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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationWed, 09 Oct 2013 10:19:33 -0400
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2013/Oct/09/t1381328496q23y7end7ysugy4.htm/, Retrieved Mon, 29 Apr 2024 07:53:42 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=214436, Retrieved Mon, 29 Apr 2024 07:53:42 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact64
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2013-10-09 14:19:33] [3d308039bd6152c26e5d01eb1ba12dd8] [Current]
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Dataseries X:
104,4
104,4
104,4
104,4
104,4
104,41
104,42
104,68
106,02
106,35
106,38
106,47
106,5
106,56
113,07
116,26
118
118,02
118,04
118,12
118,12
118,17
118,22
118,22
118,23
118,23
118,23
119,94
120,88
121,14
121,16
121,2
121,2
121,2
121,2
121,2
121,22
121,22
121,95
123,05
123,44
123,65
123,79
123,87
123,91
123,94
124,28
126,28
126,68
126,69
126,69
126,99
128,79
128,84
128,95
128,97
128,97
128,97
128,97
128,97
128,97
128,98
128,99
129,07
129,76
130,47
130,76
130,88
131,04
131,06
131,13
131,15




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net

\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 & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=214436&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]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=214436&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=214436&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'Gwilym Jenkins' @ jenkins.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean120.4608333333331.02600568530366117.407569040596
Geometric Mean120.138636331362
Harmonic Mean119.804591042085
Quadratic Mean120.770663621869
Winsorized Mean ( 1 / 24 )120.4605555555561.0259649621864117.411958493052
Winsorized Mean ( 2 / 24 )120.4586111111111.0256810269645117.442565421736
Winsorized Mean ( 3 / 24 )120.4577777777781.02555981548699117.455633458666
Winsorized Mean ( 4 / 24 )120.4488888888891.02427640697499117.594126027576
Winsorized Mean ( 5 / 24 )120.441251.02293350482876117.741035396198
Winsorized Mean ( 6 / 24 )120.4179166666671.01935435044173118.131557112092
Winsorized Mean ( 7 / 24 )120.3741666666671.0044412088414119.841923655756
Winsorized Mean ( 8 / 24 )120.4463888888890.962440500885504125.146841574176
Winsorized Mean ( 9 / 24 )120.4776388888890.952517040561931126.483447285955
Winsorized Mean ( 10 / 24 )120.4804166666670.951472202439392126.625261734161
Winsorized Mean ( 11 / 24 )120.4926388888890.948413241042451127.046559110087
Winsorized Mean ( 12 / 24 )120.4976388888890.94737237493301127.191421321959
Winsorized Mean ( 13 / 24 )120.5084722222220.945119219357946127.506106905844
Winsorized Mean ( 14 / 24 )121.7743055555560.699558541390294174.073073732389
Winsorized Mean ( 15 / 24 )122.4388888888890.591667610776062206.938636928751
Winsorized Mean ( 16 / 24 )122.8255555555560.538646687420328228.02619680776
Winsorized Mean ( 17 / 24 )122.8255555555560.537292919271173228.60073369693
Winsorized Mean ( 18 / 24 )122.8030555555560.532258807481091230.720570199148
Winsorized Mean ( 19 / 24 )122.8109722222220.527499162261245232.817378696423
Winsorized Mean ( 20 / 24 )122.3109722222220.450775594860502271.334503501843
Winsorized Mean ( 21 / 24 )122.2380555555560.436175746284305280.249547566268
Winsorized Mean ( 22 / 24 )122.2533333333330.434172805503896281.577592570423
Winsorized Mean ( 23 / 24 )122.2501388888890.433713154823872281.868644123866
Winsorized Mean ( 24 / 24 )122.1201388888890.414251521288091294.797080066631
Trimmed Mean ( 1 / 24 )120.5375714285711.01833283221766118.367558832482
Trimmed Mean ( 2 / 24 )120.6191176470591.00870286177742119.578442986191
Trimmed Mean ( 3 / 24 )120.7066666666670.99685611471371121.087351409118
Trimmed Mean ( 4 / 24 )120.80.982210971664002122.987834065168
Trimmed Mean ( 5 / 24 )120.9019354838710.964550756441001125.345332712168
Trimmed Mean ( 6 / 24 )121.01250.943115962608286128.311368694606
Trimmed Mean ( 7 / 24 )121.1355172413790.917511731873471132.026123517824
Trimmed Mean ( 8 / 24 )121.2753571428570.889480694996693136.34400142131
Trimmed Mean ( 9 / 24 )121.4135185185190.865179467307456140.333333263643
Trimmed Mean ( 10 / 24 )121.55750.836776741345451145.268736562333
Trimmed Mean ( 11 / 24 )121.71260.800577638907287152.030976241263
Trimmed Mean ( 12 / 24 )121.8789583333330.754399051590785161.557677036218
