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of Irreproducible Research!

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, 28 Nov 2011 11:36:00 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Nov/28/t132249820884azw8qvz97fjrd.htm/, Retrieved Thu, 25 Apr 2024 19:53:38 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=147850, Retrieved Thu, 25 Apr 2024 19:53:38 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact116
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
F     [Univariate Data Series] [HPC Retail Sales] [2008-03-02 15:42:48] [74be16979710d4c4e7c6647856088456]
- RMPD  [Univariate Data Series] [WS 8 inschrijving...] [2011-11-27 14:07:06] [74be16979710d4c4e7c6647856088456]
- RMPD      [Central Tendency] [WS 8 central tend...] [2011-11-28 16:36:00] [cb05b01fd3da20a46af540a30bcf4c06] [Current]
- R PD        [Central Tendency] [ws 8 central tend...] [2011-11-28 20:26:49] [620e5553455d245695b6e856984b13e0]
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Dataseries X:
20995
17382
9367
31124
26551
30651
25859
25100
25778
20418
18688
20424
24776
19814
12738
31566
30111
30019
31934
25826
26835
20205
17789
20520
22518
15572
11509
25447
24090
27786
26195
20516
22759
19028
16971
20036
22485
18730
14538
27561
25985
34670
32066
27186
29586
21359
21553
19573
24256
22380
16167
27297
28287
33474
28229
28785
25597
18130
20198
22849
23118




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'AstonUniversity' @ aston.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'AstonUniversity' @ aston.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=147850&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'AstonUniversity' @ aston.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=147850&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=147850&T=0

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'AstonUniversity' @ aston.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean23458.2950819672710.5487232880433.0143371075452
Geometric Mean22737.1887931709
Harmonic Mean21912.4338497272
Quadratic Mean24095.3185793968
Winsorized Mean ( 1 / 20 )23473.8032786885694.7652293726133.7866696349872
Winsorized Mean ( 2 / 20 )23467.9344262295673.162538069834.8622109803088
Winsorized Mean ( 3 / 20 )23549.9672131148649.75610765550836.2443183459857
Winsorized Mean ( 4 / 20 )23593.6393442623629.56793451614237.4759228523849
Winsorized Mean ( 5 / 20 )23606.1803278689611.91112720729938.5777922287589
Winsorized Mean ( 6 / 20 )23638.737704918587.00517768992140.2700667785335
Winsorized Mean ( 7 / 20 )23623.9344262295566.11421199368541.7299794383064
Winsorized Mean ( 8 / 20 )23665.2459016393554.18639308613842.7026830627381
Winsorized Mean ( 9 / 20 )23651.6721311475533.36792001307844.3440095357959
Winsorized Mean ( 10 / 20 )23611.8360655738494.21371905132347.7765694382145
Winsorized Mean ( 11 / 20 )23529.6065573771477.6573435604349.2604308812437
Winsorized Mean ( 12 / 20 )23576.8196721311466.08293693594950.5850306967388
Winsorized Mean ( 13 / 20 )23598.5573770492432.11800245560754.6113729188442
Winsorized Mean ( 14 / 20 )23602.2295081967415.34525594469156.8255666108768
Winsorized Mean ( 15 / 20 )23591.9016393443396.91015535439859.4388964884993
Winsorized Mean ( 16 / 20 )23605.2786885246386.0970808091861.1381951892845
Winsorized Mean ( 17 / 20 )23509.4098360656370.93554989142163.3786916431902
Winsorized Mean ( 18 / 20 )23488.4590163934349.27468684534467.2492450814048
Winsorized Mean ( 19 / 20 )23379.4426229508333.0793826553270.1918036372264
Winsorized Mean ( 20 / 20 )23340.7540983607319.01510289867573.1650441821687
Trimmed Mean ( 1 / 20 )23507.1016949153667.22806905857535.2309844040023
Trimmed Mean ( 2 / 20 )23542.7368421053633.26875356324537.1765332011664
Trimmed Mean ( 3 / 20 )23584.2181818182605.97545798828738.9194279585396
Trimmed Mean ( 4 / 20 )23597.358490566583.71728927495840.4260057465089
Trimmed Mean ( 5 / 20 )23598.4705882353563.9965299246241.8415173430044
Trimmed Mean ( 6 / 20 )23596.5510204082545.26186140334643.2756308311707
Trimmed Mean ( 7 / 20 )23587.4255319149529.25829076095344.5669457496859
Trimmed Mean ( 8 / 20 )23580.3555555556514.70331765749545.8134905033717
Trimmed Mean ( 9 / 20 )23565.3023255814498.91073768799647.2335040027109
Trimmed Mean ( 10 / 20 )23551.0243902439483.71987520470448.6873200739941
Trimmed Mean ( 11 / 20 )23541.5128205128473.79951982054549.6866540291753
Trimmed Mean ( 12 / 20 )23543.2972972973464.19697826669450.7183338099436
Trimmed Mean ( 13 / 20 )23538.4285714286453.4399412404351.9107966250985
Trimmed Mean ( 14 / 20 )23529.8787878788446.90047820476952.6512723423345
Trimmed Mean ( 15 / 20 )23519.7096774194440.9708989826553.3361945917087
Trimmed Mean ( 16 / 20 )23509.5862068966436.11068362009953.9073842716865
Trimmed Mean ( 17 / 20 )23496.0740740741430.24670232343254.6107011330705
Trimmed Mean ( 18 / 20 )23494.16424.20336192287155.3841909538466
Trimmed Mean ( 19 / 20 )23495419.77324953797155.9706937635022
Trimmed Mean ( 20 / 20 )23512.6666666667415.28662696947356.6179239583244
Median23118
Midrange22018.5
Midmean - Weighted Average at Xnp23393.8
