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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 computationMon, 19 Oct 2009 01:09:15 -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/2009/Oct/19/t12559362296nqpubtsek1ar61.htm/, Retrieved Mon, 29 Apr 2024 20:00:33 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=47542, Retrieved Mon, 29 Apr 2024 20:00:33 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsVraag 2
Estimated Impact171
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Workshop 3] [2009-10-19 07:09:15] [ee8fc1691ecec7724e0ca78f0c288737] [Current]
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Dataseries X:
-26
-23
-15
-15
-13
-12
-25
-30
-29
-35
-31
-48
-29
-25
-20
-17
-20
-26
-25
-26
-23
-20
-29
-21
-12
-23
-30
-21
-20
-25
-21
-20
-23
-27
-51
-39
-42
-61
-43
-45
-39
-31
-32
-42
-51
-54
-28
-20
-29
-26
-17
-2
-12
-10
0
1
3
3
15
10




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'RServer@AstonUniversity' @ vre.aston.ac.uk

\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 & 3 seconds \tabularnewline
R Server & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=47542&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=47542&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=47542&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 time3 seconds
R Server'RServer@AstonUniversity' @ vre.aston.ac.uk







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean-24.11666666666671.9642412986883-12.2778533792012
Geometric MeanNaN
Harmonic Mean0
Quadratic Mean28.4473197331489
Winsorized Mean ( 1 / 20 )-24.08333333333331.90335589249199-12.6530899598613
Winsorized Mean ( 2 / 20 )-24.21666666666671.81224517658005-13.3627982458570
Winsorized Mean ( 3 / 20 )-24.21666666666671.81224517658005-13.3627982458570
Winsorized Mean ( 4 / 20 )-24.151.73039053754619-13.9563869981897
Winsorized Mean ( 5 / 20 )-23.98333333333331.65370525022264-14.5027859892834
Winsorized Mean ( 6 / 20 )-23.98333333333331.56307889464516-15.3436486254764
Winsorized Mean ( 7 / 20 )-24.81.33780324193220-18.5378531182069
Winsorized Mean ( 8 / 20 )-25.06666666666671.28987072156195-19.4334720896002
Winsorized Mean ( 9 / 20 )-24.61666666666671.19369616994416-20.6222213713044
Winsorized Mean ( 10 / 20 )-24.61666666666671.19369616994416-20.6222213713044
Winsorized Mean ( 11 / 20 )-24.06666666666671.01815904173904-23.6374335246882
Winsorized Mean ( 12 / 20 )-23.86666666666670.841194559095786-28.3723502590427
Winsorized Mean ( 13 / 20 )-23.650.806689895542656-29.3173375923976
Winsorized Mean ( 14 / 20 )-24.11666666666670.72528648797712-33.2512283993184
Winsorized Mean ( 15 / 20 )-23.86666666666670.686210698262965-34.7803768246129
Winsorized Mean ( 16 / 20 )-24.66666666666670.560803835239726-43.9844828381433
Winsorized Mean ( 17 / 20 )-24.38333333333330.516447921618317-47.2135375371961
Winsorized Mean ( 18 / 20 )-24.38333333333330.516447921618317-47.2135375371961
Winsorized Mean ( 19 / 20 )-24.38333333333330.516447921618317-47.2135375371961
Winsorized Mean ( 20 / 20 )-24.38333333333330.516447921618317-47.2135375371961
Trimmed Mean ( 1 / 20 )-24.15517241379311.80471281340312-13.3844965439371
Trimmed Mean ( 2 / 20 )-24.23214285714291.68164094864166-14.4098196923168
Trimmed Mean ( 3 / 20 )-24.24074074074071.59180623493481-15.2284494235151
Trimmed Mean ( 4 / 20 )-24.251.47806357972225-16.4066014024626
Trimmed Mean ( 5 / 20 )-24.281.36905747408461-17.734828858251
Trimmed Mean ( 6 / 20 )-24.35416666666671.25847819254491-19.3520768265498
Trimmed Mean ( 7 / 20 )-24.43478260869571.14741977876811-21.2954169527471
Trimmed Mean ( 8 / 20 )-24.36363636363641.08033102606975-22.5520102410383
Trimmed Mean ( 9 / 20 )-24.23809523809521.00625772809061-24.087363069586
Trimmed Mean ( 10 / 20 )-24.1750.939099063614724-25.7427580717066
Trimmed Mean ( 11 / 20 )-24.10526315789470.846538826827244-28.4750827652398