Trimmed Mean ( 13 / 24 )122.0591304347830.693531732071463175.996460998565
Trimmed Mean ( 14 / 24 )122.2543181818180.610852383157523200.137253373524
Trimmed Mean ( 15 / 24 )122.3130952380950.578548434705565211.413751901935
Trimmed Mean ( 16 / 24 )122.2980.563540456536925217.017249749108
Trimmed Mean ( 17 / 24 )122.2355263157890.554488178819621220.447488305343
Trimmed Mean ( 18 / 24 )122.1661111111110.541350791088685225.66903590448
Trimmed Mean ( 19 / 24 )122.0911764705880.523511345799768233.215912988609
Trimmed Mean ( 20 / 24 )122.00593750.498609934527458244.692151221631
Trimmed Mean ( 21 / 24 )121.9693333333330.487359041415097250.265867601805
Trimmed Mean ( 22 / 24 )121.9364285714290.474050768128706257.222299317786
Trimmed Mean ( 23 / 24 )121.8965384615380.453094978091346269.030875104874
Trimmed Mean ( 24 / 24 )121.8504166666670.419178578719724290.688558176871
Median121.21
Midrange117.775
Midmean - Weighted Average at Xnp122.054054054054
Midmean - Weighted Average at X(n+1)p122.166111111111
Midmean - Empirical Distribution Function122.054054054054
Midmean - Empirical Distribution Function - Averaging122.166111111111
Midmean - Empirical Distribution Function - Interpolation122.166111111111
Midmean - Closest Observation122.054054054054
Midmean - True Basic - Statistics Graphics Toolkit122.166111111111
Midmean - MS Excel (old versions)122.235526315789
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 120.460833333333 & 1.02600568530366 & 117.407569040596 \tabularnewline
Geometric Mean & 120.138636331362 &  &  \tabularnewline
Harmonic Mean & 119.804591042085 &  &  \tabularnewline
Quadratic Mean & 120.770663621869 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 120.460555555556 & 1.0259649621864 & 117.411958493052 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 120.458611111111 & 1.0256810269645 & 117.442565421736 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 120.457777777778 & 1.02555981548699 & 117.455633458666 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 120.448888888889 & 1.02427640697499 & 117.594126027576 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 120.44125 & 1.02293350482876 & 117.741035396198 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 120.417916666667 & 1.01935435044173 & 118.131557112092 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 120.374166666667 & 1.0044412088414 & 119.841923655756 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 120.446388888889 & 0.962440500885504 & 125.146841574176 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 120.477638888889 & 0.952517040561931 & 126.483447285955 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 120.480416666667 & 0.951472202439392 & 126.625261734161 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 120.492638888889 & 0.948413241042451 & 127.046559110087 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 120.497638888889 & 0.94737237493301 & 127.191421321959 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 120.508472222222 & 0.945119219357946 & 127.506106905844 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 121.774305555556 & 0.699558541390294 & 174.073073732389 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 122.438888888889 & 0.591667610776062 & 206.938636928751 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 122.825555555556 & 0.538646687420328 & 228.02619680776 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 122.825555555556 & 0.537292919271173 & 228.60073369693 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 122.803055555556 & 0.532258807481091 & 230.720570199148 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 122.810972222222 & 0.527499162261245 & 232.817378696423 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 122.310972222222 & 0.450775594860502 & 271.334503501843 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 122.238055555556 & 0.436175746284305 & 280.249547566268 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 122.253333333333 & 0.434172805503896 & 281.577592570423 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 122.250138888889 & 0.433713154823872 & 281.868644123866 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 122.120138888889 & 0.414251521288091 & 294.797080066631 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 120.537571428571 & 1.01833283221766 & 118.367558832482 