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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, 22 Jan 2016 10:21:13 +0000
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/Jan/22/t1453458097ssx8ofne3qkk3rt.htm/, Retrieved Tue, 07 May 2024 13:51:24 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=291318, Retrieved Tue, 07 May 2024 13:51:24 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact40
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [centyral tend] [2016-01-22 10:21:13] [8acc4c3875a0c63009483cc7dfb4f316] [Current]
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Dataseries X:
3035
2552
2704
2554
2014
1655
1721
1524
1596
2074
2199
2512
2933
2889
2938
2497
1870
1726
1607
1545
1396
1787
2076
2837
2787
3891
3179
2011
1636
1580
1489
1300
1356
1653
2013
2823
3102
2294
2385
2444
1748
1554
1498
1361
1346
1564
1640
2293
2815
3137
2679
1969
1870
1633
1529
1366
1357
1570
1535
2491
3084
2605
2573
2143
1693
1504
1461
1354
1333
1492
1781
1915




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gertrude Mary Cox' @ cox.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 & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=291318&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=291318&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=291318&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'Gertrude Mary Cox' @ cox.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean2056.62571.871003154843828.6155043024663
Geometric Mean1974.01685993685
Harmonic Mean1899.5311292614
Quadratic Mean2143.93393282847
Winsorized Mean ( 1 / 24 )2047.1944444444468.868108503808729.7263056721127
Winsorized Mean ( 2 / 24 )2046.3888888888968.550004467557729.8524982570552
Winsorized Mean ( 3 / 24 )2045.2638888888968.179639343943829.9981623336434
Winsorized Mean ( 4 / 24 )2044.37567.946875932184430.0878439509187
Winsorized Mean ( 5 / 24 )2041.0416666666767.215869970273530.365472730909
Winsorized Mean ( 6 / 24 )2033.2916666666765.539626634798631.0238518445737
Winsorized Mean ( 7 / 24 )2033.2916666666765.375200480247531.1018804031202
Winsorized Mean ( 8 / 24 )2031.7361111111163.966873863740431.7623167803859
Winsorized Mean ( 9 / 24 )2033.3611111111161.655947886978232.9791557959416
Winsorized Mean ( 10 / 24 )2035.3055555555660.799687263967733.4755925095318
Winsorized Mean ( 11 / 24 )2034.5416666666760.519238451992133.6180976282542
Winsorized Mean ( 12 / 24 )2030.87559.551955648468234.1025744307734
Winsorized Mean ( 13 / 24 )2016.9722222222256.796729956338735.5121188098809
Winsorized Mean ( 14 / 24 )201655.483255379826436.3352868572491
Winsorized Mean ( 15 / 24 )2001.62552.81347813958437.8998897726407
Winsorized Mean ( 16 / 24 )1995.8472222222251.512095225373238.745215341952
Winsorized Mean ( 17 / 24 )1993.7222222222250.511186655979839.4709044513448
Winsorized Mean ( 18 / 24 )1995.4722222222250.152814100659139.7878415798805
Winsorized Mean ( 19 / 24 )1987.5555555555648.191762428022641.2426409705205
Winsorized Mean ( 20 / 24 )1985.0555555555647.349121585323641.9238095468881
Winsorized Mean ( 21 / 24 )1986.2222222222246.724097885867542.5095895285971
Winsorized Mean ( 22 / 24 )1976.7543.958401475149144.9686506711922
Winsorized Mean ( 23 / 24 )1961.4166666666740.736734209856748.1485986717139
Winsorized Mean ( 24 / 24 )1939.7535.305268052645854.9422255372066
Trimmed Mean ( 1 / 24 )2041.2285714285768.179109419631429.9392084878249
Trimmed Mean ( 2 / 24 )2034.9117647058867.328462931166430.2236480102967
Trimmed Mean ( 3 / 24 )2028.6515151515266.481886670050530.5143493478112
Trimmed Mean ( 4 / 24 )2022.42187565.600484100575930.8293742451551
Trimmed Mean ( 5 / 24 )2016.0483870967764.589618674504531.2131953782933
Trimmed Mean ( 6 / 24 )2010.0563.564222716906731.6223484546028
Trimmed Mean ( 7 / 24 )2005.2413793103462.754273132089231.9538619320725
Trimmed Mean ( 8 / 24 )2000.0892857142961.761224737125232.3842231793052
Trimmed Mean ( 9 / 24 )1994.8148148148160.834845758598332.7906611735408
Trimmed Mean ( 10 / 24 )1988.8846153846260.152681890728533.0639391772683
Trimmed Mean ( 11 / 24 )1982.259.412030665136333.363613022626
Trimmed Mean ( 12 / 24 )1975.062558.466237197767433.781248711443
Trimmed Mean ( 13 / 24 )1967.7826086956557.409529019703934.2762367554048
Trimmed Mean ( 14 / 24 )1961.5909090909156.611602048079634.6499805362327
Trimmed Mean ( 15 / 24 )1954.9285714285755.768284011400635.0544867227568
Trimmed Mean ( 16 / 24 )1949.32555.182278225243735.3251997324797
