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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 08:08:09 -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/t1224511756azrw9caqzej8roa.htm/, Retrieved Sun, 19 May 2024 14:53:52 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=17319, Retrieved Sun, 19 May 2024 14:53:52 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact157
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 vrouwen] [2008-10-13 15:46:25] [e43247bc0ab243a5af99ac7f55ba0b41]
- RMPD      [Central Tendency] [central tendancy ...] [2008-10-20 14:08:09] [f24298b2e4c2a19d76cf4460ec5d2246] [Current]
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Dataseries X:
9.0
9.1
8.7
8.2
7.9
7.9
9.1
9.4
9.5
9.1
9.0
9.3
9.9
9.8
9.4
8.3
8.0
8.5
10.4
11.1
10.9
9.9
9.2
9.2
9.5
9.6
9.5
9.1
8.9
9.0
10.1
10.3
10.2
9.6
9.2
9.3
9.4
9.4
9.2
9.0
9.0
9.0
9.8
10.0
9.9
9.3
9.0
9.0
9.1
9.1
9.1
9.2
8.8
8.3
8.4
8.1
7.8
7.9
7.9
8.0
7.9
7.5
7.2
6.9
6.6
6.7
7.3
7.5




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=17319&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=17319&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=17319&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 Mean8.917647058823530.11473795729031677.7218565627729
Geometric Mean8.86613729998557
Harmonic Mean8.81236695380352
Quadratic Mean8.96696551728818
Winsorized Mean ( 1 / 22 )8.916176470588240.11350065255519578.556169236581
Winsorized Mean ( 2 / 22 )8.907352941176470.10839065723693082.1782353593997
Winsorized Mean ( 3 / 22 )8.916176470588240.10403640997767785.70246197943
Winsorized Mean ( 4 / 22 )8.916176470588240.10147313302403787.867361585023
Winsorized Mean ( 5 / 22 )8.92352941176470.096745043114605292.2375878337643
Winsorized Mean ( 6 / 22 )8.914705882352940.095193179722509493.6485776432676
Winsorized Mean ( 7 / 22 )8.935294117647060.0870137866091518102.688257411237
Winsorized Mean ( 8 / 22 )8.947058823529410.0847832175504436105.528653925008
Winsorized Mean ( 9 / 22 )8.947058823529410.0847832175504436105.528653925008
Winsorized Mean ( 10 / 22 )8.932352941176470.0823929101552848108.411669454833
Winsorized Mean ( 11 / 22 )8.932352941176470.0823929101552848108.411669454833
Winsorized Mean ( 12 / 22 )8.897058823529410.0772090701294317115.233337334779
Winsorized Mean ( 13 / 22 )8.916176470588240.0735888697267669121.162024959667
Winsorized Mean ( 14 / 22 )8.895588235294120.0708481733555641125.558469809095
Winsorized Mean ( 15 / 22 )8.917647058823530.0667488175004704133.600075518352
Winsorized Mean ( 16 / 22 )8.941176470588240.0625137489396261143.027359936825
Winsorized Mean ( 17 / 22 )8.941176470588240.0548857578833243162.905220140994
Winsorized Mean ( 18 / 22 )8.941176470588240.0548857578833243162.905220140994
Winsorized Mean ( 19 / 22 )8.969117647058820.0500770851328693179.106224399066
Winsorized Mean ( 20 / 22 )8.99852941176470.045155698212195199.277826897481
Winsorized Mean ( 21 / 22 )9.029411764705880.0310808246761938290.513905559975
Winsorized Mean ( 22 / 22 )9.061764705882350.0260873635027499347.362227881983
Trimmed Mean ( 1 / 22 )8.919696969696970.10779025858588882.7504923609558
Trimmed Mean ( 2 / 22 )8.92343750.10083338713841588.4968536041606
Trimmed Mean ( 3 / 22 )8.932258064516130.095807795912061293.2310150701594
Trimmed Mean ( 4 / 22 )8.938333333333330.091814467388563497.3521231191797
Trimmed Mean ( 5 / 22 )8.94482758620690.0879342964651228101.721716620030
Trimmed Mean ( 6 / 22 )8.950.0847839117304202105.562480160829
Trimmed Mean ( 7 / 22 )8.95740740740740.0813324505851266110.133253614830