Midmean - Weighted Average at X(n+1)p23519.7096774194
Midmean - Empirical Distribution Function23519.7096774194
Midmean - Empirical Distribution Function - Averaging23519.7096774194
Midmean - Empirical Distribution Function - Interpolation23519.7096774194
Midmean - Closest Observation23403.90625
Midmean - True Basic - Statistics Graphics Toolkit23519.7096774194
Midmean - MS Excel (old versions)23519.7096774194
Number of observations61

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 23458.2950819672 & 710.54872328804 & 33.0143371075452 \tabularnewline
Geometric Mean & 22737.1887931709 &  &  \tabularnewline
Harmonic Mean & 21912.4338497272 &  &  \tabularnewline
Quadratic Mean & 24095.3185793968 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 23473.8032786885 & 694.76522937261 & 33.7866696349872 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 23467.9344262295 & 673.1625380698 & 34.8622109803088 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 23549.9672131148 & 649.756107655508 & 36.2443183459857 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 23593.6393442623 & 629.567934516142 & 37.4759228523849 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 23606.1803278689 & 611.911127207299 & 38.5777922287589 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 23638.737704918 & 587.005177689921 & 40.2700667785335 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 23623.9344262295 & 566.114211993685 & 41.7299794383064 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 23665.2459016393 & 554.186393086138 & 42.7026830627381 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 23651.6721311475 & 533.367920013078 & 44.3440095357959 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 23611.8360655738 & 494.213719051323 & 47.7765694382145 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 23529.6065573771 & 477.65734356043 & 49.2604308812437 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 23576.8196721311 & 466.082936935949 & 50.5850306967388 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 23598.5573770492 & 432.118002455607 & 54.6113729188442 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 23602.2295081967 & 415.345255944691 & 56.8255666108768 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 23591.9016393443 & 396.910155354398 & 59.4388964884993 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 23605.2786885246 & 386.09708080918 & 61.1381951892845 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 23509.4098360656 & 370.935549891421 & 63.3786916431902 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 23488.4590163934 & 349.274686845344 & 67.2492450814048 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 23379.4426229508 & 333.07938265532 & 70.1918036372264 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 23340.7540983607 & 319.015102898675 & 73.1650441821687 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 23507.1016949153 & 667.228069058575 & 35.2309844040023 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 23542.7368421053 & 633.268753563245 & 37.1765332011664 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 23584.2181818182 & 605.975457988287 & 38.9194279585396 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 23597.358490566 & 583.717289274958 & 40.4260057465089 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 23598.4705882353 & 563.99652992462 & 41.8415173430044 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 23596.5510204082 & 545.261861403346 & 43.2756308311707 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 23587.4255319149 & 529.258290760953 & 44.5669457496859 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 23580.3555555556 & 514.703317657495 & 45.8134905033717 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 23565.3023255814 & 498.910737687996 & 47.2335040027109 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 23551.0243902439 & 483.719875204704 & 48.6873200739941 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 23541.5128205128 & 473.799519820545 & 49.6866540291753 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 23543.2972972973 & 464.196978266694 & 50.7183338099436 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 23538.4285714286 & 453.43994124043 & 51.9107966250985 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 23529.8787878788 & 446.900478204769 & 52.6512723423345 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 23519.7096774194 & 440.97089898265 & 53.3361945917087 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 23509.5862068966 & 436.110683620099 & 53.9073842716865 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 23496.0740740741 & 430.246702323432 & 54.6107011330705 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 23494.16 & 424.203361922871 & 55.3841909538466 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 23495 & 419.773249537971 & 55.9706937635022 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 23512.6666666667 & 415.286626969473 & 56.6179239583244 \tabularnewline
Median & 23118 &  &  \tabularnewline
