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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 computationWed, 10 Dec 2008 06:28:59 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/Dec/10/t12289165906cshwdcf0ie3btw.htm/, Retrieved Sun, 19 May 2024 06:05:38 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=31950, Retrieved Sun, 19 May 2024 06:05:38 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact150
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Central Tendency] [2008-12-10 13:28:59] [5f3e73ccf1ddc75508eed47fa51813d3] [Current]
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Dataseries X:
632
1270
1211
1469
2570
2765
2487
3644
2501
1629
987
1100
690
1378
1376
1736
2800
2671
2508
3590
2691
1629
1020
1224
787
1424
1232
2021
2782
2682
3284
3194
2736
1701
1089
1240
799
1163
1180
1960
2914
2658
3254
3222
2987
1604
1032
1283
774
1109
1453
1849
2800
3310
3060
3422
3448
1670
1022
1391
767
1172
1498
1623
2646
3439




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'George Udny Yule' @ 72.249.76.132

\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 & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=31950&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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=31950&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=31950&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'George Udny Yule' @ 72.249.76.132







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean1973.62121212121111.16236841479117.7544005247967
Geometric Mean1764.38945070658
Harmonic Mean1566.73800851927
Quadratic Mean2167.57707562796
Winsorized Mean ( 1 / 22 )1973.68181818182110.81609780792617.8104251748942
Winsorized Mean ( 2 / 22 )1971.71212121212109.48127058297318.0095838376100
Winsorized Mean ( 3 / 22 )1971.62121212121109.34286607445418.0315486771555
Winsorized Mean ( 4 / 22 )1971.37878787879108.99879335777318.0862441422449
Winsorized Mean ( 5 / 22 )1963.80303030303107.15780625049318.3262713097395
Winsorized Mean ( 6 / 22 )1978.53030303030104.01630278285219.0213480973338
Winsorized Mean ( 7 / 22 )1978.84848484848102.89823483940319.231121777132
Winsorized Mean ( 8 / 22 )1975.21212121212102.12943822221819.3402818579533
Winsorized Mean ( 9 / 22 )1972.75757575758101.22111101429319.4895862729565
Winsorized Mean ( 10 / 22 )1961.0909090909196.333462531928920.3573177746094
Winsorized Mean ( 11 / 22 )1950.7575757575893.978115938450420.7575727208151
Winsorized Mean ( 12 / 22 )1939.1212121212191.536374914410821.1841600012492
Winsorized Mean ( 13 / 22 )1927.3030303030386.485540432036622.2846850545794
Winsorized Mean ( 14 / 22 )1929.2121212121286.22679888656722.3736952562745
Winsorized Mean ( 15 / 22 )1926.9393939393985.348502290653922.5773076530062
Winsorized Mean ( 16 / 22 )1930.3333333333383.712039257836223.0592080953593
Winsorized Mean ( 17 / 22 )1926.2121212121282.130970269807023.4529327351711
Winsorized Mean ( 18 / 22 )1916.1212121212179.998495076612823.9519657249325
Winsorized Mean ( 19 / 22 )1915.8333333333379.310453645771424.1561262767469
Winsorized Mean ( 20 / 22 )1921.5909090909177.632290212108424.7524696726156
Winsorized Mean ( 21 / 22 )1921.5909090909176.486063685631525.1234122465619
Winsorized Mean ( 22 / 22 )1948.5909090909172.001683408424327.0631298720847
Trimmed Mean ( 1 / 22 )1968.484375109.58530007330617.9630331229025
Trimmed Mean ( 2 / 22 )1962.95161290323108.05024691304018.1670257031715
Trimmed Mean ( 3 / 22 )1958.13333333333106.98387192107118.3030703429577
Trimmed Mean ( 4 / 22 )1953.01724137931105.67758351905418.4809036726996