Trimmed Mean ( 8 / 22 )8.961538461538460.0793617947485771112.920057943865
Trimmed Mean ( 9 / 22 )8.9640.0774470194153818115.743640848490
Trimmed Mean ( 10 / 22 )8.966666666666670.0749901490772544119.571260718915
Trimmed Mean ( 11 / 22 )8.971739130434780.0724093998941206123.90296209544
Trimmed Mean ( 12 / 22 )8.977272727272730.0690362251603723130.03713204797
Trimmed Mean ( 13 / 22 )8.988095238095240.0658370900545955136.520238525759
Trimmed Mean ( 14 / 22 )8.99750.06258199749334143.771377718609
Trimmed Mean ( 15 / 22 )9.010526315789470.0587675065389962153.324972360540
Trimmed Mean ( 16 / 22 )9.022222222222220.0547883534013419164.674089694421
Trimmed Mean ( 17 / 22 )9.032352941176470.0506148626187969178.452582380854
Trimmed Mean ( 18 / 22 )9.043750.0470795269181702192.095175801556
Trimmed Mean ( 19 / 22 )9.056666666666670.0417114701646324217.126527329787
Trimmed Mean ( 20 / 22 )9.067857142857140.0356547122187427254.324227530588
Trimmed Mean ( 21 / 22 )9.076923076923080.0284511415521645319.035461557166
Trimmed Mean ( 22 / 22 )9.083333333333330.0245736593591495369.636984080328
Median9.1
Midrange8.85
Midmean - Weighted Average at Xnp9.00857142857142
Midmean - Weighted Average at X(n+1)p9.03235294117647
Midmean - Empirical Distribution Function9.00857142857142
Midmean - Empirical Distribution Function - Averaging9.03235294117647
Midmean - Empirical Distribution Function - Interpolation9.03235294117647
Midmean - Closest Observation9.00857142857142
Midmean - True Basic - Statistics Graphics Toolkit9.03235294117647
Midmean - MS Excel (old versions)9.04736842105263
Number of observations68

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 8.91764705882353 & 0.114737957290316 & 77.7218565627729 \tabularnewline
Geometric Mean & 8.86613729998557 &  &  \tabularnewline
Harmonic Mean & 8.81236695380352 &  &  \tabularnewline
Quadratic Mean & 8.96696551728818 &  &  \tabularnewline
Winsorized Mean ( 1 / 22 ) & 8.91617647058824 & 0.113500652555195 & 78.556169236581 \tabularnewline
Winsorized Mean ( 2 / 22 ) & 8.90735294117647 & 0.108390657236930 & 82.1782353593997 \tabularnewline
Winsorized Mean ( 3 / 22 ) & 8.91617647058824 & 0.104036409977677 & 85.70246197943 \tabularnewline
Winsorized Mean ( 4 / 22 ) & 8.91617647058824 & 0.101473133024037 & 87.867361585023 \tabularnewline
Winsorized Mean ( 5 / 22 ) & 8.9235294117647 & 0.0967450431146052 & 92.2375878337643 \tabularnewline
Winsorized Mean ( 6 / 22 ) & 8.91470588235294 & 0.0951931797225094 & 93.6485776432676 \tabularnewline
Winsorized Mean ( 7 / 22 ) & 8.93529411764706 & 0.0870137866091518 & 102.688257411237 \tabularnewline
Winsorized Mean ( 8 / 22 ) & 8.94705882352941 & 0.0847832175504436 & 105.528653925008 \tabularnewline
Winsorized Mean ( 9 / 22 ) & 8.94705882352941 & 0.0847832175504436 & 105.528653925008 \tabularnewline
Winsorized Mean ( 10 / 22 ) & 8.93235294117647 & 0.0823929101552848 & 108.411669454833 \tabularnewline
Winsorized Mean ( 11 / 22 ) & 8.93235294117647 & 0.0823929101552848 & 108.411669454833 \tabularnewline
Winsorized Mean ( 12 / 22 ) & 8.89705882352941 & 0.0772090701294317 & 115.233337334779 \tabularnewline
Winsorized Mean ( 13 / 22 ) & 8.91617647058824 & 0.0735888697267669 & 121.162024959667 \tabularnewline
Winsorized Mean ( 14 / 22 ) & 8.89558823529412 & 0.0708481733555641 & 125.558469809095 \tabularnewline
Winsorized Mean ( 15 / 22 ) & 8.91764705882353 & 0.0667488175004704 & 133.600075518352 \tabularnewline
Winsorized Mean ( 16 / 22 ) & 8.94117647058824 & 0.0625137489396261 & 143.027359936825 \tabularnewline
