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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, 20 Oct 2008 08:20:21 -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/t1224512461psulm4aocufh4eg.htm/, Retrieved Sun, 19 May 2024 14:57:21 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=17347, Retrieved Sun, 19 May 2024 14:57:21 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact135
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
F     [Univariate Data Series] [werkloosheid mannen] [2008-10-13 15:39:35] [e43247bc0ab243a5af99ac7f55ba0b41]
F   PD  [Univariate Data Series] [werkloosheid onde...] [2008-10-13 15:49:45] [e43247bc0ab243a5af99ac7f55ba0b41]
- RMPD      [Central Tendency] [central tendancy ...] [2008-10-20 14:20:21] [f24298b2e4c2a19d76cf4460ec5d2246] [Current]
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Dataseries X:
21.1
21.0
20.4
19.5
18.6
18.8
23.7
24.8
25.0
23.6
22.3
21.8
20.8
19.7
18.3
17.4
17.0
18.1
23.9
25.6
25.3
23.6
21.9
21.4
20.6
20.5
20.2
20.6
19.7
19.3
22.8
23.5
23.8
22.6
22.0
21.7
20.7
20.2
19.1
19.5
18.7
18.6
22.2
23.2
23.5
21.3
20.0
18.7
18.9
18.3
18.4
19.9
19.2
18.5
20.9
20.5
19.4
18.1
17.0
17.0
17.3
16.7
15.5
15.3
13.7
14.1
17.3
18.1




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=17347&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=17347&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=17347&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 Mean20.15735294117650.32049070815603662.895280356654
Geometric Mean19.9823454726867
Harmonic Mean19.8022111926714
Quadratic Mean20.3273396019774
Winsorized Mean ( 1 / 22 )20.15882352941180.31767672933973863.4570356201728
Winsorized Mean ( 2 / 22 )20.18529411764710.30633682554386965.8924831574205
Winsorized Mean ( 3 / 22 )20.18529411764710.30222517396219866.7889238113957
Winsorized Mean ( 4 / 22 )20.20294117647060.27594494517315773.2136664572461
Winsorized Mean ( 5 / 22 )20.21764705882350.27043311582304574.7602489336134
Winsorized Mean ( 6 / 22 )20.20882352941180.26870527615792875.2081381443895
Winsorized Mean ( 7 / 22 )20.19852941176470.26672741646289675.7272337415471
Winsorized Mean ( 8 / 22 )20.23382352941180.26060147129256477.642783170231
Winsorized Mean ( 9 / 22 )20.22058823529410.25807042841201678.3529843373277
Winsorized Mean ( 10 / 22 )20.23529411764710.25561099918732379.1644106943057
Winsorized Mean ( 11 / 22 )20.30.22882683585568888.7133710698268
Winsorized Mean ( 12 / 22 )20.22941176470590.21586604900481193.7127994789725
Winsorized Mean ( 13 / 22 )20.19117647058820.20918059223391096.5250946799597
Winsorized Mean ( 14 / 22 )20.17058823529410.192712476075525104.666748339579
Winsorized Mean ( 15 / 22 )20.14852941176470.189107378844289106.545442779126
Winsorized Mean ( 16 / 22 )20.1250.178181909296938112.946370815131
Winsorized Mean ( 17 / 22 )20.1250.170695203512562117.900208007420
Winsorized Mean ( 18 / 22 )20.1250.162878181532442123.558599504572
Winsorized Mean ( 19 / 22 )20.09705882352940.158626271676548126.694390602011
Winsorized Mean ( 20 / 22 )20.03823529411760.141468365930718141.644636681045
Winsorized Mean ( 21 / 22 )20.00735294117650.137075887168949145.95822324693
Winsorized Mean ( 22 / 22 )19.9750.123516215483108161.719656984890
Trimmed Mean ( 1 / 22 )20.17272727272730.30406373898222166.3437453615829
Trimmed Mean ( 2 / 22 )20.18750.28757762927102570.1984366835937
Trimmed Mean ( 3 / 22 )20.18870967741940.27518663287352373.3637003607592
Trimmed Mean ( 4 / 22 )20.190.26208313685063677.0366237317533