Trimmed Mean ( 5 / 22 )1947.60714285714104.13752357942018.7022609710112
Trimmed Mean ( 6 / 22 )1943.64814814815102.76604666714718.9133299487865
Trimmed Mean ( 7 / 22 )1936.26923076923101.85058451058019.0108799087756
Trimmed Mean ( 8 / 22 )1928.24100.87665760214119.1148284036631
Trimmed Mean ( 9 / 22 )1920.1666666666799.718643791528519.25584417976
Trimmed Mean ( 10 / 22 )1911.7826086956598.34010250856319.4405187703479
Trimmed Mean ( 11 / 22 )1904.3863636363697.5945479444819.5132453989104
Trimmed Mean ( 12 / 22 )1897.7619047619096.992497102716419.5660691440096
Trimmed Mean ( 13 / 22 )1892.07596.554796369331519.5958675399472
Trimmed Mean ( 14 / 22 )1887.3684210526396.84530655232019.4884862079815
Trimmed Mean ( 15 / 22 )1881.8888888888996.94198705213119.4125264615929
Trimmed Mean ( 16 / 22 )1876.0588235294196.909277650742619.3589186609218
Trimmed Mean ( 17 / 22 )1869.062596.840583766902819.3004051328198
Trimmed Mean ( 18 / 22 )1861.6666666666796.690920461110819.2537898883218
Trimmed Mean ( 19 / 22 )1854.5357142857196.554731061326119.2070931574323
Trimmed Mean ( 20 / 22 )1846.3461538461595.948334531706619.2431287406664
Trimmed Mean ( 21 / 22 )183694.879366581457319.3508880397481
Trimmed Mean ( 22 / 22 )1823.7727272727392.866494776247319.6386515036120
Median1649.5
Midrange2138
Midmean - Weighted Average at Xnp1849.12121212121
Midmean - Weighted Average at X(n+1)p1876.05882352941
Midmean - Empirical Distribution Function1876.05882352941
Midmean - Empirical Distribution Function - Averaging1876.05882352941
Midmean - Empirical Distribution Function - Interpolation1869.0625
Midmean - Closest Observation1876.05882352941
Midmean - True Basic - Statistics Graphics Toolkit1876.05882352941
Midmean - MS Excel (old versions)1876.05882352941
Number of observations66

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 1973.62121212121 & 111.162368414791 & 17.7544005247967 \tabularnewline
Geometric Mean & 1764.38945070658 &  &  \tabularnewline
Harmonic Mean & 1566.73800851927 &  &  \tabularnewline
Quadratic Mean & 2167.57707562796 &  &  \tabularnewline
Winsorized Mean ( 1 / 22 ) & 1973.68181818182 & 110.816097807926 & 17.8104251748942 \tabularnewline
Winsorized Mean ( 2 / 22 ) & 1971.71212121212 & 109.481270582973 & 18.0095838376100 \tabularnewline
Winsorized Mean ( 3 / 22 ) & 1971.62121212121 & 109.342866074454 & 18.0315486771555 \tabularnewline
Winsorized Mean ( 4 / 22 ) & 1971.37878787879 & 108.998793357773 & 18.0862441422449 \tabularnewline
Winsorized Mean ( 5 / 22 ) & 1963.80303030303 & 107.157806250493 & 18.3262713097395 \tabularnewline
Winsorized Mean ( 6 / 22 ) & 1978.53030303030 & 104.016302782852 & 19.0213480973338 \tabularnewline
Winsorized Mean ( 7 / 22 ) & 1978.84848484848 & 102.898234839403 & 19.231121777132 \tabularnewline
Winsorized Mean ( 8 / 22 ) & 1975.21212121212 & 102.129438222218 & 19.3402818579533 \tabularnewline
Winsorized Mean ( 9 / 22 ) & 1972.75757575758 & 101.221111014293 & 19.4895862729565 \tabularnewline
Winsorized Mean ( 10 / 22 ) & 1961.09090909091 & 96.3334625319289 & 20.3573177746094 \tabularnewline
Winsorized Mean ( 11 / 22 ) & 1950.75757575758 & 93.9781159384504 & 20.7575727208151 \tabularnewline
Winsorized Mean ( 12 / 22 ) & 1939.12121212121 & 91.5363749144108 & 21.1841600012492 \tabularnewline
Winsorized Mean ( 13 / 22 ) & 1927.30303030303 & 86.4855404320366 & 22.2846850545794 \tabularnewline
Winsorized Mean ( 14 / 22 ) & 1929.21212121212 & 86.226798886567 & 22.3736952562745 \tabularnewline
Winsorized Mean ( 15 / 22 ) & 1926.93939393939 & 85.3485022906539 & 22.5773076530062 \tabularnewline