Midrange & 22018.5 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 23393.8 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 23519.7096774194 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 23519.7096774194 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 23519.7096774194 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 23519.7096774194 &  &  \tabularnewline
Midmean - Closest Observation & 23403.90625 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 23519.7096774194 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 23519.7096774194 &  &  \tabularnewline
Number of observations & 61 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=147850&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]23458.2950819672[/C][C]710.54872328804[/C][C]33.0143371075452[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]22737.1887931709[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]21912.4338497272[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]24095.3185793968[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]23473.8032786885[/C][C]694.76522937261[/C][C]33.7866696349872[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]23467.9344262295[/C][C]673.1625380698[/C][C]34.8622109803088[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]23549.9672131148[/C][C]649.756107655508[/C][C]36.2443183459857[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]23593.6393442623[/C][C]629.567934516142[/C][C]37.4759228523849[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]23606.1803278689[/C][C]611.911127207299[/C][C]38.5777922287589[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]23638.737704918[/C][C]587.005177689921[/C][C]40.2700667785335[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]23623.9344262295[/C][C]566.114211993685[/C][C]41.7299794383064[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]23665.2459016393[/C][C]554.186393086138[/C][C]42.7026830627381[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]23651.6721311475[/C][C]533.367920013078[/C][C]44.3440095357959[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]23611.8360655738[/C][C]494.213719051323[/C][C]47.7765694382145[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]23529.6065573771[/C][C]477.65734356043[/C][C]49.2604308812437[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]23576.8196721311[/C][C]466.082936935949[/C][C]50.5850306967388[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]23598.5573770492[/C][C]432.118002455607[/C][C]54.6113729188442[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]23602.2295081967[/C][C]415.345255944691[/C][C]56.8255666108768[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]23591.9016393443[/C][C]396.910155354398[/C][C]59.4388964884993[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]23605.2786885246[/C][C]386.09708080918[/C][C]61.1381951892845[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]23509.4098360656[/C][C]370.935549891421[/C][C]63.3786916431902[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]23488.4590163934[/C][C]349.274686845344[/C][C]67.2492450814048[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]23379.4426229508[/C][C]333.07938265532[/C][C]70.1918036372264[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]23340.7540983607[/C][C]319.015102898675[/C][C]73.1650441821687[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]23507.1016949153[/C][C]667.228069058575[/C][C]35.2309844040023[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]23542.7368421053[/C][C]633.268753563245[/C][C]37.1765332011664[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]23584.2181818182[/C][C]605.975457988287[/C][C]38.9194279585396[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]23597.358490566[/C][C]583.717289274958[/C][C]40.4260057465089[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]23598.4705882353[/C][C]563.99652992462[/C][C]41.8415173430044[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]23596.5510204082[/C][C]545.261861403346[/C][C]43.2756308311707[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]23587.4255319149[/C][C]529.258290760953[/C][C]44.5669457496859[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]23580.3555555556[/C][C]514.703317657495[/C][C]45.8134905033717[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]23565.3023255814[/C][C]498.910737687996[/C][C]47.2335040027109[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]23551.0243902439[/C][C]483.719875204704[/C][C]48.6873200739941[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]23541.5128205128[/C][C]473.799519820545[/C][C]49.6866540291753[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]23543.2972972973[/C][C]464.196978266694[/C][C]50.7183338099436[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]23538.4285714286[/C][C]453.43994124043[/C][C]51.9107966250985[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]23529.8787878788[/C][C]446.900478204769[/C][C]52.6512723423345[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]23519.7096774194[/C][C]440.97089898265[/C][C]53.3361945917087[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]23509.5862068966[/C][C]436.110683620099[/C][C]53.9073842716865[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]23496.0740740741[/C][C]430.246702323432[/C][C]54.6107011330705[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]23494.16[/C][C]424.203361922871[/C][C]55.3841909538466[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]23495[/C][C]419.773249537971[/C][C]55.9706937635022[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]23512.6666666667[/C][C]415.286626969473[/C][C]56.6179239583244[/C][/ROW]