Trimmed Mean ( 5 / 22 )20.18620689655170.25632292420942378.7530298306796
Trimmed Mean ( 6 / 22 )20.17857142857140.25096843964818280.4028245816827
Trimmed Mean ( 7 / 22 )20.17222222222220.24478368874253182.408359502417
Trimmed Mean ( 8 / 22 )20.16730769230770.23756750495512784.8908511124742
Trimmed Mean ( 9 / 22 )20.1560.23005163572998387.6151127378097
Trimmed Mean ( 10 / 22 )20.14583333333330.22113421226602591.1022908978817
Trimmed Mean ( 11 / 22 )20.13260869565220.21026907876871195.7468821071755
Trimmed Mean ( 12 / 22 )20.10909090909090.20298559561623299.0665906516319
Trimmed Mean ( 13 / 22 )20.09285714285710.196762202148833102.117464245794
Trimmed Mean ( 14 / 22 )20.080.190148390096814105.601735517068
Trimmed Mean ( 15 / 22 )20.06842105263160.185349052246500108.273664253444
Trimmed Mean ( 16 / 22 )20.05833333333330.179566276396899111.704345246866
Trimmed Mean ( 17 / 22 )20.050.174346245129429115.001042810618
Trimmed Mean ( 18 / 22 )20.0406250.168834917403591118.699527966090
Trimmed Mean ( 19 / 22 )20.030.162957578571213122.915424833996
Trimmed Mean ( 20 / 22 )20.02142857142860.155444161605295128.801418880351
Trimmed Mean ( 21 / 22 )20.01923076923080.149976329493304133.482602467109
Trimmed Mean ( 22 / 22 )20.02083333333330.142693952253282140.306109804825
Median20.1
Midrange19.65
Midmean - Weighted Average at Xnp20.0028571428571
Midmean - Weighted Average at X(n+1)p20.05
Midmean - Empirical Distribution Function20.0028571428571
Midmean - Empirical Distribution Function - Averaging20.05
Midmean - Empirical Distribution Function - Interpolation20.05
Midmean - Closest Observation20.0028571428571
Midmean - True Basic - Statistics Graphics Toolkit20.05
Midmean - MS Excel (old versions)20.0583333333333
Number of observations68

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 20.1573529411765 & 0.320490708156036 & 62.895280356654 \tabularnewline
Geometric Mean & 19.9823454726867 &  &  \tabularnewline
Harmonic Mean & 19.8022111926714 &  &  \tabularnewline
Quadratic Mean & 20.3273396019774 &  &  \tabularnewline
Winsorized Mean ( 1 / 22 ) & 20.1588235294118 & 0.317676729339738 & 63.4570356201728 \tabularnewline
Winsorized Mean ( 2 / 22 ) & 20.1852941176471 & 0.306336825543869 & 65.8924831574205 \tabularnewline
Winsorized Mean ( 3 / 22 ) & 20.1852941176471 & 0.302225173962198 & 66.7889238113957 \tabularnewline
Winsorized Mean ( 4 / 22 ) & 20.2029411764706 & 0.275944945173157 & 73.2136664572461 \tabularnewline
Winsorized Mean ( 5 / 22 ) & 20.2176470588235 & 0.270433115823045 & 74.7602489336134 \tabularnewline
Winsorized Mean ( 6 / 22 ) & 20.2088235294118 & 0.268705276157928 & 75.2081381443895 \tabularnewline
Winsorized Mean ( 7 / 22 ) & 20.1985294117647 & 0.266727416462896 & 75.7272337415471 \tabularnewline
Winsorized Mean ( 8 / 22 ) & 20.2338235294118 & 0.260601471292564 & 77.642783170231 \tabularnewline
Winsorized Mean ( 9 / 22 ) & 20.2205882352941 & 0.258070428412016 & 78.3529843373277 \tabularnewline
Winsorized Mean ( 10 / 22 ) & 20.2352941176471 & 0.255610999187323 & 79.1644106943057 \tabularnewline
Winsorized Mean ( 11 / 22 ) & 20.3 & 0.228826835855688 & 88.7133710698268 \tabularnewline
Winsorized Mean ( 12 / 22 ) & 20.2294117647059 & 0.215866049004811 & 93.7127994789725 \tabularnewline
Winsorized Mean ( 13 / 22 ) & 20.1911764705882 & 0.209180592233910 & 96.5250946799597 \tabularnewline
Winsorized Mean ( 14 / 22 ) & 20.1705882352941 & 0.192712476075525 & 104.666748339579 \tabularnewline
Winsorized Mean ( 15 / 22 ) & 20.1485294117647 & 0.189107378844289 & 106.545442779126 \tabularnewline