Winsorized Mean ( 17 / 22 ) & 8.94117647058824 & 0.0548857578833243 & 162.905220140994 \tabularnewline
Winsorized Mean ( 18 / 22 ) & 8.94117647058824 & 0.0548857578833243 & 162.905220140994 \tabularnewline
Winsorized Mean ( 19 / 22 ) & 8.96911764705882 & 0.0500770851328693 & 179.106224399066 \tabularnewline
Winsorized Mean ( 20 / 22 ) & 8.9985294117647 & 0.045155698212195 & 199.277826897481 \tabularnewline
Winsorized Mean ( 21 / 22 ) & 9.02941176470588 & 0.0310808246761938 & 290.513905559975 \tabularnewline
Winsorized Mean ( 22 / 22 ) & 9.06176470588235 & 0.0260873635027499 & 347.362227881983 \tabularnewline
Trimmed Mean ( 1 / 22 ) & 8.91969696969697 & 0.107790258585888 & 82.7504923609558 \tabularnewline
Trimmed Mean ( 2 / 22 ) & 8.9234375 & 0.100833387138415 & 88.4968536041606 \tabularnewline
Trimmed Mean ( 3 / 22 ) & 8.93225806451613 & 0.0958077959120612 & 93.2310150701594 \tabularnewline
Trimmed Mean ( 4 / 22 ) & 8.93833333333333 & 0.0918144673885634 & 97.3521231191797 \tabularnewline
Trimmed Mean ( 5 / 22 ) & 8.9448275862069 & 0.0879342964651228 & 101.721716620030 \tabularnewline
Trimmed Mean ( 6 / 22 ) & 8.95 & 0.0847839117304202 & 105.562480160829 \tabularnewline
Trimmed Mean ( 7 / 22 ) & 8.9574074074074 & 0.0813324505851266 & 110.133253614830 \tabularnewline
Trimmed Mean ( 8 / 22 ) & 8.96153846153846 & 0.0793617947485771 & 112.920057943865 \tabularnewline
Trimmed Mean ( 9 / 22 ) & 8.964 & 0.0774470194153818 & 115.743640848490 \tabularnewline
Trimmed Mean ( 10 / 22 ) & 8.96666666666667 & 0.0749901490772544 & 119.571260718915 \tabularnewline
Trimmed Mean ( 11 / 22 ) & 8.97173913043478 & 0.0724093998941206 & 123.90296209544 \tabularnewline
Trimmed Mean ( 12 / 22 ) & 8.97727272727273 & 0.0690362251603723 & 130.03713204797 \tabularnewline
Trimmed Mean ( 13 / 22 ) & 8.98809523809524 & 0.0658370900545955 & 136.520238525759 \tabularnewline
Trimmed Mean ( 14 / 22 ) & 8.9975 & 0.06258199749334 & 143.771377718609 \tabularnewline
Trimmed Mean ( 15 / 22 ) & 9.01052631578947 & 0.0587675065389962 & 153.324972360540 \tabularnewline
Trimmed Mean ( 16 / 22 ) & 9.02222222222222 & 0.0547883534013419 & 164.674089694421 \tabularnewline
Trimmed Mean ( 17 / 22 ) & 9.03235294117647 & 0.0506148626187969 & 178.452582380854 \tabularnewline
Trimmed Mean ( 18 / 22 ) & 9.04375 & 0.0470795269181702 & 192.095175801556 \tabularnewline
Trimmed Mean ( 19 / 22 ) & 9.05666666666667 & 0.0417114701646324 & 217.126527329787 \tabularnewline
Trimmed Mean ( 20 / 22 ) & 9.06785714285714 & 0.0356547122187427 & 254.324227530588 \tabularnewline
Trimmed Mean ( 21 / 22 ) & 9.07692307692308 & 0.0284511415521645 & 319.035461557166 \tabularnewline
Trimmed Mean ( 22 / 22 ) & 9.08333333333333 & 0.0245736593591495 & 369.636984080328 \tabularnewline
Median & 9.1 &  &  \tabularnewline
Midrange & 8.85 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 9.00857142857142 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 9.03235294117647 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 9.00857142857142 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 9.03235294117647 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 9.03235294117647 &  &  \tabularnewline
Midmean - Closest Observation & 9.00857142857142 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 9.03235294117647 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 9.04736842105263 &  &  \tabularnewline
