Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationMon, 10 Oct 2016 19:55:22 +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/10/t1476125998rxafzwkf3y70ukm.htm/, Retrieved Wed, 08 May 2024 12:38:54 +0200
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Wed, 08 May 2024 12:38:54 +0200
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact0
Dataseries X:
1859000
1869000
1858000
1859000
1878000
1876000
1869000
1888000
1874000
1872000
1885000
1878000
1868000
1879000
1873000
1863000
1880000
1886000
1880000
1901000
1900000
1901000
1922000
1917000
1918000
1927000
1926000
1926000
1945000
1940000
1934000
1945000
1940000
1935000
1945000
1937000
1932000
1947000
1943000
1941000
1951000
1951000
1944000
1962000
1968000
1969000
1972000
1954000
1959000
1971000
1963000
1964000
1986000
1972000
1975000
1993000
1983000
1997000
2000000
1995000
1991000
2001000
1993000
1995000
2010000
2005000
2008000
2028000
2015000
2023000
2031000
2027000




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Sir Maurice George Kendall' @ kendall.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 & 'Sir Maurice George Kendall' @ kendall.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]'Sir Maurice George Kendall' @ kendall.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'Sir Maurice George Kendall' @ kendall.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean1939888.888888895927.16471141625327.287832098286
Geometric Mean1939245.3673166
Harmonic Mean1938601.36014122
Quadratic Mean1940531.6854466
Winsorized Mean ( 1 / 24 )1939861.111111115915.59388394996327.923307307199
Winsorized Mean ( 2 / 24 )1939833.333333335909.79399824744328.240431715318
Winsorized Mean ( 3 / 24 )1939833.333333335844.28884040464331.919483500241
Winsorized Mean ( 4 / 24 )1939666.666666675708.11272319668339.80875303745
Winsorized Mean ( 5 / 24 )1939388.888888895632.92757503182344.295015878654
Winsorized Mean ( 6 / 24 )1939222.222222225603.80844613964346.054338020444
Winsorized Mean ( 7 / 24 )1939222.222222225503.20799252646352.380325231347
Winsorized Mean ( 8 / 24 )1938888.888888895410.76983303251358.338822149126
Winsorized Mean ( 9 / 24 )1938888.888888895369.287391029361.107303015365
Winsorized Mean ( 10 / 24 )19387505256.36770103184368.838351932537
Winsorized Mean ( 11 / 24 )19387505158.01752201691375.871154319363
Winsorized Mean ( 12 / 24 )19387505158.01752201691375.871154319363
Winsorized Mean ( 13 / 24 )1938569.444444445073.08967063412382.127967432937
Winsorized Mean ( 14 / 24 )1938763.888888895041.04797955946384.595404913865
Winsorized Mean ( 15 / 24 )1938347.222222224978.4417763424389.348175453867
Winsorized Mean ( 16 / 24 )1938347.222222224633.27083596104418.353964369573
Winsorized Mean ( 17 / 24 )19378754493.51547655376431.260337281897
Winsorized Mean ( 18 / 24 )19363754138.42246429213467.901722626864
Winsorized Mean ( 19 / 24 )19387503526.93359214209549.698470172357
Winsorized Mean ( 20 / 24 )1939027.777777783484.08926711324556.537915397434
Winsorized Mean ( 21 / 24 )1938736.111111113445.41569362255562.700203258406
Winsorized Mean ( 22 / 24 )1943013.888888892641.94031221083735.449578443707
Winsorized Mean ( 23 / 24 )1943013.888888892553.6108602313760.888794431622
Winsorized Mean ( 24 / 24 )1943013.888888892189.34439843867887.486633110144
Trimmed Mean ( 1 / 24 )1939757.142857145837.39056943766332.298673488282
Trimmed Mean ( 2 / 24 )1939647.058823535743.13976779234337.732866906899
Trimmed Mean ( 3 / 24 )1939545.454545455633.28361593136344.301048337114
Trimmed Mean ( 4 / 24 )1939437.55530.25924899648350.695584542792
Trimmed Mean ( 5 / 24 )1939370.967741945454.01592640918355.585864418035
Trimmed Mean ( 6 / 24 )1939366.666666675382.53960320197360.306994399627
Trimmed Mean ( 7 / 24 )1939396.551724145300.92275038497365.860180019279
Trimmed Mean ( 8 / 24 )1939428.571428575223.93698518961371.258033342869
Trimmed Mean ( 9 / 24 )1939518.518518525147.96715768102376.754252525614
Trimmed Mean ( 10 / 24 )1939615.384615385059.83458005216383.335730433186
Trimmed Mean ( 11 / 24 )19397404971.57717347692390.165923672754
Trimmed Mean ( 12 / 24 )19398754878.36308800808397.648753281315
Trimmed Mean ( 13 / 24 )1940021.739130434755.92578555582407.916739370168
Trimmed Mean ( 14 / 24 )1940204.545454554614.5944078658420.449637382513
Trimmed Mean ( 15 / 24 )1940380.952380954435.36002607684437.479920676757
Trimmed Mean ( 16 / 24 )19406254211.2011046244460.824584669909