Winsorized Mean ( 16 / 22 ) & 20.125 & 0.178181909296938 & 112.946370815131 \tabularnewline
Winsorized Mean ( 17 / 22 ) & 20.125 & 0.170695203512562 & 117.900208007420 \tabularnewline
Winsorized Mean ( 18 / 22 ) & 20.125 & 0.162878181532442 & 123.558599504572 \tabularnewline
Winsorized Mean ( 19 / 22 ) & 20.0970588235294 & 0.158626271676548 & 126.694390602011 \tabularnewline
Winsorized Mean ( 20 / 22 ) & 20.0382352941176 & 0.141468365930718 & 141.644636681045 \tabularnewline
Winsorized Mean ( 21 / 22 ) & 20.0073529411765 & 0.137075887168949 & 145.95822324693 \tabularnewline
Winsorized Mean ( 22 / 22 ) & 19.975 & 0.123516215483108 & 161.719656984890 \tabularnewline
Trimmed Mean ( 1 / 22 ) & 20.1727272727273 & 0.304063738982221 & 66.3437453615829 \tabularnewline
Trimmed Mean ( 2 / 22 ) & 20.1875 & 0.287577629271025 & 70.1984366835937 \tabularnewline
Trimmed Mean ( 3 / 22 ) & 20.1887096774194 & 0.275186632873523 & 73.3637003607592 \tabularnewline
Trimmed Mean ( 4 / 22 ) & 20.19 & 0.262083136850636 & 77.0366237317533 \tabularnewline
Trimmed Mean ( 5 / 22 ) & 20.1862068965517 & 0.256322924209423 & 78.7530298306796 \tabularnewline
Trimmed Mean ( 6 / 22 ) & 20.1785714285714 & 0.250968439648182 & 80.4028245816827 \tabularnewline
Trimmed Mean ( 7 / 22 ) & 20.1722222222222 & 0.244783688742531 & 82.408359502417 \tabularnewline
Trimmed Mean ( 8 / 22 ) & 20.1673076923077 & 0.237567504955127 & 84.8908511124742 \tabularnewline
Trimmed Mean ( 9 / 22 ) & 20.156 & 0.230051635729983 & 87.6151127378097 \tabularnewline
Trimmed Mean ( 10 / 22 ) & 20.1458333333333 & 0.221134212266025 & 91.1022908978817 \tabularnewline
Trimmed Mean ( 11 / 22 ) & 20.1326086956522 & 0.210269078768711 & 95.7468821071755 \tabularnewline
Trimmed Mean ( 12 / 22 ) & 20.1090909090909 & 0.202985595616232 & 99.0665906516319 \tabularnewline
Trimmed Mean ( 13 / 22 ) & 20.0928571428571 & 0.196762202148833 & 102.117464245794 \tabularnewline
Trimmed Mean ( 14 / 22 ) & 20.08 & 0.190148390096814 & 105.601735517068 \tabularnewline
Trimmed Mean ( 15 / 22 ) & 20.0684210526316 & 0.185349052246500 & 108.273664253444 \tabularnewline
Trimmed Mean ( 16 / 22 ) & 20.0583333333333 & 0.179566276396899 & 111.704345246866 \tabularnewline
Trimmed Mean ( 17 / 22 ) & 20.05 & 0.174346245129429 & 115.001042810618 \tabularnewline
Trimmed Mean ( 18 / 22 ) & 20.040625 & 0.168834917403591 & 118.699527966090 \tabularnewline
Trimmed Mean ( 19 / 22 ) & 20.03 & 0.162957578571213 & 122.915424833996 \tabularnewline
Trimmed Mean ( 20 / 22 ) & 20.0214285714286 & 0.155444161605295 & 128.801418880351 \tabularnewline
Trimmed Mean ( 21 / 22 ) & 20.0192307692308 & 0.149976329493304 & 133.482602467109 \tabularnewline
Trimmed Mean ( 22 / 22 ) & 20.0208333333333 & 0.142693952253282 & 140.306109804825 \tabularnewline
Median & 20.1 &  &  \tabularnewline
Midrange & 19.65 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 20.0028571428571 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 20.05 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 20.0028571428571 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 20.05 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 20.05 &  &  \tabularnewline
Midmean - Closest Observation & 20.0028571428571 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 20.05 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 20.0583333333333 &  &  \tabularnewline
