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of Irreproducible Research!

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationMon, 20 Oct 2008 10:41:23 -0600
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/Oct/20/t1224520918u17wefqk0kmupca.htm/, Retrieved Fri, 17 May 2024 06:37:59 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=17626, Retrieved Fri, 17 May 2024 06:37:59 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact118
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
F     [Central Tendency] [Q1 central tenden...] [2007-10-18 09:35:57] [b731da8b544846036771bbf9bf2f34ce]
F R  D    [Central Tendency] [Central Tendency ...] [2008-10-20 16:41:23] [270782e2502ae87124d0ebdcd1862d6a] [Current]
Feedback Forum
2008-10-24 10:41:47 [Nathalie Koulouris] [reply
De student heeft enkel een link weergegeven naar de central tendency van zijn tijdreeksen en geen verdere toelichting gegeven. Dit was niet de bedoeling. Hij had gebruik moeten maken van de verschillende berekeningsmethoden. Hieruit kon hij dan een goede conclusie trekken.

Post a new message
Dataseries X:
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2.21
2.25
2.25
2.45
2.5
2.5
2.64
2.75
2.93
3
3.17
3.25
3.39
3.5
3.5
3.65
3.75
3.75
3.9
4
4
4
4
4
4
4
4
4
4
4
4
4,18
4.25
4.25




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=17626&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=17626&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=17626&T=0

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean2.833666666666670.11486542523044524.6694482781195
Geometric Mean2.70197517270761
Harmonic Mean2.58290058710914
Quadratic Mean2.96784714341333
Winsorized Mean ( 1 / 20 )2.833666666666670.11486542523044524.6694482781195
Winsorized Mean ( 2 / 20 )2.831333333333330.11438844185880524.7519180025915
Winsorized Mean ( 3 / 20 )2.822333333333330.11269136058069925.0448066186248
Winsorized Mean ( 4 / 20 )2.822333333333330.11269136058069925.0448066186248
Winsorized Mean ( 5 / 20 )2.822333333333330.11269136058069925.0448066186248
Winsorized Mean ( 6 / 20 )2.822333333333330.11269136058069925.0448066186248
Winsorized Mean ( 7 / 20 )2.822333333333330.11269136058069925.0448066186248
Winsorized Mean ( 8 / 20 )2.822333333333330.11269136058069925.0448066186248
Winsorized Mean ( 9 / 20 )2.822333333333330.11269136058069925.0448066186248
Winsorized Mean ( 10 / 20 )2.822333333333330.11269136058069925.0448066186248
Winsorized Mean ( 11 / 20 )2.822333333333330.11269136058069925.0448066186248
Winsorized Mean ( 12 / 20 )2.822333333333330.11269136058069925.0448066186248
Winsorized Mean ( 13 / 20 )2.822333333333330.11269136058069925.0448066186248
Winsorized Mean ( 14 / 20 )2.822333333333330.11269136058069925.0448066186248
Winsorized Mean ( 15 / 20 )2.797333333333330.10831943413661325.8248517971883
Winsorized Mean ( 16 / 20 )2.757333333333330.10155065159773627.1522958243118
Winsorized Mean ( 17 / 20 )2.757333333333330.10155065159773627.1522958243118
Winsorized Mean ( 18 / 20 )2.727333333333330.096636621085590128.2225651383005
Winsorized Mean ( 19 / 20 )2.679833333333330.089081468352101630.0829497190266
Winsorized Mean ( 20 / 20 )2.679833333333330.089081468352101630.0829497190266
Trimmed Mean ( 1 / 20 )2.823620689655170.11536540707324324.4754537888687
Trimmed Mean ( 2 / 20 )2.812857142857140.11577062921994324.2968113917152
Trimmed Mean ( 3 / 20 )2.802592592592590.11635213221605324.0871614401401
Trimmed Mean ( 4 / 20 )2.7950.11758040155384123.7709683166896
Trimmed Mean ( 5 / 20 )2.78680.11879821341335123.4582652375714
Trimmed Mean ( 6 / 20 )2.777916666666670.11999222726501523.1508050978283
Trimmed Mean ( 7 / 20 )2.768260869565220.12114442386908522.8509144800320
Trimmed Mean ( 8 / 20 )2.757727272727270.12223035804036922.5617213018100
Trimmed Mean ( 9 / 20 )2.746190476190480.12321664083437722.2874967016980
Trimmed Mean ( 10 / 20 )2.73350.12405723968373922.0341836314313
Trimmed Mean ( 11 / 20 )2.719473684210530.12468791617201821.8102424653466
Trimmed Mean ( 12 / 20 )2.703888888888890.12501763544026821.6280597482646
Trimmed Mean ( 13 / 20 )2.686470588235290.12491486038319421.5064130880359
Trimmed Mean ( 14 / 20 )2.6668750.12418479133611121.4750531953787
Trimmed Mean ( 15 / 20 )2.644666666666670.12252959608073821.5839009615605
Trimmed Mean ( 16 / 20 )2.622857142857140.12093644439442721.6878969444714
Trimmed Mean ( 17 / 20 )2.603461538461540.12018439973985121.66222524801
Trimmed Mean ( 18 / 20 )2.580833333333330.11809004895348221.8547909515219
Trimmed Mean ( 19 / 20 )2.558636363636360.11590467693827922.0753504623362
Trimmed Mean ( 20 / 20 )2.53950.11471813282999322.1368665733378
Median2.475
Midrange3.125
Midmean - Weighted Average at Xnp2.42977777777778
Midmean - Weighted Average at X(n+1)p2.42977777777778
Midmean - Empirical Distribution Function2.42977777777778
Midmean - Empirical Distribution Function - Averaging2.42977777777778
Midmean - Empirical Distribution Function - Interpolation2.42977777777778
Midmean - Closest Observation2.42977777777778
