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Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationFri, 09 Oct 2015 08:31:59 +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/2015/Oct/09/t1444375944eq0zmiqj5nzvmqr.htm/, Retrieved Sat, 25 May 2024 05:12:37 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=281704, Retrieved Sat, 25 May 2024 05:12:37 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact107
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2015-10-09 07:31:59] [1faf68c5110a4cb4d7d9116a9189ca68] [Current]
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Dataseries X:
1795
1756
2237
1960
1829
2524
2077
2366
2185
2098
1836
1863
2044
2136
2931
3263
3328
3570
2313
1623
1316
1507
1419
1660
1790
1733
2086
1814
2241
1943
1773
2143
2087
1805
1913
2296
2500
2210
2526
2249
2024
2091
2045
1882
1831
1964
1763
1688
2149
1823
2094
2145
1790
1996
2097
1795
1963
2041
1746
2210
2949
3110
3716
3014
1515
1498
1366
1607
1757
1623
1451
1765




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ jenkins.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 & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=281704&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=281704&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=281704&T=0

As an alternative you can also use a QR Code:  

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

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







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean2072.9583333333358.833045516259935.2345916337175
Geometric Mean2021.72574397969
Harmonic Mean1976.84318977199
Quadratic Mean2131.41044524773
Winsorized Mean ( 1 / 24 )2071.62557.942231624219335.7532829152214
Winsorized Mean ( 2 / 24 )2066.37555.38892025743837.3066488820481
Winsorized Mean ( 3 / 24 )206554.317777663174338.0170192677084
Winsorized Mean ( 4 / 24 )2059.1111111111151.361188236869240.0907997224448
Winsorized Mean ( 5 / 24 )2053.0694444444449.389493975699141.568950786469
Winsorized Mean ( 6 / 24 )2048.3194444444447.824289711198342.830106977309
Winsorized Mean ( 7 / 24 )2055.5138888888946.040139462511744.6461264645516
Winsorized Mean ( 8 / 24 )2012.2916666666734.903311773108757.6533161021425
Winsorized Mean ( 9 / 24 )2012.0416666666734.851537561252857.7317905452646
Winsorized Mean ( 10 / 24 )2013.8472222222233.376648264072260.337011861973
Winsorized Mean ( 11 / 24 )1997.6527777777828.768680803896669.438456055559
Winsorized Mean ( 12 / 24 )1996.3194444444426.112933573981376.4494513337085
Winsorized Mean ( 13 / 24 )1995.5972222222225.26363078775378.990911440553
Winsorized Mean ( 14 / 24 )1988.4027777777823.512563316111284.5676735047976
Winsorized Mean ( 15 / 24 )1986.9444444444423.225049621588185.551784681551
Winsorized Mean ( 16 / 24 )1987.3888888888922.903387578705986.7727047826162
Winsorized Mean ( 17 / 24 )1981.4861111111121.879274615260190.5645249193537
Winsorized Mean ( 18 / 24 )1983.4861111111121.602668148830591.8167190018373
Winsorized Mean ( 19 / 24 )1981.37520.032870459956998.9061953932417
Winsorized Mean ( 20 / 24 )1971.37518.6445358152683105.7347321238
Winsorized Mean ( 21 / 24 )1971.6666666666718.2892769835814107.804516736045
Winsorized Mean ( 22 / 24 )1971.0555555555618.2078493547575108.253068067072
Winsorized Mean ( 23 / 24 )1972.0138888888917.4788547978753112.822831455102
Winsorized Mean ( 24 / 24 )1962.3472222222215.4508428408376127.005836667732
Trimmed Mean ( 1 / 24 )2060.354.621825584904637.7193544510418
Trimmed Mean ( 2 / 24 )2048.3088235294150.544646670078240.5247431424223
Trimmed Mean ( 3 / 24 )2038.4545454545547.303622681527843.0929901326683
Trimmed Mean ( 4 / 24 )2028.543.837746473478946.2729077834146
Trimmed Mean ( 5 / 24 )2019.6129032258140.789792449578649.5127035942217
Trimmed Mean ( 6 / 24 )2011.5833333333337.721371392072753.3274178296729
Trimmed Mean ( 7 / 24 )2003.9827586206934.383240013368258.283709093196
Trimmed Mean ( 8 / 24 )1994.5178571428630.612810227850465.1530467898148
Trimmed Mean ( 9 / 24 )1991.5555555555629.350238918531667.8548328374286
Trimmed Mean ( 10 / 24 )1988.4038461538527.772946291543571.5949912292629
Trimmed Mean ( 11 / 24 )1984.7426.149754125351375.8989927968716
Trimmed Mean ( 12 / 24 )1982.9791666666725.280088623980178.4403566048285
Trimmed Mean ( 13 / 24 )1981.2391304347824.771695410483579.9799568662675
Trimmed Mean ( 14 / 24 )1979.4318181818224.283308410613781.5140912725324
Trimmed Mean ( 15 / 24 )1978.3333333333324.014046089762582.382340982377
Trimmed Mean ( 16 / 24 )1977.323.683387015222783.4889029482595