Trimmed Mean ( 17 / 24 )1943.8157894736854.580657363841635.61363829893
Trimmed Mean ( 18 / 24 )1937.9444444444453.865808344830235.9772646878034
Trimmed Mean ( 19 / 24 )1931.1764705882452.816290608421436.5640306871592
Trimmed Mean ( 20 / 24 )1924.551.746571493098237.1908697420985
Trimmed Mean ( 21 / 24 )1917.2333333333350.30110904225938.1151304581103
Trimmed Mean ( 22 / 24 )1908.7857142857148.199633282070539.6016646665184
Trimmed Mean ( 23 / 24 )1900.2307692307745.912133730296641.3884220758148
Trimmed Mean ( 24 / 24 )1892.2543.564804718315143.4352916817846
Median1870
Midrange2595.5
Midmean - Weighted Average at Xnp1927.32432432432
Midmean - Weighted Average at X(n+1)p1937.94444444444
Midmean - Empirical Distribution Function1927.32432432432
Midmean - Empirical Distribution Function - Averaging1937.94444444444
Midmean - Empirical Distribution Function - Interpolation1937.94444444444
Midmean - Closest Observation1927.32432432432
Midmean - True Basic - Statistics Graphics Toolkit1937.94444444444
Midmean - MS Excel (old versions)1943.81578947368
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 2056.625 & 71.8710031548438 & 28.6155043024663 \tabularnewline
Geometric Mean & 1974.01685993685 &  &  \tabularnewline
Harmonic Mean & 1899.5311292614 &  &  \tabularnewline
Quadratic Mean & 2143.93393282847 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 2047.19444444444 & 68.8681085038087 & 29.7263056721127 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 2046.38888888889 & 68.5500044675577 & 29.8524982570552 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 2045.26388888889 & 68.1796393439438 & 29.9981623336434 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 2044.375 & 67.9468759321844 & 30.0878439509187 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 2041.04166666667 & 67.2158699702735 & 30.365472730909 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 2033.29166666667 & 65.5396266347986 & 31.0238518445737 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 2033.29166666667 & 65.3752004802475 & 31.1018804031202 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 2031.73611111111 & 63.9668738637404 & 31.7623167803859 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 2033.36111111111 & 61.6559478869782 & 32.9791557959416 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 2035.30555555556 & 60.7996872639677 & 33.4755925095318 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 2034.54166666667 & 60.5192384519921 & 33.6180976282542 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 2030.875 & 59.5519556484682 & 34.1025744307734 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 2016.97222222222 & 56.7967299563387 & 35.5121188098809 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 2016 & 55.4832553798264 & 36.3352868572491 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 2001.625 & 52.813478139584 & 37.8998897726407 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 1995.84722222222 & 51.5120952253732 & 38.745215341952 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 1993.72222222222 & 50.5111866559798 & 39.4709044513448 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 1995.47222222222 & 50.1528141006591 & 39.7878415798805 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 1987.55555555556 & 48.1917624280226 & 41.2426409705205 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 1985.05555555556 & 47.3491215853236 & 41.9238095468881 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 1986.22222222222 & 46.7240978858675 & 42.5095895285971 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 1976.75 & 43.9584014751491 & 44.9686506711922 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 1961.41666666667 & 40.7367342098567 & 48.1485986717139 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 1939.75 & 35.3052680526458 & 54.9422255372066 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 2041.22857142857 & 68.1791094196314 & 29.9392084878249 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 2034.91176470588 & 67.3284629311664 & 30.2236480102967 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 2028.65151515152 & 66.4818866700505 & 30.5143493478112 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 2022.421875 & 65.6004841005759 & 30.8293742451551 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 2016.04838709677 & 64.5896186745045 & 31.2131953782933 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 2010.05 & 63.5642227169067 & 31.6223484546028 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 2005.24137931034 & 62.7542731320892 & 31.9538619320725 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 2000.08928571429 & 61.7612247371252 & 32.3842231793052 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 1994.81481481481 & 60.8348457585983 & 32.7906611735408 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 1988.88461538462 & 60.1526818907285 & 33.0639391772683 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 1982.2 & 59.4120306651363 & 33.363613022626 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 1975.0625 & 58.4662371977674 & 33.781248711443 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 1967.78260869565 & 57.4095290197039 & 34.2762367554048 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 1961.59090909091 & 56.6116020480796 & 34.6499805362327 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 1954.92857142857 & 55.7682840114006 & 35.0544867227568 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 1949.325 & 55.1822782252437 & 35.3251997324797 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 1943.81578947368 & 54.5806573638416 & 35.61363829893 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 1937.94444444444 & 53.8658083448302 & 35.9772646878034 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 1931.17647058824 & 52.8162906084214 & 36.5640306871592 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 1924.5 & 51.7465714930982 & 37.1908697420985 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 1917.23333333333 & 50.301109042259 & 38.1151304581103 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 1908.78571428571 & 48.1996332820705 & 39.6016646665184 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 1900.23076923077 & 45.9121337302966 & 41.3884220758148 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 1892.25 & 43.5648047183151 & 43.4352916817846 \tabularnewline
Median & 1870 &  &  \tabularnewline
Midrange & 2595.5 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 1927.32432432432 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 1937.94444444444 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 1927.32432432432 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 1937.94444444444 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 1937.94444444444 &  &  \tabularnewline
Midmean - Closest Observation & 1927.32432432432 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 1937.94444444444 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 1943.81578947368 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=291318&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]2056.625[/C][C]71.8710031548438[/C][C]28.6155043024663[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]1974.01685993685[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]1899.5311292614[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]2143.93393282847[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]2047.19444444444[/C][C]68.8681085038087[/C][C]29.7263056721127[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]2046.38888888889[/C][C]68.5500044675577[/C][C]29.8524982570552[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]2045.26388888889[/C][C]68.1796393439438[/C][C]29.9981623336434[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]2044.375[/C][C]67.9468759321844[/C][C]30.0878439509187[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]2041.04166666667[/C][C]67.2158699702735[/C][C]30.365472730909[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]2033.29166666667[/C][C]65.5396266347986[/C][C]31.0238518445737[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]2033.29166666667[/C][C]65.3752004802475[/C][C]31.1018804031202[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]2031.73611111111[/C][C]63.9668738637404[/C][C]31.7623167803859[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]2033.36111111111[/C][C]61.6559478869782[/C][C]32.9791557959416[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]2035.30555555556[/C][C]60.7996872639677[/C][C]33.4755925095318[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]2034.54166666667[/C][C]60.5192384519921[/C][C]33.6180976282542[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]2030.875[/C][C]59.5519556484682[/C][C]34.1025744307734[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]2016.97222222222[/C][C]56.7967299563387[/C][C]35.5121188098809[