Midmean - True Basic - Statistics Graphics Toolkit2.42977777777778
Midmean - MS Excel (old versions)2.76035087719298
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 2.83366666666667 & 0.114865425230445 & 24.6694482781195 \tabularnewline
Geometric Mean & 2.70197517270761 &  &  \tabularnewline
Harmonic Mean & 2.58290058710914 &  &  \tabularnewline
Quadratic Mean & 2.96784714341333 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 2.83366666666667 & 0.114865425230445 & 24.6694482781195 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 2.83133333333333 & 0.114388441858805 & 24.7519180025915 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 2.82233333333333 & 0.112691360580699 & 25.0448066186248 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 2.82233333333333 & 0.112691360580699 & 25.0448066186248 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 2.82233333333333 & 0.112691360580699 & 25.0448066186248 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 2.82233333333333 & 0.112691360580699 & 25.0448066186248 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 2.82233333333333 & 0.112691360580699 & 25.0448066186248 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 2.82233333333333 & 0.112691360580699 & 25.0448066186248 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 2.82233333333333 & 0.112691360580699 & 25.0448066186248 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 2.82233333333333 & 0.112691360580699 & 25.0448066186248 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 2.82233333333333 & 0.112691360580699 & 25.0448066186248 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 2.82233333333333 & 0.112691360580699 & 25.0448066186248 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 2.82233333333333 & 0.112691360580699 & 25.0448066186248 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 2.82233333333333 & 0.112691360580699 & 25.0448066186248 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 2.79733333333333 & 0.108319434136613 & 25.8248517971883 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 2.75733333333333 & 0.101550651597736 & 27.1522958243118 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 2.75733333333333 & 0.101550651597736 & 27.1522958243118 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 2.72733333333333 & 0.0966366210855901 & 28.2225651383005 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 2.67983333333333 & 0.0890814683521016 & 30.0829497190266 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 2.67983333333333 & 0.0890814683521016 & 30.0829497190266 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 2.82362068965517 & 0.115365407073243 & 24.4754537888687 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 2.81285714285714 & 0.115770629219943 & 24.2968113917152 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 2.80259259259259 & 0.116352132216053 & 24.0871614401401 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 2.795 & 0.117580401553841 & 23.7709683166896 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 2.7868 & 0.118798213413351 & 23.4582652375714 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 2.77791666666667 & 0.119992227265015 & 23.1508050978283 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 2.76826086956522 & 0.121144423869085 & 22.8509144800320 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 2.75772727272727 & 0.122230358040369 & 22.5617213018100 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 2.74619047619048 & 0.123216640834377 & 22.2874967016980 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 2.7335 & 0.124057239683739 & 22.0341836314313 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 2.71947368421053 & 0.124687916172018 & 21.8102424653466 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 2.70388888888889 & 0.125017635440268 & 21.6280597482646 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 2.68647058823529 & 0.124914860383194 & 21.5064130880359 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 2.666875 & 0.124184791336111 & 21.4750531953787 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 2.64466666666667 & 0.122529596080738 & 21.5839009615605 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 2.62285714285714 & 0.120936444394427 & 21.6878969444714 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 2.60346153846154 & 0.120184399739851 & 21.66222524801 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 2.58083333333333 & 0.118090048953482 & 21.8547909515219 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 2.55863636363636 & 0.115904676938279 & 22.0753504623362 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 2.5395 & 0.114718132829993 & 22.1368665733378 \tabularnewline
Median & 2.475 &  &  \tabularnewline
Midrange & 3.125 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 2.42977777777778 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 2.42977777777778 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 2.42977777777778 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 2.42977777777778 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 2.42977777777778 &  &  \tabularnewline