Trimmed Mean ( 17 / 24 )1976.1052631578923.273767718865484.9069771181095
Trimmed Mean ( 18 / 24 )1975.4722222222222.926711603242986.1646561621511
Trimmed Mean ( 19 / 24 )1974.5294117647122.465471041491187.8917432052942
Trimmed Mean ( 20 / 24 )1973.7187522.177356694376388.9970241809969
Trimmed Mean ( 21 / 24 )197422.061095938846589.4787822632177
Trimmed Mean ( 22 / 24 )1974.2857142857121.886483056662490.2057086638563
Trimmed Mean ( 23 / 24 )1974.6923076923121.537999995054891.6841075376405
Trimmed Mean ( 24 / 24 )1975.0416666666721.140787486075493.4232780102232
Median1980
Midrange2516
Midmean - Weighted Average at Xnp1976.10526315789
Midmean - Weighted Average at X(n+1)p1981.81081081081
Midmean - Empirical Distribution Function1976.10526315789
Midmean - Empirical Distribution Function - Averaging1981.81081081081
Midmean - Empirical Distribution Function - Interpolation1981.81081081081
Midmean - Closest Observation1976.10526315789
Midmean - True Basic - Statistics Graphics Toolkit1981.81081081081
Midmean - MS Excel (old versions)1976.10526315789
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 2072.95833333333 & 58.8330455162599 & 35.2345916337175 \tabularnewline
Geometric Mean & 2021.72574397969 &  &  \tabularnewline
Harmonic Mean & 1976.84318977199 &  &  \tabularnewline
Quadratic Mean & 2131.41044524773 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 2071.625 & 57.9422316242193 & 35.7532829152214 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 2066.375 & 55.388920257438 & 37.3066488820481 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 2065 & 54.3177776631743 & 38.0170192677084 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 2059.11111111111 & 51.3611882368692 & 40.0907997224448 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 2053.06944444444 & 49.3894939756991 & 41.568950786469 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 2048.31944444444 & 47.8242897111983 & 42.830106977309 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 2055.51388888889 & 46.0401394625117 & 44.6461264645516 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 2012.29166666667 & 34.9033117731087 & 57.6533161021425 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 2012.04166666667 & 34.8515375612528 & 57.7317905452646 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 2013.84722222222 & 33.3766482640722 & 60.337011861973 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 1997.65277777778 & 28.7686808038966 & 69.438456055559 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 1996.31944444444 & 26.1129335739813 & 76.4494513337085 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 1995.59722222222 & 25.263630787753 & 78.990911440553 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 1988.40277777778 & 23.5125633161112 & 84.5676735047976 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 1986.94444444444 & 23.2250496215881 & 85.551784681551 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 1987.38888888889 & 22.9033875787059 & 86.7727047826162 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 1981.48611111111 & 21.8792746152601 & 90.5645249193537 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 1983.48611111111 & 21.6026681488305 & 91.8167190018373 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 1981.375 & 20.0328704599569 & 98.9061953932417 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 1971.375 & 18.6445358152683 & 105.7347321238 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 1971.66666666667 & 18.2892769835814 & 107.804516736045 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 1971.05555555556 & 18.2078493547575 & 108.253068067072 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 1972.01388888889 & 17.4788547978753 & 112.822831455102 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 1962.34722222222 & 15.4508428408376 & 127.005836667732 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 2060.3 & 54.6218255849046 & 37.7193544510418 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 2048.30882352941 & 50.5446466700782 & 40.5247431424223 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 2038.45454545455 & 47.3036226815278 & 43.0929901326683 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 2028.5 & 43.8377464734789 & 46.2729077834146 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 2019.61290322581 & 40.7897924495786 & 49.5127035942217 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 