Trimmed Mean ( 12 / 20 )-24.11111111111110.779476602760109-30.9324372607647
Trimmed Mean ( 13 / 20 )-24.14705882352940.743519060601699-32.4767179525811
Trimmed Mean ( 14 / 20 )-24.218750.702435818156387-34.4782389707355
Trimmed Mean ( 15 / 20 )-24.23333333333330.670706152718923-36.1310735485216
Trimmed Mean ( 16 / 20 )-24.28571428571430.63591192457175-38.1903740868978
Trimmed Mean ( 17 / 20 )-24.23076923076920.625872172517169-38.715204629272
Trimmed Mean ( 18 / 20 )-24.20833333333330.622579855382828-38.8839007944571
Trimmed Mean ( 19 / 20 )-24.18181818181820.61241260048354-39.486153881754
Trimmed Mean ( 20 / 20 )-24.150.590606289734273-40.8901842390903
Median-25
Midrange-23
Midmean - Weighted Average at Xnp-24.4242424242424
Midmean - Weighted Average at X(n+1)p-24
Midmean - Empirical Distribution Function-24.4242424242424
Midmean - Empirical Distribution Function - Averaging-24
Midmean - Empirical Distribution Function - Interpolation-24
Midmean - Closest Observation-24.4242424242424
Midmean - True Basic - Statistics Graphics Toolkit-24
Midmean - MS Excel (old versions)-24.4242424242424
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & -24.1166666666667 & 1.9642412986883 & -12.2778533792012 \tabularnewline
Geometric Mean & NaN &  &  \tabularnewline
Harmonic Mean & 0 &  &  \tabularnewline
Quadratic Mean & 28.4473197331489 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & -24.0833333333333 & 1.90335589249199 & -12.6530899598613 \tabularnewline
Winsorized Mean ( 2 / 20 ) & -24.2166666666667 & 1.81224517658005 & -13.3627982458570 \tabularnewline
Winsorized Mean ( 3 / 20 ) & -24.2166666666667 & 1.81224517658005 & -13.3627982458570 \tabularnewline
Winsorized Mean ( 4 / 20 ) & -24.15 & 1.73039053754619 & -13.9563869981897 \tabularnewline
Winsorized Mean ( 5 / 20 ) & -23.9833333333333 & 1.65370525022264 & -14.5027859892834 \tabularnewline
Winsorized Mean ( 6 / 20 ) & -23.9833333333333 & 1.56307889464516 & -15.3436486254764 \tabularnewline
Winsorized Mean ( 7 / 20 ) & -24.8 & 1.33780324193220 & -18.5378531182069 \tabularnewline
Winsorized Mean ( 8 / 20 ) & -25.0666666666667 & 1.28987072156195 & -19.4334720896002 \tabularnewline
Winsorized Mean ( 9 / 20 ) & -24.6166666666667 & 1.19369616994416 & -20.6222213713044 \tabularnewline
Winsorized Mean ( 10 / 20 ) & -24.6166666666667 & 1.19369616994416 & -20.6222213713044 \tabularnewline
Winsorized Mean ( 11 / 20 ) & -24.0666666666667 & 1.01815904173904 & -23.6374335246882 \tabularnewline
Winsorized Mean ( 12 / 20 ) & -23.8666666666667 & 0.841194559095786 & -28.3723502590427 \tabularnewline
Winsorized Mean ( 13 / 20 ) & -23.65 & 0.806689895542656 & -29.3173375923976 \tabularnewline
Winsorized Mean ( 14 / 20 ) & -24.1166666666667 & 0.72528648797712 & -33.2512283993184 \tabularnewline
Winsorized Mean ( 15 / 20 ) & -23.8666666666667 & 0.686210698262965 & -34.7803768246129 \tabularnewline
Winsorized Mean ( 16 / 20 ) & -24.6666666666667 & 0.560803835239726 & -43.9844828381433 \tabularnewline
Winsorized Mean ( 17 / 20 ) & -24.3833333333333 & 0.516447921618317 & -47.2135375371961 \tabularnewline
Winsorized Mean ( 18 / 20 ) & -24.3833333333333 & 0.516447921618317 & -47.2135375371961 \tabularnewline
Winsorized Mean ( 19 / 20 ) & -24.3833333333333 & 0.516447921618317 & -47.2135375371961 \tabularnewline
Winsorized Mean ( 20 / 20 ) & -24.3833333333333 & 0.516447921618317 & -47.2135375371961 \tabularnewline
Trimmed Mean ( 1 / 20 ) & -24.1551724137931 & 1.80471281340312 & -13.3844965439371 \tabularnewline
Trimmed Mean ( 2 / 20 ) & -24.2321428571429 & 1.68164094864166 & -14.4098196923168 \tabularnewline
Trimmed Mean ( 3 / 20 ) & -24.2407407407407 & 1.59180623493481 & -15.2284494235151 \tabularnewline
Trimmed Mean ( 4 / 20 ) & -24.25 & 1.47806357972225 & -16.4066014024626 \tabularnewline