Midmean - Closest Observation & 2.42977777777778 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 2.42977777777778 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 2.76035087719298 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=17626&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]2.83366666666667[/C][C]0.114865425230445[/C][C]24.6694482781195[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]2.70197517270761[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]2.58290058710914[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]2.96784714341333[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]2.83366666666667[/C][C]0.114865425230445[/C][C]24.6694482781195[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]2.83133333333333[/C][C]0.114388441858805[/C][C]24.7519180025915[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]2.82233333333333[/C][C]0.112691360580699[/C][C]25.0448066186248[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]2.82233333333333[/C][C]0.112691360580699[/C][C]25.0448066186248[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]2.82233333333333[/C][C]0.112691360580699[/C][C]25.0448066186248[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]2.82233333333333[/C][C]0.112691360580699[/C][C]25.0448066186248[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]2.82233333333333[/C][C]0.112691360580699[/C][C]25.0448066186248[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]2.82233333333333[/C][C]0.112691360580699[/C][C]25.0448066186248[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]2.82233333333333[/C][C]0.112691360580699[/C][C]25.0448066186248[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]2.82233333333333[/C][C]0.112691360580699[/C][C]25.0448066186248[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]2.82233333333333[/C][C]0.112691360580699[/C][C]25.0448066186248[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]2.82233333333333[/C][C]0.112691360580699[/C][C]25.0448066186248[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]2.82233333333333[/C][C]0.112691360580699[/C][C]25.0448066186248[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]2.82233333333333[/C][C]0.112691360580699[/C][C]25.0448066186248[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]2.79733333333333[/C][C]0.108319434136613[/C][C]25.8248517971883[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]2.75733333333333[/C][C]0.101550651597736[/C][C]27.1522958243118[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]2.75733333333333[/C][C]0.101550651597736[/C][C]27.1522958243118[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]2.72733333333333[/C][C]0.0966366210855901[/C][C]28.2225651383005[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]2.67983333333333[/C][C]0.0890814683521016[/C][C]30.0829497190266[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]2.67983333333333[/C][C]0.0890814683521016[/C][C]30.0829497190266[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]2.82362068965517[/C][C]0.115365407073243[/C][C]24.4754537888687[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]2.81285714285714[/C][C]0.115770629219943[/C][C]24.2968113917152[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]2.80259259259259[/C][C]0.116352132216053[/C][C]24.0871614401401[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]2.795[/C][C]0.117580401553841[/C][C]23.7709683166896[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]2.7868[/C][C]0.118798213413351[/C][C]23.4582652375714[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]2.77791666666667[/C][C]0.119992227265015[/C][C]23.1508050978283[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]2.76826086956522[/C][C]0.121144423869085[/C][C]22.8509144800320[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]2.75772727272727[/C][C]0.122230358040369[/C][C]22.5617213018100[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]2.74619047619048[/C][C]0.123216640834377[/C][C]22.2874967016980[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]2.7335[/C][C]0.124057239683739[/C][C]22.0341836314313[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]2.71947368421053[/C][C]0.124687916172018[/C][C]21.8102424653466[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]2.70388888888889[/C][C]0.125017635440268[/C][C]21.6280597482646[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]2.68647058823529[/C][C]0.124914860383194[/C][C]21.5064130880359[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]2.666875[/C][C]0.124184791336111[/C][C]21.4750531953787[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]2.64466666666667[/C][C]0.122529596080738[/C][C]21.5839009615605[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]2.62285714285714[/C][C]0.120936444394427[/C][C]21.6878969444714[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]2.60346153846154[/C][C]0.120184399739851[/C][C]21.66222524801[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]2.58083333333333[/C][C]0.118090048953482[/C][C]21.8547909515219[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]2.55863636363636[/C][C]0.115904676938279[/C][C]22.0753504623362[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]2.5395[/C][C]0.114718132829993[/C][C]22.1368665733378[/C][/ROW]