Winsorized Mean ( 16 / 22 ) & 1930.33333333333 & 83.7120392578362 & 23.0592080953593 \tabularnewline
Winsorized Mean ( 17 / 22 ) & 1926.21212121212 & 82.1309702698070 & 23.4529327351711 \tabularnewline
Winsorized Mean ( 18 / 22 ) & 1916.12121212121 & 79.9984950766128 & 23.9519657249325 \tabularnewline
Winsorized Mean ( 19 / 22 ) & 1915.83333333333 & 79.3104536457714 & 24.1561262767469 \tabularnewline
Winsorized Mean ( 20 / 22 ) & 1921.59090909091 & 77.6322902121084 & 24.7524696726156 \tabularnewline
Winsorized Mean ( 21 / 22 ) & 1921.59090909091 & 76.4860636856315 & 25.1234122465619 \tabularnewline
Winsorized Mean ( 22 / 22 ) & 1948.59090909091 & 72.0016834084243 & 27.0631298720847 \tabularnewline
Trimmed Mean ( 1 / 22 ) & 1968.484375 & 109.585300073306 & 17.9630331229025 \tabularnewline
Trimmed Mean ( 2 / 22 ) & 1962.95161290323 & 108.050246913040 & 18.1670257031715 \tabularnewline
Trimmed Mean ( 3 / 22 ) & 1958.13333333333 & 106.983871921071 & 18.3030703429577 \tabularnewline
Trimmed Mean ( 4 / 22 ) & 1953.01724137931 & 105.677583519054 & 18.4809036726996 \tabularnewline
Trimmed Mean ( 5 / 22 ) & 1947.60714285714 & 104.137523579420 & 18.7022609710112 \tabularnewline
Trimmed Mean ( 6 / 22 ) & 1943.64814814815 & 102.766046667147 & 18.9133299487865 \tabularnewline
Trimmed Mean ( 7 / 22 ) & 1936.26923076923 & 101.850584510580 & 19.0108799087756 \tabularnewline
Trimmed Mean ( 8 / 22 ) & 1928.24 & 100.876657602141 & 19.1148284036631 \tabularnewline
Trimmed Mean ( 9 / 22 ) & 1920.16666666667 & 99.7186437915285 & 19.25584417976 \tabularnewline
Trimmed Mean ( 10 / 22 ) & 1911.78260869565 & 98.340102508563 & 19.4405187703479 \tabularnewline
Trimmed Mean ( 11 / 22 ) & 1904.38636363636 & 97.59454794448 & 19.5132453989104 \tabularnewline
Trimmed Mean ( 12 / 22 ) & 1897.76190476190 & 96.9924971027164 & 19.5660691440096 \tabularnewline
Trimmed Mean ( 13 / 22 ) & 1892.075 & 96.5547963693315 & 19.5958675399472 \tabularnewline
Trimmed Mean ( 14 / 22 ) & 1887.36842105263 & 96.845306552320 & 19.4884862079815 \tabularnewline
Trimmed Mean ( 15 / 22 ) & 1881.88888888889 & 96.941987052131 & 19.4125264615929 \tabularnewline
Trimmed Mean ( 16 / 22 ) & 1876.05882352941 & 96.9092776507426 & 19.3589186609218 \tabularnewline
Trimmed Mean ( 17 / 22 ) & 1869.0625 & 96.8405837669028 & 19.3004051328198 \tabularnewline
Trimmed Mean ( 18 / 22 ) & 1861.66666666667 & 96.6909204611108 & 19.2537898883218 \tabularnewline
Trimmed Mean ( 19 / 22 ) & 1854.53571428571 & 96.5547310613261 & 19.2070931574323 \tabularnewline
Trimmed Mean ( 20 / 22 ) & 1846.34615384615 & 95.9483345317066 & 19.2431287406664 \tabularnewline
Trimmed Mean ( 21 / 22 ) & 1836 & 94.8793665814573 & 19.3508880397481 \tabularnewline
Trimmed Mean ( 22 / 22 ) & 1823.77272727273 & 92.8664947762473 & 19.6386515036120 \tabularnewline
Median & 1649.5 &  &  \tabularnewline
Midrange & 2138 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 1849.12121212121 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 1876.05882352941 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 1876.05882352941 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 1876.05882352941 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 1869.0625 &  &  \tabularnewline
Midmean - Closest Observation & 1876.05882352941 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 1876.05882352941 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 1876.05882352941 &  &  \tabularnewline