[ROW][C]Median[/C][C]23118[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]22018.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]23393.8[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]23519.7096774194[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]23519.7096774194[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]23519.7096774194[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]23519.7096774194[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]23403.90625[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]23519.7096774194[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]23519.7096774194[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]61[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=147850&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=147850&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 Mean23458.2950819672710.5487232880433.0143371075452
Geometric Mean22737.1887931709
Harmonic Mean21912.4338497272
Quadratic Mean24095.3185793968
Winsorized Mean ( 1 / 20 )23473.8032786885694.7652293726133.7866696349872
Winsorized Mean ( 2 / 20 )23467.9344262295673.162538069834.8622109803088
Winsorized Mean ( 3 / 20 )23549.9672131148649.75610765550836.2443183459857
Winsorized Mean ( 4 / 20 )23593.6393442623629.56793451614237.4759228523849
Winsorized Mean ( 5 / 20 )23606.1803278689611.91112720729938.5777922287589
Winsorized Mean ( 6 / 20 )23638.737704918587.00517768992140.2700667785335
Winsorized Mean ( 7 / 20 )23623.9344262295566.11421199368541.7299794383064
Winsorized Mean ( 8 / 20 )23665.2459016393554.18639308613842.7026830627381
Winsorized Mean ( 9 / 20 )23651.6721311475533.36792001307844.3440095357959
Winsorized Mean ( 10 / 20 )23611.8360655738494.21371905132347.7765694382145
Winsorized Mean ( 11 / 20 )23529.6065573771477.6573435604349.2604308812437
Winsorized Mean ( 12 / 20 )23576.8196721311466.08293693594950.5850306967388
Winsorized Mean ( 13 / 20 )23598.5573770492432.11800245560754.6113729188442
Winsorized Mean ( 14 / 20 )23602.2295081967415.34525594469156.8255666108768
Winsorized Mean ( 15 / 20 )23591.9016393443396.91015535439859.4388964884993
Winsorized Mean ( 16 / 20 )23605.2786885246386.0970808091861.1381951892845
Winsorized Mean ( 17 / 20 )23509.4098360656370.93554989142163.3786916431902
Winsorized Mean ( 18 / 20 )23488.4590163934349.27468684534467.2492450814048
Winsorized Mean ( 19 / 20 )23379.4426229508333.0793826553270.1918036372264
Winsorized Mean ( 20 / 20 )23340.7540983607319.01510289867573.1650441821687
Trimmed Mean ( 1 / 20 )23507.1016949153667.22806905857535.2309844040023
Trimmed Mean ( 2 / 20 )23542.7368421053633.26875356324537.1765332011664
Trimmed Mean ( 3 / 20 )23584.2181818182605.97545798828738.9194279585396
Trimmed Mean ( 4 / 20 )23597.358490566583.71728927495840.4260057465089
Trimmed Mean ( 5 / 20 )23598.4705882353563.9965299246241.8415173430044
Trimmed Mean ( 6 / 20 )23596.5510204082545.26186140334643.2756308311707
Trimmed Mean ( 7 / 20 )23587.4255319149529.25829076095344.5669457496859
Trimmed Mean ( 8 / 20 )23580.3555555556514.70331765749545.8134905033717
Trimmed Mean ( 9 / 20 )23565.3023255814498.91073768799647.2335040027109
Trimmed Mean ( 10 / 20 )23551.0243902439483.71987520470448.6873200739941
Trimmed Mean ( 11 / 20 )23541.5128205128473.79951982054549.6866540291753
Trimmed Mean ( 12 / 20 )23543.2972972973464.19697826669450.7183338099436
Trimmed Mean ( 13 / 20 )23538.4285714286453.4399412404351.9107966250985
Trimmed Mean ( 14 / 20 )23529.8787878788446.90047820476952.6512723423345
Trimmed Mean ( 15 / 20 )23519.7096774194440.9708989826553.3361945917087
Trimmed Mean ( 16 / 20 )23509.5862068966436.11068362009953.9073842716865
Trimmed Mean ( 17 / 20 )23496.0740740741430.24670232343254.6107011330705
Trimmed Mean ( 18 / 20 )23494.16424.20336192287155.3841909538466
Trimmed Mean ( 19 / 20 )23495419.77324953797155.9706937635022
Trimmed Mean ( 20 / 20 )23512.6666666667415.28662696947356.6179239583244
Median23118
Midrange22018.5
Midmean - Weighted Average at Xnp23393.8
Midmean - Weighted Average at X(n+1)p23519.7096774194
Midmean - Empirical Distribution Function23519.7096774194
Midmean - Empirical Distribution Function - Averaging23519.7096774194
Midmean - Empirical Distribution Function - Interpolation23519.7096774194
Midmean - Closest Observation23403.90625
Midmean - True Basic - Statistics Graphics Toolkit23519.7096774194
Midmean - MS Excel (old versions)23519.7096774194
Number of observations61



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')