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 120.619117647059 & 1.00870286177742 & 119.578442986191 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 120.706666666667 & 0.99685611471371 & 121.087351409118 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 120.8 & 0.982210971664002 & 122.987834065168 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 120.901935483871 & 0.964550756441001 & 125.345332712168 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 121.0125 & 0.943115962608286 & 128.311368694606 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 121.135517241379 & 0.917511731873471 & 132.026123517824 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 121.275357142857 & 0.889480694996693 & 136.34400142131 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 121.413518518519 & 0.865179467307456 & 140.333333263643 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 121.5575 & 0.836776741345451 & 145.268736562333 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 121.7126 & 0.800577638907287 & 152.030976241263 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 121.878958333333 & 0.754399051590785 & 161.557677036218 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 122.059130434783 & 0.693531732071463 & 175.996460998565 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 122.254318181818 & 0.610852383157523 & 200.137253373524 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 122.313095238095 & 0.578548434705565 & 211.413751901935 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 122.298 & 0.563540456536925 & 217.017249749108 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 122.235526315789 & 0.554488178819621 & 220.447488305343 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 122.166111111111 & 0.541350791088685 & 225.66903590448 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 122.091176470588 & 0.523511345799768 & 233.215912988609 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 122.0059375 & 0.498609934527458 & 244.692151221631 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 121.969333333333 & 0.487359041415097 & 250.265867601805 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 121.936428571429 & 0.474050768128706 & 257.222299317786 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 121.896538461538 & 0.453094978091346 & 269.030875104874 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 121.850416666667 & 0.419178578719724 & 290.688558176871 \tabularnewline
Median & 121.21 &  &  \tabularnewline
Midrange & 117.775 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 122.054054054054 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 122.166111111111 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 122.054054054054 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 122.166111111111 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 122.166111111111 &  &  \tabularnewline
Midmean - Closest Observation & 122.054054054054 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 122.166111111111 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 122.235526315789 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=214436&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]120.460833333333[/C][C]1.02600568530366[/C][C]117.407569040596[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]120.138636331362[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]119.804591042085[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]120.770663621869[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]120.460555555556[/C][C]1.0259649621864[/C][C]117.411958493052[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]120.458611111111[/C][C]1.0256810269645[/C][C]117.442565421736[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]120.457777777778[/C][C]1.02555981548699[/C][C]117.455633458666[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]120.448888888889[/C][C]1.02427640697499[/C][C]117.594126027576[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]120.44125[/C][C]1.02293350482876[/C][C]117.741035396198[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]120.417916666667[/C][C]1.01935435044173[/C][C]118.131557112092[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]120.374166666667[/C][C]1.0044412088414[/C][C]119.841923655756[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]120.446388