.571074970800
Trimmed Mean ( 18 / 20 )2097661657.9754853872126.519361624344
Trimmed Mean ( 19 / 20 )209914.7727272731573.87790982322133.374241684890
Trimmed Mean ( 20 / 20 )210203.851466.39688975716143.347173925615
Median211299.5
Midrange208423
Midmean - Weighted Average at Xnp208482.838709677
Midmean - Weighted Average at X(n+1)p209348.4
Midmean - Empirical Distribution Function208482.838709677
Midmean - Empirical Distribution Function - Averaging209348.4
Midmean - Empirical Distribution Function - Interpolation209348.4
Midmean - Closest Observation208482.838709677
Midmean - True Basic - Statistics Graphics Toolkit209348.4
Midmean - MS Excel (old versions)209173.375
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')