Trimmed Mean ( 17 / 24 )1940894.736842114001.20705004169485.0773060649
Trimmed Mean ( 18 / 24 )19412503750517.666666666667
Trimmed Mean ( 19 / 24 )1941823.529411763498.52797877118555.040160088647
Trimmed Mean ( 20 / 24 )1942187.53340.38023598628581.427072007134
Trimmed Mean ( 21 / 24 )1942566.666666673121.9222391714622.234161470419
Trimmed Mean ( 22 / 24 )1943035.714285712802.34319134112693.36108449866
Trimmed Mean ( 23 / 24 )1943038.461538462655.8966437436731.594155260374
Trimmed Mean ( 24 / 24 )1943041.666666672457.96484587857790.508322332066
Median1943500
Midrange1944500
Midmean - Weighted Average at Xnp1939756.75675676
Midmean - Weighted Average at X(n+1)p1941250
Midmean - Empirical Distribution Function1939756.75675676
Midmean - Empirical Distribution Function - Averaging1941250
Midmean - Empirical Distribution Function - Interpolation1941250
Midmean - Closest Observation1939756.75675676
Midmean - True Basic - Statistics Graphics Toolkit1941250
Midmean - MS Excel (old versions)1940894.73684211
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 1939888.88888889 & 5927.16471141625 & 327.287832098286 \tabularnewline
Geometric Mean & 1939245.3673166 &  &  \tabularnewline
Harmonic Mean & 1938601.36014122 &  &  \tabularnewline
Quadratic Mean & 1940531.6854466 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 1939861.11111111 & 5915.59388394996 & 327.923307307199 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 1939833.33333333 & 5909.79399824744 & 328.240431715318 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 1939833.33333333 & 5844.28884040464 & 331.919483500241 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 1939666.66666667 & 5708.11272319668 & 339.80875303745 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 1939388.88888889 & 5632.92757503182 & 344.295015878654 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 1939222.22222222 & 5603.80844613964 & 346.054338020444 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 1939222.22222222 & 5503.20799252646 & 352.380325231347 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 1938888.88888889 & 5410.76983303251 & 358.338822149126 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 1938888.88888889 & 5369.287391029 & 361.107303015365 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 1938750 & 5256.36770103184 & 368.838351932537 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 1938750 & 5158.01752201691 & 375.871154319363 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 1938750 & 5158.01752201691 & 375.871154319363 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 1938569.44444444 & 5073.08967063412 & 382.127967432937 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 1938763.88888889 & 5041.04797955946 & 384.595404913865 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 1938347.22222222 & 4978.4417763424 & 389.348175453867 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 1938347.22222222 & 4633.27083596104 & 418.353964369573 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 1937875 & 4493.51547655376 & 431.260337281897 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 1936375 & 4138.42246429213 & 467.901722626864 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 1938750 & 3526.93359214209 & 549.698470172357 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 1939027.77777778 & 3484.08926711324 & 556.537915397434 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 1938736.11111111 & 3445.41569362255 & 562.700203258406 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 1943013.88888889 & 2641.94031221083 & 735.449578443707 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 1943013.88888889 & 2553.6108602313 & 760.888794431622 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 1943013.88888889 & 2189.34439843867 & 887.486633110144 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 1939757.14285714 & 5837.39056943766 & 332.298673488282 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 1939647.05882353 & 5743.13976779234 & 337.732866906899 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 1939545.45454545 & 5633.28361593136 & 344.301048337114 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 1939437.5 & 5530.25924899648 & 350.695584542792 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 1939370.96774194 & 5454.01592640918 & 355.585864418035 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 1939366.66666667 & 