2011.58333333333 & 37.7213713920727 & 53.3274178296729 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 2003.98275862069 & 34.3832400133682 & 58.283709093196 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 1994.51785714286 & 30.6128102278504 & 65.1530467898148 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 1991.55555555556 & 29.3502389185316 & 67.8548328374286 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 1988.40384615385 & 27.7729462915435 & 71.5949912292629 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 1984.74 & 26.1497541253513 & 75.8989927968716 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 1982.97916666667 & 25.2800886239801 & 78.4403566048285 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 1981.23913043478 & 24.7716954104835 & 79.9799568662675 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 1979.43181818182 & 24.2833084106137 & 81.5140912725324 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 1978.33333333333 & 24.0140460897625 & 82.382340982377 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 1977.3 & 23.6833870152227 & 83.4889029482595 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 1976.10526315789 & 23.2737677188654 & 84.9069771181095 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 1975.47222222222 & 22.9267116032429 & 86.1646561621511 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 1974.52941176471 & 22.4654710414911 & 87.8917432052942 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 1973.71875 & 22.1773566943763 & 88.9970241809969 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 1974 & 22.0610959388465 & 89.4787822632177 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 1974.28571428571 & 21.8864830566624 & 90.2057086638563 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 1974.69230769231 & 21.5379999950548 & 91.6841075376405 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 1975.04166666667 & 21.1407874860754 & 93.4232780102232 \tabularnewline
Median & 1980 &  &  \tabularnewline
Midrange & 2516 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 1976.10526315789 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 1981.81081081081 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 1976.10526315789 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 1981.81081081081 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 1981.81081081081 &  &  \tabularnewline
Midmean - Closest Observation & 1976.10526315789 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 1981.81081081081 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 1976.10526315789 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=281704&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]2072.95833333333[/C][C]58.8330455162599[/C][C]35.2345916337175[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]2021.72574397969[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]1976.84318977199[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]2131.41044524773[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]2071.625[/C][C]57.9422316242193[/C][C]35.7532829152214[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]2066.375[/C][C]55.388920257438[/C][C]37.3066488820481[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]2065[/C][C]54.3177776631743[/C][C]38.0170192677084[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]2059.11111111111[/C][C]51.3611882368692[/C][C]40.0907997224448[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]2053.06944444444[/C][C]49.3894939756991[/C][C]41.568950786469[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]2048.31944444444[/C][C]47.8242897111983[/C][C]42.830106977309[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]2055.51388888889[/C][C]46.0401394625117[/C][C]44.6461264645516[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]2012.29166666667[/C][C]34.9033117731087[/C][C]57.6533161021425[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]2012.04166666667[/C][C]34.8515375612528[/C][C]57.7317905452646[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]2013.84722222222[/C][C]33.3766482640722[/C][C]60.337011861973[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]1997.65277777778[/C][C]28.7686808038966[/C][C]69.438456055559[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]1996.31944444444[/C][C]26.1129335739813[/C][C]76.4494513337085[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]1995.59722222222[/C][C]25.263630787753[/C][C]78.990911440553[