Number of observations & 68 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=17319&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]8.91764705882353[/C][C]0.114737957290316[/C][C]77.7218565627729[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]8.86613729998557[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]8.81236695380352[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]8.96696551728818[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 22 )[/C][C]8.91617647058824[/C][C]0.113500652555195[/C][C]78.556169236581[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 22 )[/C][C]8.90735294117647[/C][C]0.108390657236930[/C][C]82.1782353593997[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 22 )[/C][C]8.91617647058824[/C][C]0.104036409977677[/C][C]85.70246197943[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 22 )[/C][C]8.91617647058824[/C][C]0.101473133024037[/C][C]87.867361585023[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 22 )[/C][C]8.9235294117647[/C][C]0.0967450431146052[/C][C]92.2375878337643[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 22 )[/C][C]8.91470588235294[/C][C]0.0951931797225094[/C][C]93.6485776432676[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 22 )[/C][C]8.93529411764706[/C][C]0.0870137866091518[/C][C]102.688257411237[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 22 )[/C][C]8.94705882352941[/C][C]0.0847832175504436[/C][C]105.528653925008[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 22 )[/C][C]8.94705882352941[/C][C]0.0847832175504436[/C][C]105.528653925008[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 22 )[/C][C]8.93235294117647[/C][C]0.0823929101552848[/C][C]108.411669454833[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 22 )[/C][C]8.93235294117647[/C][C]0.0823929101552848[/C][C]108.411669454833[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 22 )[/C][C]8.89705882352941[/C][C]0.0772090701294317[/C][C]115.233337334779[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 22 )[/C][C]8.91617647058824[/C][C]0.0735888697267669[/C][C]121.162024959667[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 22 )[/C][C]8.89558823529412[/C][C]0.0708481733555641[/C][C]125.558469809095[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 22 )[/C][C]8.91764705882353[/C][C]0.0667488175004704[/C][C]133.600075518352[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 22 )[/C][C]8.94117647058824[/C][C]0.0625137489396261[/C][C]143.027359936825[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 22 )[/C][C]8.94117647058824[/C][C]0.0548857578833243[/C][C]162.905220140994[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 22 )[/C][C]8.94117647058824[/C][C]0.0548857578833243[/C][C]162.905220140994[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 22 )[/C][C]8.96911764705882[/C][C]0.0500770851328693[/C][C]179.106224399066[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 22 )[/C][C]8.9985294117647[/C][C]0.045155698212195[/C][C]199.277826897481[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 22 )[/C][C]9.02941176470588[/C][C]0.0310808246761938[/C][C]290.513905559975[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 22 )[/C][C]9.06176470588235[/C][C]0.0260873635027499[/C][C]347.362227881983[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 22 )[/C][C]8.91969696969697[/C][C]0.107790258585888[/C][C]82.7504923609558[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 22 )[/C][C]8.9234375[/C][C]0.100833387138415[/C][C]88.4968536041606[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 22 )[/C][C]8.93225806451613[/C][C]0.0958077959120612[/C][C]93.2310150701594[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 22 )[/C][C]8.93833333333333[/C][C]0.0918144673885634[/C][C]97.3521231191797[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 22 )[/C][C]8.9448275862069[/C][C]0.0879342964651228[/C][C]101.721716620030[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 22 )[/C][C]8.95[/C][C]0.0847839117304202[/C][C]105.562480160829[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 22 )[/C][C]8.9574074074074[/C][C]0.0813324505851266[/C][C]110.133253614830[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 22 )[/C][C]8.96153846153846[/C][C]0.0793617947485771[/C][C]112.920057943865[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 22 )[/C][C]8.964[/C][C]0.0774470194153818[/C][C]115.743640848490[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 22 )[/C][C]8.96666666666667[/C][C]0.0749901490772544[/C][C]119.571260718915[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 22 )[/C][C]8.97173913043478[/C][C]0.0724093998941206[/C][C]123.90296209544[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 22 )[/C][C]8.97727272727273[/C][C]0.0690362251603723[/C][C]130.03713204797[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 22 )[/C][C]8.98809523809524[/C][C]0.0658370900545955[/C][C]136.520238525759[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 22 )[/C][C]8.9975[/C][C]0.06258199749334[/C][C]143.771377718609[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 22 )[/C][C]9.01052631578947[/C][C]0.0587675065389962[/C][C]153.324972360540[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 22 )[/C][C]9.02222222222222[/C][C]0.0547883534013419[/C][C]164.674089694421[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 22 )[/C][C]9.03235294117647[/C][C]0.0506148626187969[/C][C]178.452582380854[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 22 )[/C][C]9.04375[/C][C]0.0470795269181702[/C][C]192.095175801556[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 22 )[/C][C]9.05666666666667[/C][C]0.0417114701646324[/C][C]217.126527329787[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 22 )[/C][C]9.06785714285714[/C][C]0.0356547122187427[/C][C]254.324227530588[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 22 )[/C][C]9.07692307692308[/C][C]0.0284511415521645[/C][C]319.035461557166[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 22 )[/C][C]9.08333333333333[/C][C]0.0245736593591495[/C][C]369.636984080328[/C][/ROW]
[ROW][C]Median[/C][C]9.1[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]8.85[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]9.00857142857142[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]9.03235294117647[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]9.00857142857142[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]9.03235294117647[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]9.03235294117647[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]9.00857142857142[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]9.03235294117647[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]9.04736842105263[/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=17319&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=17319&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 Mean8.917647058823530.11473795729031677.7218565627729
Geometric Mean8.86613729998557
Harmonic Mean8.81236695380352
Quadratic Mean8.96696551728818
Winsorized Mean ( 1 / 22 )8.916176470588240.11350065255519578.556169236581
Winsorized Mean ( 2 / 22 )8.907352941176470.10839065723693082.1782353593997
Winsorized Mean ( 3 / 22 )8.916176470588240.10403640997767785.70246197943
Winsorized Mean ( 4 / 22 )8.916176470588240.10147313302403787.867361585023