Number of observations & 68 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=17347&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]20.1573529411765[/C][C]0.320490708156036[/C][C]62.895280356654[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]19.9823454726867[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]19.8022111926714[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]20.3273396019774[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 22 )[/C][C]20.1588235294118[/C][C]0.317676729339738[/C][C]63.4570356201728[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 22 )[/C][C]20.1852941176471[/C][C]0.306336825543869[/C][C]65.8924831574205[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 22 )[/C][C]20.1852941176471[/C][C]0.302225173962198[/C][C]66.7889238113957[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 22 )[/C][C]20.2029411764706[/C][C]0.275944945173157[/C][C]73.2136664572461[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 22 )[/C][C]20.2176470588235[/C][C]0.270433115823045[/C][C]74.7602489336134[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 22 )[/C][C]20.2088235294118[/C][C]0.268705276157928[/C][C]75.2081381443895[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 22 )[/C][C]20.1985294117647[/C][C]0.266727416462896[/C][C]75.7272337415471[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 22 )[/C][C]20.2338235294118[/C][C]0.260601471292564[/C][C]77.642783170231[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 22 )[/C][C]20.2205882352941[/C][C]0.258070428412016[/C][C]78.3529843373277[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 22 )[/C][C]20.2352941176471[/C][C]0.255610999187323[/C][C]79.1644106943057[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 22 )[/C][C]20.3[/C][C]0.228826835855688[/C][C]88.7133710698268[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 22 )[/C][C]20.2294117647059[/C][C]0.215866049004811[/C][C]93.7127994789725[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 22 )[/C][C]20.1911764705882[/C][C]0.209180592233910[/C][C]96.5250946799597[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 22 )[/C][C]20.1705882352941[/C][C]0.192712476075525[/C][C]104.666748339579[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 22 )[/C][C]20.1485294117647[/C][C]0.189107378844289[/C][C]106.545442779126[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 22 )[/C][C]20.125[/C][C]0.178181909296938[/C][C]112.946370815131[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 22 )[/C][C]20.125[/C][C]0.170695203512562[/C][C]117.900208007420[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 22 )[/C][C]20.125[/C][C]0.162878181532442[/C][C]123.558599504572[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 22 )[/C][C]20.0970588235294[/C][C]0.158626271676548[/C][C]126.694390602011[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 22 )[/C][C]20.0382352941176[/C][C]0.141468365930718[/C][C]141.644636681045[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 22 )[/C][C]20.0073529411765[/C][C]0.137075887168949[/C][C]145.95822324693[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 22 )[/C][C]19.975[/C][C]0.123516215483108[/C][C]161.719656984890[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 22 )[/C][C]20.1727272727273[/C][C]0.304063738982221[/C][C]66.3437453615829[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 22 )[/C][C]20.1875[/C][C]0.287577629271025[/C][C]70.1984366835937[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 22 )[/C][C]20.1887096774194[/C][C]0.275186632873523[/C][C]73.3637003607592[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 22 )[/C][C]20.19[/C][C]0.262083136850636[/C][C]77.0366237317533[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 22 )[/C][C]20.1862068965517[/C][C]0.256322924209423[/C][C]78.7530298306796[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 22 )[/C][C]20.1785714285714[/C][C]0.250968439648182[/C][C]80.4028245816827[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 22 )[/C][C]20.1722222222222[/C][C]0.244783688742531[/C][C]82.408359502417[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 22 )[/C][C]20.1673076923077[/C][C]0.237567504955127[/C][C]84.8908511124742[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 22 )[/C][C]20.156[/C][C]0.230051635729983[/C][C]87.6151127378097[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 22 )[/C][C]20.1458333333333[/C][C]0.221134212266025[/C][C]91.1022908978817[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 22 )[/C][C]20.1326086956522[/C][C]0.210269078768711[/C][C]95.7468821071755[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 22 )[/C][C]20.1090909090909[/C][C]0.202985595616232[/C][C]99.0665906516319[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 22 )[/C][C]20.0928571428571[/C][C]0.196762202148833[/C][C]102.117464245794[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 22 )[/C][C]20.08[/C][C]0.190148390096814[/C][C]105.601735517068[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 22 )[/C][C]20.0684210526316[/C][C]0.185349052246500[/C][C]108.273664253444[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 22 )[/C][C]20.0583333333333[/C][C]0.179566276396899[/C][C]111.704345246866[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 22 )[/C][C]20.05[/C][C]0.174346245129429[/C][C]115.001042810618[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 22 )[/C][C]20.040625[/C][C]0.168834917403591[/C][C]118.699527966090[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 22 )[/C][C]20.03[/C][C]0.162957578571213[/C][C]122.915424833996[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 22 )[/C][C]20.0214285714286[/C][C]0.155444161605295[/C][C]128.801418880351[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 22 )[/C][C]20.0192307692308[/C][C]0.149976329493304[/C][C]133.482602467109[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 22 )[/C][C]20.0208333333333[/C][C]0.142693952253282[/C][C]140.306109804825[/C][/ROW]
[ROW][C]Median[/C][C]20.1[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]19.65[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]20.0028571428571[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]20.05[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]20.0028571428571[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]20.05[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]20.05[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]20.0028571428571[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]20.05[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]20.0583333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]68[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=17347&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=17347&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 Mean20.15735294117650.32049070815603662.895280356654
Geometric Mean19.9823454726867
Harmonic Mean19.8022111926714
Quadratic Mean20.3273396019774
Winsorized Mean ( 1 / 22 )20.15882352941180.31767672933973863.4570356201728
Winsorized Mean ( 2 / 22 )20.18529411764710.30633682554386965.8924831574205
Winsorized Mean ( 3 / 22 )20.18529411764710.30222517396219866.7889238113957