[ROW][C]Median[/C][C]2.475[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]3.125[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]2.42977777777778[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]2.42977777777778[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]2.42977777777778[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]2.42977777777778[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]2.42977777777778[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]2.42977777777778[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]2.42977777777778[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]2.76035087719298[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]60[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=17626&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=17626&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 Mean2.833666666666670.11486542523044524.6694482781195
Geometric Mean2.70197517270761
Harmonic Mean2.58290058710914
Quadratic Mean2.96784714341333
Winsorized Mean ( 1 / 20 )2.833666666666670.11486542523044524.6694482781195
Winsorized Mean ( 2 / 20 )2.831333333333330.11438844185880524.7519180025915
Winsorized Mean ( 3 / 20 )2.822333333333330.11269136058069925.0448066186248
Winsorized Mean ( 4 / 20 )2.822333333333330.11269136058069925.0448066186248
Winsorized Mean ( 5 / 20 )2.822333333333330.11269136058069925.0448066186248
Winsorized Mean ( 6 / 20 )2.822333333333330.11269136058069925.0448066186248
Winsorized Mean ( 7 / 20 )2.822333333333330.11269136058069925.0448066186248
Winsorized Mean ( 8 / 20 )2.822333333333330.11269136058069925.0448066186248
Winsorized Mean ( 9 / 20 )2.822333333333330.11269136058069925.0448066186248
Winsorized Mean ( 10 / 20 )2.822333333333330.11269136058069925.0448066186248
Winsorized Mean ( 11 / 20 )2.822333333333330.11269136058069925.0448066186248
Winsorized Mean ( 12 / 20 )2.822333333333330.11269136058069925.0448066186248
Winsorized Mean ( 13 / 20 )2.822333333333330.11269136058069925.0448066186248
Winsorized Mean ( 14 / 20 )2.822333333333330.11269136058069925.0448066186248
Winsorized Mean ( 15 / 20 )2.797333333333330.10831943413661325.8248517971883
Winsorized Mean ( 16 / 20 )2.757333333333330.10155065159773627.1522958243118
Winsorized Mean ( 17 / 20 )2.757333333333330.10155065159773627.1522958243118
Winsorized Mean ( 18 / 20 )2.727333333333330.096636621085590128.2225651383005
Winsorized Mean ( 19 / 20 )2.679833333333330.089081468352101630.0829497190266
Winsorized Mean ( 20 / 20 )2.679833333333330.089081468352101630.0829497190266
Trimmed Mean ( 1 / 20 )2.823620689655170.11536540707324324.4754537888687
Trimmed Mean ( 2 / 20 )2.812857142857140.11577062921994324.2968113917152
Trimmed Mean ( 3 / 20 )2.802592592592590.11635213221605324.0871614401401
Trimmed Mean ( 4 / 20 )2.7950.11758040155384123.7709683166896
Trimmed Mean ( 5 / 20 )2.78680.11879821341335123.4582652375714
Trimmed Mean ( 6 / 20 )2.777916666666670.11999222726501523.1508050978283
Trimmed Mean ( 7 / 20 )2.768260869565220.12114442386908522.8509144800320
Trimmed Mean ( 8 / 20 )2.757727272727270.12223035804036922.5617213018100
Trimmed Mean ( 9 / 20 )2.746190476190480.12321664083437722.2874967016980
Trimmed Mean ( 10 / 20 )2.73350.12405723968373922.0341836314313
Trimmed Mean ( 11 / 20 )2.719473684210530.12468791617201821.8102424653466
Trimmed Mean ( 12 / 20 )2.703888888888890.12501763544026821.6280597482646
Trimmed Mean ( 13 / 20 )2.686470588235290.12491486038319421.5064130880359
Trimmed Mean ( 14 / 20 )2.6668750.12418479133611121.4750531953787
Trimmed Mean ( 15 / 20 )2.644666666666670.12252959608073821.5839009615605
Trimmed Mean ( 16 / 20 )2.622857142857140.12093644439442721.6878969444714
Trimmed Mean ( 17 / 20 )2.603461538461540.12018439973985121.66222524801
Trimmed Mean ( 18 / 20 )2.580833333333330.11809004895348221.8547909515219
Trimmed Mean ( 19 / 20 )2.558636363636360.11590467693827922.0753504623362
Trimmed Mean ( 20 / 20 )2.53950.11471813282999322.1368665733378
Median2.475
Midrange3.125
Midmean - Weighted Average at Xnp2.42977777777778
Midmean - Weighted Average at X(n+1)p2.42977777777778
Midmean - Empirical Distribution Function2.42977777777778
Midmean - Empirical Distribution Function - Averaging2.42977777777778
Midmean - Empirical Distribution Function - Interpolation2.42977777777778
Midmean - Closest Observation2.42977777777778
Midmean - True Basic - Statistics Graphics Toolkit2.42977777777778
Midmean - MS Excel (old versions)2.76035087719298
Number of observations60



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')