5382.53960320197 & 360.306994399627 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 1939396.55172414 & 5300.92275038497 & 365.860180019279 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 1939428.57142857 & 5223.93698518961 & 371.258033342869 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 1939518.51851852 & 5147.96715768102 & 376.754252525614 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 1939615.38461538 & 5059.83458005216 & 383.335730433186 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 1939740 & 4971.57717347692 & 390.165923672754 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 1939875 & 4878.36308800808 & 397.648753281315 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 1940021.73913043 & 4755.92578555582 & 407.916739370168 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 1940204.54545455 & 4614.5944078658 & 420.449637382513 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 1940380.95238095 & 4435.36002607684 & 437.479920676757 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 1940625 & 4211.2011046244 & 460.824584669909 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 1940894.73684211 & 4001.20705004169 & 485.0773060649 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 1941250 & 3750 & 517.666666666667 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 1941823.52941176 & 3498.52797877118 & 555.040160088647 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 1942187.5 & 3340.38023598628 & 581.427072007134 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 1942566.66666667 & 3121.9222391714 & 622.234161470419 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 1943035.71428571 & 2802.34319134112 & 693.36108449866 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 1943038.46153846 & 2655.8966437436 & 731.594155260374 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 1943041.66666667 & 2457.96484587857 & 790.508322332066 \tabularnewline
Median & 1943500 &  &  \tabularnewline
Midrange & 1944500 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 1939756.75675676 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 1941250 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 1939756.75675676 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 1941250 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 1941250 &  &  \tabularnewline
Midmean - Closest Observation & 1939756.75675676 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 1941250 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 1940894.73684211 &  &  \tabularnewline
Number of observations & 72 &  &  \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]1939888.88888889[/C][C]5927.16471141625[/C][C]327.287832098286[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]1939245.3673166[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]1938601.36014122[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]1940531.6854466[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]1939861.11111111[/C][C]5915.59388394996[/C][C]327.923307307199[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]1939833.33333333[/C][C]5909.79399824744[/C][C]328.240431715318[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]1939833.33333333[/C][C]5844.28884040464[/C][C]331.919483500241[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]1939666.66666667[/C][C]5708.11272319668[/C][C]339.80875303745[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]1939388.88888889[/C][C]5632.92757503182[/C][C]344.295015878654[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]1939222.22222222[/C][C]5603.80844613964[/C][C]346.054338020444[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]1939222.22222222[/C][C]5503.20799252646[/C][C]352.380325231347[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]1938888.88888889[/C][C]5410.76983303251[/C][C]358.338822149126[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]1938888.88888889[/C][C]5369.287391029[/C][C]361.107303015365[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]1938750[/C][C]5256.36770103184[/C][C]368.838351932537[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]1938750[/C][C]5158.01752201691[/C][C]375.871154319363[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]1938750[/C][C]5158.01752201691[/C][C]375.871154319363[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]1938569.44444444[/C][C]5073.08967063412[/C][C]382.127967432937[