Winsorized Mean ( 5 / 22 )8.92352941176470.096745043114605292.2375878337643
Winsorized Mean ( 6 / 22 )8.914705882352940.095193179722509493.6485776432676
Winsorized Mean ( 7 / 22 )8.935294117647060.0870137866091518102.688257411237
Winsorized Mean ( 8 / 22 )8.947058823529410.0847832175504436105.528653925008
Winsorized Mean ( 9 / 22 )8.947058823529410.0847832175504436105.528653925008
Winsorized Mean ( 10 / 22 )8.932352941176470.0823929101552848108.411669454833
Winsorized Mean ( 11 / 22 )8.932352941176470.0823929101552848108.411669454833
Winsorized Mean ( 12 / 22 )8.897058823529410.0772090701294317115.233337334779
Winsorized Mean ( 13 / 22 )8.916176470588240.0735888697267669121.162024959667
Winsorized Mean ( 14 / 22 )8.895588235294120.0708481733555641125.558469809095
Winsorized Mean ( 15 / 22 )8.917647058823530.0667488175004704133.600075518352
Winsorized Mean ( 16 / 22 )8.941176470588240.0625137489396261143.027359936825
Winsorized Mean ( 17 / 22 )8.941176470588240.0548857578833243162.905220140994
Winsorized Mean ( 18 / 22 )8.941176470588240.0548857578833243162.905220140994
Winsorized Mean ( 19 / 22 )8.969117647058820.0500770851328693179.106224399066
Winsorized Mean ( 20 / 22 )8.99852941176470.045155698212195199.277826897481
Winsorized Mean ( 21 / 22 )9.029411764705880.0310808246761938290.513905559975
Winsorized Mean ( 22 / 22 )9.061764705882350.0260873635027499347.362227881983
Trimmed Mean ( 1 / 22 )8.919696969696970.10779025858588882.7504923609558
Trimmed Mean ( 2 / 22 )8.92343750.10083338713841588.4968536041606
Trimmed Mean ( 3 / 22 )8.932258064516130.095807795912061293.2310150701594
Trimmed Mean ( 4 / 22 )8.938333333333330.091814467388563497.3521231191797
Trimmed Mean ( 5 / 22 )8.94482758620690.0879342964651228101.721716620030
Trimmed Mean ( 6 / 22 )8.950.0847839117304202105.562480160829
Trimmed Mean ( 7 / 22 )8.95740740740740.0813324505851266110.133253614830
Trimmed Mean ( 8 / 22 )8.961538461538460.0793617947485771112.920057943865
Trimmed Mean ( 9 / 22 )8.9640.0774470194153818115.743640848490
Trimmed Mean ( 10 / 22 )8.966666666666670.0749901490772544119.571260718915
Trimmed Mean ( 11 / 22 )8.971739130434780.0724093998941206123.90296209544
Trimmed Mean ( 12 / 22 )8.977272727272730.0690362251603723130.03713204797
Trimmed Mean ( 13 / 22 )8.988095238095240.0658370900545955136.520238525759
Trimmed Mean ( 14 / 22 )8.99750.06258199749334143.771377718609
Trimmed Mean ( 15 / 22 )9.010526315789470.0587675065389962153.324972360540
Trimmed Mean ( 16 / 22 )9.022222222222220.0547883534013419164.674089694421
Trimmed Mean ( 17 / 22 )9.032352941176470.0506148626187969178.452582380854
Trimmed Mean ( 18 / 22 )9.043750.0470795269181702192.095175801556
Trimmed Mean ( 19 / 22 )9.056666666666670.0417114701646324217.126527329787
Trimmed Mean ( 20 / 22 )9.067857142857140.0356547122187427254.324227530588
Trimmed Mean ( 21 / 22 )9.076923076923080.0284511415521645319.035461557166
Trimmed Mean ( 22 / 22 )9.083333333333330.0245736593591495369.636984080328
Median9.1
Midrange8.85
Midmean - Weighted Average at Xnp9.00857142857142
Midmean - Weighted Average at X(n+1)p9.03235294117647
Midmean - Empirical Distribution Function9.00857142857142
Midmean - Empirical Distribution Function - Averaging9.03235294117647
Midmean - Empirical Distribution Function - Interpolation9.03235294117647
Midmean - Closest Observation9.00857142857142
Midmean - True Basic - Statistics Graphics Toolkit9.03235294117647
Midmean - MS Excel (old versions)9.04736842105263
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')