888889[/C][C]0.962440500885504[/C][C]125.146841574176[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]120.477638888889[/C][C]0.952517040561931[/C][C]126.483447285955[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]120.480416666667[/C][C]0.951472202439392[/C][C]126.625261734161[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]120.492638888889[/C][C]0.948413241042451[/C][C]127.046559110087[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]120.497638888889[/C][C]0.94737237493301[/C][C]127.191421321959[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]120.508472222222[/C][C]0.945119219357946[/C][C]127.506106905844[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]121.774305555556[/C][C]0.699558541390294[/C][C]174.073073732389[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]122.438888888889[/C][C]0.591667610776062[/C][C]206.938636928751[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]122.825555555556[/C][C]0.538646687420328[/C][C]228.02619680776[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]122.825555555556[/C][C]0.537292919271173[/C][C]228.60073369693[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]122.803055555556[/C][C]0.532258807481091[/C][C]230.720570199148[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]122.810972222222[/C][C]0.527499162261245[/C][C]232.817378696423[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]122.310972222222[/C][C]0.450775594860502[/C][C]271.334503501843[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]122.238055555556[/C][C]0.436175746284305[/C][C]280.249547566268[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]122.253333333333[/C][C]0.434172805503896[/C][C]281.577592570423[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]122.250138888889[/C][C]0.433713154823872[/C][C]281.868644123866[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]122.120138888889[/C][C]0.414251521288091[/C][C]294.797080066631[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]120.537571428571[/C][C]1.01833283221766[/C][C]118.367558832482[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]120.619117647059[/C][C]1.00870286177742[/C][C]119.578442986191[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]120.706666666667[/C][C]0.99685611471371[/C][C]121.087351409118[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]120.8[/C][C]0.982210971664002[/C][C]122.987834065168[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]120.901935483871[/C][C]0.964550756441001[/C][C]125.345332712168[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]121.0125[/C][C]0.943115962608286[/C][C]128.311368694606[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]121.135517241379[/C][C]0.917511731873471[/C][C]132.026123517824[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]121.275357142857[/C][C]0.889480694996693[/C][C]136.34400142131[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]121.413518518519[/C][C]0.865179467307456[/C][C]140.333333263643[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]121.5575[/C][C]0.836776741345451[/C][C]145.268736562333[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]121.7126[/C][C]0.800577638907287[/C][C]152.030976241263[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]121.878958333333[/C][C]0.754399051590785[/C][C]161.557677036218[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]122.059130434783[/C][C]0.693531732071463[/C][C]175.996460998565[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]122.254318181818[/C][C]0.610852383157523[/C][C]200.137253373524[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]122.313095238095[/C][C]0.578548434705565[/C][C]211.413751901935[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]122.298[/C][C]0.563540456536925[/C][C]217.017249749108[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]122.235526315789[/C][C]0.554488178819621[/C][C]220.447488305343[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]122.166111111111[/C][C]0.541350791088685[/C][C]225.66903590448[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]122.091176470588[/C][C]0.523511345799768[/C][C]233.215912988609[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]122.0059375[/C][C]0.498609934527458[/C][C]244.692151221631[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]121.969333333333[/C][C]0.487359041415097[/C][C]250.265867601805[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]121.936428571429[/C][C]0.474050768128706[/C][C]257.222299317786[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]121.896538461538[/C][C]0.453094978091346[/C][C]269.030875104874[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]121.850416666667[/C][C]0.419178578719724[/C][C]290.688558176871[/C][/ROW]