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]1938763.88888889[/C][C]5041.04797955946[/C][C]384.595404913865[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]1938347.22222222[/C][C]4978.4417763424[/C][C]389.348175453867[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]1938347.22222222[/C][C]4633.27083596104[/C][C]418.353964369573[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]1937875[/C][C]4493.51547655376[/C][C]431.260337281897[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]1936375[/C][C]4138.42246429213[/C][C]467.901722626864[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]1938750[/C][C]3526.93359214209[/C][C]549.698470172357[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]1939027.77777778[/C][C]3484.08926711324[/C][C]556.537915397434[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]1938736.11111111[/C][C]3445.41569362255[/C][C]562.700203258406[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]1943013.88888889[/C][C]2641.94031221083[/C][C]735.449578443707[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]1943013.88888889[/C][C]2553.6108602313[/C][C]760.888794431622[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]1943013.88888889[/C][C]2189.34439843867[/C][C]887.486633110144[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]1939757.14285714[/C][C]5837.39056943766[/C][C]332.298673488282[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]1939647.05882353[/C][C]5743.13976779234[/C][C]337.732866906899[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]1939545.45454545[/C][C]5633.28361593136[/C][C]344.301048337114[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]1939437.5[/C][C]5530.25924899648[/C][C]350.695584542792[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]1939370.96774194[/C][C]5454.01592640918[/C][C]355.585864418035[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]1939366.66666667[/C][C]5382.53960320197[/C][C]360.306994399627[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]1939396.55172414[/C][C]5300.92275038497[/C][C]365.860180019279[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]1939428.57142857[/C][C]5223.93698518961[/C][C]371.258033342869[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]1939518.51851852[/C][C]5147.96715768102[/C][C]376.754252525614[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]1939615.38461538[/C][C]5059.83458005216[/C][C]383.335730433186[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]1939740[/C][C]4971.57717347692[/C][C]390.165923672754[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]1939875[/C][C]4878.36308800808[/C][C]397.648753281315[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]1940021.73913043[/C][C]4755.92578555582[/C][C]407.916739370168[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]1940204.54545455[/C][C]4614.5944078658[/C][C]420.449637382513[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]1940380.95238095[/C][C]4435.36002607684[/C][C]437.479920676757[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]1940625[/C][C]4211.2011046244[/C][C]460.824584669909[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]1940894.73684211[/C][C]4001.20705004169[/C][C]485.0773060649[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]1941250[/C][C]3750[/C][C]517.666666666667[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]1941823.52941176[/C][C]3498.52797877118[/C][C]555.040160088647[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]1942187.5[/C][C]3340.38023598628[/C][C]581.427072007134[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]1942566.66666667[/C][C]3121.9222391714[/C][C]622.234161470419[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]1943035.71428571[/C][C]2802.34319134112[/C][C]693.36108449866[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]1943038.46153846[/C][C]2655.8966437436[/C][C]731.594155260374[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]1943041.66666667[/C][C]2457.96484587857[/C][C]790.508322332066[/C][/ROW]
[ROW][C]Median[/C][C]1943500[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]1944500[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]1939756.75675676[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]1941250[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]1939756.75675676[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]1941250[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]1941250[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]1939756.75675676[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]1941250[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]1940894.73684211[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]72[/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 Mean1939888.888888895927.16471141625327.287832098286