Trimmed Mean ( 5 / 20 ) & -24.28 & 1.36905747408461 & -17.734828858251 \tabularnewline
Trimmed Mean ( 6 / 20 ) & -24.3541666666667 & 1.25847819254491 & -19.3520768265498 \tabularnewline
Trimmed Mean ( 7 / 20 ) & -24.4347826086957 & 1.14741977876811 & -21.2954169527471 \tabularnewline
Trimmed Mean ( 8 / 20 ) & -24.3636363636364 & 1.08033102606975 & -22.5520102410383 \tabularnewline
Trimmed Mean ( 9 / 20 ) & -24.2380952380952 & 1.00625772809061 & -24.087363069586 \tabularnewline
Trimmed Mean ( 10 / 20 ) & -24.175 & 0.939099063614724 & -25.7427580717066 \tabularnewline
Trimmed Mean ( 11 / 20 ) & -24.1052631578947 & 0.846538826827244 & -28.4750827652398 \tabularnewline
Trimmed Mean ( 12 / 20 ) & -24.1111111111111 & 0.779476602760109 & -30.9324372607647 \tabularnewline
Trimmed Mean ( 13 / 20 ) & -24.1470588235294 & 0.743519060601699 & -32.4767179525811 \tabularnewline
Trimmed Mean ( 14 / 20 ) & -24.21875 & 0.702435818156387 & -34.4782389707355 \tabularnewline
Trimmed Mean ( 15 / 20 ) & -24.2333333333333 & 0.670706152718923 & -36.1310735485216 \tabularnewline
Trimmed Mean ( 16 / 20 ) & -24.2857142857143 & 0.63591192457175 & -38.1903740868978 \tabularnewline
Trimmed Mean ( 17 / 20 ) & -24.2307692307692 & 0.625872172517169 & -38.715204629272 \tabularnewline
Trimmed Mean ( 18 / 20 ) & -24.2083333333333 & 0.622579855382828 & -38.8839007944571 \tabularnewline
Trimmed Mean ( 19 / 20 ) & -24.1818181818182 & 0.61241260048354 & -39.486153881754 \tabularnewline
Trimmed Mean ( 20 / 20 ) & -24.15 & 0.590606289734273 & -40.8901842390903 \tabularnewline
Median & -25 &  &  \tabularnewline
Midrange & -23 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & -24.4242424242424 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & -24 &  &  \tabularnewline
Midmean - Empirical Distribution Function & -24.4242424242424 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & -24 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & -24 &  &  \tabularnewline
Midmean - Closest Observation & -24.4242424242424 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & -24 &  &  \tabularnewline
Midmean - MS Excel (old versions) & -24.4242424242424 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=47542&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]-24.1166666666667[/C][C]1.9642412986883[/C][C]-12.2778533792012[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]NaN[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]0[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]28.4473197331489[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]-24.0833333333333[/C][C]1.90335589249199[/C][C]-12.6530899598613[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]-24.2166666666667[/C][C]1.81224517658005[/C][C]-13.3627982458570[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]-24.2166666666667[/C][C]1.81224517658005[/C][C]-13.3627982458570[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]-24.15[/C][C]1.73039053754619[/C][C]-13.9563869981897[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]-23.9833333333333[/C][C]1.65370525022264[/C][C]-14.5027859892834[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]-23.9833333333333[/C][C]1.56307889464516[/C][C]-15.3436486254764[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]-24.8[/C][C]1.33780324193220[/C][C]-18.5378531182069[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]-25.0666666666667[/C][C]1.28987072156195[/C][C]-19.4334720896002[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]-24.6166666666667[/C][C]1.19369616994416[/C][C]-20.6222213713044[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]-24.6166666666667[/C][C]1.19369616994416[/C][C]-20.6222213713044[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]-24.0666666666667[/C][C]1.01815904173904[/C][C]-23.6374335246882[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]-23.8666666666667[/C][C]0.841194