[ROW][C]Median[/C][C]121.21[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]117.775[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]122.054054054054[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]122.166111111111[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]122.054054054054[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]122.166111111111[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]122.166111111111[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]122.054054054054[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]122.166111111111[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]122.235526315789[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]72[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=214436&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=214436&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 Mean120.4608333333331.02600568530366117.407569040596
Geometric Mean120.138636331362
Harmonic Mean119.804591042085
Quadratic Mean120.770663621869
Winsorized Mean ( 1 / 24 )120.4605555555561.0259649621864117.411958493052
Winsorized Mean ( 2 / 24 )120.4586111111111.0256810269645117.442565421736
Winsorized Mean ( 3 / 24 )120.4577777777781.02555981548699117.455633458666
Winsorized Mean ( 4 / 24 )120.4488888888891.02427640697499117.594126027576
Winsorized Mean ( 5 / 24 )120.441251.02293350482876117.741035396198
Winsorized Mean ( 6 / 24 )120.4179166666671.01935435044173118.131557112092
Winsorized Mean ( 7 / 24 )120.3741666666671.0044412088414119.841923655756
Winsorized Mean ( 8 / 24 )120.4463888888890.962440500885504125.146841574176
Winsorized Mean ( 9 / 24 )120.4776388888890.952517040561931126.483447285955
Winsorized Mean ( 10 / 24 )120.4804166666670.951472202439392126.625261734161
Winsorized Mean ( 11 / 24 )120.4926388888890.948413241042451127.046559110087
Winsorized Mean ( 12 / 24 )120.4976388888890.94737237493301127.191421321959
Winsorized Mean ( 13 / 24 )120.5084722222220.945119219357946127.506106905844
Winsorized Mean ( 14 / 24 )121.7743055555560.699558541390294174.073073732389
Winsorized Mean ( 15 / 24 )122.4388888888890.591667610776062206.938636928751
Winsorized Mean ( 16 / 24 )122.8255555555560.538646687420328228.02619680776
Winsorized Mean ( 17 / 24 )122.8255555555560.537292919271173228.60073369693
Winsorized Mean ( 18 / 24 )122.8030555555560.532258807481091230.720570199148
Winsorized Mean ( 19 / 24 )122.8109722222220.527499162261245232.817378696423
Winsorized Mean ( 20 / 24 )122.3109722222220.450775594860502271.334503501843
Winsorized Mean ( 21 / 24 )122.2380555555560.436175746284305280.249547566268
Winsorized Mean ( 22 / 24 )122.2533333333330.434172805503896281.577592570423
Winsorized Mean ( 23 / 24 )122.2501388888890.433713154823872281.868644123866
Winsorized Mean ( 24 / 24 )122.1201388888890.414251521288091294.797080066631
Trimmed Mean ( 1 / 24 )120.5375714285711.01833283221766118.367558832482
Trimmed Mean ( 2 / 24 )120.6191176470591.00870286177742119.578442986191
Trimmed Mean ( 3 / 24 )120.7066666666670.99685611471371121.087351409118
Trimmed Mean ( 4 / 24 )120.80.982210971664002122.987834065168
Trimmed Mean ( 5 / 24 )120.9019354838710.964550756441001125.345332712168
Trimmed Mean ( 6 / 24 )121.01250.943115962608286128.311368694606
Trimmed Mean ( 7 / 24 )121.1355172413790.917511731873471132.026123517824
Trimmed Mean ( 8 / 24 )121.2753571428570.889480694996693136.34400142131
Trimmed Mean ( 9 / 24 )121.4135185185190.865179467307456140.333333263643
Trimmed Mean ( 10 / 24 )121.55750.836776741345451145.268736562333
Trimmed Mean ( 11 / 24 )121.71260.800577638907287152.030976241263
Trimmed Mean ( 12 / 24 )121.8789583333330.754399051590785161.557677036218
Trimmed Mean ( 13 / 24 )122.0591304347830.693531732071463175.996460998565
Trimmed Mean ( 14 / 24 )122.2543181818180.610852383157523200.137253373524
Trimmed Mean ( 15 / 24 )122.3130952380950.578548434705565211.413751901935
Trimmed Mean ( 16 / 24 )122.2980.563540456536925217.017249749108
Trimmed Mean ( 17 / 24 )122.2355263157890.554488178819621220.447488305343
