Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationThu, 22 Nov 2007 09:53:20 -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/2007/Nov/22/t1195749933afbvckldc729fla.htm/, Retrieved Thu, 02 May 2024 19:39:22 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=6075, Retrieved Thu, 02 May 2024 19:39:22 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact171
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Mean] [2007-11-22 16:53:20] [67794d83edd3193bd9ea9816803ddb96] [Current]
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Dataseries X:
76.1666666666828
50.000000000001
215.666666666667
236.666666666667
182.5
270.499999999999
12.8333333333327
-273
213.833333333334
442.666666666666
320.5
644.333333333333
163.166666666663
431
-68.3333333333333
-44.3333333333332
105.5
-57.5
-152.166666666666
-261
-192.166666666667
-76.3333333333332
-30.5
39.3333333333333
-119.833333333336
-140.0
-53.3333333333333
-289.333333333333
-229.5
-379.5
-17.1666666666666
-43.0000000000001
-249.166666666667
-89.3333333333331
271.5
-302.666666666667
-41.8333333333365
-38.0000000000001
54.6666666666667
158.666666666667
13.5000000000000
-36.5
-66.1666666666666
178
-49.1666666666667
-187.333333333333
-754.5
-695.666666666667
49.1666666666635
-119
-36.3333333333333
15.6666666666668
-71.5
223.5
257.833333333333
224
193.833333333333
130.666666666666
333.5
193.333333333333
-126.833333333336
-184
-112.333333333333
-77.3333333333332
-0.499999999999959
-20.5000000000000
-35.1666666666666
175
82.8333333333334
-220.333333333333
-140.5
121.333333333333




Summary of compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\begin{tabular}{lllllllll}
\hline
Summary of compuational 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' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=6075&T=0

[TABLE]
[ROW][C]Summary of compuational 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' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=6075&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6075&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 compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean6.13166924641935e-1526.97492145650792.2730999444449e-16
Geometric MeanNaN
Harmonic Mean-33.9057047654961
Quadratic Mean227.294728312204
Winsorized Mean ( 1 / 24 )-1.983796296296325.8460712785525-0.0767542685662437
Winsorized Mean ( 2 / 24 )6.4745370370370623.03264946639760.281102573391861
Winsorized Mean ( 3 / 24 )5.6134259259259321.35760440638670.262830316505315
Winsorized Mean ( 4 / 24 )5.6319444444444921.0550571975730.267486542145023
Winsorized Mean ( 5 / 24 )3.3634259259259520.15556600677860.166873305606738
Winsorized Mean ( 6 / 24 )4.2800925925925319.94970877315680.214544113964791
Winsorized Mean ( 7 / 24 )4.1990740740740419.50820661115580.215246545096195
Winsorized Mean ( 8 / 24 )4.0324074074074918.69431063268710.215702385963183
Winsorized Mean ( 9 / 24 )3.5949074074074918.22063479119980.197298691763679
Winsorized Mean ( 10 / 24 )7.437517.55643378403800.423633870721629
Winsorized Mean ( 11 / 24 )6.9791666666668217.23287567962730.404991412716892
Winsorized Mean ( 12 / 24 )7.2291666666668217.09292243233000.42293333368163
Winsorized Mean ( 13 / 24 )9.3657407407408315.61155303441990.599923705225964
Winsorized Mean ( 14 / 24 )11.53703703703715.27089410372990.755491915448427
Winsorized Mean ( 15 / 24 )9.3842592592592814.88207158251580.630574796474192
Winsorized Mean ( 16 / 24 )11.310185185184614.31226664891590.790244163459692
Winsorized Mean ( 17 / 24 )12.254629629629113.97368091001470.876979352007843
Winsorized Mean ( 18 / 24 )9.504629629628813.46534316582550.705858700560354
Winsorized Mean ( 19 / 24 )10.076388888889213.04005211802410.772726120853576
Winsorized Mean ( 20 / 24 )8.6875000000000210.98033759107320.791186967426462
Winsorized Mean ( 21 / 24 )9.4652777777778710.12378499480630.934954444670023
Winsorized Mean ( 22 / 24 )4.932870370370569.343036806333380.527972914227064
Winsorized Mean ( 23 / 24 )-0.7638888888887228.07498382296145-0.0945994327216584
Winsorized Mean ( 24 / 24 )-1.930555555550027.62270711026837-0.253263771993733
Trimmed Mean ( 1 / 24 )1.5738095238095323.79658124592110.0661359506874248
Trimmed Mean ( 2 / 24 )5.3406862745098321.22999595946680.251563226140339
Trimmed Mean ( 3 / 24 )4.7222222222222520.04734338665960.235553516051639
Trimmed Mean ( 4 / 24 )4.3880208333333719.42593686053790.225884644063023
Trimmed Mean ( 5 / 24 )4.0268817204301418.79033988016130.214305954342086
Trimmed Mean ( 6 / 24 )4.1861111111111418.31187328645130.228600921687699
Trimmed Mean ( 7 / 24 )4.1666666666667117.78580177861680.234269262557291
Trimmed Mean ( 8 / 24 )4.1607142857143517.25739168873360.241097516980544
Trimmed Mean ( 9 / 24 )4.1820987654321616.80884572474130.248803447536937