Number of observations & 66 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=31950&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]1973.62121212121[/C][C]111.162368414791[/C][C]17.7544005247967[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]1764.38945070658[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]1566.73800851927[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]2167.57707562796[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 22 )[/C][C]1973.68181818182[/C][C]110.816097807926[/C][C]17.8104251748942[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 22 )[/C][C]1971.71212121212[/C][C]109.481270582973[/C][C]18.0095838376100[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 22 )[/C][C]1971.62121212121[/C][C]109.342866074454[/C][C]18.0315486771555[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 22 )[/C][C]1971.37878787879[/C][C]108.998793357773[/C][C]18.0862441422449[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 22 )[/C][C]1963.80303030303[/C][C]107.157806250493[/C][C]18.3262713097395[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 22 )[/C][C]1978.53030303030[/C][C]104.016302782852[/C][C]19.0213480973338[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 22 )[/C][C]1978.84848484848[/C][C]102.898234839403[/C][C]19.231121777132[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 22 )[/C][C]1975.21212121212[/C][C]102.129438222218[/C][C]19.3402818579533[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 22 )[/C][C]1972.75757575758[/C][C]101.221111014293[/C][C]19.4895862729565[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 22 )[/C][C]1961.09090909091[/C][C]96.3334625319289[/C][C]20.3573177746094[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 22 )[/C][C]1950.75757575758[/C][C]93.9781159384504[/C][C]20.7575727208151[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 22 )[/C][C]1939.12121212121[/C][C]91.5363749144108[/C][C]21.1841600012492[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 22 )[/C][C]1927.30303030303[/C][C]86.4855404320366[/C][C]22.2846850545794[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 22 )[/C][C]1929.21212121212[/C][C]86.226798886567[/C][C]22.3736952562745[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 22 )[/C][C]1926.93939393939[/C][C]85.3485022906539[/C][C]22.5773076530062[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 22 )[/C][C]1930.33333333333[/C][C]83.7120392578362[/C][C]23.0592080953593[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 22 )[/C][C]1926.21212121212[/C][C]82.1309702698070[/C][C]23.4529327351711[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 22 )[/C][C]1916.12121212121[/C][C]79.9984950766128[/C][C]23.9519657249325[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 22 )[/C][C]1915.83333333333[/C][C]79.3104536457714[/C][C]24.1561262767469[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 22 )[/C][C]1921.59090909091[/C][C]77.6322902121084[/C][C]24.7524696726156[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 22 )[/C][C]1921.59090909091[/C][C]76.4860636856315[/C][C]25.1234122465619[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 22 )[/C][C]1948.59090909091[/C][C]72.0016834084243[/C][C]27.0631298720847[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 22 )[/C][C]1968.484375[/C][C]109.585300073306[/C][C]17.9630331229025[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 22 )[/C][C]1962.95161290323[/C][C]108.050246913040[/C][C]18.1670257031715[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 22 )[/C][C]1958.13333333333[/C][C]106.983871921071[/C][C]18.3030703429577[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 22 )[/C][C]1953.01724137931[/C][C]105.677583519054[/C][C]18.4809036726996[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 22 )[/C][C]1947.60714285714[/C][C]104.137523579420[/C][C]18.7022609710112[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 22 )[/C][C]1943.64814814815[/C][C]102.766046667147[/C][C]18.9133299487865[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 22 )[/C][C]1936.26923076923[/C][C]101.850584510580[/C][C]19.0108799087756[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 22 )[/C][C]1928.24[/C][C]100.876657602141[/C][C]19.1148284036631[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 22 )[/C][C]1920.16666666667[/C][C]99.7186437915285[/C][C]19.25584417976[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 22 )[/C][C]1911.78260869565[/C][C]98.340102508563[/C][C]19.4405187703479[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 22 )[/C][C]1904.38636363636[/C][C]97.59454794448[/C][C]19.5132453989104[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 22 )[/C][C]1897.76190476190[/C][C]96.9924971027164[/C][C]19.5660691440096[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 22 )[/C][C]1892.075[/C][C]96.5547963693315[/C][C]19.5958675399472[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 22 )[/C][C]1887.36842105263[/C][C]96.845306552320[/C][C]19.4884862079815[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 22 )[/C][C]1881.88888888889[/C][C]96.941987052131[/C][C]19.4125264615929[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 22 )[/C][C]1876.05882352941[/C][C]96.9092776507426[/C][C]19.3589186609218[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 22 )[/C][C]1869.0625[/C][C]96.8405837669028[/C][C]19.3004051328198[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 22 )[/C][C]1861.66666666667[/C][C]96.6909204611108[/C][C]19.2537898883218[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 22 )[/C][C]1854.53571428571[/C][C]96.5547310613261[/C][C]19.2070931574323[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 22 )[/C][C]1846.34615384615[/C][C]95.9483345317066[/C][C]19.2431287406664[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 22 )[/C][C]1836[/C][C]94.8793665814573[/C][C]19.3508880397481[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 22 )[/C][C]1823.77272727273[/C][C]92.8664947762473[/C][C]19.6386515036120[/C][/ROW]
[ROW][C]Median[/C][C]1649.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]2138[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]1849.12121212121[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]1876.05882352941[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]1876.05882352941[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]1876.05882352941[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]1869.0625[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]1876.05882352941[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]1876.05882352941[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]1876.05882352941[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]66[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=31950&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=31950&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 Mean1973.62121212121111.16236841479117.7544005247967
Geometric Mean1764.38945070658
Harmonic Mean1566.73800851927
Quadratic Mean2167.57707562796
Winsorized Mean ( 1 / 22 )1973.68181818182110.81609780792617.8104251748942
Winsorized Mean ( 2 / 22 )1971.71212121212109.48127058297318.0095838376100
Winsorized Mean ( 3 / 22 )1971.62121212121109.34286607445418.0315486771555