Geometric Mean1939245.3673166
Harmonic Mean1938601.36014122
Quadratic Mean1940531.6854466
Winsorized Mean ( 1 / 24 )1939861.111111115915.59388394996327.923307307199
Winsorized Mean ( 2 / 24 )1939833.333333335909.79399824744328.240431715318
Winsorized Mean ( 3 / 24 )1939833.333333335844.28884040464331.919483500241
Winsorized Mean ( 4 / 24 )1939666.666666675708.11272319668339.80875303745
Winsorized Mean ( 5 / 24 )1939388.888888895632.92757503182344.295015878654
Winsorized Mean ( 6 / 24 )1939222.222222225603.80844613964346.054338020444
Winsorized Mean ( 7 / 24 )1939222.222222225503.20799252646352.380325231347
Winsorized Mean ( 8 / 24 )1938888.888888895410.76983303251358.338822149126
Winsorized Mean ( 9 / 24 )1938888.888888895369.287391029361.107303015365
Winsorized Mean ( 10 / 24 )19387505256.36770103184368.838351932537
Winsorized Mean ( 11 / 24 )19387505158.01752201691375.871154319363
Winsorized Mean ( 12 / 24 )19387505158.01752201691375.871154319363
Winsorized Mean ( 13 / 24 )1938569.444444445073.08967063412382.127967432937
Winsorized Mean ( 14 / 24 )1938763.888888895041.04797955946384.595404913865
Winsorized Mean ( 15 / 24 )1938347.222222224978.4417763424389.348175453867
Winsorized Mean ( 16 / 24 )1938347.222222224633.27083596104418.353964369573
Winsorized Mean ( 17 / 24 )19378754493.51547655376431.260337281897
Winsorized Mean ( 18 / 24 )19363754138.42246429213467.901722626864
Winsorized Mean ( 19 / 24 )19387503526.93359214209549.698470172357
Winsorized Mean ( 20 / 24 )1939027.777777783484.08926711324556.537915397434
Winsorized Mean ( 21 / 24 )1938736.111111113445.41569362255562.700203258406
Winsorized Mean ( 22 / 24 )1943013.888888892641.94031221083735.449578443707
Winsorized Mean ( 23 / 24 )1943013.888888892553.6108602313760.888794431622
Winsorized Mean ( 24 / 24 )1943013.888888892189.34439843867887.486633110144
Trimmed Mean ( 1 / 24 )1939757.142857145837.39056943766332.298673488282
Trimmed Mean ( 2 / 24 )1939647.058823535743.13976779234337.732866906899
Trimmed Mean ( 3 / 24 )1939545.454545455633.28361593136344.301048337114
Trimmed Mean ( 4 / 24 )1939437.55530.25924899648350.695584542792
Trimmed Mean ( 5 / 24 )1939370.967741945454.01592640918355.585864418035
Trimmed Mean ( 6 / 24 )1939366.666666675382.53960320197360.306994399627
Trimmed Mean ( 7 / 24 )1939396.551724145300.92275038497365.860180019279
Trimmed Mean ( 8 / 24 )1939428.571428575223.93698518961371.258033342869
Trimmed Mean ( 9 / 24 )1939518.518518525147.96715768102376.754252525614
Trimmed Mean ( 10 / 24 )1939615.384615385059.83458005216383.335730433186
Trimmed Mean ( 11 / 24 )19397404971.57717347692390.165923672754
Trimmed Mean ( 12 / 24 )19398754878.36308800808397.648753281315
Trimmed Mean ( 13 / 24 )1940021.739130434755.92578555582407.916739370168
Trimmed Mean ( 14 / 24 )1940204.545454554614.5944078658420.449637382513
Trimmed Mean ( 15 / 24 )1940380.952380954435.36002607684437.479920676757
Trimmed Mean ( 16 / 24 )19406254211.2011046244460.824584669909
Trimmed Mean ( 17 / 24 )1940894.736842114001.20705004169485.0773060649
Trimmed Mean ( 18 / 24 )19412503750517.666666666667
Trimmed Mean ( 19 / 24 )1941823.529411763498.52797877118555.040160088647
Trimmed Mean ( 20 / 24 )1942187.53340.38023598628581.427072007134
Trimmed Mean ( 21 / 24 )1942566.666666673121.9222391714622.234161470419
Trimmed Mean ( 22 / 24 )1943035.714285712802.34319134112693.36108449866
Trimmed Mean ( 23 / 24 )1943038.461538462655.8966437436731.594155260374
Trimmed Mean ( 24 / 24 )1943041.666666672457.96484587857790.508322332066
Median1943500
Midrange1944500
Midmean - Weighted Average at Xnp1939756.75675676
Midmean - Weighted Average at X(n+1)p1941250
Midmean - Empirical Distribution Function1939756.75675676
Midmean - Empirical Distribution Function - Averaging1941250
Midmean - Empirical Distribution Function - Interpolation1941250
Midmean - Closest Observation1939756.75675676
Midmean - True Basic - Statistics Graphics Toolkit1941250
Midmean - MS Excel (old versions)1940894.73684211
Number of observations72



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')