Trimmed Mean ( 18 / 24 )122.1661111111110.541350791088685225.66903590448
Trimmed Mean ( 19 / 24 )122.0911764705880.523511345799768233.215912988609
Trimmed Mean ( 20 / 24 )122.00593750.498609934527458244.692151221631
Trimmed Mean ( 21 / 24 )121.9693333333330.487359041415097250.265867601805
Trimmed Mean ( 22 / 24 )121.9364285714290.474050768128706257.222299317786
Trimmed Mean ( 23 / 24 )121.8965384615380.453094978091346269.030875104874
Trimmed Mean ( 24 / 24 )121.8504166666670.419178578719724290.688558176871
Median121.21
Midrange117.775
Midmean - Weighted Average at Xnp122.054054054054
Midmean - Weighted Average at X(n+1)p122.166111111111
Midmean - Empirical Distribution Function122.054054054054
Midmean - Empirical Distribution Function - Averaging122.166111111111
Midmean - Empirical Distribution Function - Interpolation122.166111111111
Midmean - Closest Observation122.054054054054
Midmean - True Basic - Statistics Graphics Toolkit122.166111111111
Midmean - MS Excel (old versions)122.235526315789
Number of observations72



Parameters (Session):
Parameters (R input):
R code (references can be found in the software module):
geomean <- function(x) {
return(exp(mean(log(x))))
}
harmean <- function(x) {
return(1/mean(1/x))
}
quamean <- function(x) {
return(sqrt(mean(x*x)))
}
winmean <- function(x) {
x <-sort(x[!is.na(x)])
n<-length(x)
denom <- 3
nodenom <- n/denom
if (nodenom>40) denom <- n/40
sqrtn = sqrt(n)
roundnodenom = floor(nodenom)
win <- array(NA,dim=c(roundnodenom,2))
for (j in 1:roundnodenom) {
win[j,1] <- (j*x[j+1]+sum(x[(j+1):(n-j)])+j*x[n-j])/n
win[j,2] <- sd(c(rep(x[j+1],j),x[(j+1):(n-j)],rep(x[n-j],j)))/sqrtn
}
return(win)
}
trimean <- function(x) {
x <-sort(x[!is.na(x)])
n<-length(x)
denom <- 3
nodenom <- n/denom
if (nodenom>40) denom <- n/40
sqrtn = sqrt(n)
roundnodenom = floor(nodenom)
tri <- array(NA,dim=c(roundnodenom,2))
for (j in 1:roundnodenom) {
tri[j,1] <- mean(x,trim=j/n)
tri[j,2] <- sd(x[(j+1):(n-j)]) / sqrt(n-j*2)
}
return(tri)
}
midrange <- function(x) {
return((max(x)+min(x))/2)
}
q1 <- function(data,n,p,i,f) {
np <- n*p;
i <<- floor(np)
f <<- np - i
qvalue <- (1-f)*data[i] + f*data[i+1]
}
q2 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
qvalue <- (1-f)*data[i] + f*data[i+1]
}
q3 <- function(data,n,p,i,f) {
np <- n*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
qvalue <- data[i+1]
}
}
q4 <- function(data,n,p,i,f) {
np <- n*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- (data[i]+data[i+1])/2
} else {
qvalue <- data[i+1]
}
}
q5 <- function(data,n,p,i,f) {
np <- (n-1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i+1]
} else {
qvalue <- data[i+1] + f*(data[i+2]-data[i+1])
}
}
q6 <- function(data,n,p,i,f) {
np <- n*p+0.5
i <<- floor(np)
f <<- np - i
qvalue <- data[i]
}
q7 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
qvalue <- f*data[i] + (1-f)*data[i+1]
}
}
q8 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
if (f == 0.5) {
qvalue <- (data[i]+data[i+1])/2
} else {
if (f < 0.5) {
qvalue <- data[i]
} else {
qvalue <- data[i+1]
}
}
}
}
midmean <- function(x,def) {
x <-sort(x[!is.na(x)])
n<-length(x)
if (def==1) {
qvalue1 <- q1(x,n,0.25,i,f)
qvalue3 <- q1(x,n,0.75,i,f)
}
if (def==2) {
qvalue1 <- q2(x,n,0.25,i,f)
qvalue3 <- q2(x,n,0.75,i,f)
}
if (def==3) {
qvalue1 <- q3(x,n,0.25,i,f)
qvalue3 <- q3(x,n,0.75,i,f)
}
if (def==4) {
qvalue1 <- q4(x,n,0.25,i,f)
qvalue3 <- q4(x,n,0.75,i,f)
}
if (def==5) {
qvalue1 <- q5(x,n,0.25,i,f)
qvalue3 <- q5(x,n,0.75,i,f)
}
if (def==6) {
qvalue1 <- q6(x,n,0.25,i,f)
qvalue3 <- q6(x,n,0.75,i,f)
}
if (def==7) {
qvalue1 <- q7(x,n,0.25,i,f)
qvalue3 <- q7(x,n,0.75,i,f)
}
if (def==8) {
qvalue1 <- q8(x,n,0.25,i,f)
qvalue3 <- q8(x,n,0.75,i,f)
}
midm <- 0
myn <- 0
roundno4 <- round(n/4)
round3no4 <- round(3*n/4)
for (i in 1:n) {
if ((x[i]>=qvalue1) & (x[i]<=qvalue3)){
midm = midm + x[i]
myn = myn + 1
}
}
midm = midm / myn
return(midm)
}
(arm <- mean(x))
sqrtn <- sqrt(length(x))
(armse <- sd(x) / sqrtn)
(armose <- arm / armse)
(geo <- geomean(x))
(har <- harmean(x))
(qua <- quamean(x))
(win <- winmean(x))
(tri <- trimean(x))
(midr <- midrange(x))
midm <- array(NA,dim=8)
for (j in 1:8) midm[j] <- midmean(x,j)
midm
bitmap(file='test1.png')
lb <- win[,1] - 2*win[,2]
ub <- win[,1] + 2*win[,2]