Trimmed Mean ( 10 / 24 )4.2724358974359516.36100816481750.261135246336673
Trimmed Mean ( 11 / 24 )3.8166666666667315.94934317202590.239299300635835
Trimmed Mean ( 12 / 24 )3.3854166666667215.49718459605190.218453658190869
Trimmed Mean ( 13 / 24 )2.8840579710145314.94585941397330.192967021241892
Trimmed Mean ( 14 / 24 )2.0681818181818514.57397647896350.141909232608350
Trimmed Mean ( 15 / 24 )0.90873015873020114.15235231636860.0642105381788131
Trimmed Mean ( 16 / 24 )-0.10833333333328913.6819587548849-0.00791796958857302
Trimmed Mean ( 17 / 24 )-1.4605263157893613.1782415978975-0.110828618897257
Trimmed Mean ( 18 / 24 )-3.0740740740738812.5650782900793-0.244652202167414
Trimmed Mean ( 19 / 24 )-4.5539215686271311.8585333352550-0.384020640654482
Trimmed Mean ( 20 / 24 )-6.2864583333330210.9722718765537-0.572940445156701
Trimmed Mean ( 21 / 24 )-8.0833333333329810.3766880329827-0.778989722697625
Trimmed Mean ( 22 / 24 )-10.23214285714259.7592919111545-1.04845135797686
Trimmed Mean ( 23 / 24 )-12.14102564102529.1269896194464-1.33023331320077
Trimmed Mean ( 24 / 24 )-13.62499999999968.6759069678611-1.57044099832695
Median-32.8333333333333
Midrange-55.0833333333335
Midmean - Weighted Average at Xnp-6.2297297297296
Midmean - Weighted Average at X(n+1)p-3.07407407407387
Midmean - Empirical Distribution Function-6.2297297297296
Midmean - Empirical Distribution Function - Averaging-3.07407407407387
Midmean - Empirical Distribution Function - Interpolation-3.07407407407387
Midmean - Closest Observation-6.2297297297296
Midmean - True Basic - Statistics Graphics Toolkit-3.07407407407387
Midmean - MS Excel (old versions)-1.46052631578935
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 6.13166924641935e-15 & 26.9749214565079 & 2.2730999444449e-16 \tabularnewline
Geometric Mean & NaN &  &  \tabularnewline
Harmonic Mean & -33.9057047654961 &  &  \tabularnewline
Quadratic Mean & 227.294728312204 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & -1.9837962962963 & 25.8460712785525 & -0.0767542685662437 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 6.47453703703706 & 23.0326494663976 & 0.281102573391861 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 5.61342592592593 & 21.3576044063867 & 0.262830316505315 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 5.63194444444449 & 21.055057197573 & 0.267486542145023 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 3.36342592592595 & 20.1555660067786 & 0.166873305606738 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 4.28009259259253 & 19.9497087731568 & 0.214544113964791 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 4.19907407407404 & 19.5082066111558 & 0.215246545096195 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 4.03240740740749 & 18.6943106326871 & 0.215702385963183 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 3.59490740740749 & 18.2206347911998 & 0.197298691763679 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 7.4375 & 17.5564337840380 & 0.423633870721629 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 6.97916666666682 & 17.2328756796273 & 0.404991412716892 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 7.22916666666682 & 17.0929224323300 & 0.42293333368163 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 9.36574074074083 & 15.6115530344199 & 0.599923705225964 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 11.537037037037 & 15.2708941037299 & 0.755491915448427 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 9.38425925925928 & 14.8820715825158 & 0.630574796474192 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 11.3101851851846 & 14.3122666489159 & 0.790244163459692 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 12.2546296296291 & 13.9736809100147 & 0.876979352007843 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 9.5046296296288 & 13.4653431658255 & 0.705858700560354 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 10.0763888888892 & 13.0400521180241 & 0.772726120853576 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 8.68750000000002 & 10.9803375910732 & 0.791186967426462 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 9.46527777777787 & 10.1237849948063 & 0.934954444670023 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 4.93287037037056 & 9.34303680633338 & 0.527972914227064 \tabularnewline
Winsorized Mean ( 23 / 24 ) & -0.763888888888722 & 8.07498382296145 & -0.0945994327216584 \tabularnewline