Winsorized Mean ( 4 / 22 )20.20294117647060.27594494517315773.2136664572461
Winsorized Mean ( 5 / 22 )20.21764705882350.27043311582304574.7602489336134
Winsorized Mean ( 6 / 22 )20.20882352941180.26870527615792875.2081381443895
Winsorized Mean ( 7 / 22 )20.19852941176470.26672741646289675.7272337415471
Winsorized Mean ( 8 / 22 )20.23382352941180.26060147129256477.642783170231
Winsorized Mean ( 9 / 22 )20.22058823529410.25807042841201678.3529843373277
Winsorized Mean ( 10 / 22 )20.23529411764710.25561099918732379.1644106943057
Winsorized Mean ( 11 / 22 )20.30.22882683585568888.7133710698268
Winsorized Mean ( 12 / 22 )20.22941176470590.21586604900481193.7127994789725
Winsorized Mean ( 13 / 22 )20.19117647058820.20918059223391096.5250946799597
Winsorized Mean ( 14 / 22 )20.17058823529410.192712476075525104.666748339579
Winsorized Mean ( 15 / 22 )20.14852941176470.189107378844289106.545442779126
Winsorized Mean ( 16 / 22 )20.1250.178181909296938112.946370815131
Winsorized Mean ( 17 / 22 )20.1250.170695203512562117.900208007420
Winsorized Mean ( 18 / 22 )20.1250.162878181532442123.558599504572
Winsorized Mean ( 19 / 22 )20.09705882352940.158626271676548126.694390602011
Winsorized Mean ( 20 / 22 )20.03823529411760.141468365930718141.644636681045
Winsorized Mean ( 21 / 22 )20.00735294117650.137075887168949145.95822324693
Winsorized Mean ( 22 / 22 )19.9750.123516215483108161.719656984890
Trimmed Mean ( 1 / 22 )20.17272727272730.30406373898222166.3437453615829
Trimmed Mean ( 2 / 22 )20.18750.28757762927102570.1984366835937
Trimmed Mean ( 3 / 22 )20.18870967741940.27518663287352373.3637003607592
Trimmed Mean ( 4 / 22 )20.190.26208313685063677.0366237317533
Trimmed Mean ( 5 / 22 )20.18620689655170.25632292420942378.7530298306796
Trimmed Mean ( 6 / 22 )20.17857142857140.25096843964818280.4028245816827
Trimmed Mean ( 7 / 22 )20.17222222222220.24478368874253182.408359502417
Trimmed Mean ( 8 / 22 )20.16730769230770.23756750495512784.8908511124742
Trimmed Mean ( 9 / 22 )20.1560.23005163572998387.6151127378097
Trimmed Mean ( 10 / 22 )20.14583333333330.22113421226602591.1022908978817
Trimmed Mean ( 11 / 22 )20.13260869565220.21026907876871195.7468821071755
Trimmed Mean ( 12 / 22 )20.10909090909090.20298559561623299.0665906516319
Trimmed Mean ( 13 / 22 )20.09285714285710.196762202148833102.117464245794
Trimmed Mean ( 14 / 22 )20.080.190148390096814105.601735517068
Trimmed Mean ( 15 / 22 )20.06842105263160.185349052246500108.273664253444
Trimmed Mean ( 16 / 22 )20.05833333333330.179566276396899111.704345246866
Trimmed Mean ( 17 / 22 )20.050.174346245129429115.001042810618
Trimmed Mean ( 18 / 22 )20.0406250.168834917403591118.699527966090
Trimmed Mean ( 19 / 22 )20.030.162957578571213122.915424833996
Trimmed Mean ( 20 / 22 )20.02142857142860.155444161605295128.801418880351
Trimmed Mean ( 21 / 22 )20.01923076923080.149976329493304133.482602467109
Trimmed Mean ( 22 / 22 )20.02083333333330.142693952253282140.306109804825
Median20.1
Midrange19.65
Midmean - Weighted Average at Xnp20.0028571428571
Midmean - Weighted Average at X(n+1)p20.05
Midmean - Empirical Distribution Function20.0028571428571
Midmean - Empirical Distribution Function - Averaging20.05
Midmean - Empirical Distribution Function - Interpolation20.05
Midmean - Closest Observation20.0028571428571
Midmean - True Basic - Statistics Graphics Toolkit20.05
Midmean - MS Excel (old versions)20.0583333333333
Number of observations68



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')