559095786[/C][C]-28.3723502590427[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]-23.65[/C][C]0.806689895542656[/C][C]-29.3173375923976[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]-24.1166666666667[/C][C]0.72528648797712[/C][C]-33.2512283993184[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]-23.8666666666667[/C][C]0.686210698262965[/C][C]-34.7803768246129[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]-24.6666666666667[/C][C]0.560803835239726[/C][C]-43.9844828381433[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]-24.3833333333333[/C][C]0.516447921618317[/C][C]-47.2135375371961[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]-24.3833333333333[/C][C]0.516447921618317[/C][C]-47.2135375371961[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]-24.3833333333333[/C][C]0.516447921618317[/C][C]-47.2135375371961[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]-24.3833333333333[/C][C]0.516447921618317[/C][C]-47.2135375371961[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]-24.1551724137931[/C][C]1.80471281340312[/C][C]-13.3844965439371[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]-24.2321428571429[/C][C]1.68164094864166[/C][C]-14.4098196923168[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]-24.2407407407407[/C][C]1.59180623493481[/C][C]-15.2284494235151[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]-24.25[/C][C]1.47806357972225[/C][C]-16.4066014024626[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]-24.28[/C][C]1.36905747408461[/C][C]-17.734828858251[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]-24.3541666666667[/C][C]1.25847819254491[/C][C]-19.3520768265498[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]-24.4347826086957[/C][C]1.14741977876811[/C][C]-21.2954169527471[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]-24.3636363636364[/C][C]1.08033102606975[/C][C]-22.5520102410383[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]-24.2380952380952[/C][C]1.00625772809061[/C][C]-24.087363069586[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]-24.175[/C][C]0.939099063614724[/C][C]-25.7427580717066[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]-24.1052631578947[/C][C]0.846538826827244[/C][C]-28.4750827652398[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]-24.1111111111111[/C][C]0.779476602760109[/C][C]-30.9324372607647[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]-24.1470588235294[/C][C]0.743519060601699[/C][C]-32.4767179525811[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]-24.21875[/C][C]0.702435818156387[/C][C]-34.4782389707355[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]-24.2333333333333[/C][C]0.670706152718923[/C][C]-36.1310735485216[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]-24.2857142857143[/C][C]0.63591192457175[/C][C]-38.1903740868978[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]-24.2307692307692[/C][C]0.625872172517169[/C][C]-38.715204629272[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]-24.2083333333333[/C][C]0.622579855382828[/C][C]-38.8839007944571[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]-24.1818181818182[/C][C]0.61241260048354[/C][C]-39.486153881754[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]-24.15[/C][C]0.590606289734273[/C][C]-40.8901842390903[/C][/ROW]
[ROW][C]Median[/C][C]-25[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]-23[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]-24.4242424242424[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]-24[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]-24.4242424242424[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]-24[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]-24[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]-24.4242424242424[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]-24[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]-24.4242424242424[/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=47542&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=47542&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 Mean-24.11666666666671.9642412986883-12.2778533792012