Winsorized Mean ( 24 / 24 ) & -1.93055555555002 & 7.62270711026837 & -0.253263771993733 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 1.57380952380953 & 23.7965812459211 & 0.0661359506874248 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 5.34068627450983 & 21.2299959594668 & 0.251563226140339 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 4.72222222222225 & 20.0473433866596 & 0.235553516051639 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 4.38802083333337 & 19.4259368605379 & 0.225884644063023 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 4.02688172043014 & 18.7903398801613 & 0.214305954342086 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 4.18611111111114 & 18.3118732864513 & 0.228600921687699 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 4.16666666666671 & 17.7858017786168 & 0.234269262557291 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 4.16071428571435 & 17.2573916887336 & 0.241097516980544 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 4.18209876543216 & 16.8088457247413 & 0.248803447536937 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 4.27243589743595 & 16.3610081648175 & 0.261135246336673 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 3.81666666666673 & 15.9493431720259 & 0.239299300635835 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 3.38541666666672 & 15.4971845960519 & 0.218453658190869 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 2.88405797101453 & 14.9458594139733 & 0.192967021241892 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 2.06818181818185 & 14.5739764789635 & 0.141909232608350 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 0.908730158730201 & 14.1523523163686 & 0.0642105381788131 \tabularnewline
Trimmed Mean ( 16 / 24 ) & -0.108333333333289 & 13.6819587548849 & -0.00791796958857302 \tabularnewline
Trimmed Mean ( 17 / 24 ) & -1.46052631578936 & 13.1782415978975 & -0.110828618897257 \tabularnewline
Trimmed Mean ( 18 / 24 ) & -3.07407407407388 & 12.5650782900793 & -0.244652202167414 \tabularnewline
Trimmed Mean ( 19 / 24 ) & -4.55392156862713 & 11.8585333352550 & -0.384020640654482 \tabularnewline
Trimmed Mean ( 20 / 24 ) & -6.28645833333302 & 10.9722718765537 & -0.572940445156701 \tabularnewline
Trimmed Mean ( 21 / 24 ) & -8.08333333333298 & 10.3766880329827 & -0.778989722697625 \tabularnewline
Trimmed Mean ( 22 / 24 ) & -10.2321428571425 & 9.7592919111545 & -1.04845135797686 \tabularnewline
Trimmed Mean ( 23 / 24 ) & -12.1410256410252 & 9.1269896194464 & -1.33023331320077 \tabularnewline
Trimmed Mean ( 24 / 24 ) & -13.6249999999996 & 8.6759069678611 & -1.57044099832695 \tabularnewline
Median & -32.8333333333333 &  &  \tabularnewline
Midrange & -55.0833333333335 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & -6.2297297297296 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & -3.07407407407387 &  &  \tabularnewline
Midmean - Empirical Distribution Function & -6.2297297297296 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & -3.07407407407387 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & -3.07407407407387 &  &  \tabularnewline
Midmean - Closest Observation & -6.2297297297296 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & -3.07407407407387 &  &  \tabularnewline
Midmean - MS Excel (old versions) & -1.46052631578935 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=6075&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]6.13166924641935e-15[/C][C]26.9749214565079[/C][C]2.2730999444449e-16[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]NaN[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]-33.9057047654961[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]227.294728312204[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]-1.9837962962963[/C][C]25.8460712785525[/C][C]-0.0767542685662437[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]6.47453703703706[/C][C]23.0326494663976[/C][C]0.281102573391861[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]5.61342592592593[/C][C]21.3576044063867[/C][C]0.262830316505315[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]5.63194444444449[/C][C]21.055057197573[/C][C]0.267486542145023[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]3.36342592592595[/C][C]20.1555660067786[/C][C]0.166873305606738[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]4.28009259259253[/C][C]19.9497087731568[/C][C]0.214544113964791[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]4.19907407407404[/C][C]19.5082066111558[/C][C]0.215246545096195[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]4.03240740740749[/C][C]18.6943106326871[/C][C]0.215702385963183[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]3.59490740740749[/C][C]18.2206347911998[/C][C]0.197298691763679[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]7.4375[/C][C]17.5564337840380[/C][C]0.423633870721629[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]6.97916666666682[/C][C]17.2328756796273[/C][C]0.404991412716892[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]7.22916666