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]2016[/C][C]55.4832553798264[/C][C]36.3352868572491[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]2001.625[/C][C]52.813478139584[/C][C]37.8998897726407[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]1995.84722222222[/C][C]51.5120952253732[/C][C]38.745215341952[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]1993.72222222222[/C][C]50.5111866559798[/C][C]39.4709044513448[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]1995.47222222222[/C][C]50.1528141006591[/C][C]39.7878415798805[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]1987.55555555556[/C][C]48.1917624280226[/C][C]41.2426409705205[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]1985.05555555556[/C][C]47.3491215853236[/C][C]41.9238095468881[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]1986.22222222222[/C][C]46.7240978858675[/C][C]42.5095895285971[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]1976.75[/C][C]43.9584014751491[/C][C]44.9686506711922[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]1961.41666666667[/C][C]40.7367342098567[/C][C]48.1485986717139[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]1939.75[/C][C]35.3052680526458[/C][C]54.9422255372066[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]2041.22857142857[/C][C]68.1791094196314[/C][C]29.9392084878249[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]2034.91176470588[/C][C]67.3284629311664[/C][C]30.2236480102967[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]2028.65151515152[/C][C]66.4818866700505[/C][C]30.5143493478112[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]2022.421875[/C][C]65.6004841005759[/C][C]30.8293742451551[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]2016.04838709677[/C][C]64.5896186745045[/C][C]31.2131953782933[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]2010.05[/C][C]63.5642227169067[/C][C]31.6223484546028[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]2005.24137931034[/C][C]62.7542731320892[/C][C]31.9538619320725[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]2000.08928571429[/C][C]61.7612247371252[/C][C]32.3842231793052[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]1994.81481481481[/C][C]60.8348457585983[/C][C]32.7906611735408[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]1988.88461538462[/C][C]60.1526818907285[/C][C]33.0639391772683[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]1982.2[/C][C]59.4120306651363[/C][C]33.363613022626[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]1975.0625[/C][C]58.4662371977674[/C][C]33.781248711443[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]1967.78260869565[/C][C]57.4095290197039[/C][C]34.2762367554048[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]1961.59090909091[/C][C]56.6116020480796[/C][C]34.6499805362327[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]1954.92857142857[/C][C]55.7682840114006[/C][C]35.0544867227568[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]1949.325[/C][C]55.1822782252437[/C][C]35.3251997324797[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]1943.81578947368[/C][C]54.5806573638416[/C][C]35.61363829893[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]1937.94444444444[/C][C]53.8658083448302[/C][C]35.9772646878034[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]1931.17647058824[/C][C]52.8162906084214[/C][C]36.5640306871592[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]1924.5[/C][C]51.7465714930982[/C][C]37.1908697420985[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]1917.23333333333[/C][C]50.301109042259[/C][C]38.1151304581103[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]1908.78571428571[/C][C]48.1996332820705[/C][C]39.6016646665184[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]1900.23076923077[/C][C]45.9121337302966[/C][C]41.3884220758148[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]1892.25[/C][C]43.5648047183151[/C][C]43.4352916817846[/C][/ROW]
[ROW][C]Median[/C][C]1870[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]2595.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]1927.32432432432[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]1937.94444444444[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]1927.32432432432[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]1937.94444444444[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]1937.94444444444[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]1927.32432432432[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]1937.94444444444[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]1943.81578947368[/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=291318&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=291318&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 Mean2056.62571.871003154843828.6155043024663