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]1988.40277777778[/C][C]23.5125633161112[/C][C]84.5676735047976[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]1986.94444444444[/C][C]23.2250496215881[/C][C]85.551784681551[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]1987.38888888889[/C][C]22.9033875787059[/C][C]86.7727047826162[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]1981.48611111111[/C][C]21.8792746152601[/C][C]90.5645249193537[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]1983.48611111111[/C][C]21.6026681488305[/C][C]91.8167190018373[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]1981.375[/C][C]20.0328704599569[/C][C]98.9061953932417[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]1971.375[/C][C]18.6445358152683[/C][C]105.7347321238[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]1971.66666666667[/C][C]18.2892769835814[/C][C]107.804516736045[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]1971.05555555556[/C][C]18.2078493547575[/C][C]108.253068067072[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]1972.01388888889[/C][C]17.4788547978753[/C][C]112.822831455102[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]1962.34722222222[/C][C]15.4508428408376[/C][C]127.005836667732[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]2060.3[/C][C]54.6218255849046[/C][C]37.7193544510418[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]2048.30882352941[/C][C]50.5446466700782[/C][C]40.5247431424223[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]2038.45454545455[/C][C]47.3036226815278[/C][C]43.0929901326683[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]2028.5[/C][C]43.8377464734789[/C][C]46.2729077834146[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]2019.61290322581[/C][C]40.7897924495786[/C][C]49.5127035942217[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]2011.58333333333[/C][C]37.7213713920727[/C][C]53.3274178296729[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]2003.98275862069[/C][C]34.3832400133682[/C][C]58.283709093196[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]1994.51785714286[/C][C]30.6128102278504[/C][C]65.1530467898148[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]1991.55555555556[/C][C]29.3502389185316[/C][C]67.8548328374286[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]1988.40384615385[/C][C]27.7729462915435[/C][C]71.5949912292629[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]1984.74[/C][C]26.1497541253513[/C][C]75.8989927968716[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]1982.97916666667[/C][C]25.2800886239801[/C][C]78.4403566048285[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]1981.23913043478[/C][C]24.7716954104835[/C][C]79.9799568662675[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]1979.43181818182[/C][C]24.2833084106137[/C][C]81.5140912725324[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]1978.33333333333[/C][C]24.0140460897625[/C][C]82.382340982377[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]1977.3[/C][C]23.6833870152227[/C][C]83.4889029482595[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]1976.10526315789[/C][C]23.2737677188654[/C][C]84.9069771181095[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]1975.47222222222[/C][C]22.9267116032429[/C][C]86.1646561621511[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]1974.52941176471[/C][C]22.4654710414911[/C][C]87.8917432052942[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]1973.71875[/C][C]22.1773566943763[/C][C]88.9970241809969[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]1974[/C][C]22.0610959388465[/C][C]89.4787822632177[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]1974.28571428571[/C][C]21.8864830566624[/C][C]90.2057086638563[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]1974.69230769231[/C][C]21.5379999950548[/C][C]91.6841075376405[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]1975.04166666667[/C][C]21.1407874860754[/C][C]93.4232780102232[/C][/ROW]
[ROW][C]Median[/C][C]1980[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]2516[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]1976.10526315789[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]1981.81081081081[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]1976.10526315789[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]1981.81081081081[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]1981.81081081081[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]1976.10526315789[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]1981.81081081081[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]1976.10526315789[/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=281704&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=281704&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 Mean2072.9583333333358.833045516259935.2345916337175