666682[/C][C]17.0929224323300[/C][C]0.42293333368163[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]9.36574074074083[/C][C]15.6115530344199[/C][C]0.599923705225964[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]11.537037037037[/C][C]15.2708941037299[/C][C]0.755491915448427[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]9.38425925925928[/C][C]14.8820715825158[/C][C]0.630574796474192[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]11.3101851851846[/C][C]14.3122666489159[/C][C]0.790244163459692[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]12.2546296296291[/C][C]13.9736809100147[/C][C]0.876979352007843[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]9.5046296296288[/C][C]13.4653431658255[/C][C]0.705858700560354[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]10.0763888888892[/C][C]13.0400521180241[/C][C]0.772726120853576[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]8.68750000000002[/C][C]10.9803375910732[/C][C]0.791186967426462[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]9.46527777777787[/C][C]10.1237849948063[/C][C]0.934954444670023[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]4.93287037037056[/C][C]9.34303680633338[/C][C]0.527972914227064[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]-0.763888888888722[/C][C]8.07498382296145[/C][C]-0.0945994327216584[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]-1.93055555555002[/C][C]7.62270711026837[/C][C]-0.253263771993733[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]1.57380952380953[/C][C]23.7965812459211[/C][C]0.0661359506874248[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]5.34068627450983[/C][C]21.2299959594668[/C][C]0.251563226140339[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]4.72222222222225[/C][C]20.0473433866596[/C][C]0.235553516051639[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]4.38802083333337[/C][C]19.4259368605379[/C][C]0.225884644063023[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]4.02688172043014[/C][C]18.7903398801613[/C][C]0.214305954342086[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]4.18611111111114[/C][C]18.3118732864513[/C][C]0.228600921687699[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]4.16666666666671[/C][C]17.7858017786168[/C][C]0.234269262557291[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]4.16071428571435[/C][C]17.2573916887336[/C][C]0.241097516980544[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]4.18209876543216[/C][C]16.8088457247413[/C][C]0.248803447536937[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]4.27243589743595[/C][C]16.3610081648175[/C][C]0.261135246336673[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]3.81666666666673[/C][C]15.9493431720259[/C][C]0.239299300635835[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]3.38541666666672[/C][C]15.4971845960519[/C][C]0.218453658190869[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]2.88405797101453[/C][C]14.9458594139733[/C][C]0.192967021241892[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]2.06818181818185[/C][C]14.5739764789635[/C][C]0.141909232608350[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]0.908730158730201[/C][C]14.1523523163686[/C][C]0.0642105381788131[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]-0.108333333333289[/C][C]13.6819587548849[/C][C]-0.00791796958857302[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]-1.46052631578936[/C][C]13.1782415978975[/C][C]-0.110828618897257[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]-3.07407407407388[/C][C]12.5650782900793[/C][C]-0.244652202167414[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]-4.55392156862713[/C][C]11.8585333352550[/C][C]-0.384020640654482[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]-6.28645833333302[/C][C]10.9722718765537[/C][C]-0.572940445156701[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]-8.08333333333298[/C][C]10.3766880329827[/C][C]-0.778989722697625[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]-10.2321428571425[/C][C]9.7592919111545[/C][C]-1.04845135797686[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]-12.1410256410252[/C][C]9.1269896194464[/C][C]-1.33023331320077[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]-13.6249999999996[/C][C]8.6759069678611[/C][C]-1.57044099832695[/C][/ROW]