Winsorized Mean ( 4 / 22 )1971.37878787879108.99879335777318.0862441422449
Winsorized Mean ( 5 / 22 )1963.80303030303107.15780625049318.3262713097395
Winsorized Mean ( 6 / 22 )1978.53030303030104.01630278285219.0213480973338
Winsorized Mean ( 7 / 22 )1978.84848484848102.89823483940319.231121777132
Winsorized Mean ( 8 / 22 )1975.21212121212102.12943822221819.3402818579533
Winsorized Mean ( 9 / 22 )1972.75757575758101.22111101429319.4895862729565
Winsorized Mean ( 10 / 22 )1961.0909090909196.333462531928920.3573177746094
Winsorized Mean ( 11 / 22 )1950.7575757575893.978115938450420.7575727208151
Winsorized Mean ( 12 / 22 )1939.1212121212191.536374914410821.1841600012492
Winsorized Mean ( 13 / 22 )1927.3030303030386.485540432036622.2846850545794
Winsorized Mean ( 14 / 22 )1929.2121212121286.22679888656722.3736952562745
Winsorized Mean ( 15 / 22 )1926.9393939393985.348502290653922.5773076530062
Winsorized Mean ( 16 / 22 )1930.3333333333383.712039257836223.0592080953593
Winsorized Mean ( 17 / 22 )1926.2121212121282.130970269807023.4529327351711
Winsorized Mean ( 18 / 22 )1916.1212121212179.998495076612823.9519657249325
Winsorized Mean ( 19 / 22 )1915.8333333333379.310453645771424.1561262767469
Winsorized Mean ( 20 / 22 )1921.5909090909177.632290212108424.7524696726156
Winsorized Mean ( 21 / 22 )1921.5909090909176.486063685631525.1234122465619
Winsorized Mean ( 22 / 22 )1948.5909090909172.001683408424327.0631298720847
Trimmed Mean ( 1 / 22 )1968.484375109.58530007330617.9630331229025
Trimmed Mean ( 2 / 22 )1962.95161290323108.05024691304018.1670257031715
Trimmed Mean ( 3 / 22 )1958.13333333333106.98387192107118.3030703429577
Trimmed Mean ( 4 / 22 )1953.01724137931105.67758351905418.4809036726996
Trimmed Mean ( 5 / 22 )1947.60714285714104.13752357942018.7022609710112
Trimmed Mean ( 6 / 22 )1943.64814814815102.76604666714718.9133299487865
Trimmed Mean ( 7 / 22 )1936.26923076923101.85058451058019.0108799087756
Trimmed Mean ( 8 / 22 )1928.24100.87665760214119.1148284036631
Trimmed Mean ( 9 / 22 )1920.1666666666799.718643791528519.25584417976
Trimmed Mean ( 10 / 22 )1911.7826086956598.34010250856319.4405187703479
Trimmed Mean ( 11 / 22 )1904.3863636363697.5945479444819.5132453989104
Trimmed Mean ( 12 / 22 )1897.7619047619096.992497102716419.5660691440096
Trimmed Mean ( 13 / 22 )1892.07596.554796369331519.5958675399472
Trimmed Mean ( 14 / 22 )1887.3684210526396.84530655232019.4884862079815
Trimmed Mean ( 15 / 22 )1881.8888888888996.94198705213119.4125264615929
Trimmed Mean ( 16 / 22 )1876.0588235294196.909277650742619.3589186609218
Trimmed Mean ( 17 / 22 )1869.062596.840583766902819.3004051328198
Trimmed Mean ( 18 / 22 )1861.6666666666796.690920461110819.2537898883218
Trimmed Mean ( 19 / 22 )1854.5357142857196.554731061326119.2070931574323
Trimmed Mean ( 20 / 22 )1846.3461538461595.948334531706619.2431287406664
Trimmed Mean ( 21 / 22 )183694.879366581457319.3508880397481
Trimmed Mean ( 22 / 22 )1823.7727272727392.866494776247319.6386515036120
Median1649.5
Midrange2138
Midmean - Weighted Average at Xnp1849.12121212121
Midmean - Weighted Average at X(n+1)p1876.05882352941
Midmean - Empirical Distribution Function1876.05882352941
Midmean - Empirical Distribution Function - Averaging1876.05882352941
Midmean - Empirical Distribution Function - Interpolation1869.0625
Midmean - Closest Observation1876.05882352941
Midmean - True Basic - Statistics Graphics Toolkit1876.05882352941
Midmean - MS Excel (old versions)1876.05882352941
Number of observations66



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')