Geometric Mean2021.72574397969
Harmonic Mean1976.84318977199
Quadratic Mean2131.41044524773
Winsorized Mean ( 1 / 24 )2071.62557.942231624219335.7532829152214
Winsorized Mean ( 2 / 24 )2066.37555.38892025743837.3066488820481
Winsorized Mean ( 3 / 24 )206554.317777663174338.0170192677084
Winsorized Mean ( 4 / 24 )2059.1111111111151.361188236869240.0907997224448
Winsorized Mean ( 5 / 24 )2053.0694444444449.389493975699141.568950786469
Winsorized Mean ( 6 / 24 )2048.3194444444447.824289711198342.830106977309
Winsorized Mean ( 7 / 24 )2055.5138888888946.040139462511744.6461264645516
Winsorized Mean ( 8 / 24 )2012.2916666666734.903311773108757.6533161021425
Winsorized Mean ( 9 / 24 )2012.0416666666734.851537561252857.7317905452646
Winsorized Mean ( 10 / 24 )2013.8472222222233.376648264072260.337011861973
Winsorized Mean ( 11 / 24 )1997.6527777777828.768680803896669.438456055559
Winsorized Mean ( 12 / 24 )1996.3194444444426.112933573981376.4494513337085
Winsorized Mean ( 13 / 24 )1995.5972222222225.26363078775378.990911440553
Winsorized Mean ( 14 / 24 )1988.4027777777823.512563316111284.5676735047976
Winsorized Mean ( 15 / 24 )1986.9444444444423.225049621588185.551784681551
Winsorized Mean ( 16 / 24 )1987.3888888888922.903387578705986.7727047826162
Winsorized Mean ( 17 / 24 )1981.4861111111121.879274615260190.5645249193537
Winsorized Mean ( 18 / 24 )1983.4861111111121.602668148830591.8167190018373
Winsorized Mean ( 19 / 24 )1981.37520.032870459956998.9061953932417
Winsorized Mean ( 20 / 24 )1971.37518.6445358152683105.7347321238
Winsorized Mean ( 21 / 24 )1971.6666666666718.2892769835814107.804516736045
Winsorized Mean ( 22 / 24 )1971.0555555555618.2078493547575108.253068067072
Winsorized Mean ( 23 / 24 )1972.0138888888917.4788547978753112.822831455102
Winsorized Mean ( 24 / 24 )1962.3472222222215.4508428408376127.005836667732
Trimmed Mean ( 1 / 24 )2060.354.621825584904637.7193544510418
Trimmed Mean ( 2 / 24 )2048.3088235294150.544646670078240.5247431424223
Trimmed Mean ( 3 / 24 )2038.4545454545547.303622681527843.0929901326683
Trimmed Mean ( 4 / 24 )2028.543.837746473478946.2729077834146
Trimmed Mean ( 5 / 24 )2019.6129032258140.789792449578649.5127035942217
Trimmed Mean ( 6 / 24 )2011.5833333333337.721371392072753.3274178296729
Trimmed Mean ( 7 / 24 )2003.9827586206934.383240013368258.283709093196
Trimmed Mean ( 8 / 24 )1994.5178571428630.612810227850465.1530467898148
Trimmed Mean ( 9 / 24 )1991.5555555555629.350238918531667.8548328374286
Trimmed Mean ( 10 / 24 )1988.4038461538527.772946291543571.5949912292629
Trimmed Mean ( 11 / 24 )1984.7426.149754125351375.8989927968716
Trimmed Mean ( 12 / 24 )1982.9791666666725.280088623980178.4403566048285
Trimmed Mean ( 13 / 24 )1981.2391304347824.771695410483579.9799568662675
Trimmed Mean ( 14 / 24 )1979.4318181818224.283308410613781.5140912725324
Trimmed Mean ( 15 / 24 )1978.3333333333324.014046089762582.382340982377
Trimmed Mean ( 16 / 24 )1977.323.683387015222783.4889029482595
Trimmed Mean ( 17 / 24 )1976.1052631578923.273767718865484.9069771181095
Trimmed Mean ( 18 / 24 )1975.4722222222222.926711603242986.1646561621511
Trimmed Mean ( 19 / 24 )1974.5294117647122.465471041491187.8917432052942
Trimmed Mean ( 20 / 24 )1973.7187522.177356694376388.9970241809969
Trimmed Mean ( 21 / 24 )197422.061095938846589.4787822632177
Trimmed Mean ( 22 / 24 )1974.2857142857121.886483056662490.2057086638563
Trimmed Mean ( 23 / 24 )1974.6923076923121.537999995054891.6841075376405
Trimmed Mean ( 24 / 24 )1975.0416666666721.140787486075493.4232780102232
Median1980
Midrange2516
Midmean - Weighted Average at Xnp1976.10526315789
Midmean - Weighted Average at X(n+1)p1981.81081081081
Midmean - Empirical Distribution Function1976.10526315789
Midmean - Empirical Distribution Function - Averaging1981.81081081081
Midmean - Empirical Distribution Function - Interpolation1981.81081081081
Midmean - Closest Observation1976.10526315789
Midmean - True Basic - Statistics Graphics Toolkit1981.81081081081
Midmean - MS Excel (old versions)1976.10526315789
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')