Geometric Mean1974.01685993685
Harmonic Mean1899.5311292614
Quadratic Mean2143.93393282847
Winsorized Mean ( 1 / 24 )2047.1944444444468.868108503808729.7263056721127
Winsorized Mean ( 2 / 24 )2046.3888888888968.550004467557729.8524982570552
Winsorized Mean ( 3 / 24 )2045.2638888888968.179639343943829.9981623336434
Winsorized Mean ( 4 / 24 )2044.37567.946875932184430.0878439509187
Winsorized Mean ( 5 / 24 )2041.0416666666767.215869970273530.365472730909
Winsorized Mean ( 6 / 24 )2033.2916666666765.539626634798631.0238518445737
Winsorized Mean ( 7 / 24 )2033.2916666666765.375200480247531.1018804031202
Winsorized Mean ( 8 / 24 )2031.7361111111163.966873863740431.7623167803859
Winsorized Mean ( 9 / 24 )2033.3611111111161.655947886978232.9791557959416
Winsorized Mean ( 10 / 24 )2035.3055555555660.799687263967733.4755925095318
Winsorized Mean ( 11 / 24 )2034.5416666666760.519238451992133.6180976282542
Winsorized Mean ( 12 / 24 )2030.87559.551955648468234.1025744307734
Winsorized Mean ( 13 / 24 )2016.9722222222256.796729956338735.5121188098809
Winsorized Mean ( 14 / 24 )201655.483255379826436.3352868572491
Winsorized Mean ( 15 / 24 )2001.62552.81347813958437.8998897726407
Winsorized Mean ( 16 / 24 )1995.8472222222251.512095225373238.745215341952
Winsorized Mean ( 17 / 24 )1993.7222222222250.511186655979839.4709044513448
Winsorized Mean ( 18 / 24 )1995.4722222222250.152814100659139.7878415798805
Winsorized Mean ( 19 / 24 )1987.5555555555648.191762428022641.2426409705205
Winsorized Mean ( 20 / 24 )1985.0555555555647.349121585323641.9238095468881
Winsorized Mean ( 21 / 24 )1986.2222222222246.724097885867542.5095895285971
Winsorized Mean ( 22 / 24 )1976.7543.958401475149144.9686506711922
Winsorized Mean ( 23 / 24 )1961.4166666666740.736734209856748.1485986717139
Winsorized Mean ( 24 / 24 )1939.7535.305268052645854.9422255372066
Trimmed Mean ( 1 / 24 )2041.2285714285768.179109419631429.9392084878249
Trimmed Mean ( 2 / 24 )2034.9117647058867.328462931166430.2236480102967
Trimmed Mean ( 3 / 24 )2028.6515151515266.481886670050530.5143493478112
Trimmed Mean ( 4 / 24 )2022.42187565.600484100575930.8293742451551
Trimmed Mean ( 5 / 24 )2016.0483870967764.589618674504531.2131953782933
Trimmed Mean ( 6 / 24 )2010.0563.564222716906731.6223484546028
Trimmed Mean ( 7 / 24 )2005.2413793103462.754273132089231.9538619320725
Trimmed Mean ( 8 / 24 )2000.0892857142961.761224737125232.3842231793052
Trimmed Mean ( 9 / 24 )1994.8148148148160.834845758598332.7906611735408
Trimmed Mean ( 10 / 24 )1988.8846153846260.152681890728533.0639391772683
Trimmed Mean ( 11 / 24 )1982.259.412030665136333.363613022626
Trimmed Mean ( 12 / 24 )1975.062558.466237197767433.781248711443
Trimmed Mean ( 13 / 24 )1967.7826086956557.409529019703934.2762367554048
Trimmed Mean ( 14 / 24 )1961.5909090909156.611602048079634.6499805362327
Trimmed Mean ( 15 / 24 )1954.9285714285755.768284011400635.0544867227568
Trimmed Mean ( 16 / 24 )1949.32555.182278225243735.3251997324797
Trimmed Mean ( 17 / 24 )1943.8157894736854.580657363841635.61363829893
Trimmed Mean ( 18 / 24 )1937.9444444444453.865808344830235.9772646878034
Trimmed Mean ( 19 / 24 )1931.1764705882452.816290608421436.5640306871592
Trimmed Mean ( 20 / 24 )1924.551.746571493098237.1908697420985
Trimmed Mean ( 21 / 24 )1917.2333333333350.30110904225938.1151304581103
Trimmed Mean ( 22 / 24 )1908.7857142857148.199633282070539.6016646665184
Trimmed Mean ( 23 / 24 )1900.2307692307745.912133730296641.3884220758148
Trimmed Mean ( 24 / 24 )1892.2543.564804718315143.4352916817846
Median1870
Midrange2595.5
Midmean - Weighted Average at Xnp1927.32432432432
Midmean - Weighted Average at X(n+1)p1937.94444444444
Midmean - Empirical Distribution Function1927.32432432432
Midmean - Empirical Distribution Function - Averaging1937.94444444444
Midmean - Empirical Distribution Function - Interpolation1937.94444444444
Midmean - Closest Observation1927.32432432432
Midmean - True Basic - Statistics Graphics Toolkit1937.94444444444
Midmean - MS Excel (old versions)1943.81578947368
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')