if ((ylimmin == '') | (ylimmax == '')) plot(win[,1],type='b',main=main, xlab='j', pch=19, ylab='Winsorized Mean(j/n)', ylim=c(min(lb),max(ub))) else plot(win[,1],type='l',main=main, xlab='j', pch=19, ylab='Winsorized Mean(j/n)', ylim=c(ylimmin,ylimmax))
lines(ub,lty=3)
lines(lb,lty=3)
grid()
dev.off()
bitmap(file='test2.png')
lb <- tri[,1] - 2*tri[,2]
ub <- tri[,1] + 2*tri[,2]
if ((ylimmin == '') | (ylimmax == '')) plot(tri[,1],type='b',main=main, xlab='j', pch=19, ylab='Trimmed Mean(j/n)', ylim=c(min(lb),max(ub))) else plot(tri[,1],type='l',main=main, xlab='j', pch=19, ylab='Trimmed Mean(j/n)', ylim=c(ylimmin,ylimmax))
lines(ub,lty=3)
lines(lb,lty=3)
grid()
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Central Tendency - Ungrouped Data',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Measure',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.element(a,'S.E.',header=TRUE)
a<-table.element(a,'Value/S.E.',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('arithmetic_mean.htm', 'Arithmetic Mean', 'click to view the definition of the Arithmetic Mean'),header=TRUE)
a<-table.element(a,arm)
a<-table.element(a,hyperlink('arithmetic_mean_standard_error.htm', armse, 'click to view the definition of the Standard Error of the Arithmetic Mean'))
a<-table.element(a,armose)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('geometric_mean.htm', 'Geometric Mean', 'click to view the definition of the Geometric Mean'),header=TRUE)
a<-table.element(a,geo)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('harmonic_mean.htm', 'Harmonic Mean', 'click to view the definition of the Harmonic Mean'),header=TRUE)
a<-table.element(a,har)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('quadratic_mean.htm', 'Quadratic Mean', 'click to view the definition of the Quadratic Mean'),header=TRUE)
a<-table.element(a,qua)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
for (j in 1:length(win[,1])) {
a<-table.row.start(a)
mylabel <- paste('Winsorized Mean (',j)
mylabel <- paste(mylabel,'/')
mylabel <- paste(mylabel,length(win[,1]))
mylabel <- paste(mylabel,')')
a<-table.element(a,hyperlink('winsorized_mean.htm', mylabel, 'click to view the definition of the Winsorized Mean'),header=TRUE)
a<-table.element(a,win[j,1])
a<-table.element(a,win[j,2])
a<-table.element(a,win[j,1]/win[j,2])
a<-table.row.end(a)
}
for (j in 1:length(tri[,1])) {
a<-table.row.start(a)
mylabel <- paste('Trimmed Mean (',j)
mylabel <- paste(mylabel,'/')
mylabel <- paste(mylabel,length(tri[,1]))
mylabel <- paste(mylabel,')')
a<-table.element(a,hyperlink('arithmetic_mean.htm', mylabel, 'click to view the definition of the Trimmed Mean'),header=TRUE)
a<-table.element(a,tri[j,1])
a<-table.element(a,tri[j,2])
a<-table.element(a,tri[j,1]/tri[j,2])
a<-table.row.end(a)
}
a<-table.row.start(a)
a<-table.element(a,hyperlink('median_1.htm', 'Median', 'click to view the definition of the Median'),header=TRUE)
a<-table.element(a,median(x))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('midrange.htm', 'Midrange', 'click to view the definition of the Midrange'),header=TRUE)
a<-table.element(a,midr)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_1.htm','Weighted Average at Xnp',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[1])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_2.htm','Weighted Average at X(n+1)p',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[2])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_3.htm','Empirical Distribution Function',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[3])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_4.htm','Empirical Distribution Function - Averaging',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[4])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_5.htm','Empirical Distribution Function - Interpolation',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[5])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_6.htm','Closest Observation',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[6])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_7.htm','True Basic - Statistics Graphics Toolkit',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[7])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_8.htm','MS Excel (old versions)',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[8])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Number of observations',header=TRUE)
a<-table.element(a,length(x))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')