[ROW][C]Median[/C][C]-32.8333333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]-55.0833333333335[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]-6.2297297297296[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]-3.07407407407387[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]-6.2297297297296[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]-3.07407407407387[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]-3.07407407407387[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]-6.2297297297296[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]-3.07407407407387[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]-1.46052631578935[/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=6075&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6075&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 Mean6.13166924641935e-1526.97492145650792.2730999444449e-16
Geometric MeanNaN
Harmonic Mean-33.9057047654961
Quadratic Mean227.294728312204
Winsorized Mean ( 1 / 24 )-1.983796296296325.8460712785525-0.0767542685662437
Winsorized Mean ( 2 / 24 )6.4745370370370623.03264946639760.281102573391861
Winsorized Mean ( 3 / 24 )5.6134259259259321.35760440638670.262830316505315
Winsorized Mean ( 4 / 24 )5.6319444444444921.0550571975730.267486542145023
Winsorized Mean ( 5 / 24 )3.3634259259259520.15556600677860.166873305606738
Winsorized Mean ( 6 / 24 )4.2800925925925319.94970877315680.214544113964791
Winsorized Mean ( 7 / 24 )4.1990740740740419.50820661115580.215246545096195
Winsorized Mean ( 8 / 24 )4.0324074074074918.69431063268710.215702385963183
Winsorized Mean ( 9 / 24 )3.5949074074074918.22063479119980.197298691763679
Winsorized Mean ( 10 / 24 )7.437517.55643378403800.423633870721629
Winsorized Mean ( 11 / 24 )6.9791666666668217.23287567962730.404991412716892
Winsorized Mean ( 12 / 24 )7.2291666666668217.09292243233000.42293333368163
Winsorized Mean ( 13 / 24 )9.3657407407408315.61155303441990.599923705225964
Winsorized Mean ( 14 / 24 )11.53703703703715.27089410372990.755491915448427
Winsorized Mean ( 15 / 24 )9.3842592592592814.88207158251580.630574796474192
Winsorized Mean ( 16 / 24 )11.310185185184614.31226664891590.790244163459692
Winsorized Mean ( 17 / 24 )12.254629629629113.97368091001470.876979352007843
Winsorized Mean ( 18 / 24 )9.504629629628813.46534316582550.705858700560354
Winsorized Mean ( 19 / 24 )10.076388888889213.04005211802410.772726120853576
Winsorized Mean ( 20 / 24 )8.6875000000000210.98033759107320.791186967426462
Winsorized Mean ( 21 / 24 )9.4652777777778710.12378499480630.934954444670023
Winsorized Mean ( 22 / 24 )4.932870370370569.343036806333380.527972914227064
Winsorized Mean ( 23 / 24 )-0.7638888888887228.07498382296145-0.0945994327216584
Winsorized Mean ( 24 / 24 )-1.930555555550027.62270711026837-0.253263771993733
Trimmed Mean ( 1 / 24 )1.5738095238095323.79658124592110.0661359506874248
Trimmed Mean ( 2 / 24 )5.3406862745098321.22999595946680.251563226140339
Trimmed Mean ( 3 / 24 )4.7222222222222520.04734338665960.235553516051639
Trimmed Mean ( 4 / 24 )4.3880208333333719.42593686053790.225884644063023
Trimmed Mean ( 5 / 24 )4.0268817204301418.79033988016130.214305954342086
Trimmed Mean ( 6 / 24 )4.1861111111111418.31187328645130.228600921687699
Trimmed Mean ( 7 / 24 )4.1666666666667117.78580177861680.234269262557291
Trimmed Mean ( 8 / 24 )4.1607142857143517.25739168873360.241097516980544
Trimmed Mean ( 9 / 24 )4.1820987654321616.80884572474130.248803447536937
Trimmed Mean ( 10 / 24 )4.2724358974359516.36100816481750.261135246336673
Trimmed Mean ( 11 / 24 )3.8166666666667315.94934317202590.239299300635835
Trimmed Mean ( 12 / 24 )3.3854166666667215.49718459605190.218453658190869
Trimmed Mean ( 13 / 24 )2.8840579710145314.94585941397330.192967021241892
Trimmed Mean ( 14 / 24 )2.0681818181818514.57397647896350.141909232608350
Trimmed Mean ( 15 / 24 )0.90873015873020114.15235231636860.0642105381788131
Trimmed Mean ( 16 / 24 )-0.10833333333328913.6819587548849-0.00791796958857302
Trimmed Mean ( 17 / 24 )-1.4605263157893613.1782415978975-0.110828618897257
Trimmed Mean ( 18 / 24 )-3.0740740740738812.5650782900793-0.244652202167414
Trimmed Mean ( 19 / 24 )-4.5539215686271311.8585333352550-0.384020640654482
Trimmed Mean ( 20 / 24 )-6.2864583333330210.9722718765537-0.572940445156701
Trimmed Mean ( 21 / 24 )-8.0833333333329810.3766880329827-0.778989722697625
Trimmed Mean ( 22 / 24 )-10.23214285714259.7592919111545-1.04845135797686
Trimmed Mean ( 23 / 24 )-12.14102564102529.1269896194464-1.33023331320077
Trimmed Mean ( 24 / 24 )-13.62499999999968.6759069678611-1.57044099832695
Median-32.8333333333333
Midrange-55.0833333333335
Midmean - Weighted Average at Xnp-6.2297297297296
Midmean - Weighted Average at X(n+1)p-3.07407407407387
Midmean - Empirical Distribution Function-6.2297297297296
Midmean - Empirical Distribution Function - Averaging-3.07407407407387
Midmean - Empirical Distribution Function - Interpolation-3.07407407407387
Midmean - Closest Observation-6.2297297297296
Midmean - True Basic - Statistics Graphics Toolkit-3.07407407407387
Midmean - MS Excel (old versions)-1.46052631578935
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')