Geometric MeanNaN
Harmonic Mean0
Quadratic Mean28.4473197331489
Winsorized Mean ( 1 / 20 )-24.08333333333331.90335589249199-12.6530899598613
Winsorized Mean ( 2 / 20 )-24.21666666666671.81224517658005-13.3627982458570
Winsorized Mean ( 3 / 20 )-24.21666666666671.81224517658005-13.3627982458570
Winsorized Mean ( 4 / 20 )-24.151.73039053754619-13.9563869981897
Winsorized Mean ( 5 / 20 )-23.98333333333331.65370525022264-14.5027859892834
Winsorized Mean ( 6 / 20 )-23.98333333333331.56307889464516-15.3436486254764
Winsorized Mean ( 7 / 20 )-24.81.33780324193220-18.5378531182069
Winsorized Mean ( 8 / 20 )-25.06666666666671.28987072156195-19.4334720896002
Winsorized Mean ( 9 / 20 )-24.61666666666671.19369616994416-20.6222213713044
Winsorized Mean ( 10 / 20 )-24.61666666666671.19369616994416-20.6222213713044
Winsorized Mean ( 11 / 20 )-24.06666666666671.01815904173904-23.6374335246882
Winsorized Mean ( 12 / 20 )-23.86666666666670.841194559095786-28.3723502590427
Winsorized Mean ( 13 / 20 )-23.650.806689895542656-29.3173375923976
Winsorized Mean ( 14 / 20 )-24.11666666666670.72528648797712-33.2512283993184
Winsorized Mean ( 15 / 20 )-23.86666666666670.686210698262965-34.7803768246129
Winsorized Mean ( 16 / 20 )-24.66666666666670.560803835239726-43.9844828381433
Winsorized Mean ( 17 / 20 )-24.38333333333330.516447921618317-47.2135375371961
Winsorized Mean ( 18 / 20 )-24.38333333333330.516447921618317-47.2135375371961
Winsorized Mean ( 19 / 20 )-24.38333333333330.516447921618317-47.2135375371961
Winsorized Mean ( 20 / 20 )-24.38333333333330.516447921618317-47.2135375371961
Trimmed Mean ( 1 / 20 )-24.15517241379311.80471281340312-13.3844965439371
Trimmed Mean ( 2 / 20 )-24.23214285714291.68164094864166-14.4098196923168
Trimmed Mean ( 3 / 20 )-24.24074074074071.59180623493481-15.2284494235151
Trimmed Mean ( 4 / 20 )-24.251.47806357972225-16.4066014024626
Trimmed Mean ( 5 / 20 )-24.281.36905747408461-17.734828858251
Trimmed Mean ( 6 / 20 )-24.35416666666671.25847819254491-19.3520768265498
Trimmed Mean ( 7 / 20 )-24.43478260869571.14741977876811-21.2954169527471
Trimmed Mean ( 8 / 20 )-24.36363636363641.08033102606975-22.5520102410383
Trimmed Mean ( 9 / 20 )-24.23809523809521.00625772809061-24.087363069586
Trimmed Mean ( 10 / 20 )-24.1750.939099063614724-25.7427580717066
Trimmed Mean ( 11 / 20 )-24.10526315789470.846538826827244-28.4750827652398
Trimmed Mean ( 12 / 20 )-24.11111111111110.779476602760109-30.9324372607647
Trimmed Mean ( 13 / 20 )-24.14705882352940.743519060601699-32.4767179525811
Trimmed Mean ( 14 / 20 )-24.218750.702435818156387-34.4782389707355
Trimmed Mean ( 15 / 20 )-24.23333333333330.670706152718923-36.1310735485216
Trimmed Mean ( 16 / 20 )-24.28571428571430.63591192457175-38.1903740868978
Trimmed Mean ( 17 / 20 )-24.23076923076920.625872172517169-38.715204629272
Trimmed Mean ( 18 / 20 )-24.20833333333330.622579855382828-38.8839007944571
Trimmed Mean ( 19 / 20 )-24.18181818181820.61241260048354-39.486153881754
Trimmed Mean ( 20 / 20 )-24.150.590606289734273-40.8901842390903
Median-25
Midrange-23
Midmean - Weighted Average at Xnp-24.4242424242424
Midmean - Weighted Average at X(n+1)p-24
Midmean - Empirical Distribution Function-24.4242424242424
Midmean - Empirical Distribution Function - Averaging-24
Midmean - Empirical Distribution Function - Interpolation-24
Midmean - Closest Observation-24.4242424242424
Midmean - True Basic - Statistics Graphics Toolkit-24
Midmean - MS Excel (old versions)-24.4242424242424
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')